Information Systems Biology 070823

Abstract

Propose Information Systems Biology as a model of systems biology in which information is a primary organizing principle and biosystems are considered as multiscalar entities of information creation, representation, and transfer. Discuss AdS/Biology and Chern-Simons Biology as models for testing the application of physics findings to biophysics in the context of complex multiscalar biosystems, genomic medicine, and Alzheimer’s Disease.

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Information Systems Biology: Biophysics, LLMs, and AdS/Biology
Melanie Swan, Renato dos Santos, 08 Jul 2023
Keywords: biophysics, information systems biology, LLMs, AI genomics, generative AI,
mathematical ecologies, topological biophysics, multiscalarity, complexity, Alzheimer’s disease
Abstract
A question in the frontiers of systems biology is how generative artificial intelligence (AI)
technologies such as large language models (LLMs) and code interpreter chat interfaces are to be
applied to outcomes in human disease and well-being. Biology is one of the last fields to digitize
due to complexity, technological constraints, and privacy concerns. At present, large data
corpora are being instantiated in LLMs, natural language for human-facing applications, and
perhaps even more powerfully, formal languages (software programs, mathematics, physics) for
human-directed AI problem solving. AI technologies may accelerate the formalization path of
biology from descriptive to quantitative, mathematical, and theoretical science. Biology is under-
theorized compared to physics and physics is possibly under-deployed in biology. The modern
computational infrastructure implies greater expediency in testing the relevance of physics
findings for biology. In the context of AI genomics, this work introduces information systems
biology to highlight information as a primary organizing principle in biology, and an example,
AdS/Biology (anti-de Sitter space) and AdS/Genomics as a model of multiscalar renormalization
physics (identifying near-and-far entropic correlations in systems) targeting Alzheimer’s disease.
Although AI has risks, the broader message is harnessing computational technologies to hasten
scientific progress, particularly in disease resolution.
“Today, biology is information, genome sequences are laid out in silico, and life is defined in
terms of information transfer” – Nick Lane, The Vital Question, 2015, 22
1 Introduction
The study of biology is becoming more digital, formal, and multidisciplinary. The large-
scale quantitative experiments that are the norm in many areas of science are also becoming
routine in biology, for example million-member whole-human genome studies (e.g. 5.4 million
individuals of diverse ancestry (Yengo et al., 2022)). Biomathematical models are starting to shift
away from small-scope individually-focused projects (possibly with heavy parameter fitting)
towards the identification of global mathematical explanations, for example, the statistical
mechanics of oscillation and avalanche pulses in the resting state of the human brain (Lombardi
et al., 2023). The mathematization of various areas of biology in turn is leading to the ability to
posit theories that are more general in scope, have greater predictive power, and focus on the
elaboration of underlying principles (Rout and Sali, 2019). Multidisciplinary study in biology
continues to grow with fields such as biochemistry and biophysics. Systems biology is defined as
the computational and mathematical study of biology as multiscalar systems comprised of
interrelated parts (Tavassoly et al., 2018), a concept including the ongoing the formalization path
of biology with digital methods.

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This work argues that the computational infrastructure is advancing in general, and that
this means the deployment of formal tools to all problem areas, especially systems biology as
problems that were previously too complex become tractable. The computational infrastructure
refers to the globally-available network of digital formal methods, tools, and knowledge bases
(programmatic code, mathematics, physics, chemistry, computational biology, bioinformatics,
algorithms, and data corpora). The formalization of the computational infrastructure means that
more formal methods are being digitized and added to the computational infrastructure, in
particular, the digitization of mathematics and physics. The point is that the computational
infrastructure includes not only the familiar range of computing platforms and data banks, but
also increasingly, formal analysis tools facilitating user engagement with mathematics, physics,
and programmatic code. The current moment is not just a computing phenomenon but a
formalization phenomenon, providing greater access to formal methods for more expedient data
analysis and problem resolution, particularly via the new and indispensable tool of human-AI
chat interaction for access to these formal methods.
The implication of the contemporary advance in computational infrastructure is first,
greater interdisciplinary connection between formal methods (code, mathematics, physics) as a
general approach, and second, greater formalization in domain-specific approaches, with biology
as the specific case of interest here. Some concrete examples are as follows. First is the field of
cancer genomics, which undertakes the routine sequencing and computational analysis of whole-
cancer genomes to assess cancers for personalized therapy interventions through known
quantitative mutagenic signatures in point mutation, copy number alteration, and structural
variation (Cortes-Ciriano et al., 2022). Second is the use of coding theory (Boolean networks and
Hamming (ordered) graphs) to prove the robustness of a genotype-phenotype mapping scheme
for folded protein and gene-regulatory network RNA sequence prediction (Mohanty et al., 2023).
Third is the use of statistical physics modeling in adaptive neural networks to explain the
coexistence of oscillatory and avalanche behavior in human brain resting states (Lombardi et al.,
2023). Fourth is the high-profile announcement of AlphaFold (Jumper et al., 2022), an
innovation employing computing platforms, algorithm development, biochemistry, and
biophysics to catalog the protein structures of the human proteome and other model organisms in
a database with over 214 million protein structures. The examples exhibit the deployment of
multiple formal methods applied in the biology context.
2 Materials and Methods
This work employs the method of describing key aspects of the formalization of the
computational infrastructure as a general situation, and then investigates how this broader
phenomenon is being applied to the formalization of systems biology (Figure 1). Two salient
points are identified and discussed regarding the computational infrastructure. First is the use of
AI chat interfaces in the scientific endeavor with generative AI tools (human-prompted AI
content generation) and code interpreter functionality (research copilot data analysis). There are
novel opportunities for humans to chat with a paper, set of equations, research area, or data
corpus, with an interactive copilot to analyze results, graph equations, generate data, and carry
out experimental lab work (especially via OpenAI’s ChatGPT Code Interpreter plug-in (Tu et al.,
2023b) and autonomous research agent systems (Boiko et al., 2023)). Second, quantum
information science is elaborated as a known potentially-emerging computation platform, but
more broadly as a method for the treatment of high-dimensional data (often deployed through

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tensor networks (mathematical structures for instantiating data in tensors for more expedient
manipulation and analysis)).
FIGURE 1 Information Systems Biology Flowchart.
After evaluating the formalization process of the computational infrastructure generally,
the method proceeds to examine the formalization process of systems biology, considering both
theory and practice. First, three new potential entrants in the theory space of biology are
presented, information systems biology (considering information as a primary organizing
principle in systems biology), the “Maxwell’s demon of biology” concept (efficiency-sorting
mechanisms directing biological activity), and genomic medicine (the theory that structural,
condition-related, and gene regulatory expression genomics substantially directs biological
processes). Second, specific practices in biophysics (biology as laws-of-physics obeying physical
systems) are framed in terms of how three research programs are applying physics research to
systems biology. These include topological biophysics (mathematical topology approaches to
problems in biology), Chern-Simons biology (Chern-Simons theory applied as a solvable
quantum field theory to formulate problems as min-max curves for the easy identification of
system events (genetic mutation, neural signal, protein docking), and AdS/Biology (the
AdS/CFT correspondence employed as a multiscalar system renormalization technique for
identifying near-far correlations in systems by describing a bulk volume from a boundary or vice
versa) with examples in AdS/Genomics, krill swarming, and neural signaling.
Following the elaboration of the formalization process of the computational infrastructure
in aggregate and as applied to systems biology through biophysics research programs, a
discussion is presented highlighting the use of computational tools in the contemporary study of
Alzheimer’s disease and proposing an SIR-type compartmental model for the realization of
precision health in large-scale populations (groups of individuals constantly cycling through the
phases of Sustaining health, Intervening on a preventive basis, and Recovering their health).
Finally, the overall project is summarized and future work is considered.

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3 Results
3.1 Information Technology and Systems Biology
“We are at the beginning of a new era of digital biology” – Demis Hassabis, Google DeepMind
AlphaFold, recipient of the 2022 Breakthrough Prize (Callaway, 2022)
Digitization is the process of converting information (text, pictures, sound, genomes,
equations) into digital form readily processed by a computer, with computational methods and
informational approaches for accessing these data. The implication is that any form of digitized
content joins the computational infrastructure and can be readily mobilized and deployed by
human and AI agents to a variety of contexts. What is different is that not only piecemeal
contents are digitizing but rather entire data corpora, all human natural language in online chat
interfaces, all software code, all academic literature, and possibly the entirety of mathematics and
other knowledge bases. The further implication is using AI tools to analyze and fill in missing
areas in these knowledge graphs. This has already been seen in the “Software 2.0” approach of
machine-designed and programmed code per human specifications, which is capable of
delivering substantially greater output (Karpathy, 2017).
The information era project of digitization is ongoing. The earliest fields where news,
entertainment, and finance in the internet boom of the 1990s, followed by the advent of academic
data science institutes in the 2000s (Donoho, 2017). Fields such as chemistry and astronomy are
conducive to automated approaches with particle-many molecular dynamics simulation and
large-scale data collection and processing free of privacy concerns. Biology has been slower to
digitize per more challenges in levels of complexity (emergence, dynamism, multiscalarity),
technological advance (genome sequencing methods), and human data use regulations. However,
modern scientific approaches and computational methods facilitate the digitization of biology in
new ways. Integrated fields such as biophysics, biochemistry, and computational biology provide
new systems-level investigatory lenses for improved multidisciplinary study.
3.1.1 Artificial Intelligence
A new phase in AI has arisen through generative technologies (AI systems which create
text, images, video, audio, or other media content per user prompts), realized through large
language models (LLMs) such as chatGPT (generative pre-trained transformer) (OpenAI, 2021).
The platform is one of the most rapidly adopted worldwide technologies, reaching 100 million
users in January 2023 two months after launch (Plumb, 2023). LLMs are computerized language
models pre-trained on large data corpora with billions of parameters (coefficients for neural
network node weighting). Transformer neural networks are an advance in machine learning as
they analyze the entirety of a data corpus simultaneously to find relations between data elements
(Vaswani et al., 2017).
Transformer neural networks operate by the self-attention mechanism of dividing input
data into small packages (tokens), assigning three weight attributions (query, key, value), and
storing the information in vectors. The network nodes then broadcast messages about the kinds
of data they have and need to the network, which allows all input data to be evaluated
simultaneously, in a computationally-intensive manner. Previous methods tended to proceed
more slowly by analyzing local data and building it into a global model of the data set. Multi-
modality is feature of generative AI and transformer neural networks. For example, the Stable

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Diffusion project takes 1D smartphone text as input and creates 2D images and 3D video as
output, producing video on demand with a few-word text prompt. An important AI technique is
self-play, in which AI systems learn by playing against their own past performance. Related
methods are generative AI networks in which one network is pitted against another, and the fill-
in-the-blanks method of the system learning data analysis from deleted elements. Reinforcement
learning models are deployed in which agents have a learned model of the environment, a
decision-making policy, and a reward prediction mechanism (Sutton and Barto, 2018). A further
technique is position evaluation in which the learning agent is able to future-cast by self-playing
to-the-end many random scenarios and by using position evaluation, a meta-level assessment
(“blink” intuition to grasp a situation at once such as who is winning at Go, traffic, stock market
activity, or ideally, a disease diagnosis in the preventive phase).
Towards the long-term goal of general-purpose problem solving artificial general
intelligence, a generalist agent transformer neural network, DeepMind’s Gato, was announced in
November 2022 (Reed et al., 2022). The Gato system is reported to be able to perform hundreds
of tasks such as playing Atari games, captioning images, chatting, and stacking blocks with a
robot arm. A single neural sequence is run for all applications, embedding tokenized forms of the
data inputs (text, images, discrete values (Atari button presses), and continuous values
(proprioception, joint torque)) into a learning space. Gato undertakes various specified tasks, but
not necessarily new ones as the reinforcement learning rewards/loss function is coded to the
tasks. Transformer neural networks are also used to seed programming code, perhaps 80% of the
code required for a new application, for example, enacting the “Software 2.0” idea of programs
developing their own code (Karpathy, 2017), via AI tools e.g. GitHub Copilot and AlphaCode.
A notable deployment of biology as an information science and AI methods in biology is
AlphaFold, a transformer neural network project which released open-source data for over 214
million protein structures predicted from the underlying amino acid sequences in July 2022
(https://alphafold.ebi.ac.uk/). The outputs were derived with machine learning techniques
(involving a novel set of thirty-two algorithms) as opposed to the previous method of painstaking
human analysis of X-ray crystallography and electron microscopy, entailing years to identify the
structure of one protein. The 23-terabyte (1012) database encompasses one million species,
including the ~20,000 human proteins and those for various animal, plant, and bacterial entities
of interest (Jumper and Hassabis, 2022). A research consortium deems ~35% of the predictions
to be highly-accurate equivalents to those determined experimentally and another 45% to be
accurate enough for many applications (Callaway, 2022). AlphaFold is now being used to target
a new class of problems beyond the simple process of obtaining information, investigating
protein-protein interactions. Also as of July 2022, over 500,000 worldwide researchers (from 190
countries) had accessed the database and examined 1.5 million protein structures with over 3,000
citations (Hassabis, 2022).
There is a contemporary proliferation in LLM applications. Although initially trained on
data corpora such as Wikipedia and social media, LLMs are now being extended to the scientific
content, in both natural language literature review and formal language analysis (genomics,
physics, mathematics, chemistry). Literature LLM examples include bioGPT (biomedical text
generation and mining (Luo et al., 2023)) and PubMed GPT (a GPT model trained on PubMed
Biomedical Papers (Chopra, 2022)). In genomics, DNAGPT is a GPT developed for DNA
sequence analysis tasks, pre-trained on 10 billion base pairs from 9 species (Zhang et al., 2023).
LLMs are seen as a crucial tool for genomic analysis given the large scope of data and
interrelated parts (Nguyen et al., 2023; Batzoglou, 2023). Targeting the complexities of biology,

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CancerGPT uses LLMs to predict the impact of drug pairs (combination drugs) in rare tissues
that lack structured data and features (Li et al., 2023). In chemistry, ChemCrow is an LLM
chemistry agent designed to perform tasks in organic synthesis, drug discovery, and materials
design (Bran et al., 2023). Another team presents an autonomous research agent project for
scientific experiment design and execution (Boiko et al., 2023). The DeepMind team extends
their platform with a generalist biomedical artificial intelligence that can encode, integrate, and
interpret large-scale multimodal biomedical data (Tu et al., 2023a).
The digitization of mathematics is an important step in making formal methods accessible
in the computational infrastructure. It is not only a matter of representing and solving sets of
equations, but the new idea of “chatting” (interactively engaging) with the mathematics to
understand, write, mobilize, and solve equations, populated with data, towards endpoints. Math
agent functionality is incorporated in OpenAI’s Code Interpreter plug-in (July 2023) which
offers the ability to upload files and “chat with a paper” or “chat with the equations” in a paper
(Figure 2). Code Interpreter can generate data to fit equations (as an important automated step
towards solving systems of equations), graph results, and write, test, and debug code.
FIGURE 2 OpenAI ChatGPT Code Interpreter Plug-In: Chatting with a Paper and its Equations.
Basic interactive “math agent” functionality exists in a tool called MathGPT, a chatbot
tutor specific to math textbooks designed as a learning aid for student interaction (Ramirez,
2023). Math agents are reinforcement learning agents: AI entities (collections of algorithms)
targeted to learning and problem-solving in a domain with an action-taking policy and rewards
function, in interactive feedback loops with the environment (Sutton and Barto, 2018). The math
agent is conceived as an AI reinforcement learning agent operating in the mathematical domain
to represent and evaluate equations, generate data to solve equations, and further in pure math, to
engage in automated theorem proving, computational proof assistance, and algorithm discovery.
Math Agent functionality is emerging in several projects as follows. There is an LLM proposed
for mathematical reasoning (Yuan et al., 2023), a self-supervised learning model computing
PDEs (partial differential equations) with Lie symmetries (Mialon et al., 2023), mathematical

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embeddings of mathematical disease models (Swan et al., 2023), and in the meta-application of
using LLMs to create instructions for LLMs in complex and formal areas with the Wizard LM
tool (Xu et al., 2023).
3.1.2 Quantum Information Science
AI may be the headline in the development of the computational infrastructure, but
quantum information science is an important corollary. The important point is the use of
quantum information science as a method for the treatment of high-dimensional problems and
data irrespective of the implementation of such problems in quantum simulators or real-life
quantum computers. Parameters such as entanglement may be likewise investigated as
correlation in classical domains (Koutny et al., 2023). Quantum computing refers to the use of
quantum objects (atoms, photons, ions) to perform computation, controlling them with lasers and
microwave pulses to progress through the same kind of programmatic logic gates as in classical
computing (although with greater potential scalability and more environmental sensitivity
requiring error correction). The term “quantum” refers to the scale of atomic and subatomic
particles (10-12 picometers to 10-15 femtometers). Just as materials at the nanoscale (10-9
nanometers) exhibit scale-specific properties (surface area tension, van der Waals forces),
materials at the quantum scale likewise have special properties, mainly superposition,
entanglement, and interference which are used in quantum computation, materials, and networks.
A potential AI-quantum computing convergence could be visible in quantum machine
learning as the first widely-deployed application of quantum computing for optimization
applications in industry (Banner et al., 2023) and science (Dawid et al., 2022). Quantum machine
learning is machine learning algorithms reformulated for the (higher-scalability) quantum
environment, available on all three machine learning architectures: neural networks, tensor
networks, and kernel learning (Biamonte et al., 2017). Quantum transformer neural networks are
likewise emerging as the quantum version of transformer neural networks, adding native
quantum capabilities. For example, a quantum attention method uses Clifford algebra to multiply
a vector with a higher-dimensional compound matrix (an inefficient classical problem) (Cherrat
et al., 2022).
There is critique of quantum computing, however, in that that it may only be useful for a
small set of linear algebra optimization-related problems and not the analysis of complex
biological systems in general. Other work argues more fundamentally that all of the quantum
speedups demonstrated thus far are due to amplitude (difficult-to-interpret complex-number
formulations) (Aaronson, 2022). It is less disputed that a theoretical breakthrough in error
correction is needed for quantum computing to scale to general-purpose machines (Preskill,
2020). Quantum information science continues as an area of worldwide competitiveness
investment, and is seen in integrated edge-cloud implementation as opposed to one-off elements
(QPUs (quantum processing units; chips) or cloud services) (Furutanpey et al., 2023).
As of May 2023, 36 universities were offering quantum information science programs
(Quantum Evangelist, 2023). There is a proliferation of quantum disciplines, prominently
cryptography, with hack-proof quantum-safe algorithms still in development (in a potential shift
in cryptographic standards to those based on 3D lattice problems as opposed to the difficulty of
factoring large numbers) (US NIST, 2022). Other quantum applications are sensing (Wang et al.,
2022), chemistry (Arrazola et al., 2021), astronomy (Khabiboulline et al., 2019), finance
(Stamatopoulos et al., 2020), and the humanities (as digital humanities expand to include
quantum humanities (Barzen and Leymann, 2020)). The quantum biology field studies the

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functional role of quantum effects in living cells, but has only confirmed two instances (avian
magneto-navigation and tunneling in enzymes) (Appendix 2: Quantum Biology). Critics in the
trend to “dequantization” argue that classical explanations are sufficient. Work ensues
investigating quantum biophysics problems such as the reaction energies of proton transfer in
DNA hydrogen bonding (Winokan et al., 2023).
Quantum computing is implicated not only as an additional platform in the computational
infrastructure, but as itself an information modeling technology. The quantum modeling of
classical data may reveal hidden correlations within a system (Bradley et al., 2020). For example,
the quantum information science formulation of a problem concerning the black hole firewall
paradox (information evaporates from black holes but the implication for entanglement
relationships between outgoing particles and those remaining inside the black hole). The
quantum information science problem formulation helped to show that although it would be
possible to compute the answer to the problem, it would not be within a useful timeframe
(Harlow and Hayden, 2013). (Appendix 3: Quantum Error Correction).
3.2 Formalization of Systems Biology
The multiscalar aspect of biosystems has been insufficiently treated with previous
methods. Advances in computational technologies (artificial intelligence, quantum computing,
simulation (e.g. molecular dynamics)) and also data science (statistical physics, complexity,
dynamics) contribute to the ability to address multiscalar biosystems in new ways. Biology
presents specific multiscalar challenges since each tier (e.g. cells, tissues, organs) involves
separate processes and outcomes, as opposed to each scale being simply more dimensionality of
the same kind (as in time and space dimensional scaling in physics; the three dimensions of
space do not differ from one another). Different scale tiers may have different spatial, temporal,
and dynamical regimes (Breakspear, 2017) (Appendix 5: The Time and Space of Multiscalar
Systems) and analog, digital, or hybrid information processing modes (Shankar, 2021).
The brain comprises nine orders of magnitude scale tiers (Sejnowski, 2020), which might
be parsed into four levels to describe electrical-chemical neural signaling processes (Table 1).
Humans have an estimated 86 billion neurons and 242 trillion synapses (~2,800 synapses per
neuron) (Martins et al., 2019), but a comprehensive understanding of how they are connected
structurally and functionally is not fully specified. Structurally, the fruit fly connectome
(neuronal wiring diagram) was completed in 2018 (Zheng et al., 2018), and scaling up from
worm to mouse entails a 10-million-fold increase in brain volume (Abbott et al., 2020). It is
estimated that one zettabyte (1021) of storage capacity will be required for each human
connectome (Lichtman et al., 2014), as compared with an estimated 101 zettabytes of total data
generated worldwide in 2022 (Burgener and Rydning, 2022, 3).
TABLE 1 Four-tier Multiscalar Model of Neural Signaling.
Tier System Event Number Math Mode Scale Microscopy
1 Ion Molecular docking Unknown PDE Chemical 10
-
4
Light sheet
2 Synapse Dendritic spike chain 242 tn PDE Chemical 10
-
6
Light field
3 Neuron Action potential 86 bn ODE Electrical 10-9 Electron
4 Network Local field potential Unknown ODE Electrical 10-12 fMRI/EEG/PET
PDE: partial differential equation (multiple unknowns); ODE ordinary differential equation (one unknown)

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The table notes the different mathematical approaches that are necessary to address the
different scale tiers of multiscalar biosystems, namely partial differential equations (PDEs) as
progressing into more detailed tiers. Partial differential equations have multiple unknown
variables whereas ordinary differential equations (ODEs) typically solve for one unknown
variable. Topology and geometry mathematical approaches to biosystems with contemporary
advance as both treat shapes, which corresponds to the literal materiality of biology, and also
invariance and shortest-length curves in the mathematical modeling of biological phenomena.
Biology exists in three-dimensional space and one-dimensional time with the contemporary
scientific method elaborating dynamical behavior in time in addition to morphological
characterization in space. Understanding the interrelation between scale tiers in time and space is
likewise a crucial element in multiscalar biosystem modeling, particularly to identify causality
and target intervention.
A successful information systems biology approach entails multiscalar model-fit analysis,
namely the informational representation of a system with the formal lens of mathematics
together with the practical lens of data substantiation. To demonstrate such an information
systems biology approach, multiscalar modeling is elaborated first from the formal lens of
topological biophysics, and then in the specific practical examples of krill swarming and neural
signaling in AdS/Biology theory. Further consideration of the biophysics of multiscalar
biosystems is elaborated in the appendix (Appendix 4: Physical Instantiation of Topologically
Modeled Multiscalar Biosystems).
3.2.1 Systems Biology Theory
The greater digitization, quantification, and mathematization of biology in a formalization
path could enable a flourishing theory space. Some of the familiar theories of biology include
Darwinian evolution, Mendelian genetics, cell theory, homeostasis, and the germ theory of
disease (Wilkin and Gray-Wilson, 2016). However, a rich “theoretical biology” domain does not
exist in the same way as theoretical physics (Davies and Walker, 2016). Novel theorizing is
implicated as biology is entering a phase beyond simply collecting data and writing equations to
predict these data. What is required is new levels of imagination and qualitative reasoning, to
rearrange the order of the world in a different way within a new conceptual structure for
understanding (Rovelli, 2023). The same formal progression seen in physics might be realized
similarly in biology (Bialek, 2017). Some of the new theoretical organizing principles could be
related to information, efficiency, and genomics.
3.2.1.1 Information Systems Biology
As discussed, systems biology is the computational and mathematical study of biology as
multiscalar systems comprised of interrelated parts (Tavassoly et al., 2018). This work names
“information systems biology” not only to identify information as a primary organizing principle
in biological systems (Davies and Davies, 2016), but also to further codify information in both
the computational and physical sense, connecting computer science and physics to the study of
biology. Information systems biology treats biology as multiscalar systems of information
creation, representation, and transfer, and can be observed in three ways. First is in the
identification of information representations in biological domains (e.g. DNA, folded proteins,
molecular knots, proton pumps). Second is the use of information technologies to study biology
(e.g. machine learning, quantum circuits, crystallography) in the advent of computational biology
and bioinformatics. Third is in the conception of biology as itself an endeavor of information

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creation, representation, and transfer (Nurse, 2020). An example of information systems biology
is the study of biochemical information processing in cells by quantifying information transfer
with information theoretic methods (Uda, 2020).
The benefit of information systems biology linking biology to computer science and
physics is that the tools of theory and practice in information-based physics are opened up for the
study of biology. Information has a specific technical definition which can be mobilized
computationally (the number of bits required to send a message) (Shannon, 1948). Information-
based formulations are more readily portable between classical and quantum computing
platforms than might be thought, which could facilitate the study of biosystem complexity as
quantum computing evolves. Quantum states are relevant to the quantum computing of any
problem, but have nothing to do with potential quantum effects in biological processes.
Formulating biological problems with information theory and studying them with quantum
computing methods is different than a potential claim of quantum effects being present in
biological systems (which has only been confirmed in a few cases, avian magneto-navigation and
tunneling in enzymes (Appendix 2: Quantum Biology)).
Biology has been formally conceived as an information science since the 1953 discovery of
the structure of DNA (Nurse, 2008). Information theory (the encoding and transmission of
information in sequences of symbols, states, pulses, and signals) is now further applied in
systems biology in the methodological study of gene regulatory networks, protein-protein
interactions, and metabolic networks (Chanda et al., 2020). However, long before the human
observer, evolutionary biology indicates the origins of DNA and RNA as four-letter code bases
for transmitting information (Wills, 2016). About four billion years ago on Earth, the purine
amino acids (G then A) likely arose first, then the pyrimidines (C then U) (Harrison et al., 2022).
3.2.1.2 “Maxwell’s Demon of Biology”
One puzzle in biological theorizing is providing an explanation for why some processes are
efficient and others are not. The “Maxwell’s demon of biology” (efficient sorting mechanism)
concept denotes the situation that biology often quickly arrives at efficient solutions (Davies,
2019). Protein folding is one example in which the final conformation of amino acids occurs in
one millisecond on average, for example, without cycling through the entire possibility space
(Street, 2016). Other biological processes likewise are not random but have a built-in efficiency
mechanism that is still being elaborated, one model purports to describe iron displacement in
heme proteins on the basis of temperature and forces (Seyedi and Matyushov, 2017). However,
in other cases, biology is tremendously wasteful, proceeding by massive proliferation in the
possibility space, followed by an equally massive prune back (Chaitin, 2012). In two examples, it
is not mathematically clear how the Cambrian explosion of body plans resulted in today’s form
factors, and how out of the vast field of examples in the Burgess Shale fossils in the Canadian
Rockies, one worm became the ancestor of all descendant vertebrates including humans (Morris
and Caron, 2012).
3.2.1.3 Genomic Medicine
Genomics is emerging as a high-level explanatory mechanism for various aspects of
disease even though it is complex in application and not fully enumerated. The routine use of
whole-human sequencing and cancer tumor sequencing (Zhao et al., 2019) helps in the
realization of precision health (individually-targeted interventions such as CAR T-cell
immunotherapies (chimeric antigen receptor)). DNA is implicated in the contemporary study of

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disease in three ways, assessing structural variation (insertions, deletions, transposed elements),
disorder-associated variants, and underlying gene regulatory mechanisms (Liu et al., 2022). RNA
is also implicated in identifying mRNA and proteins circulating in the blood (through expression
quantitative trait loci (eQTLs)). A comprehensive investigation of DNA, RNA, epigenomics, and
proteins is required to illuminate how gene regulatory elements influence expression in cells
(Schreiber et al., 2023). In Alzheimer’s disease, 2,676 differentially expressed genes have been
found, upregulating and downregulating certain proteins in certain cell types (upregulation of
APOD, INSR and COL4A1 in brain tissues and downregulation of SLC6A1 in GABAergic
neurons and astrocytes, PDGFRB in pericytes and ABCB1 and ATP10A in endothelial cells)
(Sun et al., 2022).
3.2.2 Systems Biology Practice: Biophysics
Interest in biology as a physical system and the relation between physics and biology is
long-standing. Physicist Niels Bohr wondered how living processes might be understood in
terms of physics and chemistry, and how light’s dual nature as a particle and a wave might have
a conceptual equivalent in biology (Bohr, 1933). Max Delbrück pondered biological
organization, noting that “the same matter with orderly properties in physics arranges itself in the
most astounding fashion in the living organism” (1949, paraphrase), which has inspired the
current Max Delbrück Prize in Biological Physics. Erwin Schrödinger studied DNA, identifying
it as an aperiodic crystal with a “hereditary code-script of chromosomes” (Schrödinger, 1944, 5;
20). Linus Pauling discussed “The Nature of Forces between Large Molecules of Biological
Interest” in 1948. Elucidating the biophysics of the mitotic cleavage furrow in cell division in
1967, Ray Rappaport commented on the evolutionary nature of biology being more like an “old
Maine fishing boat engine: overbuilt, inefficient, never-failed and repaired by simple measures”
rather than an elegant “beautifully made Swiss watch” (Pollard, 2004; Canman and Wells, 2004).
Natural philosopher Immanuel Kant likewise considered “the contingency of nature and its
form” (Kant, 1790, §61, 188). Biophysics ensues as the science studying the application of the
laws of physics to biological phenomena.
3.2.2.1 Topological Biophysics
Topological biophysics is a growing field of topological mathematical approaches to
biology. Topology is concerned with invariance (the properties that remain invariant when
objects are perturbed (deformed or stretched, like a piece of clay)), and identifying conserved
invariant properties across multiscalar system tiers, including in a system-wide renormalization
picture, that is relevant for characterizing biological behavior. Like geometry, topology can be
studied with curves, in particular through Chern-Simons theory (a solvable quantum field
theory), in which system events (folded protein, genetic mutation, neural signal) are read as min-
max curvature. Topological biophysics is implicated in genomic medicine, in examples of the
DNA-RNA-protein synthesis value chain in the practical consideration of pathogenesis as
topological biophysics problems involving knotting, compaction, and misfolding (Table 2).
TABLE 2 Topological Biophysics and Genomic Medicine in Multiscalar Biosystems Study.
Domain Topological Method Description Practical Outcome
1
DNA
Topographical features
Same
mutagenic signature 40 cancer types
Identify cancer/precursors
2 DNA Liquid-crystal chirality
inversion
Reverse DNA chirality in doped solutions Lower-cost chemical bond
breaking process

Page 12
3 DNA Topological associated
domains
(TADs)
Study DNA’s liquid, gel, solid phases DNA repair methods
4 DNA DNA nanotechnology,
molecular nanoweaving
Weave 90° kagome lattices of weft-warp
threads
in a 7
4
knot
using
zinc
&
iron ions
Molecularly-precise
collagen peptide
5
Protein
Reaction
-
diffusion
Fisher
–
Kolmogorov, Smoluchowski
AD, PD, ALS
6 Protein Homotopy, non-convex
optimization
Solve PDEs with homotopy instead of
Newton’s method (root
-
finding)
AI/AD: identify fast build-
up
phosphorylated plaques
7 Protein Vassiliev topological
complexity
Develop new metric of topological
complexity to explain protein folding rate
Protein folding identified as
a continuous process
AD: Alzheimer’s disease, PD: Parkinson’s disease, ALS: Amyotrophic lateral sclerosis
These kinds of methods appear in the study of the topographical features of cancer
genomes. One project found similarity in mutational signatures in 5,120 whole-genome-
sequenced tumors from 40 cancer types. Various areas of histone modification, binding,
replication, and transcription asymmetries highlighted distinct mutagenic signatures persisting
into etiology (1) (Otlu et al., 2023).
A second line of topological biophysics research engages DNA as a liquid crystal (a state
between a liquid and a crystal), familiar from LCD computer screens as a form of matter in
which molecules retain order yet flow like a liquid. Promulgated by Schrödinger’s identification
of genes being in the form of an aperiodic crystal, contemporary methods manipulate DNA’s
liquid-crystal behavior with doped solutions. In the liquid-crystal phase, DNA’s chirality (right
or left-handed orientation) can be reversed by adding dopant (LuIII (Lutetium)) to a solution (2)
(Katsonis et al., 2020). The liquid-crystal DNA unfolds and refolds into the opposite chirality,
and then returns to its initial chirality upon dopant removal. The result is a lower-cost alternative
to the expensive covalent bond-breaking method used in chemical processing.
DNA is further studied through its phase transitions between liquid, gel, and solid forms
(3) (Eshghi et al., 2021). Topological associated domains (TADs) are implicated in DNA’s
natural compaction process of cycling between resting-state condensed form, decondensing for
transcription and repair, and then recondensing to resting-state. There is a potential link between
liquid-crystal DNA phases and topological materials, for example through AdS/Floquet-
engineered tools identifying novel electronic liquid crystalline ground states in short-range
interactions with spontaneously broken rotational symmetry (Esin et al, 2021), suggesting the
examination of correlated electron states in neurodegenerative plaques.
Topological advance is further seen in the field of DNA nanotechnology which brings
together topological knotting and molecular biology by using DNA as a building material. A
molecular nanoweaving project produces a molecularly-precise collagen peptide for use in
nanomedical applications (4) (Leigh et al., 2020). Zinc and iron ions are used to weave ligand
strands to form a 74 knot (7 is the number of crossings and 4 is the order of complexity; the basic
trefoil knot has three crossings (31)). Another team nanoweaves synthetic fabric in a precise 90-
degree kagome (triangle-hexagon tiling pattern) lattice of weft-warp threads (Lewandowska et
al., 2017).
Protein misfolding is the main near-term target of topological biophysics since protein
aggregates are a factor in neural disease pathogenesis. One research program investigates the
hypothesis that neurodegenerative disease adopts prion-like mechanisms (misfolding) and
spreads out systemically through anatomically-connected brain networks (5) (Fornari et al.,
2019). The project simulates misfolded protein spread using three kinetic models of nonlinear
reaction–diffusion (Fisher–Kolmogorov, Heterodimer, and Smoluchowski) to calculate the
concentration of misfolded-to-healthy proteins with one, two, and multiple unknowns. The result

Page 13
is further confirmation that protein clearance is an issue in various neuropathologies: amyloid
beta plaque build-up in Alzheimer’s disease, alpha-synuclein protein build-up in Parkinson’s
disease (Madsen et al., 2021), and mutant TDP-43 and KIF5A deposits in amyotrophic lateral
sclerosis (ALS) (Baron et al., 2022). Other research develops the hypothesis that Alzheimer’s
disease is type 3 Diabetes, as diabetes is often an associated precursor and mutations in the ApoE
gene (a cholesterol transporter) may lead to poorly controlled blood sugar in the brain (de la
Monte and Wands, 2008). Viral infections (pneumonia, encephalitis) are likewise indicated as a
systems-level precursor to Alzheimer’s and Parkinson’s disease risk, as a study of 450,000
participants indicates (Levine et al., 2023).
Further research in topological protein folding uses machine learning to measure the pace
of protein aggregate build-up in Alzheimer’s disease, in order to identify intervention candidates
(6) (Hao et al., 2022). The work solves a problem in the machine learning field to enable not
only convex optimization but also nonconvex optimization (the ability to consider multiple
feasible regions in a landscape with different regions of curvature, saddle points, and local
minima). Instead of calculating PDEs (partial differential equations) with Newton’s method (a
root-finding algorithm finding successively better approximations), homotopy (same topology) is
applied as an alternative to gradient descent to map inputs to outputs as a continuous
deformation. The method is resource-costly but accommodates a wider range of specialty
situations such the complexities of assessing amyloid beta accumulation that then initiates tau
protein phosphorylation in neurodegenerative disease.
Finally, other work uses continuous versus discrete time to examine why proteins have
different folding rates since sequence length alone does not account for folding time. A study
formulates the second Vassiliev measure (a continuous-function real number) as a new metric of
topological complexity which describes protein folding as a continuous process in 95% of
proteins studied (7) (Wang and Panagiotou, 2022).
3.2.2.2 Chern-Simons Biology
A specific form of topological biophysics appears in the Chern-Simons biology research
program, inspired by the AdS/CFT correspondence (Bajardi et al., 2021, 4), but developed
through Chern-Simons theory. The method is deployed across the DNA-RNA-protein synthesis
system, analyzing problems primarily as topological min-max curves, but also as knotting
polynomials, and with Wilson loop expectation values. Projects include DNA mutation in cancer
(KRAS oncogene) (1), RNA (DNA-RNA transcription in host-pathogen interaction) (2), and
protein (unknotted RNA-knotted protein interaction, protein docking as a time series of knots)
(3) (Ibid.; Capozziello et al., 2018; Capozziello and Pincak, 2018) (Table 3).
TABLE 3 Chern-Simons Biology.
Domain Topological Method Description Practical Outcome
1
DNA
Chern
-
Simons
Analyze
DNA mutation (KRAS oncogene)
Cancer (colorectal, lung)
2 RNA Chern-Simons Formulate DNA-RNA as a knot
polynomial
in quaternionic projective space
DNA-RNA transcription in
host
-
pathogen
relation
3
Protein
Chern
-
Simons
Protein
-
d
ocking
per
knots in
time serie
s
Stable protein behavior
3.2.2.3 AdS/Biology
Another multiscalar physics model applied to systems biology is AdS/CFT. AdS/Biology
is introduced as the life sciences interpretation of the AdS/CFT correspondence for renormalized
multiscalar biosystems modeling in successive tiers of bulk-boundary relationships to identify

Page 14
near-far entropic correlations in systems (e.g. cis-trans (near-far) gene regulatory networks in
genomic medicine) (Liu et al., 2022). The AdS/CFT correspondence (anti-de Sitter
space/conformal field theory) is a theory that a bulk volume may be described by a boundary
field theory in one fewer dimensions (Maldacena, 1999), a substantial benefit for the
computational realization of the model (Vidal, 2008). Although developed in the context of
quantum gravity theories relating general relativity and quantum mechanics, the AdS/CFT
correspondence pertains to any physical system, whether the universe, a black hole, a classroom,
a brain, a cell, or an ecological food-web, and has been widely applied to physical systems
(Appendix 1: AdS/CFT Studies). The correspondence is defined in the frame of a two-tier bulk-
boundary gravity-gauge system, applied to black holes (unknown bulk and known event
horizon). However, the model might be deployed likewise to any number of nested tiers in a
multiscalar system, particularly biosystems with various mathematically unknown bulk-
boundary levels, such as the nine orders of magnitude scale tiers of the brain.
In the AdS/CFT correspondence, the bulk-boundary regions are connected in a duality
relation such that a system can be solved from either side. The two main examples are first, in
the boundary-to-bulk direction, calculating an unknown theory of emergent bulk structure such
as quantum gravity from a known field theory on the boundary, and second, in the bulk-to-
boundary direction, starting with a known gravity theory in the bulk (Einsteinian gravity) to
formulate an unknown quantum field theory for an exotic topological material on the boundary
(Sachdev, 2010). The AdS/CFT correspondence continues to be an active discovery frontier in
physics, and the research question is whether these findings are relevant for application to
biosystem modeling. In early work, it was articulated that the boundary region identifies the
maximum amount of information in a region, obtained by calculating the bulk entropy (number
of possible quantum states) from the boundary surface (Bousso, 2002). Further work suggests
that the entropy of bulk volumes may be computed from geometric curvature alone (Almheiri et
al., 2019). More recent work investigates the time conditions under which isometric codes
(inner-product preserving mappings) are unavailable (Akers et al., 2022).
Mathematically, the AdS/CFT correspondence includes both geometry and topology. On
the geometry side, the correspondence is used to study models of gravity (the geometric
curvature of space-time) through geodesic (shortest-length) curves through the bulk. On the
topology side, topological entanglement entropy formulations help to identify correlations in
subsystem layers in the measure of long-range quantum entanglement in many-body quantum
states (interrelatedness) and are quantum conducive (Kitaev and Preskill, 2006). Integrated
formulations of topology and geometry are arising in complex biosystems study, with the
mathematical method of persistent homology (computing the features of a space at different
spatial resolutions) being applied in the multiscalar multidimensional modeling of high
dimensional data (molecular dynamics) of the transition from partially-folded to fully-folded
protein (Xia and Wei, 2015). AdS/Biology is conceived as a mathematical modeling technique in
which problems are structured in the frame of geodesic curves from which shortest-length
distances are readily computable, and curve min-max values correspond to system events
(genetic mutation, neural signal).
An important feature of the AdS/CFT correspondence for AdS/Biology is that it is a
renormalization technology which offers the ability to view a multiscalar system in one picture.
Renormalization is the mathematical process of identifying a salient quantity (“gauge
symmetry”) that is conserved across system tiers, thus allowing a system to be rolled up or
zoomed in for relative viewing at any scale tier. In renormalization, an iterative coarse-graining

Page 15
method is applied to extract the relevant features as a physical system when examined at
different length scales (Wilson, 1975). The conserved quantity is a property which remains
invariant across system scales. An example of gauge symmetry is a gauged shotgun, which has
structural invariance but may accept different “scale tiers” of bullet size. In neural signaling, a
neuronal gauge theory is proposed based on rebalancing free energy as the gauge symmetry that
is conserved across the system (Sengupta et al., 2016). In the universe, symmetry is a conserved
quantity, the property that objects look the same from different points of view, for example, a
face, a cube, or the laws of nature.
Another useful feature of the AdS/CFT correspondence for AdS/Biology is the built-in
“formalization package,” namely, access to the large suite of computational methods that have
been developed to instantiate the correspondence. The AdS/CFT formalizations include a variety
of classical-quantum and quantum information science methods such as Multi-scale
Entanglement Renormalization Ansatz (MERA) tensor networks, quantum error correction codes
(QECC) and the computational ease of computing systems in one fewer dimensions. MERA
tensor networks are the leading tool for implementing the AdS/CFT correspondence,
renormalizing entanglement as the key property (there could be others) for eliciting cross-tier
correlation relationships in multiscalar systems (Vidal, 2008). The MERA tensor network has an
architecture familiar from machine learning of alternating layers of disentanglers and isometries
which renormalize or coarse-grain (consolidate) a system between microscale and macroscale.
MERA tensor networks are applied to bulk-boundary problems as follows. Each two
starting nodes (data inputs) on the boundary are renormalized to one node in the next tensor
network tier on the way to the bulk center (Swingle, 2012). Each node corresponds to the
entanglement entropy at that point in space. The renormalization geometry (read as shortest-
length bulk curves (geodesics)) ends when the coarse-grained states are completely factorized
into one final network kernel at the center of the bulk. The same process is then reversed to
provide a renormalized description of the boundary. Boundary entropy is calculated (as the
reduced density matrix of boundary blocks of states), and also the entropy contribution of each
scale tier. This metric could signal the relevant scale tier of a system-wide phenomenon. MERA
tensor networks use boundary properties as shorthand for describing behavior inside the volume
(McMahon et al., 2020). In a specific example of AdS/ML (the correspondence instantiated in a
machine learning architecture), the emergent network structure (weights) indicates the bulk
emergence in the physical system (e.g. the bulk metric (measure) of chiral condensate threshold
temperature) (Hashimoto et al., 2021).
Overall, AdS/Biology is an information systems biology approach to multiscalar
biosystems which applies the AdS/CFT correspondence in the context of multi-tiered biosystem
complexity. The requirement is a framework that is flexible yet mathematically formal which can
articulate multiple system levels and cross-tier interactions, considering various informational,
temporal, and spatial properties, and modes of information processing in the different scale tiers.
Solving bidirectional bulk-boundary problems could help to identify the relevant scale tier of
causal behavior in multiscalar biosystems, for example in the following cases. The pathogenesis
(unknown) of a tumor (known) needs to be elicited (boundary-to-bulk), neural waveform data
from EEG and fMRI imaging (known) needs to be built into a theory of neural signaling
(unknown) (bulk-to-boundary), and the role of thousands of ions and molecules observed at
synapses (chemical signaling) (known) needs to be related in a theory (unknown) of subsequent
larger-scale behavior (e.g. dendritic spike trains (electrical signaling) (bulk-to-boundary)).

Page 16
3.2.2.3.1 AdS/Biology: General Application
The general use case of AdS/Biology would be starting with a known phenomenon in
either the bulk or the boundary and solving for the unknown mathematics on the other side
(Table 4). This could be a tumor detected at the macroscale on the boundary, but whose complex
oncogenesis is unknown (1). This could be having detailed microscale data of bulk activity from
EEG and fMRI imaging, and attempting to generate a boundary theory to explain aggregated
behavior in healthy resting states as compared to epilepsy (2) (Lombardi et al., 2023; Bialek,
2023). A third example is the clinical presentation of Alzheimer’s disease as a detectable
pathology on the boundary, and wishing to understand the complex interrelations in the bulk
which produce the disease (3) (Sun et al., 2023). Finally, in the bulk-to-boundary direction, the
bulk locations of cis-trans (near-far) regulatory element locations are known through whole
genome sequencing, but not how they are activated to incite inflammation and pathologies of
aging (4) (Khorsand and Hormozdiari, 2021).
TABLE 4 AdS/Biology: General Application Examples in Systems Biology.
Formulation Direction Bulk Boundary
1 Cancer Boundary-
to
-
Bulk
Oncogenesis (unknown) Tumor (known)
2 Epilepsy, resting
state
Bulk-to-
boundary
Molecular, waveform data (EEG,
fMRI) (known)
Theory of dendritic
spiking, neural signaling
(unknown)
3 Alzheimer’s disease Boundary-
to
-
Bulk
Regulatory gene interactions
(unknown)
Condition (known)
4 Pathologies of Aging
(inflammation)
Bulk-to-
boundary
Regulatory gene locations (known);
cis-trans (near-far) analysis per
GWAS, EWAS, eQTL
variants
Condition activation,
predictive precursors
(unknown)
The AdS/Genomics research program develops nested tiers of bulk-boundary
relationships in the context of genomic medicine (Figure 3). Specifically in the DNA-RNA-
Protein synthesis chain, a blood test measure of Aβ42/Aβ40 amyloid plaque is a known
boundary value, triggered by emergent structure in the bulk as the aggregate of a complexity of
unknown factors in gene regulatory network operations and RNA expression patterns. The
diagnosed condition (Alzheimer’s disease) is a known boundary value, to the unknown bulk
relations of biomarkers, themselves the known boundary to the unknown RNA bulk activity,
which in turn is the known boundary to the unknown bulk of DNA operations. In the future, the
schema of genomic factors could be analyzed in bulk-boundary relations such that precision
health initiatives are able to intervene and prevent disease occurrence.

Page 17
FIGURE 3 AdS/Genomics for Precision Health.
Although there is not yet a generalized set of equations for the AdS/CFT mathematics,
the program often includes four main functions. These are the Metric (ds = ) (specifying the
space time and distance measurement properties of the system), the Action (S = ) (predicting
system dynamics over time), Operators (O = ) (mathematical functions that can act on the
system), and the Hamiltonian (H = ) (summary of system energy or states) (Zaffaroni, 2000).
There are tools for the execution of AdS/CFT research such as MERA tensor networks
(https://www.tensors.net/mera), a format supporting high-dimensional entangled (correlated)
models in classical and quantum domains.
Some examples of applied AdS/CFT with mathematics and data have been established as
prototypes. One project evaluates holographic superfluids at zero temperature in a model using a
bulk gravitational mapped to a boundary dual to assess a second-order phase transition system
event (Guo et al., 2016). Holographic superfluids are fluids with more than one kind of collective
propagating motion, and models for their study could be relevant to the nematic liquid crystal
modeling of biological processes. Another project implements the AdS/CFT correspondence in a
machine learning architecture in which the emergent network structure (weights) describes the
bulk emergence in the physical system (chiral condensate threshold temperature) (Hashimoto et
al., 2021).
One line of contemporary AdS/CFT research involves describing how a bulk
entanglement wedge influences the boundary state. Two projects which could be tested for
relevance to the biological domain are a random tensor network program defining entanglement
purification as a strong measure of correlation (Akers et al., 2023) and a project using asymptotic
codes to prove a relation between the bulk and the boundary since the mapping between the two
domains is not isometric (one-to-one) (Faulkner and Li, 2022). The idea is to investigate new
kinds of bulk-boundary relationships being enumerated in physics to biology, specifically
genomic medicine.
3.2.2.3.2 AdS/Biology Example: Krill Swarming
Two examples of multiscalar ecosystems in which an AdS/Biology program of integrated
mathematical ecologies is implicated for mathematical modeling operates are krill swarming and
neural signaling. Whereas it is difficult to obtain human data for neuroscience projects, a similar
four-tier ecosystem model is krill swarming, in which data and mathematics are extant. Real-life

Page 18
data have been modeled with biophysics methods at four ecosystem scale tiers. Hence, a parallel
approach in neuroscience might be formulated to examine the multi-tier biosystems at their
respective scale levels of light-phytoplankton-krill-whale and ion-synapse-neuron-network.
Some of the proposed mathematics for krill swarming is advection-diffusion-Lagrangian-
predation (Table 5), and for neural signaling is harmonic curvature-oscillation-kinetics-neural
field theory master equations (Table 6). A set of equations has been proposed for each scale tier
in these real-life ecosystems (Reynolds et al., 2006; Heggerud et al., 2021; Hofmann et al., 2004;
Miller et al., 2019), but whether the mathematics are correct, and might be joined in an aggregate
systems-level view is unclear. Such a project is the target of an integrated multitier renormalized
mathematical program such as AdS/Biology.
TABLE 5 AdS/Biomathematics in Multiscalar Ecosystems: Krill Swarming.
AdS/Krill Swarming
Tier
Event Mathematics Reference
1 Light rays (gradient) Incidence angle Advection Reynolds, 2006
2 Phyto-plankton Food availability Diffusion Heggerud, 2021
3
Krill
Swarm
Lagrangian
Hofmann, 2004
4 Whale Predation Lotka-Volterra Miller, 2019
Krill swarms comprise the largest known animal aggregations with up to 30,000
individuals per square meter. In the prevailing krill ecosystem mathematics, the first two bulk-
boundary pairs, light-phytoplankton (phytoplankton food availability) and phytoplankton-krill
(krill swarm formation) are modeled with Brownian motion, and the third tier, krill-whale (whale
predation), with statistical distributions. Phytoplankton food availability is a diffusion problem
interpreted as dissolved nutrients and light (Reynolds, 2006), modeling the incident light gradient
with Brownian motion (Heggerud et al., 2021). Specifically, the rate of change of the
phytoplankton density is modeled as an expression of diffusion – buoyancy + absorbed photons
– death rate. Krill swarm formation is a Lagrangian expression based on four factors: random
displacement + response to food gradients + nearest neighbor interaction (per attraction-
repulsion) – Lotka-Volterra predation (Hofmann et al., 2004; Lagzi et al., 2019).
An alternative model for krill swarm formation applies a Kuramoto oscillator to describe
synchronized movement in time and space per krill self-positioning to draft in the hydrodynamic
propulsion jet of the nearest front neighbor per metachronal pleopod (fin) stimulation (O’Keeffe
et al., 2022). The predation of krill by whales is modeled with hotspot clustering and statistical
field theory (Miller et al., 2019). Topological models are used to describe the photosynthetic
light-phytoplankton interaction. Plankton do not swim but manage their buoyancy (sinking,
rising, levitation) by adjusting their cell volume, including by inflating topological structures in
their cytoplasm five-fold within fifteen minutes (ten-fold in longer timeframes; without dilution)
(Larson et al., 2022). Toroidal versus spherical cytoplasm modeling provides a better account of
the inflationary behavior, as observed in the model organism (bio-luminescent dinoagellate
Pyrocystis noctiluca) with live-cell light-sheet microscopy.
3.2.2.3.3 AdS/Biology Example: Neural Signaling
Neural signaling is a multiscalar domain of interest as it is related to pathologies of
neurodegeneration, memory, and plasticity. AdS/Neuroscience research programs study the
multi-tier complexity of the brain with the AdS/CFT correspondence. One project, AdS/Neural
Signaling, outlines the study of neural signaling behavior at the scale tiers of ion, synapse,

Page 19
neuron, and brain network (Swan et al., 2022). Another project, AdS/Memory, hypothesizes that
greater storage capacity may be available in critically excited states as opposed to in the more-
frequently studied ground states (Dvali and Gomez, 2014).
In neuroscience modeling, various bodies of mathematics have been proposed for the
different scale tiers, which might be tested and joined into one systems-level picture with the aid
of computational methods. The most general proposed mathematics for neural signaling across
scales consists of harmonic curvature-oscillation-kinetics-neural field theory master equations. In
the direct phenomenon of neural signaling, the traditional proposed mathematical structures are
bifurcation and reaction-diffusion equations, formalized with path integrals (Bressloff, 2021),
oscillation and avalanche synchronization models (Lombardi et al., 2023; Budzinski et al., 2022),
neural mass and neural field theories of whole-brain collective behavior (Buice and Cowan,
2009; Byrne et al., 2020), and network neuroscience (Chen et al., 2022; Papadopoulos et al.,
2020).
TABLE 6 AdS/Biomathematics in Multiscalar Ecosystems: Neural Signaling.
AdS/Neural Signaling
Tier Event Mathematics Scale Reference
1
Ion
Docking
Harmonic curvature
10
-10
Cugno
, 2018
2
Synapse
Dendritic spike chain
Synchronous oscillation
10
-6
Garcia, 2022
3
Neuron
Action potential
Protein kinetics
10
-4
Fornari, 2019
4
Network
Local field potential
Neural field theory, networks
10
-2
Byrne, 2020
One multiscalar model of neural signaling consists of three tiers to describe behavior at
the microscale (molecular dynamics of Ca2+ and neurotransmitters), mesoscale (neurotransmitter
release from vesicles), and macroscale (information processing in neural circuits) (Garcia et al.,
2022). In the neural signaling process, a neuron issues an electrical spike (action potential) which
travels down the axon and enters the presynaptic terminal by causing a calcium channel to open
and calcium ions (Ca2+) to be released. The presynaptic terminal is a storage depot located at the
end of the neuron (synapse). In response to incoming calcium ions, certain vesicles (storage
sacks) are moved to the active zone at the edge of the synapse and their cargo (neurotransmitter
molecules) is disgorged into the synaptic cleft between neurons.
There are different neurotransmitter molecules; primarily glutamate for excitatory signals
and GABA for inhibitory signals, with the glutamate receptor NMDA (N-methyl-D-aspartate)
being the most-studied. The usual applied mathematics is Markov chain Monte Carlo methods
(deployed in the MCell axonal simulation software (Tapia et al., 2019)) applied to molecular
dynamics in the context of relating calcium waveforms to neurotransmitter release (as defined by
the curvature of release-rate functions). Both fast and slow mechanisms for neurotransmitter
release are implicated depending on the situation, and synchronous release occurs close to the
calcium influx, while asynchronous release occurs at all distances (Garcia et al., 2022).
On the other side of the 20-nanometer synaptic cleft, there is also a need to integrate
multiscalar behavior from the neurotransmitter molecules received at the dendrites into the
progressively expanding electrical dendritic spike chains that appear to communicate all the way
to the axon of the receiving neuron, for another potential outbound signal. One project finds that
the curvature of dendritic spine geometries gives rise to pseudo-harmonic functions per the
localization of fluxes on the spine head (Cugno et al., 2018), a finding which can be considered
in the AdS/Biology frame of the “boundary” neurotransmitter pulse being received at the post-

Page 20
synaptic density “bulk” in which dendrites reconfigure their shape (emergent bulk structure) to
process the signal, modeled as shortest-length geometric curves.
4 Discussion
4.1 Precision Health
4.1.1 Alzheimer’s Genomics
The aim of this work and the AdS/Biology approach is to connect scale tiers of
multiscalar biosystems into one renormalized picture of behavior for precision intervention. The
formalization path of systems biology improves the ability to address unsolved pathologies such
as Alzheimer’s disease. The contemporary situation is that formal methods are being applied to
the diagnosis and treatment of Alzheimer’s disease in new ways. A four-fold approach may be
employed involving the health data streams of genomics, imaging, biomarkers (CSF (Jansen et
al., 2022) and plasma (Li et al., 2022)), and cognitive assessment.
The genomic medicine approach to Alzheimer’s disease is a systems-level view which
comprises GWAS, EWAS, eQTL, and biomarker analysis to identify structural, condition-
specific, and gene-regulatory variants in the genome, and how they may be expressed in the
epigenome and biomarker fluids (blood plasma and CSF) (Sun et al., 2022). Whole-human
genome sequencing is first used to identify condition-specific variants (in GWAS (genome-wide
association studies)) (Bellenguez et al., 2022; Wightman et al., 2021). Genome sequencing is
also used to identify structural aspects which contribute to disease risk (transposable elements,
insertions, deletions, CpG islands) (Khorsand and Hormozdiari, 2021). Genome sequencing is
further used to assess epigenetic signatures in regulatory gene networks (in EWAS (epigenomic-
wide association studies) (Smith et al., 2021), and expressed transcripts in blood plasma (via
eQTL analysis (expression quantitative trait loci) indicating mRNA transcript abundance)
(Reddy et al., 2022).
Imaging (MRI and PET scans) may be used to identify and confirm the presence and
level of amyloid beta accumulation and tau protein phosphorylation (Arboleda-Velasquez et al.,
2019). Blood tests may be employed to measure the existing ratio of Aβ42/Aβ40 amyloid plaque
in the blood. One is consumer-orderable, Quest AD-Detect, Beta-Amyloid 42/40 Ratio, Plasma
(Test code: 11786) $399, possibly covered by insurance in the U.S. (Quest Diagnostics, 2023).
The other is Precivity ADTM ($1250, not covered by insurance) (Li et al., 2022). Other blood
tests could become available such as SOBA (soluble oligomer binding assay) which identifies
the presence of misfolded amyloid beta proteins clumped into oligomers (alpha sheets) by
determining whether existing proteins bind to other alpha sheets (Shea et al., 2022).
Other systems biology research investigate approaches involving the immune system and
neurodegenerative disease, finding that those treated with the BCG vaccine (Bacillus Calmette-
Guerin), a low-cost worldwide-administered tuberculosis vaccine (though not appropriate for
immunocompromised individuals), had a more than four-fold decrease in Alzheimer’s risk
(Gofrit et al., 2019). The mechanism is that the innate immune system is stimulated to upregulate
the CAMP gene (cathelicidin antimicrobial peptide), producing the immunomodulatory peptide
LL-37, which may slow Aβ fibril formulation (Armiento et al., 2020).
In the application of formal methods to biology, many machine learning projects target
neurodegenerative disease. Transformer neural networks for Alzheimer’s obtain predictive
results in two US NIH initiatives involving a vision transformer with 3D input (Zhang and

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Khalvati, 2022), and two-mode fMRI data analysis (resting-state and structural) (Sarraf et al.,
2021). Another project uses transformer neural networks in natural language speech prediction to
assess degradation of function (Roshanzamir et al., 2021). Quantum machine learning for
Alzheimer’s also demonstrates improved predictive classification of dementia via the (standard)
VQC (Variational Quantum Classification) algorithm run on an IBM quantum computing
platform (Sierra-Sosa et al., 2020).
4.1.2 Precision Health SIR Model
There is an opportunity to deploy computational methods and AI-based tools to mobilize
information systems biology approaches towards broadly humanity-benefiting use cases in
global disease prevention and healthy well-being. Future work could elaborate an SIR
(Sustaining, Intervening, Recovering) model for the realization of Precision Health based on two
tiers of ongoing circular network cycling of individuals in the population through, at the basic
tier, the usual SIR progression through the different compartmental states, and at the second
level, an information network modeling the spread of information leading to interventional
action-taking. The traditional SIR model tracks infectious disease spread, with each person being
in the state of Susceptible, Infected, or Recovering (Wyss and Hidalgo, 2023). However, in the
SIR Precision Health model, “infection” could be the “positive infection” of the spread of
information triggering interventional behavior (willfully undertaken or managed in the
background by technology). There could be a two-tier model, the underlying tier of the health
graph of individuals in SIR states, and the secondary tier of the information flow of inputs from
physicians, apps, clinical trials, health research studies, advocacy groups, health social networks,
virtual patient modeling, and quantified-self citizen science efforts to implement necessary
preventive initiatives. The aim of precision medicine is to prevent conditions in the 80% of their
lifecycle before they become clinically detectable.
4.2 Risks and Limitations
There are several risks and limitations associated with information systems biology
approaches such as AdS/Biology. First is at the level of AI and computational technologies in
general as to beneficially incorporating AI into the study of biology and ensuring outcomes that
promote human well-being. AI Alignment (producing AI that has broadly humanity-benefiting
values) is central to any AI-related project. This work supports initiatives underway to establish
global AI regulatory agencies with innovation sandboxes, registries, and accountability
frameworks (FLI, 2023). Second, at the level of the current project, there are issues related to
whether the AdS/CFT correspondence, although cast for the treatment of any physical system,
may pertain to biology. Critics of the model’s use in cosmological physics are quick to point out
that AdS/CFT is itself a toy model, based on a hyperbolic (inwardly-curving) model of space
which is employed as a simplification of the regular “de Sitter space” that constitutes everyday
reality at the macroscale on earth (de Sitter space is flat Euclidean space). The correspondence
relies on a negative-valued cosmological constant which has been empirically proven to be
positive. Although it is true that AdS/CFT is a simplified model in this sense, it is nevertheless a
known and computationally accessible structure to deploy as a first-line step for modeling
multiscalar systems, and as such, could be helpful in illuminating more of the intricacies of
biosystems. A third risk is that of complexity, that the AdS/CFT model is complex, and likewise
biology is complex. However, it is not too early to begin to conceive and model long-standing
biological problems such as chronic disease pathogenesis with the new slate of AI-enabled

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computational tools, keeping improved human health outcomes as the constant goal. Finally, a
fourth limitation is that informational models may exclude important aspects of biology. There is
also the possibility of inadvertent inaccuracies and omissions (an exhaustive survey of all
approaches to multiscalarity was not conducted). Future work could include a broader
canvassing of these topics.
“Biology will be the leading science for the next hundred years” – physicist Freeman Dyson, 1996
5 Conclusion
Biology is complex but finite. The implication is that modern computational methods may
continue to elucidate the mysteries of biosystems towards disease resolution and well-being.
Contemporary success in generative AI technologies, LLMs such as GPT-4 (OpenAI), LaMDA
(Google), and LLaMA (Meta AI) suggests their application to biology, both in natural language
human-facing research assistant chat applications, as well as formal language (software
programs, mathematics, physics) human-AI problem solving. The continued use of
computational techniques in medicine is suggested given the mathematical complexity of drug
development and dosing (Braakman et al., 2021), as seen in the high cost of bringing a new drug
to market (on average ten years and US $1.3 billion (Wouters et al., 2020)), and the high human
cost of disease, for example, as of 2020, an estimated 50 million people worldwide had
Alzheimer's disease at an estimated global annual cost of US $1 trillion (Breijyeh and Karaman,
2020).
This work introduces a variety of novel concepts. Within biophysics, information systems
biology is proposed as a conceptual approach for the treatment of biosystems as multiscalar
entities of information creation, representation, and transfer, and AdS/Biology as a flexible yet
formal life sciences interpretation of the AdS/CFT correspondence for renormalized multiscalar
biosystems modeling in successive tiers of bulk-boundary relationships to identify near-far
entropic correlations in systems (e.g. cis-trans gene regulatory networks). The benefit could be a
more immediate analysis pipeline for the application of relevant foundational findings in physics
to biosystems study. AI technologies may accelerate the ongoing formalization path of biology
from descriptive science to quantitative, mathematical, and theoretical science.
One hundred years after Ramón y Cajal’s drawings appeared portraying individual neurons
as the basic units of the nervous system (Ramón y Cajal, 1921), many of the brain’s inner
workings and ailments remain unsolved. An urgent challenge is deploying the new slate of
computational technologies in generative AI and quantum information science towards disease
resolution. In the short term, computational approaches with genomic variant and eQTL
expression analysis are indicated to address the practical challenge of Alzheimer’s disease as the
top-five human killer with no survivors. In the longer term, human-AI entities operating in
partnership could facilitate the realization of precision health initiatives such that conditions are
prevented before occurring.
6 Conflict of Interest
The authors declare that the research was conducted in the absence of any commercial or
financial relationships that could be construed as a potential conflict of interest.

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7 Glossary
AdS/Biology: life sciences interpretation of the AdS/CFT correspondence for renormalized multiscalar biosystems
modeling in successive tiers of bulk-boundary relationships to identify near-far entropic correlations in systems (e.g.
cis-trans gene regulatory networks)
AdS/CFT correspondence (anti-de Sitter space/conformal field theory): holographic theory describing a physical
system bulk volume with a boundary theory in one fewer dimensions
AdS/Genomics: nested bulk-boundary analysis tiers of transposon activation, gene regulatory expression, epigenetic
methylation, disease variants, condition prevention; multiscalar renormalization program identifies correlation-
causation
AdS/Neuroscience: application of AdS/Biology to neuroscience problems such as neural signaling, memory, and
neuropathology (Alzheimer’s disease, Parkinson’s disease, ALS), aging, inflammation, immune system maladies
Agent: (reinforcement learning agent): AI entity targeted to learning and problem-solving in a domain with an
action-taking policy and rewards function, in interactive feedback loops with the environment
Biology 1.0: biology as a descriptive science involving collecting data and writing equations to predict these data
Biology 2.0: formalization path instantiating biology as a quantitative, mathematical, and theoretical science
Biophysics: the science of the application of the laws of physics to biological phenomena
Biology as an information science: idea that the organizing principles of biological systems involve the physical
representation and transfer of information (analyzed computationally)
Bulk-boundary: mathematical relationship between a bulk volume and an edge surface
Chern-Simons biology: application of Chern-Simons theory as a solvable quantum field theory used to formulate
problems as topological min-max curves to identify biosystem events (genetic mutation, neural signal, protein
docking)
Code interpreter: ChatGPT data science analysis plug-in with a larger context window allowing file upload
(enabling the ability to chat with a paper or a set of equations), analyze results, graph equations, write code, and
generate data)
Context window: scope of targeted consideration in generative AI chat interfaces (e.g. upload a file and “chat with
a paper” or “chat with a set of equations”) a specified range of tokens surrounding a target text or sequence
Computational infrastructure: global network architecture of formal methods (program code, mathematics,
physics)
CpG island: cytosine-guanine bases separated by a phosphate (methylation) which can inactivate gene expression
Entanglement: correlations within a system; interrelated particles even when separated
Entropy: number of possible system configurations; Shannon (von Neumann) entropy: minimum number of bits
(qubits) required to send information from one location to another in a noisy (uncertain) channel
Entanglement entropy: degree of subsystem interconnection in a multiscalar system
eQTL: expression QTL (quantitative trait loci) indicating mRNA transcript abundance
Generative AI: AI with can be used to create text, images, video, audio, or other media content per user prompts
Genomic medicine: structural, condition-related, gene regulatory expression genomics directing biological
processes
Information systems: study of systems from an informational perspective
Information systems biology: model of systems biology in which information is a primary organizing principle and
biosystems are considered as multiscalar entities of information creation, representation, and transfer
Information theory: mathematical study of information encoding/transmission as sequences of symbols, states,
pulses
Knowledge: computational layer above information (in AI chips as the sum of the relationships in a set of
information)
Large language models (LLMs): computerized language model neural networks pre-trained on large data corpora
with billions of parameters (coefficients for neural network node weighting)
Math Agent: AI agent operating in digital mathematical domain to identify, represent, analyze, integrate, write,
discover, solve, theorem-prove, steward, and care-take mathematical ecologies
Mathematical ecology (mathscape): set of equations, implicated for AI-aided digital representation and evaluation
MathGPT: a chatbot tutor built specifically to a math textbook for student interaction
“Maxwell’s demon of biology”: idea of efficiency-sorting mechanisms involved in the direction of biological
activity
MERA (multi-scale entanglement renormalization ansatz): tensor network with alternating layers of disentanglers
and isometries consolidating a multiscalar system via entanglement

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Non-ergodicity (efficiency): a system not cycling through all possible configurations
Random tensor networks: tensor networks with each tensor chosen independently at random for improved
calculation of network properties such as entanglement
Quantum biology: study of the functional role of quantum effects (superposition, entanglement, tunneling,
coherence) in living cells, particularly through the use of quantum (computational) methods to model biological
interactions
Quantum computing: manipulation of quantum objects (atoms, ions, photons) in computation with
laser/microwaves
Quantum information: the information of a quantum state (physical state of quantum objects)
Quantum information science: quantum information methods applied to high-dimensional scientific problems
SIR model (Susceptible, Infected, Recovering): epidemiological model of population health based on
compartments
Software 2.0: machine (vs human) designed and programmed code; human-specified data set, objective, framework,
and problem space; machine learning optimized node weights and network architecture to write transferrable
algorithms
Surface code: standard method of quantum error-correction using topology to correct a bit-flip or a phase-flip error
by applying Pauli operators to act on the three-dimensional (XYZ) axes
Systems biology: computational-mathematical study of biology as multiscalar systems comprised of of interrelated
parts
Tensor network: mathematical structure for efficient representation and manipulation of high-dimensional data as
the factorization (contraction) of high-order tensors (tensors with a large number of indices) into a set of low-order
tensors
Topological biophysics: topological mathematical approaches to biology and biophysics problems
Topological entanglement entropy: long-range quantum entanglement in many-body quantum states
(interrelatedness)
Transformer neural networks: neural networks model processing all input data simultaneously, data are divided
into groups of tokens with three weights (query, key, value), and stored in node vectors to broadcast messages to the
network
UV-IR correlations (ultraviolet-infrared) (cis-trans (DNA analysis): short-range and long-range correlations in a
system
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9 Supplementary Material
Appendix 1: ADS/CFT Correspondence Studies
Appendix 2: Quantum Biology
Appendix 3: Quantum Error Correction
Appendix 4: Physical Instantiation of Topologically Modeled Multiscalar Biosystems
Appendix 5: The Time and Space of Multiscalar Systems

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Information Systems Biology: Biophysics, LLMs, and AdS/Biology
Supplementary Material
10 APPENDIX: AdS/CFT Correspondence Studies
The AdS/CFT correspondence (anti-de Sitter space/conformal field theory) is the theory
that a bulk volume may be described by a boundary field theory in one fewer dimensions,
describing multiscalar physical systems through the informational properties of entropy,
entanglement, renormalization, and quantum error-correction codes (Maldacena, 1999).
AdS/CFT was initially proposed to connect a gravity theory with a gauge theory in the context of
relating General Relativity and Quantum Mechanics. AdS5 is a frequently-used model system of
the correspondence, and also its first instantiation as an AdS5/CFT4 that equates a five-
dimensional bulk gravity theory with a four-dimensional Yang-Mills boundary quantum field
theory. Another notable implementation is AdS2/CFT1 as a basic model of gravity (Almheiri and
Polchinski, 2015).
A more general information-related formulation of the holographic principle appeared in
2002 (Bousso, 2002). The so-called holographic bound can be used to identify the maximum
energy or information possible in a region, and is obtained by measuring the bulk entropy
(number of possible quantum states) from the boundary surface. Further work suggests that the
entropy of bulk volumes may be described by gravity (geometric curvature of space-time) alone
(Almheiri et al., 2019).
The AdS/CFT correspondence has been applied successfully to many areas of physics and
science more generally (Natsuume, 2016). Field-specific applications include AdS/QCD
(quantum chromodynamics) to study the strong force in nuclei, AdS/CMT (condensed matter
theory) to analyze exotic materials, and AdS/Geometry to compute high-dimensional problems.
The correspondence is bidirectional in that problems can be solved from either direction, bulk-to-
boundary or boundary-to-bulk, investigating the unknown theory from the known theory, hence
the name holographic duality. Representative examples of AdS/CFT Studies are listed in Table
SI-1. There are two quintessential use cases. First is attempting to calculate an unknown theory
of emergent bulk structure such as quantum gravity from a known quantum field theory on the
boundary, as in the initial correspondence formulation (1) (Maldacena, 1999). Second is starting
with a known classical gravity theory in the bulk (Einsteinian gravity) to formulate an unknown
quantum field theory for an exotic topological material on the boundary (2) (Sachdev, 2010).
TABLE SI-1 AdS/CFT Studies Extend to Physics and Beyond.
Formulation Direction Bulk Boundary
1 AdS/CFT Boundary-to-bulk Quantum gravity theory
(unknown)
Quantum field theory (known)
2 AdS/CMT Bulk-to-boundary Classical gravity theory
(known)
Unconventional materials
quantum field theory (
unknown
)
3 AdS/QCD Boundary-to-Bulk
Identify bulk thermal phase
transition
(unknown)
Lattice chiral condensate
at
finite
-
temperature
(known)
4 AdS/QCD
AdS/Floquet
Bulk-to-boundary Low viscosity of quark-gluon
plasma
s &
black holes
(known)
Separate features of quark-gluon
plasmas (unknown)
5 AdS/ML Boundary-to-Bulk Optimal neural network
architecture
(unknown)
Empirical data (known)
6 AdS/Math Boundary-to-Bulk Complex geometry (unknown) Level-one equations (known)
CMT: condensed matter theory; QCD: quantum chromodynamics; ML: machine learning

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A recent extension is using Chern-Simons topological gravity in the bulk instead of
Einsteinian gravity, to formulate a quantum gravity theory and to study the range and limitations
of the correspondence itself. One AdS/Studies project finds that the correspondence (employed
as an AdS3/CFT2 with a Chern-Simons topological gravity bulk) accurately models certain
quantum systems (massless free bosons in two dimensions and toroidal orbifolds) in the
boundary, but not others (Calabi-Yau sigma models) (Benjamin et al., 2021). Another project
solves a spherically symmetric solution for Lovelock gravity using an AdS5 Chern-Simons
topological gravity correspondence; Lovelock gravity is an alternative to General Relativity with
better coverage in ultraviolet (near) and infrared (far) scales (Bajardi et al., 2021).
There are holographic applications in QCD (quantum chromodynamics; the study of the
strong force) in both directions, computing the bulk thermal phase transition from known finite-
temperature lattice chiral condensate data (4) (Hashimoto et al., 2021), and using bulk-related
black hole viscosity to characterize quark-gluon plasmas on the boundary (5) (Natsuume, 2016).
Quark-gluon plasmas cannot be separated experimentally in particle accelerators, but behave like
a fluid with low viscosity, a parameter similar to that of black holes, which allows the
holographic correspondence to be applied.
An extension of AdS/QCD is AdS/Floquet as a holographic approach to the study of
topological matter phases created with periodically-driven lasers. The AdS5 model system is used
as a known bulk gravity from which to compute the edge field theory when rotating electric
fields (periodic) are applied to create Floquet Weyl semimetals (Hashimoto et al., 2017) and
meson (massive quark) excitations on the boundary (Kinoshita et al., 2018). A useful standard
tool is topological invariants as a holographic metric for predicting edge behavior (modes) from
bulk dynamics. Whereas in static systems, Chern numbers (a set of numbers characterizing the
conduction of edge states) are used as a topological invariant (Thouless et al., 1982), in
periodically-driven systems, winding numbers are required (Rudner et al., 2013). Chern numbers
only consider the system during one cycle, but winding numbers examine the system at all times.
An important application of the holographic is in information-theoretic fields such as
machine learning (AdS/ML). Empirical data (known) is input on the boundary, and bulk
structure (unknown) emerges as the optimal neural network architecture is machine learned by
the system (5) (Hu et al., 2019). AdS/ML also sees deployment in the quantum domain in
AdS/QIS (quantum information science) programs such as AdS/QML (quantum machine
learning) and AdS/TN (tensor networks). Tensor networks are a quantum-ready formulation as
they provide an efficient classical representation of strongly correlated quantum many-body
systems. In general, tensor networks are a high dimensionality technology, in which high-
dimensional data is represented as tensors (multidimensional arrays of numbers). The more
complex high-order tensors (having a large number of indices) are factored into a set of low-
order tensors whose indices are summed to form a network structure per the contraction pattern.
The basic tensor network structure for AdS/CFT is MERA (multiscalar entanglement
renormalization ansatze (guess)), a significant advance in allowing entanglement to be computed
per the area law (Vidal, 2008). The area law refers to entropy scaling by area instead of volume
in quantum systems, greatly facilitating computation as area is one less dimension than volume
to calculate (Eisert et al., 2011)).
A holographic quantum simulator is proposed to instantiate a two-dimensional quantum
many-body system with a one-dimensional quantum simulator (Kim, 2017). Holography is
employed in another sense in that the history of a quantum system (memory) conveys additional
dimensionality to that of the system at the present point value, thus allowing the state of the

Page 33
device to be used to guess the low-energy configuration of the system. From the ground state
energy, the other system energy tiers (eigenstates) can be computed (Peruzzo et al., 2014).
AdS/MERA further formalizes the method of ascribing quantum states to the network structure
itself (McMahon et al., 2020).
Another advance in AdS/TN projects develops holographic MPS (matrix product states)
as an all-purpose tool for simulating quantum many-body dynamics (with the1 holoQUADS
algorithm (holographic quantum dynamics simulation) (Foss-Feig et al., 2021)). Whereas the
previous method for many-body quantum simulation requires a number of gates related to the
thermodynamic limit L, namely (nb+2L) qubits, the holographic MPS method only requires
(nb+2) qubits; one dimension less, (2L) versus (2) (Chertkov et al., 2022, 1075). The method has
been tested in a trapped-ion quantum processor using 11 qubits, simulating the dynamics of an
infinite entangled state and recapitulating the hallmarks of quantum systems (chaos and the light
cone propagation of correlations) in conformity with theoretical predictions. AdS/Mathematics
employs known equations on the boundary to solve higher-dimensional mathematics in the bulk
and to derive proofs such as demonstrating the correspondence for the Lie group SO(4, 2) (6)
(Hazboun, 2018).
11 APPENDIX: Quantum Biology
Quantum biology is the study of the functional role of non-trivial quantum effects
(superposition, entanglement, tunneling, and coherence) in living cells (McFadden and Al-
Khalili, 2018), and the use of quantum (computational) methods to model these and other
biological interactions. Some of the main research topics in quantum biology are avian magneto-
navigation, photosynthesis, and energy transfer (Ball, 2011). Biology requires an open quantum
systems approach as entities are not isolated but rather constantly measure and interact with their
environment, which calls for the Schrödinger wavefunction to be recast as a master equation
with a density matrix (Hayden and Sorce, 2022). Dedicated quantum biology research centers are
emerging such as the Quantum Foundations Centre (Surrey U.K.), the Quantum Biology Center
(UCLA) and the Quantum Biology focus area of the Theoretical and Computational Biophysics
Group (University of Illinois). The field is early-stage with theoretical results preceding
empirical demonstration, and critiques that quantum explanations are not needed in all of these
situations. A list of quantum biology applications and their mechanisms appears in Table SI-2,
only the first two for which a quantum explanation has been confirmed empirically.
TABLE SI-2 Quantum Biology Applications with Purported Description and Quantum Property.
Application Description Property
1
Magneto
-
navigation*
M
agnetically sensitive
pairs in
retinal cryptochrome
protein
Entanglement
2
Tunneling in enzymes*
E
lectron, proton, hydrogen
atom
tunneling in enzyme reactions
Tunneling
3
DNA mutation
Proton exchange in DNA
double hydrogen bond
between bases
Coherence
4
Photosynthesis
Oscillatory signals in light harvesting (but are not quantum)
Coherence
5
Olfaction (vibrational)
O
lfactory sensory neurons detect odorous molecule vibrations
Vibration
6
Oil and gas exploration
Chiral probe electron transport sensing of cellular temperature
Chirality
*Quantum effects empirically confirmed
In magneto-navigation, birds are guided by an internal magnetic compass that is light-
sensitive and wavelength-dependent. The mechanism is thought to operate via a Floquet-based
(time periodization) theory of radical pairs of magnetically sensitive chemical intermediates
formed by photoexcitation of cryptochrome (hidden color) proteins in the retina (1) (Hore and

Page 34
Mouritsen, 2016). A photon entering the retina hits one of a pair of spin-up/spin-down entangled
electrons in the cryptochrome protein, knocking it off to an adjacent atom in the same molecule.
The resulting magnetic field of different radical pairs of electrons (in single or triplet spin states)
signals the bird which direction to travel. Recent empirical research (in the European robin) finds
that the nasal quadrant contains double cones with intensely colorized oil droplets as compared
to the rest of the retina, possibly implicated in magneto-navigation (Rotov et al., 2022).
Other work has experimentally confirmed electron, proton, and hydrogen atom tunneling
in enzyme reactions in protein catalysis (2) (Klinman and Kohen, 2013). Recent theoretical work
in this area proposes that a similar quantum tunneling mechanisms of proton transfer across the
DNA hydrogen bond between bases might be implicated in DNA mutation (3) (Slocombe et al.,
2022). The work attempts to identify the mathematics for the idea that hydrogen bonds in DNA
consist of a proton shared between two electron pairs, which might mutate in transcription
depending on the asymmetric double-well potentials acting on the protons (Löwdin, 1966).
In photosynthesis, there is considerable debate about the definition of what constitutes
“quantum” in biology. What was taken to be quantum, the presence of oscillatory signals in light
harvesting, has been confirmed empirically, but is argued not to be an example of quantum
coherence, but rather a classically explainable phenomenon by an MIT team (4) (Cao et al.,
2020). Another contentious area is olfaction in which a hypothesis proposes that (contra the
usual lock and key receptor shape explanation) olfactory sensory neurons detect intramolecular
vibrations of the odorous molecule (Turin, 1996), but against which much of the recent literature
argues (5) (Hoehn et al., 2018). In other areas of potential empirical practical application, chiral
quantum sensors are proposed to assess electron transport and cellular temperature in
applications such as oil and gas exploration (6) (Aiello et al., 2020).
Whether non-trivial quantum effects are found or not, debates over quantum biology are
motivating new levels of scientific discovery in molecular biology, and quantum methods are
being used to study biological systems. Such projects and research topics now extend to
wavefunction analysis in imaging (EEG, fMRI, PET scans), energy landscape assessment in
protein folding, topology-based condensation in genomics, and various diffusion, oscillation, and
field theory models used to describe collective behavior (neural signaling, krill swarmalators
(self-synchronized behavior in time and space)). The greater scalability afforded by the quantum
domain is implicated for modeling biological systems in their native three-dimensional
complexity. Quantum computation more readily accommodates computational complexity (such
as NP-hard problems) and partial differential equations (PDEs) to solve biological problems that
are not solvable classically and involve multiple unknown variables as opposed to ordinary
differential equations (ODEs) which are solvable classically and entail just one unknown
variable. Further, quantum is an important contemporary platform for big data analysis. The
fast-paced growth of health and biology data, even as compared with other fields (comprising
30% of the world’s data volume in 2018 with an expected compound annual growth rate of 36%
(Reinsel et al., 2018, 22)), requires new platforms and conceptual modes of investigation.
12 APPENDIX: Quantum Error-correction
An important advance in the informational understanding of physics is connecting
holography with quantum error-correction codes (QECC) (Hayden and Preskill, 2007). The
technique was developed to address the black hole information problem (whether information
disappears forever in black holes or evaporates out later, possibly violating either General
Relativity or quantum mechanics). The methods result is that otherwise classically intractable

Page 35
problems can be instantiated as quantum circuits and analyzed as quantum error-correction
codes. Using this approach, it is argued that information is not lost in a black hole but emitted
later as Hawking radiation. The outgoing qubits are not themselves error-corrected, QECC is
used as a computable model of the situation. The challenge is to understand how black hole
dynamics impact quantum information bits, but the usual method for doing this (random unitary
transformations) is not computationally feasible as it would require quantum circuits that are
exponential in size. Thus, QECC is applied as a quantum computational method for efficiently
encoding and solving problems of interest. Holographic codes is a further advance instantiating
QECC in tensor networks, contracting AdS space to protect one logical qubit in the bulk with an
ancilla of physical qubits on the boundary (Pastawski et al., 2015).
The main deployment of QECC (not regarding black holes) is in the area of quantum
computing and quantum networks, to restore a qubit to its original position or to calculate the
capacity of a quantum communications channel (the number of qubits that can be transferred
reliably). Quantum information is more sensitive to environmental noise than classical
information and quantum error correction is required for scalable quantum computing, with a
technical breakthrough implicated to migrate from 100-qubit chips at present to million-qubit
general-purpose fault-tolerant computational platforms (Preskill, 2020).
Quantum error-correction entails protecting one logical qubit with an ancillary number of
physical qubits. The ancilla is used to correct the atom (or other quantum object) to its original
position by making comparison measures with the ancillary qubits (this is tricky since a quantum
bit cannot be viewed directly or copied per the no-cloning and no-measurement principles of
quantum mechanics). Once a positional error is detected, Pauli operators (acting on the three-
dimensional (XYZ) axes) or other methods are applied to correct errors such as a bit-flip (e.g. a
qubit value flipped from |1> to |0> or vice versa) or a phase-flip (e.g. superpositioned states are
flipped from |0> + |1> to |0> - |1>); the bra-ket notation (|1>) indicates a complex amplitude-
valued vector as opposed to a point value. QECC methods seek the break-even point at which the
logical qubit lifetime is at least as long as that of the best uncorrected physical qubit.
Given the importance of QECC to the potential future of quantum computing, many
methods are being explored. On the photonic platform, bosonic codes (based on the state space
of a harmonic oscillator) are a method of QECC which is able to break even, but has high control
overhead (Ofek et al., 2016; Albert, 2022). On the superconducting circuit platform (registers of
qubits), in July 2022, two teams from China and Switzerland (Zhao et al., 2022; Krinner et al.,
2022) realized surface codes as a standard proposed method for topological (lattice-based)
QECC (Kitaev, 2003). The teams both featured 17-qubit demonstrations (9 qubits to encode the
logical information and 8 qubits for stabilizer measurement read-out). Although not yet breaking
even, surface codes are promising as they are straightforward to implement, and may tolerate
large error rates. Another superconducting circuit approach is quantum LDPC (low-density
parity-check) codes, which may facilitate breaking even by scaling by the full number of
protected qubits (as opposed to only by the square root of the number of protected qubits in
surface codes) (Breuckmann and Eberhardt, 2021).
In the black hole setting, to analyze boundary dynamics, the surface code QECC model is
applied (as a stabilizer code (a surface code with stabilizer operators defined on lattice spins)) to
model the black hole horizon as a quantum information circuit. The QECC problem formulation
helps to show that the local dynamics of a black hole can thermalize quantum information
quickly enough to emanate as Hawking radiation. Further work finds that although it may be
possible to compute these kinds of black hole information problems with AdS/QIS (quantum

Page 36
information science) and QECC, it may not be within a useful timeframe (Harlow and Hayden,
2013). AdS/QIS research continues with a widespread application in information-theoretic
domains such as tensor networks, machine learning, blockchain ledgers, and biology.
13 APPENDIX: Physical Instantiation of Topologically Modeled
Multiscalar Biosystems
Topology can help in the investigation of multiscalarity as a property of biosystems. The
information systems biology conceptual approach to high-dimensional information systems can
be seen in the collective behavior domain in which, along with time and space, cellularity is a
dimension of multiscalar biosystems. One implication is biosystem multiscalarity as itself a
domain of study to investigate a growing class of biophysics motifs identified at multiple scale
levels (Table SI-3).
Biology is a unique kind of multiscalar system since each tier (e.g. cells, tissues, and
organs) involves separate processes, goals, and outcomes, as opposed to each scale being simply
more dimensionality of the previous kind (as in basic time and space system scaling in physics,
the three dimensions of space do not differ from each other). Scale tiers are interdependent, but
also coarse-grain in the sense that any tier calls the full competency of all previous tiers without
having to specify or micromanage tasks and outcomes specific to the lower-scale tiers, a property
called multiscale competency architecture (Levin, 2022). Biology is multi-computational in this
way, deploying its competency at multiple scales simultaneously. This idea might describe how
evolution has developed to scale minimal goal-directed behavior (homeostatic loops) at one tier
into higher-level activity at another tier, including with feedback built on error correction as a
design principle (Pio-Lopez et al., 2022). Another use of multiscalar competency could be to
identify the salient scale tier of multiscalar processes, for example in the electrical-chemical
levels of neural signaling.
Explaining cross-tier causality and behavior is an important contemporary research topic,
particularly towards the aim of harnessing nature’s own techniques in creating the complex
multicellular structures of tissues and organs. Substantial piecemeal progress has been made in
controlling specific limited operations in biological systems, for example in ion channel blocking
drugs, and optogenetics which allows a few neurons to be switched on or off at a time via light-
sensitive rhodopsin proteins. However, for modern goals such as organ replacement in
regenerative medicine, methods for orchestrating multicellular operations are needed.
TABLE SI-3 Cellularity as a Dimension of Multiscalarity: Cell-Tissue-Organ.
Phenomenon/Domain Description of Scale Tier Involvement
Bioelectrici
ty
1 Voltage-gated potassium
and ion channels
Electric current mechanisms themselves provide start-stop signals for the
formation of
bioelectric signaling apparatus
(horse
-
cart problem)
2
Topological deformation
T
opological defects
in proliferation signal time
-
location to create
body part
s
Liquid crystal matter phase
s
3
Nematic flow
S
ubcellular filaments, individual cells, multicellular tissues
4
Active turbulence
C
ell monolayers, cytoskeletal components, bacterial
suspensions, sperm
5
Active migration
Guided
-
track and open
-
space random walks via chemical footprint
Phase transition
6
Cancer: chaotic dynamics
Holographic bulk
-
boundary relationships in cancer cell proliferation
7 Soft materials (tissues,
foams, films, emulsions
)
Jamming, packing, floppy-to-rigid glass phase; vibrational frequency (time)
and particle density (space); holographic
interfacial
-
bulk relation
s
8
Ciliary carpets
Metachronal wave synchrony in ciliated cells, tissues, organs

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Multiscalar
microscopy
9
Expansion revealing
Transsynaptic nanocolumn imaging (neurotransmitter & electrical potential)
10 Scale-free vertical tracking Active sinking particles alter water-column flows in multidimensional data
sets: multiple time and length
scales (microns (10
-6
) to meters)
Bioelectricity refers to the generation of electric currents in biological processes, which is
implicated in multicellular behavior in development (development is one instance of
regeneration). Electricity has long been known to operate in biological systems (a field in a
current is created whenever a net ion flux occurs). Bioelectric communication enables the
organization of growth and developmental processes across multiple length scales (Schofield et
al., 2021), but how these processes coordinate large-scale patterning and plasticity is unclear.
The bioelectric code concept is proposed as a mapping of physiological properties to anatomical
outcomes (1) (Tseng and Levin, 2013), and its primary action may be providing start-stop signals
in the formation of bioelectric signaling apparatuses themselves (both voltage-gated potassium
channels and ion channels).
Notably, bioelectric signaling is an emergent process implied by multiscalarity, arising
during regeneration (development) per the self-goal-directed behavior of cells, as distinct from
the cues delivered by the hardware platform (the lower-level biochemistry scale tier). Bioelectric
codes may perform live error correction via feedback as tissues and organs are generated (Fields
and Levin, 2018). The idea of bioholography could be used to model the role of bioelectric
signals in coordinating edge and bulk multicellular behavior. A practical example of
bioelectricity is the finding that electrical fields introduce topological defects to signal cells
uniformly proliferating to separate off and create body parts (mouth, tentacles) in the Hydra (2)
(Maroudas-Sacks et al., 2021).
Another collective behavior coordination mechanism is the flow of active matter systems
in biology, which obey the physics of liquid crystals, controlling temporal and spatial order in
cells at various scale tiers (subcellular filaments, individual cells, and multicellular tissues). The
relevant analogy is nematic liquid crystals, which describe the biological behavior of rod-shaped
molecules self-orienting their long axes in parallel to flow through liquid (3) (Doostmohammadi
and Ladoux, 2022). The puzzling situation of active turbulence has arisen in active biofluids (cell
monolayers, cytoskeletal components, bacterial suspensions, sperm) in which fluids exhibit
complex turbulent-like flows despite having low Reynolds numbers (the ratio of inertial and
viscous forces which usually determines turbulence). Research seeks to establish universal
scaling laws (scaling laws with universal exponents) in active turbulence per experimental
demonstration in active nematic biofilms (4) (Martinez-Prat et al., 2021).
Further topological biophysics advance in cell biology studies the active migration of
cells in shaping, patrolling, and invading tissues with an approach involving random walks and
footprint fields (tracking the time and location of cells) (5) (d’Alessandro et al., 2021). Cells
migrate per external cues and by themselves depositing a chemical footprint on the
environmental substrate (extracellular matrix). In self-attracting walks, cells retrace their steps by
modifying the underlying chemical footprint and reversing direction by changing polarization
(shifting proteins from front to back within the cell). Modeling these processes with quantum
walks (the quantum version of random walks) could be a helpful investigatory tool as all paths
can be walked simultaneously in superposition, and various time and space environments can be
tested (different lattice graph space and discrete-continuous time specifications) (Kendon, 2020).
In cancer, a topological approach to cell proliferation examines the role of chirality and
boundaries in collective cellular flows. The finding is that in the presence of a boundary, human

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malignant fibrosarcoma (connective tissue) cells self-organize into a novel collective state
characterized by the existence of chiral edge currents, whereas in the bulk, the cell flow exhibits
highly chaotic dynamics (disordered flows with no net motion) (6) (Yashunsky et al., 2022). To
study breast cancer, the team bioengineered a method of patient-derived xenografted cells as an
alternative approach to cell lines (deployed through spheroids/organoids, tumor-on-chip, and
mouse model solutions). The most frequent metastasis site for breast cancer is bone, and the
xenografted cells create a biomimetic bone niche model that better recapitulates the underlying
biology and can be used in drug testing (Han et al., 2021).
Topological methods are likewise indicated in the basic form of multi-entity coordination
in the domain of particles. Soft materials are an important research topic in biological and other
systems, focusing on amorphous solids (tissues, foams, emulsions) that deform under stress (7).
Particles exhibit different kinds of jamming and packing behavior, and phase transitions (such as
floppy-to-rigid and network glasses (a solid material with a non-crystalline structure)) based on
the stimuli received and the size and the shape of particles. The surprising finding is that
vibrational frequency (time) rather than the number of interparticle contacts (space) is a key
factor in stabilizing configuration packing (Treado et al., 2021). At higher-level scale tiers in
human soft tissue, metachronal (sequential traveling) waves coordinate flow pumping in form of
large ciliary carpets coordinating synchrony in ciliated cells, tissues, and organs (lung and brain)
(8) (Kanale et al., 2022). Holography is implicated as an analytical approach to these wide-
ranging situations of interfacial-bulk relations in soft materials, particularly cancer tumors.
Microscopy is likewise a crucial tool for multiscalar biosystems study with direct
application to practical real-life problems such as neurodegenerative disease. Topology is again
implicated in the challenge of seeing into the dense cellular environment. An ongoing program in
expansion microscopy realizes a new technique (revealing expansion), which is carried out by
inserting a swellable hydrogel mesh into a sample to decrowd proteins and identify biological
nanostructures in the brain at 20-nanometer resolution (9) (Sarkar et al., 2022). The result is the
first imaging of transsynaptic nanocolumns (the alignment of pre-synaptic calcium channels with
post-synaptic scaffolding proteins (Tang et al., 2016)) (in intact brain tissue), and also periodic
amyloid nanoclusters containing ion-channel proteins in Alzheimer’s disease (mouse model).
Another team has developed a scale-free vertical tracking microscope (GravityMachine.org)
which captures multiple time and microns-to-meter length scales in fluid microscopy, for
example to examine active sinking particles (10) (Krishnamurthy et al, 2020).
14 APPENDIX: The Time and Space of Multiscalar Systems
The immediate implication of modern information science is the need to work in multiple
spatial (Table SI-4) and temporal (Table SI-5) regimes. In space, a useful model for realizing
high-dimensional systems is the four-dimensional number system of quaternions (the result of
dividing two vectors, yielding a number in the form of w + xi + yj + zk). Just as complex
numbers are a two-dimensional extension of real numbers (decimals), quaternions are a four-
dimensional extension of complex numbers. In a biology example, host-virus DNA-RNA
interactions are considered in a time series in projective quaternionic space (Capozziello et al.,
2018).
Space multiplicity is also seen in the model of spherical-flat-hyperbolic space with
positive-neutral-negative curvature, based on the sum of the degrees in a triangle. In spherical
space, a triangle is stretched out on the outside of the sphere, with the angles summing to more
than 180°. Conversely, hyperbolic space is the inwardly curved space of a triangle squashed

Page 39
underneath a saddle, with the angles summing to less than 180°. Hyperbolic space is also known
as AdS (anti-de Sitter space), which is employed as a closely related yet simplified version of the
regular Euclidean (de Sitter space) that constitutes everyday macroscale reality on Earth.
Hyperbolic space is represented in the Escher Circle Limits image of successive rings of frogs or
other figures becoming smaller and smaller in size as they extend from the center of a bulk
region to the edge of the circle. Hyperbolic space is proving to be a useful explanatory
mechanism in the quantum domain. The hyperbolic Bloch theorem, for example, is a solvable
model of wavefunction activity in materials accommodating more than four squares meeting at
one vertex in a lattice (Maciejko and Rayan, 2022).
A consistent progression in mathematical and computational models of reality is adding
dimensionality, from scalars to vectors to tensors. Tensors are mathematical entities that may be
represented by random matrices, tensor field theory, and topological models. Graphical methods
such as same-coloring non-adjacent regions and melon-shaped diagrams help to identify the
relationships in systems modeled with triangle/tetrahedron-based algebra. An example is a model
of quiescent-to-firing states in neural signaling, modeled as the planar-to-melonic phase
transition, in projects testing up to 5D systems (Benedetti et al., 2019).
TABLE SI-4 Models of Space.
Model of Space Description
1
Real
-
complex
-
quaternion numbers
1D, 2D, 4D number systems
Ex: time series of host
-
virus DNA interaction
Biological processes in quaternionic projective space
2
Spherical
-
flat
-
hyperbolic
Positive
-
neutral
-
negative curvature
Ex: hyperbolic Bloch
theorem
More than four squares meeting at
a
lattice vertex
3
Scalar
-
vector
-
tensor space
0D to
3+D dimensional spaces
Ex: quiescent
-
to
-
firing neural signaling
Matrix
-
to
-
tensor phase transition (planar
-
to
-
melonic)
Time also has multiple flavors such as graduating models from discrete to continuous
time. In biology, various temporal organizing patterns include oscillation, periodicity, and
episodes. Circadian rhythms are produced by ~24-hour cycles of expressing and blocking
mechanisms carried out by the circadian proteins clock (CLK) and cycle (CYC) influencing other
genes such as period (PER) and timeless (TIM) (Takahashi et al., 2008). TIM is further regulated
by cryptochrome (CRY) to coordinate the internal circadian clock with the external light-dark
cycle.
Particularly relevant to biosystems is the time crystal, the idea of structure repeating in
time as opposed to space. Wilczek develops the concept in physics (2012), and Winfree invents
the term to discuss the results of laboratory experiments carried out 1969-1970 (1980). The
biological time crystal captures temporal patterns in biological systems modeled in one, two, and
three-dimensional complexity as a ring, torus, and sphere. The time crystal structure emerges
when plotting experimental data along three temporal axes: the time (phase) of a light pulse
delivered to a system, the duration (energy) of the pulse, and the hatching time (Ibid., 414-415).
The experimental data plot resembles a crystal lattice (Ibid., 52). Winfree ran the “pinwheel
experiment” 510 times to document the internal time clock adjustment of an organism from an
old phase of oscillation to a new one in the metamorphosis of pupae to butterflies, moths, flies,
and wasps (induced in the laboratory with light pulses delivered through three variously
overlapping pinwheel structures). A contemporary biotime crystal proposal calls for
supplementing the human brain connectome project (focused on spatial reconstruction) with an
alongside project for the brain’s temporal map (Singh et al., 2020). Multi-time processes are
common in biology, for example in neural signaling, rapid electrical axonal signaling impulses

Page 40
are coordinated with slower-acting wider-ranging calcium (chemical) neurotransmitter network
signals. Also, wrapped cells, myelinated neurons and ensheathed astrocytes, have a faster-time
but weaker signal effect, potentially dampening signal transmission in order to synchronize
multicellular behavior (Handy and Borisyuk, 2022).
The biggest contemporary study of time is in the area of topological materials.
Topological materials are novel quantum matter phases emerging at low temperature (zero
Kelvin), produced in the laboratory by applying external fields (laser or microwave) to quantum
objects (atoms, ions, photons) on a time periodic (Floquet) or quasiperiodic basis. The fact that
topological materials are organized in time suggests the possibility of manipulating time in
multiple dimensions, and therefore holography as a projective viewing frame. These ideas are
incorporated in research realizing error-resistant topological materials created in Fibonacci time,
by delivering laser pulses in a Fibonacci sequence (each number is the sum of the last two
numbers) based on two recursive circuit layers generating a quasiperiodic sequence by which the
system evolves (Dumitrescu et al., 2022). The two offsetting laser pulses create what is
essentially a second time dimension (Merali, 2022). The Fibonacci time sequence is
quasiperiodic (ordered but not regular), an innovation in the larger field of study using periodic
(Floquet) engineering to shape quantum system energy bands on demand.
TABLE SI-5 Models of Time.
Domain Description Simultaneity
Physics Chaos (ballistic spread followed by saturation), first-
passage (stochastic process first reaches threshold)
Physics
Time crystal
(
structure repeating in time, not space
)
X
Cosmology
Page
curve
time
(black hole entropy halfway evaporated)
Quantum mechanics Superposition, entanglement, interference (coherence); hill
branching (asynchronous parallel time)
X
Quantum
information
Scrambling (a local measurement is no longer possible)
Topological materials
P
eriodic
(
Floquet
),
quasiperiodic
time engineering
X
Geology
Time capsule (snapshot of multiple historical regimes)
X
Computing
Clock time, event time, episodic, interval, no time
Computing
Multi
-
computational time
(asynchronously parallel)
Mathematics
Time series, Fibonacci time, high dimensional time
Biology
Oscillation, periodicity, episodic, circadian rhythm
Biology
Biotime crystal
, multi
-
time regimes, compound time
X
Phenomenology
Chronos
vs
Kairos
(clock time vs experienced time)
X
The models of time reveal simultaneity increasingly emerging as a property of time. It is
possible that traditional methods of organizing time into neat forward-linear single-threaded
packages of minutes, hours, years, and light years is merely a human convenience, a filter to
parse time into manageability from its native simultaneity. Modern information systems methods
indicate the greater presence of simultaneity, in its basic modes of time capsules, superposition,
concurrency, and multitasking. In quantum mechanics, time is implicated as simultaneity through
superposition. In geology, time capsules are nature’s blockchain, an immutable record of the
past, visible to all parties at all times, as evidence of time simultaneity (Barbour, 1999). These
kinds of simultaneity-informed analysis proceed in the chronobiological investigation of the
origins of DNA, for example, with the finding that the purine amino acids (G then A) likely
arose first, followed by the pyrimidines (C then U), as opposed to the previous hypothesis that
the genetic code coevolved with metabolic processes (Harrison et al., 2022).