Roberto Mulet

University of Havana · Department of Theoretical Physics

The data for provide evidences of the multi steady state of the human cell line HEK 293 was obtained from 2 L bioreactor continuous culture. A HEK 293 cell line transfected to produce soluble HER1 receptor was used. The bioreactor was operated at three different dilution rates in sequential manner. Daily samples of culture broth were collected, a t...

The great complexity of the human connectome motivates the study of a simpler neural network. For that purpose, the Ising Model was applied on experimental data on the synaptic connectivity of Caenorhabditis elegans (C. elegans) in resting-state, assigning a binary variable (representing active or inactive states) to each neuron in the network. The...

We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the continuous-time relaxation of the system, that translates into a set of differential equations for the evolution of...

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner using the theory of Random Point...

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner, and which performs better on se...

The study of cellular metabolism is limited by the amount of experimental data available. Formulations able to extract relevant predictions from accessible measurements are needed. Maximum Entropy (ME) inference has been successfully applied to genome-scale models of cellular metabolism, and recent data-driven studies have suggested that in chemost...

This is a review to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific. It showcases a selection of contributions from the spin glass community at large to high-dimensional statistics, by focusing on three important graph-based models and methodologies having d...

The study of cellular metabolism is often hindered by limitations in the amount of exper- imental data available. Therefore computational methods that exploit maximally the possible measurements, and are able to extract relevant predictions from a minimum of information are always welcome. Maximum Entropy (ME) inference has been succesfully applied...

We introduce an approach to characterize the dynamics of disordered quantum networks. Each quantum element (i.e., each node) of the network experiences the other nodes as an effective environment that can be self-consistently represented by a Feynman-Vernon influence functional. For networks having the topology of locally treelike graphs, these Fey...

The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from the measured properties of contemporary populations. Standard algorithms for this problem assume independent (factorized) evolution of the characters of the sequences, which is generally wrong (e.g. proteins and genome s...

We start from the theory of random point processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that generalize and improve the cavity master equation (CME), a recently obtained closure for the usual master equati...

We solve MacArthur's resource-competition model with random species-resource couplings in the `thermodynamic' limit of infinitely many species and resources using dynamical path-integrals a la De Domincis. We analyze how the steady state picture changes upon modifying several parameters, including the degree of heterogeneity of metabolic strategies...

We solve MacArthur’s resource-competition model with random species-resource couplings in the “thermodynamic” limit of infinitely many species and resources using dynamical path integrals à la De Domincis. We analyze how the steady state picture changes upon modifying several parameters, including the degree of heterogeneity of metabolic strategies...

We propose a new scheme to infer the metabolic fluxes of cell cultures in a chemostat. Our approach is based on the Maximum Entropy Principle and exploits the understanding of the chemostat dynamics and its connection with the actual metabolism of cells. We show that, in continuous cultures with limiting nutrients, the inference can be done with {\...

We study a quantum system of coupled oscillators subject to a periodic excitation of its parameters. Using Floquet-Lyapunov theory we derive the linear integrals of motion of the system and relate their covariance matrix to that for the canonical observables. The operator integrals allows us to construct the intelligent (minimum uncertainty) states...

The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent (factorized) evolution of the characters of the sequences, which is generally wrong (e.g. proteins and genome seque...

quantum system interacting with other quantum systems experiences these other systems asan effective environment. The environment is the result of integrating out all the other degrees of freedom in the network, and can be represented by a Feynman-Vernon influence functional (IF)acting on system of interest. A network is characterized by the consti...

We exploit the quantum cluster variational method (QCVM) to study the J1−J2 model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other mean field approximations. The phase diagram of the model is studied at the level of the Kikuchi approximation in square lattices as a function of the ratio between g=J2/J1, the...

We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that generalize and improve the Cavity Master Equation (CME) recently obtained in other publications. Our derivation...

The cell culture is the central piece of a biotechnological industrial process. It includes upstream (e.g. media preparation, fixed costs, etc.) and downstream steps (e.g. product purification, waste disposal, etc.). In the continuous mode of cell culture, a constant flow of fresh media replaces culture fluid until the system reaches a steady state...

We exploit the Quantum Cluster Variational Method (QCVM) to study the $J_1$-$J_2$ model for quantum Ising spins. We first describe the QCVM and discuss how it is related to other Mean Field approximations. The phase diagram of the model is studied at the level of the Kikuchi approximation in square lattices as a function of the ratio between $g = J...

The Cavity Master Equation (CME) is a closure scheme to the usual Master Equation representing the dynamics of discrete variables in continuous time. In this work we explore the CME for a ferromagnetic model in a random graph. We first derive and average equation of the CME that describes the dynamics of mean magnetization of the system. We show th...

The Cavity Master Equation (CME) is a closure scheme to the usual Master Equation representing the dynamics of discrete variables in continuous time. In this work we explore the CME for a ferromagnetic model in a random graph. We first derive and average equation of the CME that describes the dynamics of mean magnetization of the system. We show th...

We cast the metabolism of interacting cells within a statistical mechanics framework considering both the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the m...

We study local search algorithms to solve instances of the random k-satisfiability problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that the best such algorithms are akin to nonequilibrium processes in a high-dimensional space. In particular, algorit...

In this work, we propose a natural model for information flow in the brain through a neural message-passing dynamics on a structural network of macroscopic regions, such as the human connectome (HC). In our model, each brain region is assumed to have a binary behavior (active or not), the strengths of interactions among them are encoded in the anat...

We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the...

Abstract A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic parti...

Understanding the relationship between the structure and function of the human brain is one of the most important open questions in Neurosciences. In particular, Resting State Networks (RSN) and more specifically the Default Mode Network (DMN) of the brain, which are defined from the analysis of functional data lack a definitive justification consi...

We study local search algorithms to solve instances of the random $k$-satisfiabi lity problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that the best such algorithms are akin to non-equilibrium processes in a high-dimensional space. In particular, alg...

Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal popu...

Supplementary text. Additional mathematical derivations. (PDF)

Reduced CHO-K1 model. Metabolite parameters. (TXT)

Reduced CHO-K1 model. Stoichiometric matrix. (TXT)

Reduced CHO-K1 model. Reaction parameters. (TXT)

Culture media definition. Concentrations of metabolites in the media. (TXT)

We have designed a systemic model to understand the effect of Photodynamic Therapy (PDT) on long time scales. The model takes into account cell necrosis due to oxygen reactive species, cell apoptosis through the caspase pathway and the competition between healthy and tumor cells. We attempted to describe the system using state of the art computatio...

Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal popu...

A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. It is generally assumed that regulatory mechanisms must be in place to enforce some asymmetry at cell division and, therefore, at the single cell level. Here we show that population bimodality can emerge...

We introduce a new solution to Glauber multi-spin dynamics on random graphs. The solution is based on the recently introduced Cavity Master Equation (CME), a time-closure turning the in principle exact Dynamic Cavity Method into a practical method of analysis and of fast simulation. Running CME once is of comparable computational complexity as one...

We present a scattering theory for the efficient transmission of an excitation across a finite network with designed disorder. We show that the presence of randomly positioned networks sites allows to significantly accelerate the excitation transfer processes as compared to a dimer structure, if only the disordered Hamiltonians are constrained to b...

Source code. Contains the source code of scripts used in the manuscript. (ZIP)

Supplementary note. Contains mathematical derivations. (PDF)

We present a general framework to study quantum disordered systems in the context of the Kikuchi's Cluster Variational Method (CVM). The method relies in the solution of message passing-like equations for single instances or in the iterative solution of complex population dynamic algorithms for an average case scenario. We first show how a standard...

Photodynamic therapy (PDT) is an emergent technique used for the treatment of several diseases. After PDT, cells die by necrosis, apoptosis or autophagy. Necrosis is produced immediately during photodynamic therapy by high concentration of reactive oxygen species, apoptosis and autophagy are triggered by mild or low doses of light and photosensitiz...

The search of binary sequences with low auto-correlations (LABS) is a discrete combinatorial optimization problem contained in the NP-hard computational complexity class. We study this problem using Warning Propagation (WP) , a message passing algorithm, and compare the performance of the algorithm in the original problem and in two different disor...

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrient...

We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic net...

We present a new implementation of the Cluster Variational Method (CVM) as a message passing algorithm. The kind of message passing algorithms used for CVM, usually named Generalized Belief Propagation, are a generalization of the Belief Propagation algorithm in the same way that CVM is a generalization of the Bethe approximation for estimating the...

We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean field ferrom...

Photodynamic therapy (PDT) is an emergent technique used for the treatment of several diseases. It requires the interaction of three components: a photosensitizer, a light source and tissue oxygen. Knowledge of the biophysical aspects of PDT is important for improving dosimetry protocols and treatment planning. In this paper we propose a model to s...

In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find th...

We study two free energy approximations (Bethe and plaquette-CVM) for the Random Field Ising Model in two dimensions. We compare results obtained by these two methods in single instances of the model on the square grid, showing the difficulties arising in defining a robust critical line. We also attempt average case calculations using a replica-sym...

Materials capable to perform upconversion of light transform the photon spectrum and can be used to increase the efficiency of solar cells by upconverting sub-bandgap photons, increasing the density of photons able to generate an electron-hole pair in the cell. Incoherent solar radiation suffices to activate upconverters based on sensitized triplet...

We explain how centrosymmetry, together with a dominant doublet in the local density of states, can guarantee interference-assisted, strongly enhanced, strictly coherent quantum excitation transport between two predefined sites of a random network of two-level systems. Starting from a generalisation of the chaos assisted tunnelling mechanism, we fo...

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conser...

Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in the Edwards-Anderson model in 2-dimensions these approximations predict a spin glass transition at finite $T$. H...

For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit quantum efficiency. However, recent experimental evidence of quantum coherence during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despite numerous...

We establish a general mechanism for highly efficient quantum transport through finite, disordered 3D networks. It relies on the interplay of disorder with centrosymmetry and a dominant doublet spectral structure and can be controlled by the proper tuning of only coarse-grained quantities. Photosynthetic light harvesting complexes are discussed as...

We establish a general mechanism for highly efficient quantum transport through finite, disordered 3D networks. It relies on the interplay of disorder with centrosymmetry and a dominant doublet spectral structure and can be controlled by the proper tuning of only coarse-grained quantities. Photosynthetic light harvesting complexes are discussed as...

The stoichiometry of metabolic networks usually gives rise to a family of conservation laws for the aggregate concentration of specific pools of metabolites, which not only constrain the dynamics of the network, but also provide key insight into a cell's production capabilities. When the conserved quantity identifies with a chemical moiety, extract...

Through simulations of quantum coherent transport on disordered molecular networks, we show that three dimensional structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations. Furthermore, configurations that optimize constructive quantum interference from input to output sit...

form only given. Under which general conditions can fundamental principles of quantum mechanics be exploited to enhance transport in complex systems? Common wisdom suggests that quantum interference can enhance transport across perfectly periodic potentials [1], while it tends to suppress transport in disordered systems [2]. In general, multi-path...

A very promising approach to obtain efficient upconversion of light is the use of triplet-triplet annihilation of excitations in molecular systems. In real materials, besides upconversion, many other physical processes take place - fluorescence, phosphorescence, non-radiative decay, annihilation, diffusion - and compete with upconversion. The main...

We propose a model for fast and highly efficient quantum transport of excitations, through finite, disordered systems. The presented mechanism is statistically robust against configurational changes which alter the realization of disorder. We furthermore discuss the potential relevance of our findings for excitation transport in photosynthetic ligh...

La revista cubana “Juventud Técnica” publicó en diciembre de 2011 un artículo del Dr. Jorge Bergado que dio lugar a un debate donde se discutió acerca de diversos temas vinculados a la denominada en Cuba 'Medicina Natural y Tradicional', que agrupa terapias con diferente denominación en otros lugares. También se incluyen asuntos históricos, epistem...

The protein p53 has a well established role in protecting genomic integrity in human cells. When DNA is damaged p53 induces the cell cycle arrest to prevent the transmission of the damage to cell progeny, triggers the production of proteins for DNA repair and ultimately calls for apoptosis. In particular, the p53-Mdm2 feedback loop seems to be the...

A very promising approach to obtain efficient upconversion of light is the use of triplet-triplet annihilation of excitations in molecular systems. In real materials, besides upconversion, many other physical processes take place - fluorescence, non-radiative decay, annihilation, diffusion - and compete with upconversion. The main objective of this...

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with...

Reactions (abbreviation, enzyme name, formula) appearing in the reduced model of hRBC metabolism. (PDF)

For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit {\it quantum efficiency}. However, recent experimental evidence of {\it quantum coherence} during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despi...

We present and solve the Replica Symmetric equations in the context of the Replica Cluster Variational Method for the 2D random bond Ising model (including the 2D Edwards-Anderson spin glass model). First we solve a linearized version of these equations to obtain the phase diagrams of the model on the square and triangular lattices. In both cases t...