Alain Goriely

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• Dr
• Professor at University of Oxford

How mechanical and biological processes are coordinated across cells, tissues, and organs to produce complex traits is a key question in biology. Cardamine hirsuta, a relative of Arabidopsis thaliana, uses an explosive mechanism to disperse its seeds. We show that this trait evolved through morphomechanical innovations at different spatial scales....

When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening....

Controlling crystal orientations and macroscopic morphology is vital to develop the electronic properties of hybrid perovskites. Here we show that a large-area, orientationally pure crystalline (OPC) methylammonium lead iodide (MAPbI 3) hybrid perovskite film can be fabricated using a thermal-gradient-assisted directional crystallization method tha...

Prion disease is characterized by a chain reaction in which infectious misfolded proteins force native proteins into a similar pathogenic structure. Recent studies have reinforced the hypothesis that the prion paradigm–the templated growth and spreading of misfolded proteins–could help explain the progression of a variety of neurodegenerative disor...

Many neurodegenerative diseases are related to the propagation and accumulation of toxic proteins throughout the brain. The lesions created by aggregates of these toxic proteins further lead to cell death and accelerated tissue atrophy. A striking feature of some of these diseases is their characteristic pattern and evolution, leading to well-codif...

The entorhinal cortex is the earliest site of tau pathology in both Alzheimer's disease and primary age-related tauopathy, yet the mechanisms underlying this selective vulnerability remain poorly understood. Here, we use a computational model integrating neuronal activity and amyloid-beta deposition with interneuronal tau transport to predict regio...

Information processing in the human brain can be modeled as a complex dynamical system operating out of equilibrium with multiple regions interacting nonlinearly. Yet, despite extensive study of the global level of nonequilibrium in the brain, quantifying the irreversibility of interactions among brain regions at multiple levels remains an unresolv...

Brain tumors can induce pathological changes in neuronal dynamics that are reflected in functional connectivity measures. Here, we use a whole-brain modeling approach to investigate pathological alterations to neuronal activity in glioma patients. By fitting a Hopf whole-brain model to empirical functional connectivity, we investigate glioma-induce...

A notable feature of the elephant trunk is the pronounced wrinkling that enables its great flexibility. Here, we devise a general mathematical model that accounts for the characteristic skin wrinkles formed during morphogenesis in the elephant trunk. Using physically realistic parameters and operating within the theoretical framework of nonlinear m...

Neurodegenerative diseases are associated with the assembly of specific proteins into oligomers and fibrillar aggregates. At the brain scale, these protein assemblies can diffuse through the brain and seed other regions, creating an autocatalytic protein progression. The growth and transport of these assemblies depend on various mechanisms that can...

Background A generative model of tau PET was applied to multiple cohorts across the Alzheimer's disease (AD) spectrum, revealing longitudinal changes in tau production and transport. A generalisation of the model accounts for amyloid, tau and neurodegeneration (ATN) interactions and accurately explains longitudinal ATN biomarker data, adding potent...

During neurodevelopment, neuronal axons navigate through the extracellular environment, guided by various cues to establish connections with distant target cells. Among other factors, axon trajectories are influenced by heterogeneities in environmental stiffness, a process known as durotaxis, the guidance by substrate stiffness gradients. Here, we...

Most theories and applications of elasticity rely on an energy function that depends on the strains from which the stresses can be derived. This is the traditional setting of Green elasticity, also known as hyper-elasticity. However, in its original form the theory of elasticity does not assume the existence of a strain-energy function. In this cas...

A notable feature of the elephant trunk is the pronounced wrinkling that enables its great flexibility. Here, we devise a general mathematical model that accounts for the characteristic skin wrinkles formed during morphogenesis in the elephant trunk. Using physically realistic parameters and operating within the theoretical framework of nonlinear m...

Through statistical analysis and comparison of different studies, Alain Goriely challenges the widely accepted figure of 86 billion neurons in the human brain, and argues that the actual number is uncertain, with estimates ranging between 61 and 99 billion.

Rapid movement is rare in the plant kingdom, but a prerequisite for ballistic seed dispersal. A particularly dramatic example of rapid motion in plants is the squirting cucumber ( Ecballium elaterium ) which launches its seeds explosively via a high-pressure jet. Despite intriguing scientists for centuries, the exact mechanism of seed dispersal and...

In a recent article we introduced a new class of shapes, called \emph{soft cells} which fill space as \emph{soft tilings} without gaps and overlaps while minimizing the number of sharp corners. We defined the \textit{edge bending algorithm} deforming a polyhedral tiling into a soft tiling and we proved that by this algorithm an infinite class of po...

Capsular contracture is a pathological response to implant-based reconstructive breast surgery, where the ``capsule'' (tissue surrounding an implant) painfully thickens, contracts and deforms. It is known to affect breast-cancer survivors at higher rates than healthy women opting for cosmetic cosmetic breast augmentation with implants. We model the...

With more than 90,000 muscle fascicles, the elephant trunk is a complex biological structure and the largest known muscular hydrostat. It achieves an unprecedented control through intricately orchestrated contractions of a wide variety of muscle architectures. Fascinated by the elephant trunk's unique performance, scientists of all disciplines are...

Constitutive modelling of nonlinear isotropic elastic materials requires a general formulation of the strain-energy function in terms of invariants, or equivalently in terms of the principal stretches {λ 1 , λ 2 , λ 3 }. Yet, when choosing a particular form of a model, the representation in terms of either the principal invariants or stretches beco...

The structure of a complex network plays a crucial role in determining its dynamical properties. In this paper , we show that the the degree to which a network is directed and hierarchically organized is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes an...

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, nonflat faces...

Disentangling irreversible and reversible forces from random fluctuations is a challenging problem in the analysis of stochastic trajectories measured from real-world dynamical systems. We present an approach to approximate the dynamics of a stationary Langevin process as a discrete-state Markov process evolving over a graph-representation of phase...

For a given material, controllable deformations are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, universal deformations are those deformations that are controllable for any material within the class. In this paper, we characterize the universal defor...

Alzheimer's disease is a neurodegenerative disorder characterized by the presence of amyloid-beta plaques and the accumulation of misfolded tau proteins and neurofibrillary tangles in the brain. A thorough understanding of the local accumulation of tau is critical to develop effective therapeutic strategies. Tau pathology has traditionally been des...

Plants are a paradigm for active shape control in response to stimuli. For instance, it is well known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along...

Neurodegenerative diseases are associated with the assembly of specific proteins into oligomers and fibrillar aggregates. At the brain scale, these protein assemblies can diffuse through the brain and seed other regions, creating an autocatalytic protein progression. The growth and transport of these assemblies depend on various mechanisms that can...

Les mollusques sécrètent des coquilles, dont le développement soulève des questions déroutantes. Comment les bivalves produisent-ils une coquille dont les deux valves s’emboitent parfaitement l’une dans l’autre comme les pièces d’un puzzle ? Comment certaines ammonites, des céphalopodes fossiles, ont-elles formé de surprenantes coquilles asymétriqu...

One of the key problems in active materials is the control of shape through actuation. A fascinating example of such control is the elephant trunk, a long, muscular, and extremely dexterous organ with multiple vital functions. The elephant trunk is an object of fascination for biologists, physicists, and children alike. Its versatility relies on th...

For a given material, \emph{controllable deformations} are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, \emph{universal deformations} are those deformations that are controllable for any material within the class. In this paper, we characterize the u...

Dynamical systems on networks typically involve several dynamical processes evolving at different timescales. For instance, in Alzheimer’s disease, the spread of toxic protein throughout the brain not only disrupts neuronal activity but is also influenced by neuronal activity itself, establishing a feedback loop between the fast neuronal activity a...

Information processing in the human brain can be modelled as a complex dynamical system operating out of equilibrium with multiple regions interacting nonlinearly. Yet, despite extensive study of non-equilibrium at the global level of the brain, quantifying the irreversibility of interactions among brain regions at multiple levels remains an unreso...

Topology is providing new insights for neuroscience. For instance, graphs, simplicial complexes, directed graphs, flag complexes, persistent homology and convex covers have been used to study functional brain networks, synaptic connectivity, and hippocampal place cell codes. We propose a topological framework to study the evolution of Alzheimer’s d...

Correction to: Biomechanics and Modeling in Mechanobiology (2022) 21:89–118 https://doi.org/10.1007/s10237-021-01539-0

We initiate the study of the classical mechanics of nonrelativistic fractons in its simplest setting—that of identical one-dimensional particles with local Hamiltonians characterized by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the N -body proble...

Brain tumors can induce pathological changes in neuronal dynamics both on a local and global level. Here, we use a whole-brain modeling approach to investigate these pathological alterations in neuronal activity. By fitting a Hopf whole-brain model to empirical functional connectivity, we demonstrate that phase correlations are largely determined b...

Centrioles duplicate when a mother centriole gives birth to a daughter that grows from its side. Polo-like-kinase 4 (PLK4), the master regulator of centriole duplication, is recruited symmetrically around the mother centriole, but it then concentrates at a single focus that defines the daughter centriole assembly site. How PLK4 breaks symmetry is u...

We consider the 'anti-Hertz' elastic problem of inverse indentation which happens when the surface of an elastic material is pressed down with a plate with a round hole to form a bulge. This classical problem takes on a new life when a polydomain nematic liquid crystal elastomer is used. In this case, the nematic director aligns with the leading pr...

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the def...

This paper is part of the Physical Review Research collection titled Physics of Neuroscience.

Dynamical systems on networks typically involve several dynamical processes evolving at different timescales. For instance, in Alzheimer's disease, the spread of toxic protein throughout the brain not only disrupts neuronal activity but is also influenced by neuronal activity itself, establishing a feedback loop between the fast neuronal activity a...

Aggregation of the hyperphosphorylated tau protein is a central driver of Alzheimer’s disease, and its accumulation exhibits a rich spatio-temporal pattern that unfolds during the course of the disease, sequentially progressing through the brain across axonal connections. It is unclear how this spatio-temporal process is orchestrated – namely, to w...

Plants are a paradigm for active shape control in response to stimuli. For instance, it is well-known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along...

Carnivorous pitcher plants (Nepenthes) are a striking example of a natural pitfall trap. The trap’s slippery rim, or peristome, plays a critical role in insect capture via an aquaplaning mechanism that is well documented. While the peristome has received significant research attention, the conspicuous variation in peristome geometry across the genu...

We initiate the study of the classical mechanics of non-relativistic fractons in its simplest setting - that of identical one dimensional particles with local Hamiltonians characterized by by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the $N$ body...

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the gra...

The separation of double-stranded peptide chains can occur in two ways: cooperatively or non-cooperatively. These two regimes can be driven either by chemical or thermal effects, or through non-local mechanical interactions. Here, we show explicitly that local mechanical interactions in biological systems may regulate the stability, the reversibili...

The Finite Element Method (FEM) suffers from important drawbacks in problems involving excessive deformation of elements despite being universally applied to a wide range of engineering applications. While dynamic remeshing is often offered as the ideal solution, its computational cost, numerical noise and mathematical limitations in complex geomet...

Carnivorous pitcher plants ( Nepenthes ) are a striking example of a natural pitfall trap. The trap’s slippery rim, or peristome, plays a critical role in insect capture via an aquaplaning mechanism that is well documented. Whilst the peristome has received significant research attention, the conspicuous variation in peristome geometry across the g...

The design of versatile soft actuators remains a challenging task, as it is a complex trade-off between robotic adaptability and structural complexity. Recently, researchers have used statistical and physical models to simulate the mechanical behavior of soft actuators. These simulations can help identify optimal actuator designs that fulfill speci...

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970 s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry h...

Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will...

Under an external field a double-stranded peptide chain can separate in a fragile or ductile transition. It is usually believed that these two regimes are driven either by chemical and thermal fields, or through non-local mechanical interactions. Here, we show explicitly that local mechanical interactions regulates the stability and reversibility o...

Centrioles are barrel-shaped structures that duplicate when a mother centriole gives birth to a single daughter that grows from its side. Polo-like-kinase 4 (PLK4), the master regulator of centriole biogenesis, is initially recruited around the mother centriole but it quickly concentrates at a single focus that defines the daughter centriole assemb...

Due to an infinite number of degrees of freedom, soft robotic arms remain challenging to control when underactuated. Past work has drawn inspiration from biological structures–for example the elephant trunk–to design and control biomimetic soft robotic arms. However, to date, the models used to inform the control of biomimetic arms lack generalizab...

Following the experimental lead, we construct a general mathematical model which, depending on whether the uniaxial scalar order parameter is constant or not, can predict either the classical shear striping instability or the molecular auxetic response and mechanical Fréedericksz transition observed in different liquid crystal elastomers. Our theor...

Alzheimer’s disease is the most common cause of dementia and is linked to the spreading of pathological amyloid- β and tau proteins throughout the brain. Recent studies have highlighted stark differences in how amyloid- β and tau affect neurons at the cellular scale. On a larger scale, Alzheimer’s patients are observed to undergo a period of early-...

The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can help classify and characterize the morphology of broad groups of neurons. We study the stability of topological m...

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modellin...

We develop a mathematical model that builds on the surprising nonlinear mechanical response observed in recent experiments on nematic liquid crystal elastomers. Namely, under uniaxial tensile loads, the material, rather than thinning in the perpendicular directions, becomes thicker in one direction for a sufficiently large strain, while its volume...

We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of a toxic protein in a specific region represented by a vertex. Over time, the accumulation of toxic proteins a...

The growth of axons is a key process in neural system development, which relies upon a subtle balance between external mechanical forces and remodeling of cellular constituents. A key problem in the biophysics of axons is therefore to understand the overall response of the axon under stretch, which is often modeled phenomenologically using morphoel...

For a given class of materials, universal deformations are those that can be maintained in the absence of body forces by applying only boundary tractions. Universal deformations play a crucial role in nonlinear elasticity. To date, their classification has been accomplished for homogeneous isotropic solids following Ericksen’s seminal work, and hom...

In linear elasticity, universal displacements for a given symmetry class are those displacements that can be maintained by only applying boundary tractions (no body forces) and for arbitrary elastic constants in the symmetry class. In a previous work, we showed that the larger the symmetry group, the larger the space of universal displacements. Her...

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry ha...

Alzheimer's disease is the most common cause of dementia and is linked to the spreading of pathological amyloid-β and tau proteins throughout the brain. Recent studies have highlighted stark differences in how amyloid-beta and tau affect neurons at the cellular scale. On a larger scale, Alzheimer's patients are observed to undergo a period of early...

Misfolded tau proteins are a classical hallmark of Alzheimer’s disease. Increasing evidence indicates that tau—and not amyloid—is the main agent in driving neurodegeneration and tissue atrophy in Alzheimer’s brains. However, the precise correlation between tau and atrophy remains insufficiently understood. Here we explore tau-atrophy interactions b...

Universal displacements are those displacements that can be maintained, in the absence of body forces, by applying only boundary tractions for any material in a given class of materials. Therefore, equilibrium equations must be satisfied for arbitrary elastic moduli for a given anisotropy class. These conditions can be expressed as a set of partial...

Mitotic centrosomes are formed when centrioles start to recruit large amounts of pericentriolar material (PCM) around themselves in preparation for mitosis. This centrosome "maturation" requires the centrioles and also Polo/PLK1 protein kinase. The PCM comprises several hundred proteins and, in Drosophila, Polo cooperates with the conserved centros...

In many filamentary structures, such as hydrostatic arms, roots, and stems, the active or growing part of the material depends on contractile or elongating fibers. Through their activation by muscular contraction or growth, these fibers will generate internal stresses that are partially relieved by the filament acquiring intrinsic torsion and curva...

The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topological morphology descriptor, assign a morphology descriptor called a barcode to a neuron equipped with a given function, such as the Euclidean distance from the root of...

The growth of axons is a key process in neural system development, which relies upon a subtle balance between external mechanical forces and remodeling of cellular onstituents. A key problem in the biophysics of axons is therefore to understand the overall response of the axon under stretch, which is often modeled phenomenologically using morphoela...

Alzheimer's disease, the most common form of dementia, is a systemic neurological disorder associated with the formation of toxic, pathological aggregates of proteins within the brain that lead to severe cognitive decline, and eventually, death. In normal physiological conditions, the brain rids itself of toxic proteins using various clearance mech...

We derive a general constitutive model for nematic liquid crystalline rods. Our approach consists in reducing the three-dimensional strain-energy density of a nematic cylindrical structure to a one-dimensional energy of a nematic rod. The reduced one-dimensional model connects directly the optothermal stimulation to the generation of intrinsic curv...

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. The...

Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key question is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when wil...

Significance A theoretical model suggests that a mechanically induced twist of the soft body underlies the formation of helicospiral shells in snails and ammonites and also accounts for the startling and unique meandering shells observed in certain species. This theory addresses fundamental developmental issues of chirality and symmetry breaking: i...

A hallmark of Alzheimer’s disease is the aggregation of insoluble amyloid-beta plaques and tau protein neurofibrillary tangles. A key histopathological observation is that tau protein aggregates follow a structured progression pattern through the brain. Mathematical network models of prion-like propagation have the ability to capture such patterns,...

Mitotic centrosomes are formed when centrioles recruit large amounts of pericentriolar material (PCM) around themselves. This centrosome “maturation” requires the centrioles and also Polo/PLK1 protein kinase. The PCM comprises several hundred proteins and, in Drosophila , Polo cooperates with the conserved centrosome proteins Spd-2/CEP192 and Cnn/C...

For more than 25 years, the amyloid hypothesis–the paradigm that amyloid is the primary cause of Alzheimer’s disease–has dominated the Alzheimer’s community. Now, increasing evidence suggests that tissue atrophy and cognitive decline in Alzheimer’s disease are more closely linked to the amount and location of misfolded tau protein than to amyloid p...

For more than 25 years, the amyloid hypothesis--the paradigm that amyloid is the primary cause of Alzheimer's disease--has dominated the Alzheimer's community. Now, increasing evidence suggests that tissue atrophy and cognitive decline in Alzheimer's disease are more closely linked to the amount and location of misfolded tau protein than to amyloid...

Continuum models describing ideal nematic solids are widely used in theoretical studies of liquid crystal elastomers. However, experiments on nematic elastomers show a type of anisotropic response that is not predicted by the ideal models. Therefore, their description requires an additional term coupling elastic and nematic responses, to account fo...

Cover image of Proc. R. Soc. A, vol 477, issue 2253, September 2021 (https://royalsocietypublishing.org/toc/rspa/2021/477/2253). For more details, see the article "Nematic liquid crystalline elastomers are aeolotropic materials" by L.A. Mihai, H. Wang, J. Guilleminot & A. Goriely (https://doi.org/10.1098/rspa.2021.0259) or (https://www.researchgate...