We argue that energy minimization can explain the pattern of cell movements in the morphogenetic ... more We argue that energy minimization can explain the pattern of cell movements in the morphogenetic process known as convergent extension provided that the cell-cell adhesive energy has a certain type of anisotropy, which we describe. This single simple property suffices to cause the cell elongation, cell alignment, and lengthening of a cellular array that characterize convergent extension. We show that the final aspect ratio of the array of cells depends on the anisotropy and is independent of the initial configuration and of the degree of cell elongation.
The simulated tumour initially grows exponentially, then forms three concentric shells as the nut... more The simulated tumour initially grows exponentially, then forms three concentric shells as the nutrient level supplied to the core by diffusion decreases: the outer shell consists of live proliferating cells, the middle of quiescent cells and the centre is a necrotic core, where the nutrient ...
Digital twins, customized simulation models pioneered in industry, are beginning to be deployed i... more Digital twins, customized simulation models pioneered in industry, are beginning to be deployed in medicine and healthcare, with some major successes, for instance in cardiovascular diagnostics and in insulin pump control. Personalized computational models are also assisting in applications ranging from drug development to treatment optimization. More advanced medical digital twins will be essential to making precision medicine a reality. Because the immune system plays an important role in such a wide range of diseases and health conditions, from fighting pathogens to autoimmune disorders, digital twins of the immune system will have an especially high impact. However, their development presents major challenges, stemming from the inherent complexity of the immune system and the difficulty of measuring many aspects of a patient’s immune state in vivo. This perspective outlines a roadmap for meeting these challenges and building a prototype of an immune digital twin. It is structure...
We study the equilibrium energies of 2D non-coarsening uid foams which consist of bubbles with xe... more We study the equilibrium energies of 2D non-coarsening uid foams which consist of bubbles with xed areas. The equilibrium states correspond to local minima of the total perimeter. (i) We nd an approximate value of the global minimum perimeter, and a marker to determine directly from an image how far a foam is from its ground state. (ii) For (small) area disorder, small bubbles tend to sort inwards and large bubbles sort outwards. (iii) Topological charges of the same signs `repel' while charges of the opposite signs `attract'. (iv) We also discuss : boundary conditions; uniqueness of pattern when topology is prescribed; extensions to 3D.
Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indi... more Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.
Flow at Ultra-High Reynolds and Rayleigh Numbers, 1998
We have studied the scaling properties of thermal turbulence in a low Prandtl number, Pr, fluid u... more We have studied the scaling properties of thermal turbulence in a low Prandtl number, Pr, fluid using liquid Hg (Pr = 0.024). The length scale of thermal and viscous boundary layers are analyzed from time series of movable thermistors near the boundary. It revealed that the thermal and viscous layer had crossed over the observed range of Rayleigh numbers (106 < Ra < 108). The frequency spectrum of the temperature fluctuations and the scaling of the cutoff frequency differed from those of He. The cascade range was smaller than expected. Characters of high Rayleigh number flow of a low Prandtl number fluid is discussed.
The evolution of a liquid foam usually mixes quasi-equilibrium topological and geometrical featur... more The evolution of a liquid foam usually mixes quasi-equilibrium topological and geometrical features in an intricate way. We take advantage of special properties of ferro¯uid froths and of constrained area evolution simulations, to distinguish the e ects of side swapping (T1 processes) from other rearrangements in the froth. Cell elongation characterizes the froth and its deviation from mechanical equilibrium as robustly as the usually measured total wall length, that is surface energy.
A common goal in physical, chemical and life sciences is to understand the connection between the... more A common goal in physical, chemical and life sciences is to understand the connection between the growth and the morphology of developing patterns. A general process is fusion or coalescence of interacting domains, especially in mixtures of immiscible liquids or tissues, where the coalescence of two drops or clusters is the basic phenomenon which governs the morphology and the kinetics of developing patterns (Steinberg, 1963).
Abstract We study the center of mass motion of single endodermal Hydra cells in two kinds of cell... more Abstract We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggregates: endodermal and ectodermal. The mean square displacement displays anomalous super-di usion with x 2 ∼ t where ¿1. The velocity distribution function is non-Gaussian and ÿts well the q-distribution function of velocities within the framework of the non-extensive thermostatistics proposed by Tsallis. Our results indicate that cell motion in two-dimensional cellular aggregates can be described by a &quot;correlated-type&quot; anomalous di usion.
Physica A: Statistical Mechanics and its Applications, 2001
We present experimental results and a simulation in two dimensions of the expansion and bursting ... more We present experimental results and a simulation in two dimensions of the expansion and bursting of aggregates of Hydra cells formed from an initially disordered mixture. In the experiments, after cell sorting, the aggregate rounds and swells until violent bursts occur, forcibly expelling internal uid and loose cells. We use Monte Carlo techniques to simulate the bursts in two dimensions. Initially, we consider a ring made of a monolayer of cells enveloping an internal uid. Each cell and the internal medium have their areas controlled by target area size. Increasing the target area of the internal cavity causes the aggregate to swell. We observe that aggregates of cells with higher surface tension generate higher internal pressure. In the simulations the cell ring bursts when it is too thin to endure uctuations in the cellular membranes. The process is relevant to embryonic development.
Foams have unique rheological properties that range from solid-like to fluid-like flow behavior. ... more Foams have unique rheological properties that range from solid-like to fluid-like flow behavior. We study foams under periodic shear stress in a Monte Carlo simulation (using the extended large-Q Potts model) and find three different types of hysteresis in the stress-strain relationship, which correspond to elastic, viscoelastic and fluid-like properties of foams. We relate this wide-ranging mechanical response of foams
We study the evolution of cellular patterns in 2D, specifically a hexagonal-rectangular transform... more We study the evolution of cellular patterns in 2D, specifically a hexagonal-rectangular transformation induced by applied fields (such as stress). We impose an area constraint so as to prevent the destruction of cells. When sufficiently stressed, the system undergoes irreversible local cellular rearrangement via neighbor switching (T1 switches). Monte Carlo based simulations of the large-Q Potts model display both topological
We show that differential adhesion with fluctuations is sufficient to explain a wide variety of c... more We show that differential adhesion with fluctuations is sufficient to explain a wide variety of cell rearrangement, by using the extended large-Q Potts model with differential adhesivity to simulate different biological phenomena. Different values of relative surface energies correspond to different biological cases, including complete and partial cell sorting, checkerboard, position reversal, and dispersal. We examine the convergence and temperature dependence of the simulation and distinguish spontaneous, neutral, and activated processes by performing simulations at different temperatures. We discuss the biological and physical implications of our quantitative results.
We present a simulation in two dimensions of an important process of biological development: the ... more We present a simulation in two dimensions of an important process of biological development: the burst of an aggregate of cells due to the expansion of an internal cavity by influx of external medium. The burst is quantitatively characterized by discontinuous change of the pressure of the aggregate. The influence of dimensionality on the process and its relevance for development are discussed.
Proceedings of the Royal Society of London. Series B: Biological Sciences, 2004
We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experim... more We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experiments on chondrogenesis in the early vertebrate limb and additional hypotheses. Cellular differentiation of mesenchymal cells into subtypes with different fibroblast growth factor (FGF) receptors occurs in the presence of spatio-temporal variations of FGFs and transforming growth factor-betas (TGF-βs). One class of differentiated cells produces elevated quantities of the extracellular matrix protein fibronectin, which initiates adhesion-mediated preskeletal mesenchymal condensation. The same class of cells also produces an FGFdependent laterally acting inhibitor that keeps condensations from expanding beyond a critical size. We show that this 'reactor-diffusion' mechanism leads naturally to patterning consistent with skeletal form, and describe simulations of spatio-temporal distribution of these differentiated cell types and the TGF-β and inhibitor concentrations in the developing limb bud.
Physica A: Statistical Mechanics and its Applications, 2001
We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggr... more We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggregates: endodermal and ectodermal. The mean square displacement displays anomalous super-di usion with x 2 ∼ t where ¿1. The velocity distribution function is non-Gaussian and ÿts well the q-distribution function of velocities within the framework of the non-extensive thermostatistics proposed by Tsallis. Our results indicate that cell motion in two-dimensional cellular aggregates can be described by a "correlated-type" anomalous di usion.
We study the vertical liquid profile of foam drainage using the threedimensional large-Q Potts mo... more We study the vertical liquid profile of foam drainage using the threedimensional large-Q Potts model extended to include gravity. Forced drainage with constant-rate liquid input from the top of the foam produces a constant profile. In free drainage, without liquid input from the top, homogeneously distributed liquid drains to the bottom of the foam until capillary effects and gravity balance. For pulsed drainage, as liquid drains from the top of the foam into the dry foam, a sharp interface between the wet and dry foam develops. The fixed profile moves downwards at a constant velocity with a flat interface. The results of our simulations are suggested in both experiments and simplified meanfield analytical results.
Many materials. including soap froths. polycrystalline alloys, ceramics, lipid monolayers and gar... more Many materials. including soap froths. polycrystalline alloys, ceramics, lipid monolayers and garnet films. have structures composed of either two-or three-dimensional polygonal domains separated by well defined boundaries. Usually. the surface energy 01 these boundaries makes the pattern unstable. causing certain grains toshrink and eventually to disappear. Thus the pattern coarsens continuously unless other factors arrest the motion of the boundaries. We review recent theoretical, computational and experimental progress in our understanding of the asymptotic scaling laws that describe coarsening. In most cases the elementary expectation. that the mean grain radius scales with the square root of time. is confirmed. We pay particular attention to the history 01 the field. to understand why this elementary result has remained in doubt until now.
We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomple... more We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomplete image using the extended Potts model on a pinned lattice. The initial information consists of the positions of the vertices only. We locate the centers of the bubbles using the Euclidean distance-map construction and assign at each vertex position a continuous pinning field with a potential falling off as 1/r. We nucleate a bubble at each center using the extended Potts model and let the structure evolve under the constraint of scaled target areas until the bubbles contact each other. The target area constraint and pinning centers prevent further coarsening. We then turn the area constraint off and let the edges relax to a minimum energy configuration. The result is a reconstructed structure very close to the simulation. We repeated this procedure for various stages of the coarsening of the same simulated foam and investigated the simulation and reconstruction dynamics, topology and area distribution, finding that they agreed to good accuracy.
We argue that energy minimization can explain the pattern of cell movements in the morphogenetic ... more We argue that energy minimization can explain the pattern of cell movements in the morphogenetic process known as convergent extension provided that the cell-cell adhesive energy has a certain type of anisotropy, which we describe. This single simple property suffices to cause the cell elongation, cell alignment, and lengthening of a cellular array that characterize convergent extension. We show that the final aspect ratio of the array of cells depends on the anisotropy and is independent of the initial configuration and of the degree of cell elongation.
The simulated tumour initially grows exponentially, then forms three concentric shells as the nut... more The simulated tumour initially grows exponentially, then forms three concentric shells as the nutrient level supplied to the core by diffusion decreases: the outer shell consists of live proliferating cells, the middle of quiescent cells and the centre is a necrotic core, where the nutrient ...
Digital twins, customized simulation models pioneered in industry, are beginning to be deployed i... more Digital twins, customized simulation models pioneered in industry, are beginning to be deployed in medicine and healthcare, with some major successes, for instance in cardiovascular diagnostics and in insulin pump control. Personalized computational models are also assisting in applications ranging from drug development to treatment optimization. More advanced medical digital twins will be essential to making precision medicine a reality. Because the immune system plays an important role in such a wide range of diseases and health conditions, from fighting pathogens to autoimmune disorders, digital twins of the immune system will have an especially high impact. However, their development presents major challenges, stemming from the inherent complexity of the immune system and the difficulty of measuring many aspects of a patient’s immune state in vivo. This perspective outlines a roadmap for meeting these challenges and building a prototype of an immune digital twin. It is structure...
We study the equilibrium energies of 2D non-coarsening uid foams which consist of bubbles with xe... more We study the equilibrium energies of 2D non-coarsening uid foams which consist of bubbles with xed areas. The equilibrium states correspond to local minima of the total perimeter. (i) We nd an approximate value of the global minimum perimeter, and a marker to determine directly from an image how far a foam is from its ground state. (ii) For (small) area disorder, small bubbles tend to sort inwards and large bubbles sort outwards. (iii) Topological charges of the same signs `repel' while charges of the opposite signs `attract'. (iv) We also discuss : boundary conditions; uniqueness of pattern when topology is prescribed; extensions to 3D.
Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indi... more Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.
Flow at Ultra-High Reynolds and Rayleigh Numbers, 1998
We have studied the scaling properties of thermal turbulence in a low Prandtl number, Pr, fluid u... more We have studied the scaling properties of thermal turbulence in a low Prandtl number, Pr, fluid using liquid Hg (Pr = 0.024). The length scale of thermal and viscous boundary layers are analyzed from time series of movable thermistors near the boundary. It revealed that the thermal and viscous layer had crossed over the observed range of Rayleigh numbers (106 < Ra < 108). The frequency spectrum of the temperature fluctuations and the scaling of the cutoff frequency differed from those of He. The cascade range was smaller than expected. Characters of high Rayleigh number flow of a low Prandtl number fluid is discussed.
The evolution of a liquid foam usually mixes quasi-equilibrium topological and geometrical featur... more The evolution of a liquid foam usually mixes quasi-equilibrium topological and geometrical features in an intricate way. We take advantage of special properties of ferro¯uid froths and of constrained area evolution simulations, to distinguish the e ects of side swapping (T1 processes) from other rearrangements in the froth. Cell elongation characterizes the froth and its deviation from mechanical equilibrium as robustly as the usually measured total wall length, that is surface energy.
A common goal in physical, chemical and life sciences is to understand the connection between the... more A common goal in physical, chemical and life sciences is to understand the connection between the growth and the morphology of developing patterns. A general process is fusion or coalescence of interacting domains, especially in mixtures of immiscible liquids or tissues, where the coalescence of two drops or clusters is the basic phenomenon which governs the morphology and the kinetics of developing patterns (Steinberg, 1963).
Abstract We study the center of mass motion of single endodermal Hydra cells in two kinds of cell... more Abstract We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggregates: endodermal and ectodermal. The mean square displacement displays anomalous super-di usion with x 2 ∼ t where ¿1. The velocity distribution function is non-Gaussian and ÿts well the q-distribution function of velocities within the framework of the non-extensive thermostatistics proposed by Tsallis. Our results indicate that cell motion in two-dimensional cellular aggregates can be described by a &quot;correlated-type&quot; anomalous di usion.
Physica A: Statistical Mechanics and its Applications, 2001
We present experimental results and a simulation in two dimensions of the expansion and bursting ... more We present experimental results and a simulation in two dimensions of the expansion and bursting of aggregates of Hydra cells formed from an initially disordered mixture. In the experiments, after cell sorting, the aggregate rounds and swells until violent bursts occur, forcibly expelling internal uid and loose cells. We use Monte Carlo techniques to simulate the bursts in two dimensions. Initially, we consider a ring made of a monolayer of cells enveloping an internal uid. Each cell and the internal medium have their areas controlled by target area size. Increasing the target area of the internal cavity causes the aggregate to swell. We observe that aggregates of cells with higher surface tension generate higher internal pressure. In the simulations the cell ring bursts when it is too thin to endure uctuations in the cellular membranes. The process is relevant to embryonic development.
Foams have unique rheological properties that range from solid-like to fluid-like flow behavior. ... more Foams have unique rheological properties that range from solid-like to fluid-like flow behavior. We study foams under periodic shear stress in a Monte Carlo simulation (using the extended large-Q Potts model) and find three different types of hysteresis in the stress-strain relationship, which correspond to elastic, viscoelastic and fluid-like properties of foams. We relate this wide-ranging mechanical response of foams
We study the evolution of cellular patterns in 2D, specifically a hexagonal-rectangular transform... more We study the evolution of cellular patterns in 2D, specifically a hexagonal-rectangular transformation induced by applied fields (such as stress). We impose an area constraint so as to prevent the destruction of cells. When sufficiently stressed, the system undergoes irreversible local cellular rearrangement via neighbor switching (T1 switches). Monte Carlo based simulations of the large-Q Potts model display both topological
We show that differential adhesion with fluctuations is sufficient to explain a wide variety of c... more We show that differential adhesion with fluctuations is sufficient to explain a wide variety of cell rearrangement, by using the extended large-Q Potts model with differential adhesivity to simulate different biological phenomena. Different values of relative surface energies correspond to different biological cases, including complete and partial cell sorting, checkerboard, position reversal, and dispersal. We examine the convergence and temperature dependence of the simulation and distinguish spontaneous, neutral, and activated processes by performing simulations at different temperatures. We discuss the biological and physical implications of our quantitative results.
We present a simulation in two dimensions of an important process of biological development: the ... more We present a simulation in two dimensions of an important process of biological development: the burst of an aggregate of cells due to the expansion of an internal cavity by influx of external medium. The burst is quantitatively characterized by discontinuous change of the pressure of the aggregate. The influence of dimensionality on the process and its relevance for development are discussed.
Proceedings of the Royal Society of London. Series B: Biological Sciences, 2004
We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experim... more We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experiments on chondrogenesis in the early vertebrate limb and additional hypotheses. Cellular differentiation of mesenchymal cells into subtypes with different fibroblast growth factor (FGF) receptors occurs in the presence of spatio-temporal variations of FGFs and transforming growth factor-betas (TGF-βs). One class of differentiated cells produces elevated quantities of the extracellular matrix protein fibronectin, which initiates adhesion-mediated preskeletal mesenchymal condensation. The same class of cells also produces an FGFdependent laterally acting inhibitor that keeps condensations from expanding beyond a critical size. We show that this 'reactor-diffusion' mechanism leads naturally to patterning consistent with skeletal form, and describe simulations of spatio-temporal distribution of these differentiated cell types and the TGF-β and inhibitor concentrations in the developing limb bud.
Physica A: Statistical Mechanics and its Applications, 2001
We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggr... more We study the center of mass motion of single endodermal Hydra cells in two kinds of cellular aggregates: endodermal and ectodermal. The mean square displacement displays anomalous super-di usion with x 2 ∼ t where ¿1. The velocity distribution function is non-Gaussian and ÿts well the q-distribution function of velocities within the framework of the non-extensive thermostatistics proposed by Tsallis. Our results indicate that cell motion in two-dimensional cellular aggregates can be described by a "correlated-type" anomalous di usion.
We study the vertical liquid profile of foam drainage using the threedimensional large-Q Potts mo... more We study the vertical liquid profile of foam drainage using the threedimensional large-Q Potts model extended to include gravity. Forced drainage with constant-rate liquid input from the top of the foam produces a constant profile. In free drainage, without liquid input from the top, homogeneously distributed liquid drains to the bottom of the foam until capillary effects and gravity balance. For pulsed drainage, as liquid drains from the top of the foam into the dry foam, a sharp interface between the wet and dry foam develops. The fixed profile moves downwards at a constant velocity with a flat interface. The results of our simulations are suggested in both experiments and simplified meanfield analytical results.
Many materials. including soap froths. polycrystalline alloys, ceramics, lipid monolayers and gar... more Many materials. including soap froths. polycrystalline alloys, ceramics, lipid monolayers and garnet films. have structures composed of either two-or three-dimensional polygonal domains separated by well defined boundaries. Usually. the surface energy 01 these boundaries makes the pattern unstable. causing certain grains toshrink and eventually to disappear. Thus the pattern coarsens continuously unless other factors arrest the motion of the boundaries. We review recent theoretical, computational and experimental progress in our understanding of the asymptotic scaling laws that describe coarsening. In most cases the elementary expectation. that the mean grain radius scales with the square root of time. is confirmed. We pay particular attention to the history 01 the field. to understand why this elementary result has remained in doubt until now.
We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomple... more We discuss a method to reconstruct an approximate two-dimensional foam structure from an incomplete image using the extended Potts model on a pinned lattice. The initial information consists of the positions of the vertices only. We locate the centers of the bubbles using the Euclidean distance-map construction and assign at each vertex position a continuous pinning field with a potential falling off as 1/r. We nucleate a bubble at each center using the extended Potts model and let the structure evolve under the constraint of scaled target areas until the bubbles contact each other. The target area constraint and pinning centers prevent further coarsening. We then turn the area constraint off and let the edges relax to a minimum energy configuration. The result is a reconstructed structure very close to the simulation. We repeated this procedure for various stages of the coarsening of the same simulated foam and investigated the simulation and reconstruction dynamics, topology and area distribution, finding that they agreed to good accuracy.
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Papers by James Glazier