The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit of discrete one dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified numerically by comparing Monte Carlo simulations for the CPM with numerics for the Keller-Segel model.
The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article clarifies the form of biologically relevant model equations: We derive Patlak-Keller-Segel-like equations involving nonlocal, fractional Laplacians from a microscopic model for cell movement. Starting from a power-law distribution of run times, we derive a kinetic equation in which the collision term takes into account the long range behaviour of the individuals. A fractional chemotactic equation is obtained in a bi…
In chemotaxis, cells are modulating their migration patterns in response to concentration gradients of a guiding substance. Immune cells are believed to use such chemotactic sensing for remotely detecting and homing in on pathogens. Considering that an immune cells may encounter a multitude of targets with vastly different migration properties, ranging from immobile to highly mobile, it is not clear which strategies of chemotactic pursuit are simultaneously efficient and versatile. We takle this problem theoretically and define a tunable response function that maps temporal or spatial concentr…
We consider an inertial model of chemotactic aggregation generalizing the Keller-Segel model and we study the linear dynamical stability of an infinite and homogeneous distribution of cells (bacteria, amoebae, endothelial cells,...) when inertial effects are accounted for. These inertial terms model cells directional persistance. We determine the condition of instability and the growth rate of the perturbation as a function of the cell density and the wavelength of the perturbation. We discuss the differences between overdamped (Keller-Segel) and inertial models. Finally, we show the analogy b…
We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean field Fokker-Planck equation governing the evolution of the distribution function of the system in phase space. By taking the successive moments of this kinetic equation and using a local thermodynamic equilibrium condition, we derive a set of hydrodynamic equations involvin…
Chemical signaling is one of the ubiquitous mechanisms by which inter-cellular communication takes place at the microscopic level, particularly via chemotaxis. Such multi-cellular systems are popularly studied using continuum, mean-field equations. In this letter we study a stochastic model of chemotactic signaling. The Langevin formalism of the model makes it amenable to calculation via non-perturbative analysis, which enables a quantification of the effect of fluctuations on both the weak and strongly-coupled biological dynamics. In particular we show that the (i) self-localization due to au…
We perform a linear dynamical stability analysis of a general hydrodynamic model of chemotactic aggregation [Chavanis & Sire, Physica A, in press (2007)]. Specifically, we study the stability of an infinite and homogeneous distribution of cells against "chemotactic collapse". We discuss the analogy between the chemotactic collapse of biological populations and the gravitational collapse (Jeans instability) of self-gravitating systems. Our hydrodynamic model involves a pressure force which can take into account several effects like anomalous diffusion or the fact that the organisms cannot inter…
The multiscale approach to the assessment of biodamage resulting upon irradiation of biological media with ions is reviewed, explained and compared to other approaches. The processes of ion propagation in the medium concurrent with ionization and excitation of molecules, transport of secondary products, dynamics of the medium, and biological damage take place on a number of different temporal, spatial and energy scales. The multiscale approach, a physical phenomenon-based analysis of the scenario that leads to radiation damage, has been designed to consider all relevant effects on a variety of…
We describe a recent multiscale approach based on the concurrent coupling of constrained molecular dynamics for long biomolecules with a mesoscopic lattice Boltzmann treatment of solvent hydrodynamics. The multiscale approach is based on a simple scheme of exchange of space-time information between the atomistic and mesoscopic scales and is capable of describing self-consistent hydrodynamic effects on molecular motion at a computational cost which scales linearly with both solute size and solvent volume. For an application of our multiscale method, we consider the much studied problem of biopo…
Relative biological effectiveness (RBE) is a key quantity for the description of radiobiological effects induced by charged-particle irradiation in the context of ion-beam cancer therapy. Since RBE is a complex function that depends on different physical, chemical and biological parameters, a fundamental understanding of these effects becomes increasingly important for clinical applications. The phenomenon-based MultiScale Approach to the physics of radiation damage with ions (MSA) provides a tool for a molecular-level understanding of physical and chemical mechanisms of radiation biodamage an…
Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, classical machine learning techniques often ignore the fundamental laws of physics and result in ill-posed pr…
We review the computation models for biofilm and bacteria cells, providing perspectives on biofilm's various properties and potential serving as engineering living materials (ELMs), considering the omnipresence of such biological matter. The minireview starts from the molecular regime, bottom-up to the mesoscale, to continuum, with an emphasis on the mesoscale algorithms such as dissipative particles dynamics (DPD) and individual-based modeling (IbM). Some representative works are highlighted considering different modeling methods on each scale. The advantages and limitations of each algorithm…
Collective migration -- the directed, coordinated motion of many self-propelled agents -- is a fascinating emergent behavior exhibited by active matter that has key functional implications for biological systems. Extensive studies have elucidated the different ways in which this phenomenon may arise. Nevertheless, how collective migration can persist when a population is confronted with perturbations, which inevitably arise in complex settings, is poorly understood. Here, by combining experiments and simulations, we describe a mechanism by which collectively migrating populations smooth out la…
Zhejiang University（浙江大学）；Ningbo Institute of Technology, Beihang University（北京航空航天大学宁波研究院）
By imitating biological microswimmers, microrobots can be designed to accomplish targeted delivery of cargos and biomedical manipulations at microscale. However, it is still a great challenge to enable microrobots to maneuver in a complex environment. Machine learning algorithms offer a tool to boost mobility and flexibility of a synthetic microswimmer, hence could help us design truly smart microrobots. In this work, we investigate how a model of sea urchin sperm cell can self-learn chemotactic motion in a chemoattractant concentration field. We employ an artificial neural network to act as a…
Interfacing atomistic-based with continuum-based simulation codes is now required in many multiscale physical and biological systems. We present the first results from coupled atomistic-continuum simulations on 190,000 processors. Platelet aggregation in the patient-specific model of an aneurysm has been modeled using a high-order spectral/hp element Navier-Stokes solver with a stochastic (coarse-grained) Molecular Dynamics solver based on Dissipative Particle Dynamics (DPD).
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information…
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas i…
Various biological processes such as transport of oxygen and nutrients, thrombus formation, vascular angiogenesis and remodeling are related to cellular/subcellular level biological processes, where mesoscopic simulations resolving detailed cell dynamics provide a key to understanding and identifying the cellular basis of disease. To break this bottleneck and achieve a biologically meaningful timescale, we propose a multiscale parareal algorithm in which a continuum-based solver supervises a mesoscopic simulation in the time-domain. Using an iterative prediction-correction strategy, the parall…
Similarly to their biological counterparts, suspensions of chemically-active autophoretic swimmers exhibit nontrivial dynamics involving self-organization processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a differ…
Biological processes such as embryogenesis, wound healing and cancer progression, crucially rely on the ability of epithelial cells to coordinate their mechanical activity over length scales order of magnitudes larger than the typical cellular size. While regulated by various signalling pathways, it has recently become evident that this behavior can additionally hinge on a minimal toolkit of physical mechanisms, of which liquid crystal order is the most prominent example. Yet, experimental and theoretical studies have given so far inconsistent results in this respect: whereas nematic order is …
How self-organized networks develop, mature and degenerate is a key question for sociotechnical, cyberphysical and biological systems with potential applications from tackling violent extremism through to neurological diseases. So far, it has proved impossible to measure the continuous-time evolution of any in vivo organism network from birth to death. Here we provide such a study which crosses all organizational and temporal scales, from individual components (10^1) through to the mesoscopic (10^3) and entire system scale (10^6). These continuous-time data reveal a lifespan driven by punctuat…
Macromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of deformable membranes, the diffusion of proteins and the molecular binding and unbinding. Because these stochastic processes couple over a multitude of time and length scales, theoretical modeling of membrane adhesion has been a major challenge. Here we present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local r…
