1,130 research outputs found
Universal features of cell polarization processes
Cell polarization plays a central role in the development of complex
organisms. It has been recently shown that cell polarization may follow from
the proximity to a phase separation instability in a bistable network of
chemical reactions. An example which has been thoroughly studied is the
formation of signaling domains during eukaryotic chemotaxis. In this case, the
process of domain growth may be described by the use of a constrained
time-dependent Landau-Ginzburg equation, admitting scale-invariant solutions
{\textit{\`a la}} Lifshitz and Slyozov. The constraint results here from a
mechanism of fast cycling of molecules between a cytosolic, inactive state and
a membrane-bound, active state, which dynamically tunes the chemical potential
for membrane binding to a value corresponding to the coexistence of different
phases on the cell membrane. We provide here a universal description of this
process both in the presence and absence of a gradient in the external
activation field. Universal power laws are derived for the time needed for the
cell to polarize in a chemotactic gradient, and for the value of the smallest
detectable gradient. We also describe a concrete realization of our scheme
based on the analysis of available biochemical and biophysical data.Comment: Submitted to Journal of Statistical Mechanics -Theory and Experiment
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
3D stochastic bicontinuous microstructures: Generation, topology and elasticity
Motivated by recent experimental investigations of the mechanical behavior of nanoporous metal we explore an efficient and robust method for generating 3D representative volume elements (RVEs) with strikingly similar behavior. Our approach adopts Cahn's method of generating a Gaussian random field by taking a superposition of standing sinusoidal waves of fixed wavelength but random in direction and phase. In its theory part, our study describes closed-form expressions for how the solid volume fraction affects the binarization level, mean structure size, specific surface area, averages of mean and Gaussian curvature, and the scaled topological genus. Based on numerical studies we report on criteria for achieving representative realizations of the structure by proper choice of the number of waves and element size. We also show that periodic structures are readily created. We analyze the mechanical properties considering linear and infinitesimal elasticity and evaluate the residual anisotropy (which can be made small) and the effective values of the Young's modulus and Poisson's ratio. The numerical results are in excellent agreement with experimental findings for the variation of stiffness with solid fraction of nanoporous gold made by dealloying. We propose scaling relations that achieve naturally a perfect agreement with the numerical and experimental data. The scaling relation for the stiffness accounts for a percolation-to-cluster transition in the random field microstructure at a finite solid fraction. We propose that this transition is the origin of the previously reported anomalous compliance of nanoporous gold
Pattern formation at cellular membranes by phosphorylation and dephosphorylation of proteins
We consider a classical model on activation of proteins, based in two reciprocal enzymatic biochemical reactions. The combination of phosphorylation and dephosphorylation reactions of proteins is a well established mechanism for protein activation in cell signalling. We introduce different affinity of the two versions of the proteins to the membrane and to the cytoplasm. The difference in the diffusion coefficient at the membrane and in the cytoplasm together with the high density of proteins at the membrane which reduces the accessible area produces domain formation of protein concentration at the membrane. We differentiate two mechanisms responsible for the pattern formation inside of living cells and discuss the consequences of these models for cell biology.Peer ReviewedPreprin
Tensegrity and Motor-Driven Effective Interactions in a Model Cytoskeleton
Actomyosin networks are major structural components of the cell. They provide
mechanical integrity and allow dynamic remodeling of eukaryotic cells,
self-organizing into the diverse patterns essential for development. We provide
a theoretical framework to investigate the intricate interplay between local
force generation, network connectivity and collective action of molecular
motors. This framework is capable of accommodating both regular and
heterogeneous pattern formation, arrested coarsening and macroscopic
contraction in a unified manner. We model the actomyosin system as a motorized
cat's cradle consisting of a crosslinked network of nonlinear elastic filaments
subjected to spatially anti-correlated motor kicks acting on motorized (fibril)
crosslinks. The phase diagram suggests there can be arrested phase separation
which provides a natural explanation for the aggregation and coalescence of
actomyosin condensates. Simulation studies confirm the theoretical picture that
a nonequilibrium many-body system driven by correlated motor kicks can behave
as if it were at an effective equilibrium, but with modified interactions that
account for the correlation of the motor driven motions of the actively bonded
nodes. Regular aster patterns are observed both in Brownian dynamics
simulations at effective equilibrium and in the complete stochastic
simulations. The results show that large-scale contraction requires correlated
kicking.Comment: 38 pages, 13 figure
Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms
Traffic-like collective movements are observed at almost all levels of
biological systems. Molecular motor proteins like, for example, kinesin and
dynein, which are the vehicles of almost all intra-cellular transport in
eukayotic cells, sometimes encounter traffic jam that manifests as a disease of
the organism. Similarly, traffic jam of collagenase MMP-1, which moves on the
collagen fibrils of the extracellular matrix of vertebrates, has also been
observed in recent experiments. Traffic-like movements of social insects like
ants and termites on trails are, perhaps, more familiar in our everyday life.
Experimental, theoretical and computational investigations in the last few
years have led to a deeper understanding of the generic or common physical
principles involved in these phenomena. In particular, some of the methods of
non-equilibrium statistical mechanics, pioneered almost a hundred years ago by
Einstein, Langevin and others, turned out to be powerful theoretical tools for
quantitaive analysis of models of these traffic-like collective phenomena as
these systems are intrinsically far from equilibrium. In this review we
critically examine the current status of our understanding, expose the
limitations of the existing methods, mention open challenging questions and
speculate on the possible future directions of research in this
interdisciplinary area where physics meets not only chemistry and biology but
also (nano-)technology.Comment: 33 page Review article, REVTEX text, 29 EPS and PS figure
Structure formation in active networks
Structure formation and constant reorganization of the actin cytoskeleton are
key requirements for the function of living cells. Here we show that a minimal
reconstituted system consisting of actin filaments, crosslinking molecules and
molecular-motor filaments exhibits a generic mechanism of structure formation,
characterized by a broad distribution of cluster sizes. We demonstrate that the
growth of the structures depends on the intricate balance between
crosslinker-induced stabilization and simultaneous destabilization by molecular
motors, a mechanism analogous to nucleation and growth in passive systems. We
also show that the intricate interplay between force generation, coarsening and
connectivity is responsible for the highly dynamic process of structure
formation in this heterogeneous active gel, and that these competing mechanisms
result in anomalous transport, reminiscent of intracellular dynamics
Challenges in Quantitative Abstractions for Collective Adaptive Systems
Like with most large-scale systems, the evaluation of quantitative properties
of collective adaptive systems is an important issue that crosscuts all its
development stages, from design (in the case of engineered systems) to runtime
monitoring and control. Unfortunately it is a difficult problem to tackle in
general, due to the typically high computational cost involved in the analysis.
This calls for the development of appropriate quantitative abstraction
techniques that preserve most of the system's dynamical behaviour using a more
compact representation. This paper focuses on models based on ordinary
differential equations and reviews recent results where abstraction is achieved
by aggregation of variables, reflecting on the shortcomings in the state of the
art and setting out challenges for future research.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
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