458 research outputs found
Symmetry-Breaking Motility
Locomotion of bacteria by actin polymerization, and in vitro motion of
spherical beads coated with a protein catalyzing polymerization, are examples
of active motility. Starting from a simple model of forces locally normal to
the surface of a bead, we construct a phenomenological equation for its motion.
The singularities at a continuous transition between moving and stationary
beads are shown to be related to the symmetries of its shape. Universal
features of the phase behavior are calculated analytically and confirmed by
simulations. Fluctuations in velocity are shown to be generically
non-Maxwellian and correlated to the shape of the bead.Comment: 4 pages, 2 figures, REVTeX; formatting of references correcte
The Force-Velocity Relation for Growing Biopolymers
The process of force generation by the growth of biopolymers is simulated via
a Langevin-dynamics approach. The interaction forces are taken to have simple
forms that favor the growth of straight fibers from solution. The
force-velocity relation is obtained from the simulations for two versions of
the monomer-monomer force field. It is found that the growth rate drops off
more rapidly with applied force than expected from the simplest theories based
on thermal motion of the obstacle. The discrepancies amount to a factor of
three or more when the applied force exceeds 2.5kT/a, where a is the step size
for the polymer growth. These results are explained on the basis of restricted
diffusion of monomers near the fiber tip. It is also found that the mobility of
the obstacle has little effect on the growth rate, over a broad range.Comment: Latex source, 9 postscript figures, uses psfig.st
Single cell mechanics: stress stiffening and kinematic hardening
Cell mechanical properties are fundamental to the organism but remain poorly
understood. We report a comprehensive phenomenological framework for the
nonlinear rheology of single fibroblast cells: a superposition of elastic
stiffening and viscoplastic kinematic hardening. Our results show, that in
spite of cell complexity its mechanical properties can be cast into simple,
well-defined rules, which provide mechanical cell strength and robustness via
control of crosslink slippage.Comment: 4 pages, 6 figure
Dynamic Phase Transitions in Cell Spreading
We monitored isotropic spreading of mouse embryonic fibroblasts on
fibronectin-coated substrates. Cell adhesion area versus time was measured via
total internal reflection fluorescence microscopy. Spreading proceeds in
well-defined phases. We found a power-law area growth with distinct exponents
a_i in three sequential phases, which we denote basal (a_1=0.4+-0.2), continous
(a_2=1.6+-0.9) and contractile (a_3=0.3+-0.2) spreading. High resolution
differential interference contrast microscopy was used to characterize local
membrane dynamics at the spreading front. Fourier power spectra of membrane
velocity reveal the sudden development of periodic membrane retractions at the
transition from continous to contractile spreading. We propose that the
classification of cell spreading into phases with distinct functional
characteristics and protein activity patterns serves as a paradigm for a
general program of a phase classification of cellular phenotype. Biological
variability is drastically reduced when only the corresponding phases are used
for comparison across species/different cell lines.Comment: 4 pages, 5 figure
Mathematical modelling of extracellular matrix dynamics using discrete cells: Fiber orientation and tissue regeneration
Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the factors involved in orientation and alignment. Within this framework, cells are considered as discrete objects, while the matrix is modelled as a continuum. Using numerical simulations, we investigate the effect on alignment of changing cell properties and of varying cell interactions with collagen and fibrin
An Experimental and Computational Study of the Effect of ActA Polarity on the Speed of Listeria monocytogenes Actin-based Motility
Listeria monocytogenes is a pathogenic bacterium that moves within infected cells and spreads directly between cells by harnessing the cell's dendritic actin machinery. This motility is dependent on expression of a single bacterial surface protein, ActA, a constitutively active Arp2,3 activator, and has been widely studied as a biochemical and biophysical model system for actin-based motility. Dendritic actin network dynamics are important for cell processes including eukaryotic cell motility, cytokinesis, and endocytosis. Here we experimentally altered the degree of ActA polarity on a population of bacteria and made use of an ActA-RFP fusion to determine the relationship between ActA distribution and speed of bacterial motion. We found a positive linear relationship for both ActA intensity and polarity with speed. We explored the underlying mechanisms of this dependence with two distinctly different quantitative models: a detailed agent-based model in which each actin filament and branched network is explicitly simulated, and a three-state continuum model that describes a simplified relationship between bacterial speed and barbed-end actin populations. In silico bacterial motility required a cooperative restraining mechanism to reconstitute our observed speed-polarity relationship, suggesting that kinetic friction between actin filaments and the bacterial surface, a restraining force previously neglected in motility models, is important in determining the effect of ActA polarity on bacterial motility. The continuum model was less restrictive, requiring only a filament number-dependent restraining mechanism to reproduce our experimental observations. However, seemingly rational assumptions in the continuum model, e.g. an average propulsive force per filament, were invalidated by further analysis with the agent-based model. We found that the average contribution to motility from side-interacting filaments was actually a function of the ActA distribution. This ActA-dependence would be difficult to intuit but emerges naturally from the nanoscale interactions in the agent-based representation
A phenomenological approach to the simulation of metabolism and proliferation dynamics of large tumour cell populations
A major goal of modern computational biology is to simulate the collective
behaviour of large cell populations starting from the intricate web of
molecular interactions occurring at the microscopic level. In this paper we
describe a simplified model of cell metabolism, growth and proliferation,
suitable for inclusion in a multicell simulator, now under development
(Chignola R and Milotti E 2004 Physica A 338 261-6). Nutrients regulate the
proliferation dynamics of tumor cells which adapt their behaviour to respond to
changes in the biochemical composition of the environment. This modeling of
nutrient metabolism and cell cycle at a mesoscopic scale level leads to a
continuous flow of information between the two disparate spatiotemporal scales
of molecular and cellular dynamics that can be simulated with modern computers
and tested experimentally.Comment: 58 pages, 7 figures, 3 tables, pdf onl
In Silico Reconstitution of Actin-Based Symmetry Breaking and Motility
Computational modeling and experimentation in a model system for actin-based force generation explain how actin networks initiate and maintain directional movement
Parameter identification problems in the modelling of cell motility
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree
Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics
This paper is devoted to estimates of the exponential decay of eigenfunctions
of difference operators on the lattice Z^n which are discrete analogs of the
Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our
investigation of the essential spectra and the exponential decay of
eigenfunctions of the discrete spectra is based on the calculus of so-called
pseudodifference operators (i.e., pseudodifferential operators on the group
Z^n) with analytic symbols and on the limit operators method. We obtain a
description of the location of the essential spectra and estimates of the
eigenfunctions of the discrete spectra of the main lattice operators of quantum
mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on
Z^3, and square root Klein-Gordon operators on Z^n
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