Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers
1
Citation
26
Reference
10
Related Paper
Citation Trend
Abstract:
The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, p c . A cell can only grow and divide if the pressure it experiences, due to interaction with its neighbors, is less than p c . Because temperature is an irrelevant variable in the model, the cell dynamics is driven by self-generated active forces (SGAFs) that are created by cell division. It is shown that even in the absence of intercellular interactions , cells undergo diffusive behavior. The SGAF-driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function ( FAF ) that extends over timescale of several cell division times. The time-dependence of the FAF reveals memory effects, which increases as p c increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback, and is inherently a non-equilibrium phenomenon.Keywords:
Negative feedback
Dynamics
Positive feedback
Brownian dynamics
The relaxation of initially straight semiflexible polymers has been discussed mainly with respect to the longest relaxation time. The biologically relevant nonequilibrium dynamics on shorter times is comparatively poorly understood, partly because ``initially straight'' can be realized in manifold ways. Combining Brownian dynamics simulations and systematic theory, we demonstrate how different experimental preparations give rise to specific short-time and universal long-time dynamics. We also discuss boundary effects and the onset of the stretch-coil transition.
Dynamics
Brownian dynamics
Manifold (fluid mechanics)
Cite
Citations (18)
The growth of a tissue, which depends on cell-cell interactions and biologically relevant process such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, p c . A cell can only grow and divide if the pressure it experiences, due to interaction with its neighbors, is less than p c . Because temperature is an irrelevant variable in the model, the cell dynamics is driven by self-generated active forces (SGAFs) that are created by cell division. It is shown that even in the absence of intercellular interactions , cells undergo diffusive behavior. The SGAF-driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force-force autocorrelation function ( FAF ) that extends over timescale of several cell division times. The time-dependence of the FAF reveals memory effects, which increases as p c increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback, and is inherently a non-equilibrium phenomenon.
Negative feedback
Dynamics
Positive feedback
Brownian dynamics
Cite
Citations (1)
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow down our survey for the case of the diffusion coefficient for a Brownian particle which can be modeled in the framework of Langevin dynamics. Our main focus will center on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds we consider a number of physical situations away from free Brownian motion and end with surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
Anomalous Diffusion
Langevin equation
Particle (ecology)
Brownian dynamics
Cite
Citations (0)
Recent experimental data reveal the complexity of diffusion dynamics beyond the scope of classical Brownian dynamics. The particles exhibit diverse diffusive motions from the anomalous toward classical diffusion over a wide range of temporal scales. Here a dressed diffusion model is developed to account for non-Brownian phenomena. By coupling the particle dynamics with a local field, the dressed diffusion model generalizes the Langevin equation through coupled damping kernels and generates the salient feature of time-dependent diffusion dynamics reported in the experimental measurements of biomolecules. The dressed diffusion model provides one quantitative aspect for future endeavors in this rapid-growing field.
Brownian dynamics
Langevin dynamics
Anomalous Diffusion
Dynamics
Langevin equation
Cite
Citations (5)
Describes an approach to the dynamics of particles in liquid suspension, based on Langevin equations, which allows rather direct calculation of power series expansions in time tau of such quantities as the particle velocity autocorrelation function, mean-square displacement and dynamic structure factors. The expansions are evaluated to order tau 3 if hydrodynamic interactions are neglected, but only to order tau in their presence. The longer-time diffusion coefficients are also considered, and the importance of the structural relaxation time tau I to the theoretical development is emphasised. Further similarities between the dynamics of particle suspensions and atoms in simple fluids are pointed out.
Brownian dynamics
Langevin equation
Mean squared displacement
Langevin dynamics
Particle (ecology)
Dynamics
Cite
Citations (84)
We describe in detail how to implement a coarse-grained hybrid Molecular Dynamics and Stochastic Rotation Dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length-scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number, the Schmidt number, the Mach number, the Knudsen number, and the Peclet number. The many Brownian and hydrodynamic time-scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant physical processes. We also show how to control a number of numerical artifacts, such as finite size effects and solvent induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity auto-correlation functions and related self diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity auto-correlation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems, and from this extract more general lessons that may be relevant for other coarse-graining schemes such as Lattice Boltzmann or Dissipative Particle Dynamics.
Lattice Boltzmann methods
Péclet number
Granularity
Brownian dynamics
Dimensionless quantity
Dissipative particle dynamics
Cite
Citations (439)
Confined diffusion is ubiquitous in nature. Ever since the "anomalous yet Brownian" motion was observed, the non-Gaussianity in confined diffusion has been unveiled as an important issue. In this Letter, we experimentally investigate the characteristics and source of non-Gaussian behavior in confined diffusion of nanoparticles suspended in polymer solutions. A time-varied and size-dependent non-Gaussianity is reported based on the non-Gaussian parameter and displacement probability distribution, especially when the nanoparticle's size is smaller than the typical polymer mesh size. This non-Gaussianity does not vanish even at the long-time Brownian stage. By inspecting the displacement autocorrelation, we observe that the nanoparticle-structure interaction, indicated by the anticorrelation, is limited in the short-time stage and makes little contribution to the non-Gaussianity in the long-time stage. The main source of the non-Gaussianity can therefore be attributed to hopping diffusion that results in an exponential probability distribution with the large displacements, which may also explain certain processes dominated by rare events in the biological environment.
Anomalous Diffusion
Brownian dynamics
Cite
Citations (96)
A simple stochastic model is used to show that the time autocorrelation function which determines dynamic susceptibility is generally nonexponential. The nonexponential character is caused by environmental fluctuations which arise in ordinary Brownian motion. Some computations of dynamic susceptibility are presented which indicate the kind of experimental results anticipated for substances which conform to this model.
Brownian dynamics
Stochastic modelling
Cite
Citations (9)
Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow down our survey for the case of the diffusion coefficient for a Brownian particle which can be modeled in the framework of Langevin dynamics. Our main focus will center on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds we consider a number of physical situations away from free Brownian motion and end with surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
Particle (ecology)
Cite
Citations (31)
We use Time Resolved Correlation (TRC), a recently introduced light scattering method, to study the dynamics of a variety of jammed, or glassy, soft materials. The output of a TRC experiment is cI(t,r), the time series of the degree of correlation between the speckle patterns generated by the light scattered at time t and t + r. We characterize the fluctuations of cI by calculating their Probability Density Function, their variance as a function of the lag r, and their time autocorrelation function. The comparison between these quantities for a Brownian sample and for jammed materials indicate unambiguously that the slow dynamics measured in soft glasses is temporally heterogeneous. The analogies with recent experimental, numerical and theoretical work on temporal heterogeneity in glassy dynamics are briefly discussed.
Brownian dynamics
Dynamics
Cite
Citations (10)