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Register a new userMacroscopic dynamics of biological cells interacting via chemotaxis and direct contact
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A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called chemotaxis) with their shapes randomly fluctuating. Nonlinear diffusion equation is derived from microscopic dynamics in dimensions one and two using excluded volume approach. Nonlinear diffusion coefficient depends on cellular volume fraction and it is demonstrated to prevent collapse of cellular density. A very good agreement is shown between Monte Carlo simulations of the microscopic Cellular Potts Model and numerical solutions of the macroscopic equations for relatively large cellular volume fractions. Combination of microscopic and macroscopic models were used to simulate growth of structures similar to early vascular networks.
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Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically; and the frequency spectrum of this chemical fluctuation carries valuable information about the mechanism and the dynamics of the intracellular reactions creating these biomolecules. Although recent advances in single-cell experimental techniques enable the direct monitoring of the time-traces of the biological noise in each cell, the development of the theoretical tools needed to extract the information encoded in the stochastic dynamics of intracellular chemical fluctuation is still in its adolescence. Here, we present a simple and general equation that relates the power-spectrum of the product number fluctuation to the product lifetime and the reaction dynamics of the product creation process. By analyzing the time traces of the protein copy number using this theory, we can extract the power spectrum of the mRNA number, which cannot be directly measured by currently available experimental techniques. From the power spectrum of the mRNA number, we can further extract quantitative information about the transcriptional regulation dynamics. Our power spectrum analysis of gene expression noise is demonstrated for the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. Additionally, we investigate how the non-Poisson reaction dynamics and the cell-to-cell heterogeneity in transcription and translation affect the power-spectra of the mRNA and protein number.
Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical Andronov Hopf bifurcation, with the emergence of limit cycle. The increase of the population of the oxidized PUFA fragments, take as the control parameter, involves an inverse Feigenbaum, (a cascade of saddle foci Shilnikovs bifurcations) scenario, which results in the stabilization of the dynamics and in a decrease of complexity.
Periodic reversals of the direction of motion in systems of self-propelled rod shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize their swarming rate. In this paper, a connection is found between a microscopic one dimensional cell-based stochastic model of reversing non-overlapping bacteria and a macroscopic non-linear diffusion equation describing dynamics of the cellular density. Boltzmann-Matano analysis is used to determine the nonlinear diffusion equation corresponding to the specific reversal frequency. Macroscopically (ensemble-vise) averaged stochastic dynamics is shown to be in a very good agreement with the numerical solutions of the nonlinear diffusion equation. Critical density $p_0$ is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities $p>p_0$. An analytical approximation of the pairwise collision time and semi-analytical fit for the total jam time per reversal period are also obtained. It is shown that cell populations with high reversal frequencies are able to spread out effectively at high densities. If the cells rarely reverse then they are able to spread out at lower densities but are less efficient at spreading out at at higher densities.
Contact between particles and motile cells underpins a wide variety of biological processes, from nutrient capture and ligand binding, to grazing, viral infection and cell-cell communication. The window of opportunity for these interactions is ultimately determined by the physical mechanism that enables proximity and governs the contact time. Jeanneret et al. (Nat. Comm. 7: 12518, 2016) reported recently that for the biflagellate microalga Chlamydomonas reinhardtii contact with microparticles is controlled by events in which the object is entrained by the swimmer over large distances. However, neither the universality of this interaction mechanism nor its physical origins are currently understood. Here we show that particle entrainment is indeed a generic feature for microorganisms either pushed or pulled by flagella. By combining experiments, simulations and analytical modelling we reveal that entrainment length, and therefore contact time, can be understood within the framework of Taylor dispersion as a competition between advection by the no slip surface of the cell body and microparticle diffusion. The existence of an optimal tracer size is predicted theoretically, and observed experimentally for C. reinhardtii. Spatial organisation of flagella, swimming speed, swimmer and tracer size influence entrainment features and provide different trade-offs that may be tuned to optimise microbial interactions like predation and infection.
In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a continuous limit of a two-dimensional Cellular Potts Model (CPM) with excluded volume is derived, describing cells moving in a medium and reacting to each other through both direct contact and long range chemotaxis. The continuous macroscopic model is obtained as a Fokker-Planck equation describing evolution of the cell probability density function. All coefficients of the general macroscopic model are derived from parameters of the CPM and a very good agreement is demonstrated between CPM Monte Carlo simulations and numerical solution of the macroscopic model. It is also shown that in the absence of contact cell-cell interactions, the obtained model reduces to the classical macroscopic Keller-Segel model. General multiscale approach is demonstrated by simulating spongy bone formation from loosely packed mesenchyme via the intramembranous route suggesting that self-organizing physical mechanisms can account for this developmental process.
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