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Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
The work is devoted to the analysis of cell population dynamics where cells make a choice between differentiation and apoptosis. This choice is based on the values of intracellular proteins whose concentrations are described by a system of…
The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
For various species of biological cells, experimental observations indicate the existence of universal distributions of the cellular size, scaling relations between the cell-size moments and simple rules for the cell-size control. We…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
The spatial structure of the cell is highly organized at all levels: from small complexes and assemblies, to local nano- and micro-clusters, to global, micrometer scales across and between cells. We suggest that this multiscale spatial cell…
Many cytoskeletal biopolymers are "active," consuming energy in large quantities. In this Letter, we identify a fundamental difference between active polymers and passive, equilibrium polymers: for equal mean lengths, active polymers can…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
Cellular behavior is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
A fundamental issue discussed in evolutionary biology is the transition from unicellular to multicellular organisms. Here we develop non-robust models provided in [1] and attempt to get robust models investigated how differentiation of…
Emergence and maintenance of polymers with complex sequences is a major question in the study of origins of life. To answer this, we studied a model polymerization reaction, where polymers are synthesized by stepwise ligation from two types…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Nonlinear dynamics of two biomolecules is studied. These are a microtubule and DNA molecule. Two mathematical procedures are explained, yielding to three kinds of solitary waves moving through the systems. These waves are kinks, modulated…
Unlike many physical nonequilibrium systems, in biological systems, the coupling to external energy sources is not a fixed parameter but adaptively controlled by the system itself. We do not have theoretical frameworks that allow for such…
Phase separation within polymer networks plays a central role in shaping the structure and mechanics of both synthetic materials and living cells, including the formation of biomolecular condensates within cytoskeletal networks. Previous…