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A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article,…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
Cell polarity refers to the spatial asymmetry of molecules on the cell membrane. Altschuler, Angenent, Wang and Wu have proposed a stochastic model for studying the emergence of polarity in the presence of feedback between molecules. We…
Diverse processes--e.g. bioremediation, biofertilization, and microbial drug delivery--rely on bacterial migration in disordered, three-dimensional (3D) porous media. However, how pore-scale confinement alters bacterial motility is unknown…
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 effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases…
In this paper we propose a Stochastic model for studying a spatial cholera epidemic spreading where communities (Humans and Bacteria) are spatially distributed on a one-dimensional lattice and the bacteria are transported along a network…
We explore the joint effect of the intrinsic noise and time delay on the spatial pattern formation within a multi-scale mobile lattice model of the epithelium. The protein fluctuations are driven by transcription/translation processes in…
Bacteria can spontaneously develop collective motions by aligning their motions in dense systems. Here, we show that bacteria can also respond collectively to an alternating electrical field and form dynamic clusters oscillating at the same…
The proper functioning of multicellular organisms requires the robust establishment of precise proportions between distinct cell-types. This developmental differentiation process typically involves intracellular regulatory and stochastic…
Navigation of microorganisms is controlled by internal processes ultimately sensitive to mechanical or chemical signaling encountered along the path. In many natural environments, such as porous soils or physiological ducts, motile species…
Heterogeneity in gene expression across isogenic cell populations can give rise to phenotypic diversity, even when cells are in homogenous environments. This diversity arises from the discrete, stochastic nature of biochemical reactions,…
A recent burst of dynamic single-cell growth-division data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different modeling frameworks were used to infer specific mechanisms from such data,…
The dynamical behavior of two types of non-equilibrium systems is discussed: $(a)$ two-dimensional cellular structures, and $(b)$ living polymers. Simple models governing their evolution are introduced and steady state distributions (cell…
Modelling, analysing and inferring triggering mechanisms in population reproduction is fundamental in many biological applications. It is also an active and growing research domain in mathematical biology. In this chapter, we review the…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
We demonstrate 'differential dynamic microscopy' (DDM) for the fast, high throughput characterization of the dynamics of active particles. Specifically, we characterize the swimming speed distribution and the fraction of motile cells in…
Synchronization of mobile oscillators occurs in numerous contexts, including physical, chemical, biological and engineered systems. In vertebrate embryonic development, a segmental body structure is generated by a population of mobile…