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Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks and theoretical methods, we can begin to probe the complex lives of microscopic motile…

We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…

A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…

Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…

Phase separation, crucial for spatially segregating biomolecules in cells, is well-understood in the simple case of a few components with pairwise interactions. Yet, biological cells challenge the simple picture in at least two ways: First,…

In this paper we present a network model to study the impact of spatial distribution of constituents, coupling between them and diffusive processes in the context of biological situations. The model is in terms of network of mobile elements…

Biochemical signalling cascades transduce extracellular stimuli into cellular responses through sequences of discrete, node-to-node activations. While signal fidelity depends critically on local interaction kinetics, the mechanisms…

We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending…

Biomolecular condensates constitute a newly recognized form of spatial organization in living cells. Although many condensates are believed to form as a result of phase separation, the physicochemical properties that determine the phase…

Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…

Different types of synchronization states are found when non-linear chemical oscillators are embedded into an active medium that interconnects the oscillators but also contributes to the system dynamics. Using different theoretical tools,…

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…

Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…

Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks…

Local interactions among biomolecules, and the role played by their environment, have gained increasing attention in modelling biochemical reactions. By defining the automaton of molecular perceptions, we explore an agent-based…

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the…

Biological systems are known to communicate by diffusing chemical signals in the surrounding medium. However, most of the recent literature has neglected the electron transfer mechanism occurring amongst living cells, and its role in…

Cells continuously sense their surroundings to detect modifications and generate responses. Very often changes in extracellular concentrations initiate signaling cascades that eventually result in changes in gene expression. Increasing…

Materials undergoing both phase separation and chemical reactions (defined here as all processes that change particle type or number) form an important class of non-equilibrium systems. Examples range from suspensions of self-propelled…

Systems biology models are useful models of complex biological systems that may require a large amount of experimental data to fit each model's parameters or to approximate a likelihood function. These models range from a few to thousands…