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The large scale behaviour of a population of cells that grow and interact through the concentration field of the chemicals they secrete is studied using dynamical renormalization group methods. The combination of the effective long-range…

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,…

Dysregulation in signal transduction pathways can lead to a variety of complex disorders, including cancer. Computational approaches such as network analysis are important tools to understand system dynamics as well as to identify critical…

Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple…

Cellular reprogramming, the conversion of one cell type to another, has fundamentally transformed our conception of cell types. Cellular reprogramming induces global changes in gene expression involving hundreds of transcription factors and…

Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Among these mechanisms, interspecies recognition…

Biomolecular condensates are small droplets forming spontaneously in biological cells via phase separation. They play a role in many cellular processes, but it is unclear how cells control them. Cellular regulation often relies on…

Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated routing information. Various cellular level mechanisms influence the network dynamics and…

Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to…

Phase separation and transitions among different molecular states are ubiquitous in living cells. Such transitions can be governed by local equilibrium thermodynamics or by active processes controlled by biological fuel. It remains largely…

The process of programmed cell death, namely apoptosis, is a natural mechanism that regulates healthy tissue, multicellular structures, and homeostasis. An improved understanding of apoptosis can significantly enhance our knowledge of…

Irreversibility, in which a transient perturbation leaves a system in a new state, is an emergent property in systems of interacting entities. This property has well-established implications in statistical physics but remains underexplored…

While bacterial chromosomes were long thought to be amorphous, recent experiments reveal pronounced organizational features. However, the extent of bacterial chromosome organization remains unclear. Here, we develop a fully data-driven…

Cell sorting, the segregation of cells with different properties into distinct domains, is a key phenomenon in biological processes such as embryogenesis. We use a phase-field model of a confluent cell layer to study the role of activity in…

We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random…

A new approach to the modular, complex systems analysis of nonlinear dynamics in cell cycling network transformations involved in carcinogenesis is proposed. Carcinogenesis is a complex process that involves dynamically inter-connected…

Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data…

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…

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…

Droplet formation has emerged as an essential concept for the spatiotemporal organisation of biomolecules in cells. However, classical descriptions of droplet dynamics based on passive liquid-liquid phase separation cannot capture the…