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The cell cycle is a tightly controlled process, yet its underlying genetic network shows marked differences across species. Which of the associated structural features follow solely from the ability to impose the appropriate gene expression…
Cellular differentiation is governed by gene regulatory networks, the high-dimensional stochastic biochemical systems that determine the transcriptional landscape and mediate cellular responses to signals and perturbations. Although…
Single-cell data provide high-dimensional measurements of the transcriptional states of cells, but extracting insights into the regulatory functions of genes, particularly identifying transcriptional mechanisms affected by biological…
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…
Life is characterized by a myriad of complex dynamic processes allowing organisms to grow, reproduce, and evolve. Physical approaches for describing systems out of thermodynamic equilibrium have been increasingly applied to living systems,…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the…
Characterization of pluripotent states, in which cells can both self-renew and differentiate, and the irreversible loss of pluripotency are important research areas in developmental biology. In particular, an understanding of these…
A blood cell lineage consists of several consecutive developmental stages from the pluripotent or multipotent stem cell to a particular stage of terminally differentiated cells. There is considerable interest in identifying the key…
Cellular development follows a stochastic yet rule-governed trajectory, though the underlying principles remain elusive. Here, we propose that cellular development follows paths of least action, aligning with foundational physical laws that…
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
Models of transcriptional regulation that assume equilibrium binding of transcription factors have been very successful at predicting gene expression from sequence in bacteria. However, analogous equilibrium models do not perform as well in…
Bacteria are highly adaptive microorganisms that thrive in a wide range of growth conditions via changes in cell morphologies and macromolecular composition. How bacterial morphologies are regulated in diverse environmental conditions is a…
To attain the targeted data rates of next generation cellular networks requires dense deployment of small cells in addition to macro cells which provide wide coverage. Dynamic radio resource management is crucial to the success of such…
Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells…
The innumerable shapes of plant leaves present a challenge to the explanatory power of biophysical theory. A model is needed that can produce these shapes with a small set of parameters. This paper presents a simple model of leaf shape…
We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical…