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Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent to the indispensability of proteins for living cells is the fact that a given protein…
The phenomenon of cell sorting/segregation, by which cells organise spatially into clusters of specific cell type or function, is essential for tissue morphogenesis. This self-organization process involves an interplay between mechanical,…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
We present a machine learning framework for modeling protein dynamics. Our approach uses L1-regularized, reversible hidden Markov models to understand large protein datasets generated via molecular dynamics simulations. Our model is…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…
Temporally and spatially resolved measurements of protein transport inside cells provide important clues to the functional architecture and dynamics of biological systems. Fluorescence Recovery After Photobleaching (FRAP) technique has been…
Collective behavior of bacterial colonies plays critical roles in adaptability, survivability, biofilm expansion and infection. We employ an individual-based model of an interstitial biofilm to study emergent pattern formation based on the…
Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language…
A dynamic model for cell differentiation is studied, where cells with internal chemical reaction dynamics interact with each other and replicate. It leads to spontaneous differentiation of cells and determination, as is discussed in the…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Life on earth is distinguished by long-lived correlations in time. The patterns of material organization that characterize living organisms today are contingent on events that occurred billions of years ago. This contingency is a necessary…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
The molecular machinery of life is largely created via self-organisation of individual molecules into functional assemblies. Minimal coarse-grained models, where a whole macromolecule is represented by a small number of particles, can be of…
The metabolism is the motor behind the biological complexity of an organism. One problem of characterizing its large-scale structure is that it is hard to know what to compare it to. All chemical reaction systems are shaped by the same…
The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organization. Many of these transitions are achieved…