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Despite having advanced a reaction-diffusion model of ODE's in his 1952 paper on morphogenesis, reflecting his interest in mathematical biology, Alan Turing has never been considered to have approached a definition of Cellular Automata.…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
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…
This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular…
To advance understanding of cellular metabolism and reduce batch-to-batch variability in cell culture processes, this study introduces a multi-scale hybrid modeling framework designed to simulate and predict the dynamic behavior of CHO cell…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and…
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
We investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction diffusion advection (RDA) equation, which was previously introduced to model synaptogenesis in \textit{C. elegans}. The model describes…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…
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…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
Understanding how living organisms spontaneously develop complex functional structures inspires innovative approaches in engineering design. Here, we introduce a decentralized generative model based on morphogenesis to autonomously grow…
Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently,…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
We investigate Turing pattern formation in a stochastic reaction-diffusion model defined on $N$ lattice sites, where each lattice site is associated with a reaction vessel of volume $\Omega$. We focus on a regime where spatial discreteness…
Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is…