Related papers: Quantitative Modelling of Diffusion-driven Pattern…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
The current paper presents a novel recurrent neural network model, the predictive multiple spatio-temporal scales RNN (P-MSTRNN), which can generate as well as recognize dynamic visual patterns in the predictive coding framework. The model…
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate…
Multi-sample microarray experiments have become a standard experimental method for studying biological systems. A frequent goal in such studies is to unravel the regulatory relationships between genes. During the last few years, regression…
From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially or simultaneously. These growth patterns are manifested in all types of bacteria and yeasts. The ubiquity of these growth…
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…
We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying…
We investigate the nature of genetic drift acting at the leading edge of range expansions, building on recent results in [Hallatschek et al., Proc.\ Natl.\ Acad.\ Sci., \textbf{104}(50): 19926 - 19930 (2007)]. A well mixed population of two…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
We investigate proteins within heterogeneous cell membranes where non-equilibrium phenomena arises from spatial variations in concentration and temperature. We develop simulation methods building on non-equilibrium statistical mechanics to…
Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these…
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…
Gene regulatory networks arise in all living cells, allowing the control of gene expression patterns. The study of their topology has revealed that certain subgraphs of interactions or "motifs" appear at anomalously high frequencies. We ask…
Piebaldism usually manifests as white areas of fur, hair or skin due to the absence of pigment-producing cells in those regions. The distribution of the white and colored zones does not follow the classical Turing patterns. Here we present…
Genes are frequently regulated in complex manners, necessitating modelling approaches which go beyond simple (linear) gene-to-gene interactions and address the modularity of cis-regulatory regions and alternate transcription initiation…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…