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Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. These changes in cell shape may in turn affect the dynamics of…
An important task for many if not all the scientific domains is efficient knowledge integration, testing and codification. It is often solved with model construction in a controllable computational environment. In spite of that, the…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic…
Important cellular processes, such as cell motility and cell division, are coordinated by cell polarity, which is determined by the non-uniform distribution of certain proteins. Such protein patterns form via an interplay of protein…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Spatial organization of proteins in cells is important for many biological functions. In general, the nonlinear, spatially coupled models for protein-pattern formation are only accessible to numerical simulations, which has limited insight…
Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane,…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…
A fast and accurate grid-based method with low memory requirement is presented to calculate volume characteristics in molecular systems. The distribution of volume and packing density is characterized in globular proteins, where void space…
Spatial profiling technologies in biology, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate high-dimensional, multi-channel data with strong spatial alignment and complex inter-channel relationships.…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing…
The evolution of occupied volume under progressive fragmentation of granular matter is studied using a purely geometric model. Rather than modelling disorder directly, properties are investigated by analysing highly ordered reference…
The self-organization of proteins into enriched compartments and the formation of complex patterns are crucial processes for life on the cellular level. Liquid-liquid phase separation is one mechanism for forming such enriched compartments.…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Most models of biological pattern formation are simulated on continuous domains even though cells are discrete objects that provide internal boundaries to the diffusion of regulatory components. In our previous papers on simulating…
Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also…
In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in…