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Inferring concerted changes among biological traits along an evolutionary history remains an important yet challenging problem. Besides adjusting for spurious correlation induced from the shared history, the task also requires sufficient…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
Rhythmic activity in the gamma band (30-100Hz) has been observed in numerous animal species ranging from insects to humans, and in relation to a wide range of cognitive tasks. Various experimental and theoretical studies have investigated…
We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we…
Bipolar Disorder (BD) is a complex disease. It is heterogeneous, both at the phenotypic and genetic level, although the extent and impact of this heterogeneity is not fully understood. In this paper, we leverage recent advances in…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
We present a vector field method for obtaining the spatial organization of 3D patterns of gene expression based on gradients and lines of force obtained by numerical integration. The convergence of these lines of force in local maxima are…
Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with a kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and…
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population…
Phenotype transition takes place in many biological processes such as differentiation, and understanding how a cell reprograms its global gene expression profile is a problem of rate theories. A cell phenotype transition accompanies with…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…
Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external…
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In…
The ability of a cancer cell population to achieve heterogeneity in their phenotype distributions offers advantages in tumor invasiveness and drug resistance. Studying the mechanisms behind such observed heterogeneity in mammalian cells…
In multicellular organisms, cells differentiate into several distinct types during early development. Determination of each cellular state, along with the ratio of each cell type, as well as the developmental course during cell…
Non-genetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong…
The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through…
In a wide variety of natural systems, closely-related microbial strains coexist stably, resulting in high levels of fine-scale biodiversity. However, the mechanisms that stabilize this coexistence are not fully understood. Spatial…
We propose a probabilistic model for interpreting gene expression levels that are observed through single-cell RNA sequencing. In the model, each cell has a low-dimensional latent representation. Additional latent variables account for…
We consider a reaction-diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evolution of a population of organisms which can switch their…