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A model to describe the arising of new structures in an initial homogeneous biological system is proposed. The essay is motivated by the intention to work on a non-equilibrium situation grouping together several mechanisms and processes as:…
To study how a zygote develops into an embryo with different tissues, large-scale 4D confocal movies of C. elegans embryos have been produced recently by experimental biologists. However, the lack of principled statistical methods for the…
Mechanism of two-tone suppression is studied using a coupled-oscillator model of the cochlea with feed-forward coupling. Local amplification of sound signals is modeled by using Stuart-Landau oscillators near the Hopf bifurcation, and…
We present a model for evolving agents using both genetic and cultural inheritance mechanisms. Within each agent our model maintains two distinct information stores we call the genome and the memome. Processes of adaptation are modeled as…
Gene co-expression network differential analysis is designed to help biologists understand gene expression patterns under different condition. By comparing different gene co-expression networks we may find conserved part as well as…
In this paper we consider discrete-time dynamical systems generated by gonosomal evolution operators of sex linked inheritance. Mainly we study dynamical systems of a hemophilia, which biologically is a group of hereditary genetic disorders…
Identifying latent structure in large data matrices is essential for exploring biological processes. Here, we consider recovering gene co-expression networks from gene expression data, where each network encodes relationships between genes…
How patterns and structures undergo symmetry breaking and self-organize within biological systems from initially homogeneous states is a key issue for biological development. The activator-inhibitor (AI) mechanism, derived from…
Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted…
Tissue boundaries pattern embryos, suppress tumours, and provide directional cues. Tissue boundaries are associated with supracellular cables formed by actin and the molecular motor non-muscle myosin II. Actomyosin cables generate tension…
A wide range of organisms use circadian clocks to keep internal sense of daily time and regulate their behavior accordingly. Most of these clocks use intracellular genetic networks based on positive and negative regulatory elements. The…
We propose a mechanism enabling the appearance of border cells -- neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows…
A model of population growth and dispersal is considered where the spatial habitat is a lattice and reproduction occurs generationally. The resulting discrete dynamical systems exhibits velocity locking, where rational speed invasion fronts…
In a developing embryo, information about the position of cells is encoded in the concentrations of "morphogen" molecules. In the fruit fly, the local concentrations of just a handful of proteins encoded by the gap genes are sufficient to…
A model for morphoelastic growth, that is, growth influenced by elastic stress, driven by the absorption of nutrients is considered. The model features a multiplicative decomposition of the deformation gradient into an elastic contribution…
Accurate computational identification of DNA methylation is essential for understanding epigenetic regulation. Although deep learning excels in this binary classification task, its "black-box" nature impedes biological insight. We address…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume…
We derive novel anti-concentration bounds for the difference between the maximal values of two Gaussian random vectors across various settings. Our bounds are dimension-free, scaling with the dimension of the Gaussian vectors only through…
From a coarse-grained perspective the motif of a self-activating species, activating a second species which acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory…