Related papers: Neutral evolution of model proteins: diffusion in …
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
Emergence of new protein structures has proved difficult to trace in nature and engineer in the laboratory. However, one aspect of structure evolution has proved immensely helpful for determining the three-dimensional structure of proteins…
The accurate prediction of biological features from genomic data is paramount for precision medicine and sustainable agriculture. For decades, neural network models have been widely popular in fields like computer vision, astrophysics and…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
We consider a reaction-diffusion model for a population structured in phenotype. We assume that the population lives in a heterogeneous periodic environment, so that a given phenotypic trait may be more or less fit according to the spatial…
Scientific studies in many areas of biology routinely employ evolutionary analyses based on the probabilistic inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly…
In this paper, we mathematically describe the time evolution of protein folding features via Iori et al.'s heteropolymer model. More specifically, we identify that the folding amino acid chain evolve according to a power law $D \sim…
Known by many names and arising in many settings, the forced linear diffusion model is central to the modeling of power and influence within social networks (while also serving as the mechanistic justification for the widely used…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we…
An all-atom model of proteins is used to show that the same sequence of amino acids can have many alternative structures, that are very distant from, and that can be as stable as, the corresponding native structure. Such alternative…
MOTIVATION: Proteins fold into complex structures that are crucial for their biological functions. Experimental determination of protein structures is costly and therefore limited to a small fraction of all known proteins. Hence, different…
In this work we propose a physical model of organismal evolution, where phenotype, organism life expectancy, is directly related to genotype i.e. the stability of its proteins which can be determined exactly in the model. Simulating the…
It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other…
In this review some simple models of asexual populations evolving on smooth landscapes are studied. The basic model is based on a cellular automaton, which is analyzed here in the spatial mean-field limit. Firstly, the evolution on a fixed…
Theoretical studies of protein folding on lattice models relie on the assumption that water close to amino-acids is always in thermal equilibrium all along the folding pathway. Within this framework, it has always been considered that…
We present a sequence-based probabilistic formalism that directly addresses co-operative effects in networks of interacting positions in proteins, providing significantly improved contact prediction, as well as accurate quantitative…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…