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Gene duplication is a fundamental evolutionary mechanism that contributes to biological complexity and diversity (Fortna et al., 2004). Traditionally, research has focused on the duplication of gene sequences (Zhang, 1914). However,…
Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the…
We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose a novel…
There is increasing evidence that protein binding to specific sites along DNA can activate the reading out of genetic information without coming into direct physical contact with the gene. There also is evidence that these distant but…
Epistasis describes the phenomenon that mutations at different loci do not have independent effects with regard to certain phenotypes. Understanding the global epistatic landscape is vital for many genetic and evolutionary theories. Current…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
The architecture of the eukaryotic genome is characterized by a high degree of spatial organization. Chromosomes occupy preferred territories correlated to their state of activity and, yet, displace their genes to interact with remote sites…
Structural changes in a network representation of a system (e.g.,different experimental conditions, time evolution), can provide insight on its organization, function and on how it responds to external perturbations. The deeper…
Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. We here analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation…
A theoretical framework for evaluating the approximate energy and dynamic properties associated with the folding of DNA into nucleosomes and chromatin is presented. For this purpose experimentally determined elastic constants of linear DNA…
We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…
Electronic properties of DNA are believed to play a crucial role in many phenomena in living organisms, for example the location of DNA lesions by base excision repair (BER) glycosylases and the regulation of tumor-suppressor genes such as…
Modeling of DNA-protein interactions is a complex process involving many important time and length scales. This can be facilitated through the use of coarse-grained models which reduce the number of degrees of freedom and allow efficient…
To ensure fast gene activation, Transcription Factors (TF) use a mechanism known as facilitated diffusion to find their DNA promoter site. Here we analyze such a process where a TF alternates between 3D and 1D diffusion. In the latter (TF…
The genomic reality is a highly complex and dynamic system. The recent development of high-throughput technologies has enabled researchers to measure the abundance of many genes (in the order of thousands) simultaneously. The challenge is…
Autoregressive models capture stochastic processes in which past realizations determine the generative distribution of new data; they arise naturally in a variety of industrial, biomedical, and financial settings. A key challenge when…
Spatial transcriptomics is a modern sequencing technology that allows the measurement of the activity of thousands of genes in a tissue sample and map where the activity is occurring. This technology has enabled the study of the so-called…
Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in…
Recent experiments at the level of a single cell have shown that gene expression occurs in abrupt stochastic bursts. Further, in an ensemble of cells, the levels of proteins produced have a bimodal distribution. In a large fraction of…