Related papers: Mean-field vs. stochastic models for transcription…
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
Signal-processing molecules inside cells are often present at low copy number, which necessitates probabilistic models to account for intrinsic noise. Probability distributions have traditionally been found using simulation-based approaches…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
Oscillations in a stochastic dynamical system, whose deterministic counterpart has a stable steady state, are a widely reported phenomenon. Traditional methods of finding parameter regimes for stochastically-driven resonances are, however,…
The regulatory process of Drosophila is thoroughly studied for understanding a great variety of biological principles. While pattern-forming gene networks are analysed in the transcription step, post-transcriptional events (e.g.…
Living cells must control the reading out or "expression" of information encoded in their genomes, and this regulation often is mediated by transcription factors--proteins that bind to DNA and either enhance or repress the expression of…
Motivation: Cell-biological processes are regulated through a complex network of interactions between genes and their products. The processes, their activating conditions, and the associated transcriptional responses are often unknown.…
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term. Our main insight…
We consider a stochastic model of gene expression in which transcription depends on a multistate promoter, including the famous two-state model and refractory promoters as special cases, and focus on deriving the exact stationary…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…
In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on…
Gene regulatory networks, as a powerful abstraction for describing complex biological interactions between genes through their expression products within a cell, are often regarded as virtually deterministic dynamical systems. However, this…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in…
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…
Gaussian macroscopic fluctuation theory underpins the understanding of noise in a broad class of nonequilibrium systems. We derive exact fluctuation-response relations linking the power spectral density of stationary fluctuations to the…
We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model,…
The dynamics of gene transcription is tightly regulated in eukaryotes. Recent experiments have revealed various kinds of transcriptional dynamics, such as RNA polymerase II pausing, that involves regulation at the transcription initiation…
Deciphering gene regulatory networks is a central problem in computational biology. Here, we explore the use of multi-modal neural networks to learn predictive models of gene expression that include cis and trans regulatory components. We…
Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks…