Related papers: Path integral approach to generating functions for…

This paper analyzes, in the context of a prokaryotic cell, the stochastic variability of the number of proteins when there is a control of gene expression by an autoregulation scheme. The goal of this work is to estimate the efficiency of…

Purpose: This work proposes a novel approach to efficiently generate MR fingerprints for MR fingerprinting (MRF) problems based on the unsupervised deep learning model generative adversarial networks (GAN). Methods: The GAN model is adopted…

Gene regulation is a series of processes that control gene expression and its extent. The connections among genes and their regulatory molecules, usually transcription factors, and a descriptive model of such connections, are known as gene…

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative…

Inference of gene regulatory networks (GRNs) based on experimental data is a challenging task in bioinformatics. In this paper, we present a bi-objective minimization model (BoMM) for inference of GRNs, where one objective is the fitting…

Modelling gene regulatory networks not only requires a thorough understanding of the biological system depicted but also the ability to accurately represent this system from a mathematical perspective. Throughout this chapter, we aim to…

In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN)…

Single-cell RNA sequencing allows the quantification of gene expression at the individual cell level, enabling the study of cellular heterogeneity and gene expression dynamics. Dimensionality reduction is a common preprocessing step…

Generative Flow Networks (GFlowNets or GFNs) are probabilistic models predicated on Markov flows, and they employ specific amortization algorithms to learn stochastic policies that generate compositional substances including biomolecules,…

Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled…

The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to…

Graph generation is a fundamental task with broad applications, such as drug discovery. Recently, discrete flow matching-based graph generation, \aka, graph flow model (GFM), has emerged due to its superior performance and flexible…

Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…

A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…

An interpretable generative model for handwritten digits synthesis is proposed in this work. Modern image generative models, such as Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), are trained by backpropagation…

A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness…

Enzyme kinetics has historically been described by deterministic models, with the Michaelis-Menten (MM) equation serving as a paradigm. However, recent experimental and theoretical advances have made it clear that stochastic fluctuations,…

This paper presents a novel method, called Modular Grammatical Evolution (MGE), towards validating the hypothesis that restricting the solution space of NeuroEvolution to modular and simple neural networks enables the efficient generation…

[Context] The stochasticity of grain chemistry requires special care in modeling. Previously methods based on the modified rate equation, the master equation, the moment equation, and Monte Carlo simulations have been used. [Aims] We…

Molecular systems often remain trapped for long times around some local minimum of the potential energy function, before switching to another one -- a behavior known as metastability. Simulating transition paths linking one metastable state…