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We derive exact solutions of simplified models for the temporal evolution of the protein concentration within a cell population arbitrarily far from the stationary state. We show that monitoring the dynamics can assist in modeling and…
Feed-forward dynamics, which is well-known to have several important implications in nonlinear dynamical systems, frequently occurs in gene expression motifs, and has been well explored experimentally and mathematically. However, dependency…
Regulatory networks consist of interacting molecules with a high degree of mutual chemical specificity. How can these molecules evolve when their function depends on maintenance of interactions with cognate partners and simultaneous…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
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…
Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research…
A novel deep neural network framework -- that we refer to as Deep Dynamic Factor Model (D$^2$FM) --, is able to encode the information available, from hundreds of macroeconomic and financial time-series into a handful of unobserved latent…
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability,…
Gene expression is a random or noisy process. The process consists of several random events among which the reinitiation of transcription by RNAP is an important one. The RNAP molecules can bind the gene only after the promoter gets…
Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can…
The transcription of DNA into mRNA is initiated and aided by a number of transcription factors (TFs), proteins with DNA-binding regions that attach themselves to binding sites in the DNA (transcription factor binding sites, TFBSs). As it…
Motivation: Alternative splicing is an important mechanism in which the regions of pre-mRNAs are differentially joined in order to form different transcript isoforms. Alternative splicing is involved in the regulation of normal…
Neuroscience is experiencing a data revolution in which many hundreds or thousands of neurons are recorded simultaneously. Currently, there is little consensus on how such data should be analyzed. Here we introduce LFADS (Latent Factor…
Consider learning a generative model for time-series data. The sequential setting poses a unique challenge: Not only should the generator capture the conditional dynamics of (stepwise) transitions, but its open-loop rollouts should also…
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to…
Force fields for molecular dynamics are usually developed manually, limiting their transferability and making systematic exploration of functional forms challenging. We developed a graph neural network that assigns all force field…
Transcription Factors (TFs) are proteins crucial for regulating gene expression. Effective regulation requires the TFs to rapidly bind to their correct target, enabling the cell to respond efficiently to stimuli such as nutrient…
Generative artificial intelligence models learn probability distributions from data and produce novel samples that capture the salient properties of their training sets. Proteins are particularly attractive for such approaches given their…
In this article, we introduce a novel backward method to model stochastic gene expression and protein level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation…