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Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions…
Transcription factor binding sites vary in their specificity, both within and between species. Binding specificity has a strong impact on the evolution of gene expression, because it determines how easily regulatory interactions are gained…
Understanding the molecular processes that drive cellular life is a fundamental question in biological research. Ambitious programs have gathered a number of molecular datasets on large populations. To decipher the complex cellular…
Gene networks exhibiting oscillatory dynamics are widespread in biology. The minimal regulatory designs giving rise to oscillations have been implemented synthetically and studied by mathematical modeling. However, most of the available…
Noise in the expression of a gene produces fluctuations in the concentration of the gene product. These fluctuations can interfere with optimal function or can be exploited to generate beneficial diversity between cells; gene expression…
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…
Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, biological responses should also…
Gene regulatory networks are powerful tools for modeling interactions among genes to regulate their expression for homeostasis and differentiation. Single-cell sequencing offers a unique opportunity to build these networks with…
Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The…
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…
Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to…
Gene promoters are the key DNA regulatory elements positioned around the transcription start sites and are responsible for regulating gene transcription process. Various alignment-based, signal-based and content-based approaches are…
The solution of high-dimensional inference and prediction problems in computational biology is almost always a compromise between mathematical theory and practical constraints such as limited computational resources. As time progresses,…
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…
Phenotype transition takes place in many biological processes such as differentiation, and understanding how a cell reprograms its global gene expression profile is a problem of rate theories. A cell phenotype transition accompanies with…
It often is emphasized that gene expression is noisy. A seemingly contradictory view is that control mechanisms have been optimized to squeeze as much information as possible out of a limited number of molecules. Here we revisit these…
To survive environmental conditions, cells transcribe their response activities into encoded mRNA sequences in order to produce certain amounts of protein concentrations. The external conditions are mapped into the cell through the…
Gene regulatory networks (GRNs) play a crucial role in the control of cellular functions. Numerous methods have been developed to infer GRNs from gene expression data, including mechanism-based approaches, information-based approaches, and…
Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. What mechanisms might be responsible for these low in-degrees? Starting with an accepted framework of the…
Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises…