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Biological structure and function depend on complex regulatory interactions between many genes. A wealth of gene expression data is available from high-throughput genome-wide measurement technologies, but effective gene regulatory network…
Epigenetic modifications of histones crucially affect the eukaryotic gene activity, while the epigenetic histone state is largely determined by the binding of specific factors such as the transcription factors (TFs) to DNA. Here, the way…
Evolving biomolecular networks have to combine the stability against perturbations with flexibility allowing their constituents to assume new roles in the cell. Gene duplication followed by functional divergence of associated proteins is a…
A wealth of new research has highlighted the critical roles of small RNAs (sRNAs) in diverse processes such as quorum sensing and cellular responses to stress. The pathways controlling these processes often have a central motif comprising…
Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing…
Allostery, the phenomenon by which the perturbation of a molecule at one site alters its behavior at a remote functional site, enables control over biomolecular function. Allosteric modulation is a promising avenue for drug discovery and is…
Models of transcriptional regulation that assume equilibrium binding of transcription factors have been very successful at predicting gene expression from sequence in bacteria. However, analogous equilibrium models do not perform as well in…
Multipotent stem or progenitor cells undergo a sequential series of binary fate decisions, which ultimately generate the diversity of differentiated cells. Efforts to understand cell fate control have focused on simple gene regulatory…
Gene expression has a stochastic component owing to the single molecule nature of the gene and the small number of copies of individual DNA binding proteins in the cell. We show how the statistics of such systems can be mapped on to quantum…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
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…
Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells…
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…
Systematic characterization of biological effects to genetic perturbation is essential to the application of molecular biology and biomedicine. However, the experimental exhaustion of genetic perturbations on the genome-wide scale is…
We examine immunostaining experimental data for the formation of the strip 2 of $even-skipped$ ($eve$) transcripts on $D.$ $melanogaster$ embryos. An estimate of the factor converting immunofluorescence intensity units into molecular…
We present a detailed dynamical model of the behavior of transcription-translation circuits in vitro that makes explicit the roles played by essential molecular resources. A set of simple two-gene test circuits operating in a cell-free…
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics…
Elucidating the architecture and dynamics of large scale genetic regulatory networks of cells is an important goal in systems biology. We study the system level dynamical properties of the genetic network of Escherichia coli that regulates…
The intricate pattern of chemical modifications on DNA and histones, the "histone code", is considered to be a key gene regulation factor. Multivalency is seen by many as an essential instrument to transmit the "encoded" information to the…