Stochastic gene expression with delay

Analytic delay distributions for a family of gene transcription models

Models intended to describe the time evolution of a gene network must somehow include transcription, the DNA-templated synthesis of RNA, and translation, the RNA-templated synthesis of proteins. In eukaryotes, the DNA template for transcription can be very long, often consisting of tens of thousands of nucleotides, and lengthy pauses may punctuate this process. Accordingly, transcription can last for many minutes, in some cases hours. There is a long history of introducing delays in gene expression models to take the transcription and translation times into account. Here we study a family of detailed transcription models that includes initiation, elongation, and termination reactions. We establish a framework for computing the distribution of transcription times, and work out these distributions for some typical cases. For elongation, a fixed delay is a good model provided elongation is fast compared to initiation and termination, and there are no sites where long pauses occur. The initiation and termination phases of the model then generate a nontrivial delay distribution, and elongation shifts this distribution by an amount corresponding to the elongation delay. When initiation and termination are relatively fast, the distribution of elongation times can be approximated by a Gaussian. A convolution of this Gaussian with the initiation and termination time distributions gives another analytic approximation to the transcription time distribution. If there are long pauses during elongation, because of the modularity of the family of models considered, the elongation phase can be partitioned into reactions generating a simple delay (elongation through regions where there are no long pauses), and reactions whose distribution of waiting times must be considered explicitly (initiation, termination, and motion through regions where long pauses are likely). In these cases, the distribution of transcription times again involves a nontrivial part and a shift due to fast elongation processes.

A Markovian arrival stream approach to stochastic gene expression in cells

We analyse a generalisation of the stochastic gene expression model studied recently in Fromion et al. (SIAM J Appl Math 73:195-211, 2013) and Robert (Probab Surv 16:277-332, 2019) that keeps track of the production of both mRNA and protein molecules, using techniques from the theory of point processes, as well as ideas from the theory of matrix-analytic methods. Here, both the activity of a gene and the creation of mRNA are modelled with an arbitrary Markovian Arrival Process governed by finitely many phases, and each mRNA molecule during its lifetime gives rise to protein molecules in accordance with a Poisson process. This modification is important, as Markovian Arrival Processes can be used to approximate many types of point processes on the nonnegative real line, meaning this framework allows us to further relax our assumptions on the overall process of transcription.

Coexistence of Hopf-born rotation and heteroclinic cycling in a time-delayed three-gene auto-regulated and mutually-repressed core genetic regulation network

In this work, we study the behavior of a time-delayed mutually repressive auto-activating three-gene system. Delays are introduced to account for the location difference between DNA transcription that leads to production of messenger RNA and its translation that result in protein synthesis. We study the dynamics of the system using numerical simulations, computational bifurcation analysis and mathematical analysis. We find Hopf bifurcations leading to stable and unstable rotation in the system, and we study the rotational behavior as a function of cyclic mutual repression parameter asymmetry between each gene pair in the network. We focus on how rotation co-exists with a stable heteroclinic flow linking the three saddles in the system. We find that this coexistence allows for a transition between two markedly different types of rotation leading to strikingly different phenotypes. One type of rotation belongs to Hopf-induced rotation while the other type, belongs to heteroclinic cycling between three saddle nodes in the system. We discuss the evolutionary and biological implications of our findings.

An Intracellular Model of Hepatitis B Viral Infection: An In Silico Platform for Comparing Therapeutic Strategies

Hepatitis B virus (HBV) is a major focus of antiviral research worldwide. The International Coalition to Eliminate HBV, together with the World Health Organisation (WHO), have prioritised the search for a cure, with the goal of eliminating deaths from viral hepatitis by 2030. We present here a comprehensive model of intracellular HBV infection dynamics that includes all molecular processes currently targeted by drugs and agrees well with the observed outcomes of several clinical studies. The model reveals previously unsuspected kinetic behaviour in the formation of sub-viral particles, which could lead to a better understanding of the immune responses to infection. It also enables rapid comparative assessment of the impact of different treatment options and their potential synergies as combination therapies. A comparison of available and currently developed treatment options reveals that combinations of multiple capsid assembly inhibitors perform best.

Transcranial Current Stimulation Alters the Expression of Immune-Mediating Genes

Despite its extensive use in clinical studies, the molecular mechanisms underlying the effects of transcranial direct current stimulation (tDCS) remain to be elucidated. We previously described subacute effects of tDCS on immune- and stem cells in the rat brain. To investigate the more immediate effects of tDCS regulating those cellular responses, we treated rats with a single session of either anodal or cathodal tDCS, and analyzed the gene expression by microarray; sham-stimulated rats served as control. Anodal tDCS increased expression of several genes coding for the major histocompatibility complex I (MHC I), while cathodal tDCS increased the expression of the immunoregulatory protein osteopontin (OPN). We confirmed the effects of gene upregulation by immunohistochemistry at the protein level. Thus, our data show a novel mechanism for the actions of tDCS on immune- and inflammatory processes, providing a target for future therapeutic studies.

Time-Delayed Models of Gene Regulatory Networks

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 the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Molecular characterization of a novel ovary-specific gene fem-1 homolog from the oriental river prawn, Macrobrachium nipponense

The feminization-1 (fem-1) gene is characterized by one of the most common protein-protein interaction motifs, ankyrin repeat motifs, displays many expression patterns in vertebrates and invertebrates, and plays an essential role in the sex-determination/differentiation pathway in Caenorhabditis elegans. In this study, a fem-1 homolog, designated as Mnfem-1, was first cloned from the oriental river prawn Macrobrachium nipponense. The prawn Mnfem-1 gene consists of six exons and five introns. The full-length cDNA (2603bp) of Mnfem-1 contains an open reading frame (ORF) encoding a protein of 622 amino acids. The Mnfem-1 RNA and protein are exclusively expressed in the ovary in adult prawns as revealed by RT-PCR and immunofluorescence analysis, respectively. In situ hybridization results showed that strong positive signals were concentrated at the edge of the previtellogenic and vitellogenic oocyte. During embryogenesis, Mnfem-1 is highly expressed in both unfertilized eggs and embryos at cleavage stage and thereafter dropped to a low level from blastula to zoea, indicating that the Mnfem-1 in early embryos is maternal. After hatching, the Mnfem-1 expression significantly increased in the larvae at length of 2cm, an important stage of sex differentiation. Yeast two hybridization results showed that the Mnfem-1 protein can be potentially interactive with cathepsin L and proteins containing the domains of insulinase, ankyrin or ubiquitin. Our results suggested that Mnfem-1 could have roles in prawn ovarian development and sex determination/differentiation.