Mesoscopic Biochemical Basis of Isogenetic Inheritance and Canalization: Stochasticity, Nonlinearity, and Emergent Landscape

Biochemical reaction systems in mesoscopic volume, under sustained environmental chemical gradient(s), can have multiple stochastic attractors. Two distinct mechanisms are known for their origins: ($a$) Stochastic single-molecule events, such as gene expression, with slow gene on-off dynamics; and ($b$) nonlinear networks with feedbacks. These two mechanisms yield different volume dependence for the sojourn time of an attractor. As in the classic Arrhenius theory for temperature dependent transition rates, a landscape perspective provides a natural framework for the system's behavior. However, due to the nonequilibrium nature of the open chemical systems, the landscape, and the attractors it represents, are all themselves {\em emergent properties} of complex, mesoscopic dynamics. In terms of the landscape, we show a generalization of Kramers' approach is possible to provide a rate theory. The emergence of attractors is a form of self-organization in the mesoscopic system; stochastic attractors in biochemical systems such as gene regulation and cellular signaling are naturally inheritable via cell division. Delbr\"{u}ck-Gillespie's mesoscopic reaction system theory, therefore, provides a biochemical basis for spontaneous isogenetic switching and canalization.Comment: 24 pages, 6 figure

Biological applications of the theory of birth-and-death processes

In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer, and somatic evolution of cancers. We further describe how empirical data, e.g., distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. It is concluded that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological process, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.Comment: 29 pages, 4 figures; submitted to "Briefings in Bioinformatics

Epigenetic regulation of Mash1 expression

Mash1 is a proneural gene important for specifying the neural fate. The Mash1 locus undergoes specific epigenetic changes in ES cells following neural induction. These include the loss of repressive H3K27 trimethylation and acquisition of H3K9 acetylation at the promoter, switch to an early replication timing and repositioning of the locus away from the nuclear periphery. Here I examine the relationship between nuclear localization and gene expression during neural differentiation and the role of the neuronal repressor REST in silencing Mash1 expression in ES cells. Following neural induction of ES cells, I observed that relocation of the Mash1 locus occurs from day 4-6 whereas overt expression begins at day 6. Mash1 expression was unaffected by REST removal in ES cells as well as the locus localization at the nuclear periphery. In contrast bona fide REST target genes were upregulated in REST -/- cells. Interestingly, among REST targets, loci that were more derepressed upon REST removal showed an interior location (Sthatmin, Synaptophysin), while those more resistant to REST withdrawal, showed a peripheral location (BDNF, Calbidin, Complexin). To ask whether the insulator protein CTCF together with the cohesin complex might be involved in regulating Mash1 in ES cells, I performed ChIP analysis of CTCF and cohesin binding across the Mash1 locus in ES cells and used RNAi to deplete CTCF and cohesin expression. A slight increase in the transcription of Mash1 was seen in cells upon Rad21 knock down, although it was not possible to exclude this was a consequence of delayed cell cycle progression. Finally ES cell lines that carried a Mash1 transgene were created as a tool to look at whether activation of Mash1 can affect the epigenetic properties of neighbouring genes

Transcriptional Regulation: a Genomic Overview

The availability of the Arabidopsis thaliana genome sequence allows a comprehensive analysis of transcriptional regulation in plants using novel genomic approaches and methodologies. Such a genomic view of transcription first necessitates the compilation of lists of elements. Transcription factors are the most numerous of the different types of proteins involved in transcription in eukaryotes, and the Arabidopsis genome codes for more than 1,500 of them, or approximately 6% of its total number of genes. A genome-wide comparison of transcription factors across the three eukaryotic kingdoms reveals the evolutionary generation of diversity in the components of the regulatory machinery of transcription. However, as illustrated by Arabidopsis, transcription in plants follows similar basic principles and logic to those in animals and fungi. A global view and understanding of transcription at a cellular and organismal level requires the characterization of the Arabidopsis transcriptome and promoterome, as well as of the interactome, the localizome, and the phenome of the proteins involved in transcription

Universal Features in the Genome-level Evolution of Protein Domains

Protein domains are found on genomes with notable statistical distributions, which bear a high degree of similarity. Previous work has shown how these distributions can be accounted for by simple models, where the main ingredients are probabilities of duplication, innovation, and loss of domains. However, no one so far has addressed the issue that these distributions follow definite trends depending on protein-coding genome size only. We present a stochastic duplication/innovation model, falling in the class of so-called Chinese Restaurant Processes, able to explain this feature of the data. Using only two universal parameters, related to a minimal number of domains and to the relative weight of innovation to duplication, the model reproduces two important aspects: (a) the populations of domain classes (the sets, related to homology classes, containing realizations of the same domain in different proteins) follow common power-laws whose cutoff is dictated by genome size, and (b) the number of domain families is universal and markedly sublinear in genome size. An important ingredient of the model is that the innovation probability decreases with genome size. We propose the possibility to interpret this as a global constraint given by the cost of expanding an increasingly complex interactome. Finally, we introduce a variant of the model where the choice of a new domain relates to its occurrence in genomic data, and thus accounts for fold specificity. Both models have general quantitative agreement with data from hundreds of genomes, which indicates the coexistence of the well-known specificity of proteomes with robust self-organizing phenomena related to the basic evolutionary ``moves'' of duplication and innovation

The inference of gene trees with species trees

Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are tightly linked, they are seldom identical, because genes duplicate, are lost or horizontally transferred, and because alleles can co-exist in populations for periods that may span several speciation events. Building models describing the relationship between gene and species trees can thus improve the reconstruction of gene trees when a species tree is known, and vice-versa. Several approaches have been proposed to solve the problem in one direction or the other, but in general neither gene trees nor species trees are known. Only a few studies have attempted to jointly infer gene trees and species trees. In this article we review the various models that have been used to describe the relationship between gene trees and species trees. These models account for gene duplication and loss, transfer or incomplete lineage sorting. Some of them consider several types of events together, but none exists currently that considers the full repertoire of processes that generate gene trees along the species tree. Simulations as well as empirical studies on genomic data show that combining gene tree-species tree models with models of sequence evolution improves gene tree reconstruction. In turn, these better gene trees provide a better basis for studying genome evolution or reconstructing ancestral chromosomes and ancestral gene sequences. We predict that gene tree-species tree methods that can deal with genomic data sets will be instrumental to advancing our understanding of genomic evolution.Comment: Review article in relation to the "Mathematical and Computational Evolutionary Biology" conference, Montpellier, 201