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Register a new userSolvable model for template coexistence in protocells
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Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is a selective pressure favoring protocells with a mixed template composition. Here we study analytically a group selection model for the coexistence between two template types using the diffusion approximation of population genetics. The model combines competition at the template and protocell levels as well as genetic drift inside protocells. At the steady state, we find a continuous phase transition separating the coexistence and segregation regimes, with the order parameter vanishing linearly with the distance to the critical point. In addition, we derive explicit analytical expressions for the critical steady-state probability density of protocell compositions.
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The compartmentalization of distinct templates in protocells and the exchange of templates between them (migration) are key elements of a modern scenario for prebiotic evolution. Here we use the diffusion approximation of population genetics to study analytically the steady-state properties of such prebiotic scenario. The coexistence of distinct template types inside a protocell is achieved by a selective pressure at the protocell level (group selection) favoring protocells with a mixed template composition. In the degenerate case, where the templates have the same replication rate, we find that a vanishingly small migration rate suffices to eliminate the segregation effect of random drift and so to promote coexistence. In the non-degenerate case, a small migration rate greatly boosts coexistence as compared with the situation where there is no migration. However, increase of the migration rate beyond a critical value leads to the complete dominance of the more efficient template type (homogeneous regime). In this case, we find a continuous phase transition separating the homogeneous and the coexistence regimes, with the order parameter vanishing linearly with the distance to the transition point.
Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, much of physical behavior of transcription remains largely unknown. Understanding torsional mechanics of DNA and RNAP together with its nascent RNA and RNA-bound proteins in transcription maybe the first step towards deciphering the mechanism of gene expression. In this study, based on the balance between viscous drag on RNA synthesis and torque resulted from untranscribed supercoiled DNA template, a simple model is presented to describe mechanical properties of transcription. With this model, the rotation and supercoiling density of the untranscribed DNA template are discussed in detail. Two particular cases of transcription are considered, transcription with constant velocity and transcription with torque dependent velocity. Our results show that, during the initial stage of transcription, rotation originated from the transcribed part of DNA template is mainly released by the rotation of RNAP synthesis. During the intermediate stage, the rotation is usually released by both the supercoiling of the untranscribed part of DNA template and the rotation of RNAP synthesis, with proportion depending on the friction coefficient in environment and the length of nascent RNA. However, with the approaching to the upper limit of twisting of the untranscribed DNA template, the rotation resulted from transcription will then be mainly released by the rotation of RNAP synthesis.
Microbial communities are ubiquitous in nature and come in a multitude of forms, ranging from communities dominated by a handful of species to communities containing a wide variety of metabolically distinct organisms. This huge range in diversity is not a curiosity - microbial diversity has been linked to outcomes of substantial ecological and medical importance. However, the mechanisms underlying microbial diversity are still under debate, as simple mathematical models only permit as many species to coexist as there are resources. A plethora of mechanisms have been proposed to explain the origins of microbial diversity, but many of these analyses omit a key property of real microbial ecosystems: the propensity of the microbes themselves to change their growth properties within and across generations. In order to explore the impact of this key property on microbial diversity, we expand upon a recently developed model of microbial diversity in fluctuating environments. We implement changes in growth strategy in two distinct ways. First, we consider the regulation of a cells enzyme levels within short, ecological times, and second we consider evolutionary changes driven by mutations across generations. Interestingly, we find that these two types of microbial responses to the environment can have drastically different outcomes. Enzyme regulation may collapse diversity over long enough times while, conversely, strategy-randomizing mutations can produce a rich-get-poorer effect that promotes diversity. This work makes explicit, using a simple serial-dilutions framework, the conflicting ways that microbial adaptation and evolution can affect community diversity.
In this paper I will review twenty years of work on the question: When is there coexistence in stochastic spatial models? The answer, announced in Durrett and Levin [Theor. Pop. Biol. 46 (1994) 363--394], and that we explain in this paper is that this can be determined by examining the mean-field ODE. There are a number of rigorous results in support of this picture, but we will state nine challenging and important open problems, most of which date from the 1990s.
The two most fundamental processes describing change in biology, development and evolu-tion, occur over drastically different timescales, difficult to reconcile within a unified framework. Development involves temporal sequences of cell states controlled by hierarchies of regulatory structures. It occurs over the lifetime of a single individual, and is associated to the gene expression level change of a given genotype. Evolution, by contrast entails genotypic change through the acquisition/loss of genes and changes in the network topology of interactions among genes. It involves the emergence of new, environmentally selected phenotypes over the lifetimes of many individuals. Here we present a model of regulatory network evolution that accounts for both timescales. We extend the framework of Boolean models of gene regulatory networks (GRN)-currently only applicable to describing development to include evolutionary processes. As opposed to one-to-one maps to specific attractors, we identify the phenotypes of the cells as the relevant macrostates of the GRN. A phenotype may now correspond to multiple attractors, and its formal definition no longer requires a fixed size for the genotype. This opens the possibility for a quantitative study of the phenotypic change of a genotype, which is itself changing over evolutionary timescales. We show how the realization of specific phenotypes can be controlled by gene duplication events (used here as an archetypal evolutionary event able to change the genotype), and how successive events of gene duplication lead to new regulatory structures via selection. At the same time, we show that our generalized framework does not inhibit network controllability and the possibility for network control theory to describe epigenetic signaling during development.
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