Abstract: Simulations of evolution have a long history, but their relation to biology is questioned because of the perceived contingency of evolution. Here we provide an example of a biological process, adaptation, where simulations are argued to approach closer to biology. Adaptation is a common feature of sensory systems, and a plausible component of other biochemical networks because it rescales upstream signals to facilitate downstream processing. We create random gene networks numerically, by linking genes with interactions that model transcription, phosphorylation and protein-protein association. We define a fitness function for adaptation in terms of two functional metrics, and show that any reasonable combination of them will yield the same adaptive networks after repeated rounds of mutation and selection. Convergence to these networks is driven by positive selection and thus fast. There is always a path in parameter space of continuously improving fitness that leads to perfect adaptation, implying that the actual mutation rates we use in the simulation do not bias the results. Our results imply a kinetic view of evolution, i.e., it favors gene networks that can be learned quickly from the random examples supplied by mutation. This formulation allows for deductive predictions of the networks realized in nature.
Abstract: Segmentation is a common feature of disparate clades of metazoans, and its evolution is a central problem of evolutionary developmental biology. We evolved in silico regulatory networks by a mutation/selection process that just rewards the number of segment boundaries. For segmentation controlled by a static gradient, as in long-germ band insects, a cascade of adjacent repressors reminiscent of gap genes evolves. For sequential segmentation controlled by a moving gradient, similar to vertebrate somitogenesis, we invariably observe a very constrained evolutionary path or funnel. The evolved state is a cell autonomous 'clock and wavefront' model, with the new attribute of a separate bistable system driven by an autonomous clock. Early stages in the evolution of both modes of segmentation are functionally similar, and simulations suggest a possible path for their interconversion. Our computation illustrates how complex traits can evolve by the incremental addition of new functions on top of pre-existing traits.
Abstract: Circadian clocks are important biological oscillators that generally involve two feedback loops. Here, we propose a new model for the Neurospora crassa circadian clock. First, we model its main negative feedback loop, including only experimentally well-documented reactions, the transcriptional activation of frequency (frq) by the white-collar complex (WCC), and the post-transcriptional dimerization of FRQ with WCC. This main loop is sufficient for oscillations and a similar one lies at the core of almost all known circadian clocks. Second, the model is refined to include the less characterized enhancement of white-collar 1 (WC-1) protein synthesis by FRQ, the positive second feedback loop. Numerical testing of different hypotheses led us to propose that the synthesis of WC-1 is enhanced by FRQ monomers and repressed by FRQ dimers. We demonstrate that this second loop contributes significantly to the robustness of the oscillator period against parameter variation. A phase response curve to light pulses is also computed and agrees well with experiments. On a general level, our results show that explicit time delays are not required for sustained oscillations but that it is crucial to take into account mRNA dynamics and protein-protein interactions.
Abstract: The so-called mixed feedback loop (MFL) is a small two-gene network where protein A regulates the transcription of protein B and the two proteins form a heterodimer. It has been found to be statistically over-represented in statistical analyses of gene and protein interaction databases and to lie at the core of several computer-generated genetic networks. Here, we propose and mathematically study a model of the MFL and show that, by itself, it can serve both as a bistable switch and as a clock (an oscillator) depending on kinetic parameters. The MFL phase diagram as well as a detailed description of the nonlinear oscillation regime are presented and some biological examples are discussed. The results emphasize the role of protein interactions in the function of genetic modules and the usefulness of modeling RNA dynamics explicitly.
Abstract: Recent studies have provided insights into the modular structure of genetic regulatory networks and emphasized the interest of quantitative functional descriptions. Here, to provide a priori knowledge of the structure of functional modules, we describe an evolutionary procedure in silico that creates small gene networks performing basic tasks. We used it to create networks functioning as bistable switches or oscillators. The obtained circuits provide a variety of functional designs, demonstrate the crucial role of posttranscriptional interactions, and highlight design principles also found in known biological networks. The procedure should prove helpful as a way to understand and create small functional modules with diverse functions as well as to analyze large networks.
