Mutational robustness of gene regulatory networks

Potential for evolution of complex defense strategies in a multi-scale model of virus-host coevolution

Background

Host resistance and viral pathogenicity are determined by molecular interactions that are part of the evolutionary arms race between viruses and their hosts. Viruses are obligate intracellular parasites and entry to the host cell is the first step of any virus infection. Commonly, viruses enter host cells by binding cell surface receptors. We adopt a computational modeling approach to study the evolution of the first infection step, where we consider two possible levels of resistance mechanism: at the level of the binding interaction between the host receptor and a virus binding protein, and at the level of receptor protein expression where we use a standard gene regulatory network model. At the population level we adopted the Susceptible-Infected-Susceptible (SIS) model. We used our multi-scale model to understand what conditions might determine the balance between use of resistance mechanisms at the two different levels.

Results

We explored a range of different conditions (model parameters) that affect host evolutionary dynamics and, in particular, the balance between the use of different resistance mechanisms. These conditions include the complexity of the receptor binding protein-protein interaction, selection pressure on the host population (pathogenicity), and the number of expressed cell-surface receptors. In particular, we found that as the receptor binding complexity (understood as the number of amino acids involved in the interaction between the virus entry protein and the host receptor) increases, viruses tend to become specialists and target one specific receptor. At the same time, on the host side, the potential for resistance shifts from the changes at the level of receptor binding (protein-protein) interaction towards changes at the level of gene regulation, suggesting a mechanism for increased biological complexity.

Conclusions

Host resistance and viral pathogenicity depend on quite different evolutionary conditions. Viruses may evolve cell entry strategies that use small receptor binding regions, represented by low complexity binding in our model. Our modeling results suggest that if the virus adopts a strategy based on binding to low complexity sites on the host receptor, the host will select a defense strategy at the protein (receptor) level, rather than at the level of the regulatory network - a virus-host strategy that appears to have been selected most often in nature.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-016-0804-z) contains supplementary material, which is available to authorized users.

Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks

Stochastic noise in gene expression causes variation in the development of phenotypes, making such noise a potential target of stabilizing selection. Here, we develop a new simulation model of gene networks to study the adaptive landscape underlying the evolution of robustness to noise. We find that epistatic interactions between the determinants of the expression of a gene and its downstream effect impose significant constraints on evolution, but these interactions do allow the gradual evolution of increased robustness. Despite strong sign epistasis, adaptation rarely proceeds via deleterious intermediate steps, but instead occurs primarily through small beneficial mutations. A simple mathematical model captures the relevant features of the single-gene fitness landscape and explains counterintuitive patterns, such as a correlation between the mean and standard deviation of phenotypes. In more complex networks, mutations in regulatory regions provide evolutionary pathways to increased robustness. These results chart the constraints and possibilities of adaptation to reduce expression noise and demonstrate the potential of a novel modeling framework for gene networks.

Models of buffering of dosage imbalances in protein complexes

Background

Stoichiometric imbalances in macromolecular complexes can lead to altered function. Such imbalances stem from under- or over-expression of a subunit of a complex consequent to a deletion, duplication or regulatory mutation of an allele encoding the relevant protein. In some cases, the phenotypic perturbations induced by such alterations can be subtle or be lacking because nonlinearities in the process of protein complex assembly can provide some degree of buffering.

Results

We explore with biochemical models of increasing plausibility how buffering can be elicited. Specifically, we analyze the formation of a dimer AB and show that there are particular sets of parameters so that decreasing/increasing the input amount of either A or B translates into a non proportional (buffered) change of AB. The buffer effect also appears in higher-order structures provided that there are intermediate subcomplexes in the assembly process.

Conclusions

We highlight the importance of protein degradation and/or conformational inactivation for buffering to appear. The models sketched here have experimental support but can be further tested with existing biological resources.

Reviewers

This article was reviewed by Eugene Koonin, Berend Snel and Csaba Pal.

Genetic code evolution reveals the neutral emergence of mutational robustness, and information as an evolutionary constraint

The standard genetic code (SGC) is central to molecular biology and its origin and evolution is a fundamental problem in evolutionary biology, the elucidation of which promises to reveal much about the origins of life. In addition, we propose that study of its origin can also reveal some fundamental and generalizable insights into mechanisms of molecular evolution, utilizing concepts from complexity theory. The first is that beneficial traits may arise by non-adaptive processes, via a process of "neutral emergence". The structure of the SGC is optimized for the property of error minimization, which reduces the deleterious impact of point mutations. Via simulation, it can be shown that genetic codes with error minimization superior to the SGC can emerge in a neutral fashion simply by a process of genetic code expansion via tRNA and aminoacyl-tRNA synthetase duplication, whereby similar amino acids are added to codons related to that of the parent amino acid. This process of neutral emergence has implications beyond that of the genetic code, as it suggests that not all beneficial traits have arisen by the direct action of natural selection; we term these "pseudaptations", and discuss a range of potential examples. Secondly, consideration of genetic code deviations (codon reassignments) reveals that these are mostly associated with a reduction in proteome size. This code malleability implies the existence of a proteomic constraint on the genetic code, proportional to the size of the proteome (P), and that its reduction in size leads to an "unfreezing" of the codon - amino acid mapping that defines the genetic code, consistent with Crick's Frozen Accident theory. The concept of a proteomic constraint may be extended to propose a general informational constraint on genetic fidelity, which may be used to explain variously, differences in mutation rates in genomes with differing proteome sizes, differences in DNA repair capacity and genome GC content between organisms, a selective pressure in the evolution of sexual reproduction, and differences in translational fidelity. Lastly, the utility of the concept of an informational constraint to other diverse fields of research is explored.

Evolving robust gene regulatory networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of 'parts' and 'devices'. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.

Biophysical fitness landscapes for transcription factor binding sites

Phenotypic states and evolutionary trajectories available to cell populations are ultimately dictated by complex interactions among DNA, RNA, proteins, and other molecular species. Here we study how evolution of gene regulation in a single-cell eukaryote S. cerevisiae is affected by interactions between transcription factors (TFs) and their cognate DNA sites. Our study is informed by a comprehensive collection of genomic binding sites and high-throughput in vitro measurements of TF-DNA binding interactions. Using an evolutionary model for monomorphic populations evolving on a fitness landscape, we infer fitness as a function of TF-DNA binding to show that the shape of the inferred fitness functions is in broad agreement with a simple functional form inspired by a thermodynamic model of two-state TF-DNA binding. However, the effective parameters of the model are not always consistent with physical values, indicating selection pressures beyond the biophysical constraints imposed by TF-DNA interactions. We find little statistical support for the fitness landscape in which each position in the binding site evolves independently, indicating that epistasis is common in the evolution of gene regulation. Finally, by correlating TF-DNA binding energies with biological properties of the sites or the genes they regulate, we are able to rule out several scenarios of site-specific selection, under which binding sites of the same TF would experience different selection pressures depending on their position in the genome. These findings support the existence of universal fitness landscapes which shape evolution of all sites for a given TF, and whose properties are determined in part by the physics of protein-DNA interactions.

Specialized proteins called transcription factors turn genes on and off by binding to short stretches of DNA in their regulatory regions. Precise gene regulation is essential for cellular survival and proliferation, and its evolution and maintenance under mutational pressure are central issues in biology. Here we discuss how evolution of gene regulation is shaped by the need to maintain favorable binding energies between transcription factors and their genomic binding sites. We show that, surprisingly, transcription factor binding is not affected by many biological properties, such as the essentiality of the gene it regulates. Rather, all sites for a given factor appear to evolve under a universal set of constraints, which can be rationalized in terms of a simple model inspired by transcription factor – DNA binding thermodynamics.

On the contributions of topological features to transcriptional regulatory network robustness

BACKGROUND

Because biological networks exhibit a high-degree of robustness, a systemic understanding of their architecture and function requires an appraisal of the network design principles that confer robustness. In this project, we conduct a computational study of the contribution of three degree-based topological properties (transcription factor-target ratio, degree distribution, cross-talk suppression) and their combinations on the robustness of transcriptional regulatory networks. We seek to quantify the relative degree of robustness conferred by each property (and combination) and also to determine the extent to which these properties alone can explain the robustness observed in transcriptional networks.

RESULTS

To study individual properties and their combinations, we generated synthetic, random networks that retained one or more of the three properties with values derived from either the yeast or E. coli gene regulatory networks. Robustness of these networks were estimated through simulation. Our results indicate that the combination of the three properties we considered explains the majority of the structural robustness observed in the real transcriptional networks. Surprisingly, scale-free degree distribution is, overall, a minor contributor to robustness. Instead, most robustness is gained through topological features that limit the complexity of the overall network and increase the transcription factor subnetwork sparsity.

CONCLUSIONS

Our work demonstrates that (i) different types of robustness are implemented by different topological aspects of the network and (ii) size and sparsity of the transcription factor subnetwork play an important role for robustness induction. Our results are conserved across yeast and E Coli, which suggests that the design principles examined are present within an array of living systems.

Digital IIR filters design using differential evolution algorithm with a controllable probabilistic population size

Design of a digital infinite-impulse-response (IIR) filter is the process of synthesizing and implementing a recursive filter network so that a set of prescribed excitations results a set of desired responses. However, the error surface of IIR filters is usually non-linear and multi-modal. In order to find the global minimum indeed, an improved differential evolution (DE) is proposed for digital IIR filter design in this paper. The suggested algorithm is a kind of DE variants with a controllable probabilistic (CPDE) population size. It considers the convergence speed and the computational cost simultaneously by nonperiodic partial increasing or declining individuals according to fitness diversities. In addition, we discuss as well some important aspects for IIR filter design, such as the cost function value, the influence of (noise) perturbations, the convergence rate and successful percentage, the parameter measurement, etc. As to the simulation result, it shows that the presented algorithm is viable and comparable. Compared with six existing State-of-the-Art algorithms-based digital IIR filter design methods obtained by numerical experiments, CPDE is relatively more promising and competitive.