Joshua L. Payne

The robustness and evolvability of transcription factor binding sites

Robust to Change The variation in genetic sequences determining the binding of transcription factors is believed to be an important facet of evolution. However, the degree to which a genome is robust, that is, able to withstand changes and how robustness affects evolution is unclear. Payne and Wagner (p. 875) investigated the empirical support for mutational robustness by examining transcription factor (TF) binding in the mouse and yeast genomes. A network analysis of the degree of variation revealed that the sites with the highest affinity for TF binding exhibit the greatest tolerance for nucleotide substitutions, whereas low-affinity sites exhibit greater sensitivity to mutation. Thus, while mutational robustness and evolvability are antagonistic at the genotypic level, they are synergistic at the phenotypic level. Transcription factor binding sites form connected networks. Robustness, the maintenance of a character in the presence of genetic change, can help preserve adaptive traits but also may hinder evolvability, the ability to bring forth novel adaptations. We used genotype networks to analyze the binding site repertoires of 193 transcription factors from mice and yeast, providing empirical evidence that robustness and evolvability need not be conflicting properties. Network vertices represent binding sites where two sites are connected if they differ in a single nucleotide. We show that the binding sites of larger genotype networks are not only more robust, but the sequences adjacent to such networks can also bind more transcription factors, thus demonstrating that robustness can facilitate evolvability.

Robustness, evolvability, and the logic of genetic regulation

In gene regulatory circuits, the expression of individual genes is commonly modulated by a set of regulating gene products, which bind to a genes cis-regulatory region. This region encodes an input-output function, referred to as signal-integration logic, that maps a specific combination of regulatory signals (inputs) to a particular expression state (output) of a gene. The space of all possible signal-integration functions is vast and the mapping from input to output is many-to-one: For the same set of inputs, many functions (genotypes) yield the same expression output (phenotype). Here, we exhaustively enumerate the set of signal-integration functions that yield identical gene expression patterns within a computational model of gene regulatory circuits. Our goal is to characterize the relationship between robustness and evolvability in the signal-integration space of regulatory circuits, and to understand how these properties vary between the genotypic and phenotypic scales. Among other results, we find that the distributions of genotypic robustness are skewed, so that the majority of signal-integration functions are robust to perturbation. We show that the connected set of genotypes that make up a given phenotype are constrained to specific regions of the space of all possible signal-integration functions, but that as the distance between genotypes increases, so does their capacity for unique innovations. In addition, we find that robust phenotypes are (i) evolvable, (ii) easily identified by random mutation, and (iii) mutationally biased toward other robust phenotypes. We explore the implications of these latter observations for mutation-based evolution by conducting random walks between randomly chosen source and target phenotypes. We demonstrate that the time required to identify the target phenotype is independent of the properties of the source phenotype.

Constraint and contingency in multifunctional gene regulatory circuits.

Gene regulatory circuits drive the development, physiology, and behavior of organisms from bacteria to humans. The phenotypes or functions of such circuits are embodied in the gene expression patterns they form. Regulatory circuits are typically multifunctional, forming distinct gene expression patterns in different embryonic stages, tissues, or physiological states. Any one circuit with a single function can be realized by many different regulatory genotypes. Multifunctionality presumably constrains this number, but we do not know to what extent. We here exhaustively characterize a genotype space harboring millions of model regulatory circuits and all their possible functions. As a circuits number of functions increases, the number of genotypes with a given number of functions decreases exponentially but can remain very large for a modest number of functions. However, the sets of circuits that can form any one set of functions becomes increasingly fragmented. As a result, historical contingency becomes widespread in circuits with many functions. Whether a circuit can acquire an additional function in the course of its evolution becomes increasingly dependent on the function it already has. Circuits with many functions also become increasingly brittle and sensitive to mutation. These observations are generic properties of a broad class of circuits and independent of any one circuit genotype or phenotype.

Mechanisms of mutational robustness in transcriptional regulation

Robustness is the invariance of a phenotype in the face of environmental or genetic change. The phenotypes produced by transcriptional regulatory circuits are gene expression patterns that are to some extent robust to mutations. Here we review several causes of this robustness. They include robustness of individual transcription factor binding sites, homotypic clusters of such sites, redundant enhancers, transcription factors, redundant transcription factors, and the wiring of transcriptional regulatory circuits. Such robustness can either be an adaptation by itself, a byproduct of other adaptations, or the result of biophysical principles and non-adaptive forces of genome evolution. The potential consequences of such robustness include complex regulatory network topologies that arise through neutral evolution, as well as cryptic variation, i.e., genotypic divergence without phenotypic divergence. On the longest evolutionary timescales, the robustness of transcriptional regulation has helped shape life as we know it, by facilitating evolutionary innovations that helped organisms such as flowering plants and vertebrates diversify.

Exploiting Graphics Processing Units for Computational Biology and Bioinformatics

Advances in the video gaming industry have led to the production of low-cost, high-performance graphics processing units (GPUs) that possess more memory bandwidth and computational capability than central processing units (CPUs), the standard workhorses of scientific computing. With the recent release of generalpurpose GPUs and NVIDIA’s GPU programming language, CUDA, graphics engines are being adopted widely in scientific computing applications, particularly in the fields of computational biology and bioinformatics. The goal of this article is to concisely present an introduction to GPU hardware and programming, aimed at the computational biologist or bioinformaticist. To this end, we discuss the primary differences between GPU and CPU architecture, introduce the basics of the CUDA programming language, and discuss important CUDA programming practices, such as the proper use of coalesced reads, data types, and memory hierarchies. We highlight each of these topics in the context of computing the all-pairs distance between instances in a dataset, a common procedure in numerous disciplines of scientific computing. We conclude with a runtime analysis of the GPU and CPU implementations of the all-pairs distance calculation. We show our final GPU implementation to outperform the CPU implementation by a factor of 1700.

A thousand empirical adaptive landscapes and their navigability

The adaptive landscape is an iconic metaphor that pervades evolutionary biology. It was mostly applied in theoretical models until recent years, when empirical data began to allow partial landscape reconstructions. Here, we exhaustively analyse 1,137 complete landscapes from 129 eukaryotic species, each describing the binding affinity of a transcription factor to all possible short DNA sequences. We find that the navigability of these landscapes through single mutations is intermediate to that of additive and shuffled null models, suggesting that binding affinity—and thereby gene expression—is readily fine-tuned via mutations in transcription factor binding sites. The landscapes have few peaks that vary in their accessibility and in the number of sequences they contain. Binding sites in the mouse genome are enriched in sequences found in the peaks of especially navigable landscapes and the genetic diversity of binding sites in yeast increases with the number of sequences in a peak. Our findings suggest that landscape navigability may have contributed to the enormous success of transcriptional regulation as a source of evolutionary adaptations and innovations.

The Influence of Assortativity on the Robustness of Signal-Integration Logic in Gene Regulatory Networks

Gene regulatory networks (GRNs) drive the cellular processes that sustain life. To do so reliably, GRNs must be robust to perturbations, such as gene deletion and the addition or removal of regulatory interactions. GRNs must also be robust to genetic changes in regulatory regions that define the logic of signal-integration, as these changes can affect how specific combinations of regulatory signals are mapped to particular gene expression states. Previous theoretical analyses have demonstrated that the robustness of a GRN is influenced by its underlying topological properties, such as degree distribution and modularity. Another important topological property is assortativity, which measures the propensity with which nodes of similar connectivity are connected to one another. How assortativity influences the robustness of the signal-integration logic of GRNs remains an open question. Here, we use computational models of GRNs to investigate this relationship. We separately consider each of the three dynamical regimes of this model for a variety of degree distributions. We find that in the chaotic regime, robustness exhibits a pronounced increase as assortativity becomes more positive, while in the critical and ordered regimes, robustness is generally less sensitive to changes in assortativity. We attribute the increased robustness to a decrease in the duration of the gene expression pattern, which is caused by a reduction in the average size of a GRNs in-components. This study provides the first direct evidence that assortativity influences the robustness of the signal-integration logic of computational models of GRNs, illuminates a mechanistic explanation for this influence, and furthers our understanding of the relationship between topology and robustness in complex biological systems.

Evolutionary dynamics on multiple scales: a quantitative analysis of the interplay between genotype, phenotype, and fitness in linear genetic programming

Redundancy is a ubiquitous feature of genetic programming (GP), with many-to-one mappings commonly observed between genotype and phenotype, and between phenotype and fitness. If a representation is redundant, then neutral mutations are possible. A mutation is phenotypically-neutral if its application to a genotype does not lead to a change in phenotype. A mutation is fitness-neutral if its application to a genotype does not lead to a change in fitness. Whether such neutrality has any benefit for GP remains a contentious topic, with reported experimental results supporting both sides of the debate. Most existing studies use performance statistics, such as success rate or search efficiency, to investigate the utility of neutrality in GP. Here, we take a different tack and use a measure of robustness to quantify the neutrality associated with each genotype, phenotype, and fitness value. We argue that understanding the influence of neutrality on GP requires an understanding of the distributions of robustness at these three levels, and of the interplay between robustness, evolvability, and accessibility amongst genotypes, phenotypes, and fitness values. As a concrete example, we consider a simple linear genetic programming system that is amenable to exhaustive enumeration and allows for the full characterization of these quantities, which we then relate to the dynamical properties of simple mutation-based evolutionary processes. Our results demonstrate that it is not only the distribution of robustness amongst phenotypes that affects evolutionary search, but also (1) the distributions of robustness at the genotypic and fitness levels and (2) the mutational biases that exist amongst genotypes, phenotypes, and fitness values. Of crucial importance is the relationship between the robustness of a genotype and its mutational bias toward other phenotypes.

Function does not follow form in gene regulatory circuits.

Gene regulatory circuits are to the cell what arithmetic logic units are to the chip: fundamental components of information processing that map an input onto an output. Gene regulatory circuits come in many different forms, distinct structural configurations that determine who regulates whom. Studies that have focused on the gene expression patterns (functions) of circuits with a given structure (form) have examined just a few structures or gene expression patterns. Here, we use a computational model to exhaustively characterize the gene expression patterns of nearly 17 million three-gene circuits in order to systematically explore the relationship between circuit form and function. Three main conclusions emerge. First, function does not follow form. A circuit of any one structure can have between twelve and nearly thirty thousand distinct gene expression patterns. Second, and conversely, form does not follow function. Most gene expression patterns can be realized by more than one circuit structure. And third, multifunctionality severely constrains circuit form. The number of circuit structures able to drive multiple gene expression patterns decreases rapidly with the number of these patterns. These results indicate that it is generally not possible to infer circuit function from circuit form, or vice versa.

Robustness, evolvability, and accessibility in linear genetic programming

Whether neutrality has positive or negative effects on evolutionary search is a contentious topic, with reported experimental results supporting both sides of the debate. Most existing studies use performance statistics, e.g., success rate or search efficiency, to investigate if neutrality, either embedded or artificially added, can benefit an evolutionary algorithm. Here, we argue that understanding the influence of neutrality on evolutionary optimization requires an understanding of the interplay between robustness and evolvability at the genotypic and phenotypic scales. As a concrete example, we consider a simple linear genetic programming system that is amenable to exhaustive enumeration, and allows for the full characterization of these properties. We adopt statistical measurements from RNA systems to quantify robustness and evolvability at both genotypic and phenotypic levels. Using an ensemble of random walks, we demonstrate that the benefit of neutrality crucially depends upon its phenotypic distribution.