Robustness, evolvability, and the logic of genetic regulation

Probabilistic Genotype-Phenotype Maps Reveal Mutational Robustness of RNA Folding, Spin Glasses, and Quantum Circuits

Recent studies of genotype-phenotype (GP) maps have reported universally enhanced phenotypic robustness to genotype mutations, a feature essential to evolution. Virtually all of these studies make a simplifying assumption that each genotype-represented as a sequence-maps deterministically to a single phenotype, such as a discrete structure. Here, we introduce probabilistic genotype-phenotype (PrGP) maps, where each genotype maps to a vector of phenotype probabilities, as a more realistic and universal language for investigating robustness in a variety of physical, biological, and computational systems. We study three model systems to show that PrGP maps offer a generalized framework which can handle uncertainty emerging from various physical sources: (1) thermal fluctuation in RNA folding, (2) external field disorder in spin glass ground state finding, and (3) superposition and entanglement in quantum circuits, which are realized experimentally on IBM quantum computers. In all three cases, we observe a novel biphasic robustness scaling which is enhanced relative to random expectation for more frequent phenotypes and approaches random expectation for less frequent phenotypes. We derive an analytical theory for the behavior of PrGP robustness, and we demonstrate that the theory is highly predictive of empirical robustness.

Evolutionary Implications of Self-Assembling Cybernetic Materials with Collective Problem-Solving Intelligence at Multiple Scales

In recent years, the scientific community has increasingly recognized the complex multi-scale competency architecture (MCA) of biology, comprising nested layers of active homeostatic agents, each forming the self-orchestrated substrate for the layer above, and, in turn, relying on the structural and functional plasticity of the layer(s) below. The question of how natural selection could give rise to this MCA has been the focus of intense research. Here, we instead investigate the effects of such decision-making competencies of MCA agential components on the process of evolution itself, using in silico neuroevolution experiments of simulated, minimal developmental biology. We specifically model the process of morphogenesis with neural cellular automata (NCAs) and utilize an evolutionary algorithm to optimize the corresponding model parameters with the objective of collectively self-assembling a two-dimensional spatial target pattern (reliable morphogenesis). Furthermore, we systematically vary the accuracy with which the uni-cellular agents of an NCA can regulate their cell states (simulating stochastic processes and noise during development). This allows us to continuously scale the agents' competency levels from a direct encoding scheme (no competency) to an MCA (with perfect reliability in cell decision executions). We demonstrate that an evolutionary process proceeds much more rapidly when evolving the functional parameters of an MCA compared to evolving the target pattern directly. Moreover, the evolved MCAs generalize well toward system parameter changes and even modified objective functions of the evolutionary process. Thus, the adaptive problem-solving competencies of the agential parts in our NCA-based in silico morphogenesis model strongly affect the evolutionary process, suggesting significant functional implications of the near-ubiquitous competency seen in living matter.

Maximum mutational robustness in genotype-phenotype maps follows a self-similar blancmange-like curve

Phenotype robustness, defined as the average mutational robustness of all the genotypes that map to a given phenotype, plays a key role in facilitating neutral exploration of novel phenotypic variation by an evolving population. By applying results from coding theory, we prove that the maximum phenotype robustness occurs when genotypes are organized as bricklayer's graphs, so-called because they resemble the way in which a bricklayer would fill in a Hamming graph. The value of the maximal robustness is given by a fractal continuous everywhere but differentiable nowhere sums-of-digits function from number theory. Interestingly, genotype-phenotype maps for RNA secondary structure and the hydrophobic-polar (HP) model for protein folding can exhibit phenotype robustness that exactly attains this upper bound. By exploiting properties of the sums-of-digits function, we prove a lower bound on the deviation of the maximum robustness of phenotypes with multiple neutral components from the bricklayer's graph bound, and show that RNA secondary structure phenotypes obey this bound. Finally, we show how robustness changes when phenotypes are coarse-grained and derive a formula and associated bounds for the transition probabilities between such phenotypes.

Robustness and innovation in synthetic genotype networks

Genotype networks are sets of genotypes connected by small mutational changes that share the same phenotype. They facilitate evolutionary innovation by enabling the exploration of different neighborhoods in genotype space. Genotype networks, first suggested by theoretical models, have been empirically confirmed for proteins and RNAs. Comparative studies also support their existence for gene regulatory networks (GRNs), but direct experimental evidence is lacking. Here, we report the construction of three interconnected genotype networks of synthetic GRNs producing three distinct phenotypes in Escherichia coli. Our synthetic GRNs contain three nodes regulating each other by CRISPR interference and governing the expression of fluorescent reporters. The genotype networks, composed of over twenty different synthetic GRNs, provide robustness in face of mutations while enabling transitions to innovative phenotypes. Through realistic mathematical modeling, we quantify robustness and evolvability for the complete genotype-phenotype map and link these features mechanistically to GRN motifs. Our work thereby exemplifies how GRN evolution along genotype networks might be driving evolutionary innovation.

Cellular Competency during Development Alters Evolutionary Dynamics in an Artificial Embryogeny Model

Biological genotypes do not code directly for phenotypes; developmental physiology is the control layer that separates genomes from capacities ascertained by selection. A key aspect is cellular competency, since cells are not passive materials but descendants of unicellular organisms with complex context-sensitive behavioral capabilities. To probe the effects of different degrees of cellular competency on evolutionary dynamics, we used an evolutionary simulation in the context of minimal artificial embryogeny. Virtual embryos consisted of a single axis of positional information values provided by cells' 'structural genes', operated upon by an evolutionary cycle in which embryos' fitness was proportional to monotonicity of the axial gradient. Evolutionary dynamics were evaluated in two modes: hardwired development (genotype directly encodes phenotype), and a more realistic mode in which cells interact prior to evaluation by the fitness function ("regulative" development). We find that even minimal ability of cells with to improve their position in the embryo results in better performance of the evolutionary search. Crucially, we observed that increasing the behavioral competency masks the raw fitness encoded by structural genes, with selection favoring improvements to its developmental problem-solving capacities over improvements to its structural genome. This suggests the existence of a powerful ratchet mechanism: evolution progressively becomes locked in to improvements in the intelligence of its agential substrate, with reduced pressure on the structural genome. This kind of feedback loop in which evolution increasingly puts more effort into the developmental software than perfecting the hardware explains the very puzzling divergence of genome from anatomy in species like planaria. In addition, it identifies a possible driver for scaling intelligence over evolutionary time, and suggests strategies for engineering novel systems in silico and in bioengineering.

Robustness and stability of spin-glass ground states to perturbed interactions

Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ±J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.

Early effects of gene duplication on the robustness and phenotypic variability of gene regulatory networks

Background

Research on gene duplication is abundant and comes from a wide range of approaches, from high-throughput analyses and experimental evolution to bioinformatics and theoretical models. Notwithstanding, a consensus is still lacking regarding evolutionary mechanisms involved in evolution through gene duplication as well as the conditions that affect them. We argue that a better understanding of evolution through gene duplication requires considering explicitly that genes do not act in isolation. It demands studying how the perturbation that gene duplication implies percolates through the web of gene interactions. Due to evolution’s contingent nature, the paths that lead to the final fate of duplicates must depend strongly on the early stages of gene duplication, before gene copies have accumulated distinctive changes.

Methods

Here we use a widely-known model of gene regulatory networks to study how gene duplication affects network behavior in early stages. Such networks comprise sets of genes that cross-regulate. They organize gene activity creating the gene expression patterns that give cells their phenotypic properties. We focus on how duplication affects two evolutionarily relevant properties of gene regulatory networks: mitigation of the effect of new mutations and access to new phenotypic variants through mutation.

Results

Among other observations, we find that those networks that are better at maintaining the original phenotype after duplication are usually also better at buffering the effect of single interaction mutations and that duplication tends to enhance further this ability. Moreover, the effect of mutations after duplication depends on both the kind of mutation and genes involved in it. We also found that those phenotypes that had easier access through mutation before duplication had higher chances of remaining accessible through new mutations after duplication.

Conclusion

Our results support that gene duplication often mitigates the impact of new mutations and that this effect is not merely due to changes in the number of genes. The work that we put forward helps to identify conditions under which gene duplication may enhance evolvability and robustness to mutations.

Endless forms most beautiful 2.0: teleonomy and the bioengineering of chimaeric and synthetic organisms

The rich variety of biological forms and behaviours results from one evolutionary history on Earth, via frozen accidents and selection in specific environments. This ubiquitous baggage in natural, familiar model species obscures the plasticity and swarm intelligence of cellular collectives. Significant gaps exist in our understanding of the origin of anatomical novelty, of the relationship between genome and form, and of strategies for control of large-scale structure and function in regenerative medicine and bioengineering. Analysis of living forms that have never existed before is necessary to reveal deep design principles of life as it can be. We briefly review existing examples of chimaeras, cyborgs, hybrots and other beings along the spectrum containing evolved and designed systems. To drive experimental progress in multicellular synthetic morphology, we propose teleonomic (goal-seeking, problem-solving) behaviour in diverse problem spaces as a powerful invariant across possible beings regardless of composition or origin. Cybernetic perspectives on chimaeric morphogenesis erase artificial distinctions established by past limitations of technology and imagination. We suggest that a multi-scale competency architecture facilitates evolution of robust problem-solving, living machines. Creation and analysis of novel living forms will be an essential testbed for the emerging field of diverse intelligence, with numerous implications across regenerative medicine, robotics and ethics.

Heuristic algorithms in evolutionary computation and modular organization of biological macromolecules: Applications to in vitro evolution

Evolutionary computing (EC) is an area of computer sciences and applied mathematics covering heuristic optimization algorithms inspired by evolution in Nature. EC extensively study all the variety of methods which were originally based on the principles of selectionism. As a result, many new algorithms and approaches, significantly more efficient than classical selectionist schemes, were found. This is especially true for some families of special problems. There are strong arguments to believe that EC approaches are quite suitable for modeling and numerical analysis of those methods of synthetic biology and biotechnology that are known as in vitro evolution. Therefore, it is natural to expect that the new algorithms and approaches developed in EC can be effectively applied in experiments on the directed evolution of biological macromolecules. According to the John Holland's Schema theorem, the effective evolutionary search in genetic algorithms (GA) is provided by identifying short schemata of high fitness which in the further search recombine into the larger building blocks (BBs) with higher and higher fitness. The multimodularity of functional biological macromolecules and the preservation of already found modules in the evolutionary search have a clear analogy with the BBs in EC. It seems reasonable to try to transfer and introduce the methods of EC, preserving BBs and essentially accelerating the search, into experiments on in vitro evolution. We extend the key instrument of the Holland's theory, the Royal Roads fitness function, to problems of the in vitro evolution (Biological Royal Staircase, BioRS, functions). The specific version of BioRS developed in this publication arises from the realities of experimental evolutionary search for (DNA-) RNA-devices (aptazymes). Our numerical tests showed that for problems with the BioRS functions, simple heuristic algorithms, which turned out to be very effective for preserving BBs in GA, can be very effective in in vitro evolution approaches. We are convinced that such algorithms can be implemented in modern methods of in vitro evolution to achieve significant savings in time and resources and a significant increase in the efficiency of evolutionary search.

Light Induced Regulation Pathway of Anthocyanin Biosynthesis in Plants

Anthocyanins are natural pigments with antioxidant effects that exist in various fruits and vegetables. The accumulation of anthocyanins is induced by environmental signals and regulated by transcription factors in plants. Numerous evidence has indicated that among the environmental factors, light is one of the most signal regulatory factors involved in the anthocyanin biosynthesis pathway. However, the signal transduction of light and molecular regulation of anthocyanin synthesis remains to be explored. Here, we focus on the research progress of signal transduction factors for positive and negative regulation in light-dependent and light-independent anthocyanin biosynthesis. In particular, we will discuss light-induced regulatory pathways and related specific regulators of anthocyanin biosynthesis in plants. In addition, an integrated regulatory network of anthocyanin biosynthesis controlled by transcription factors is discussed based on the significant progress.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

On the evolution and development of morphological complexity: A view from gene regulatory networks

How does morphological complexity evolve? This study suggests that the likelihood of mutations increasing phenotypic complexity becomes smaller when the phenotype itself is complex. In addition, the complexity of the genotype-phenotype map (GPM) also increases with the phenotypic complexity. We show that complex GPMs and the above mutational asymmetry are inevitable consequences of how genes need to be wired in order to build complex and robust phenotypes during development. We randomly wired genes and cell behaviors into networks in EmbryoMaker. EmbryoMaker is a mathematical model of development that can simulate any gene network, all animal cell behaviors (division, adhesion, apoptosis, etc.), cell signaling, cell and tissues biophysics, and the regulation of those behaviors by gene products. Through EmbryoMaker we simulated how each random network regulates development and the resulting morphology (i.e. a specific distribution of cells and gene expression in 3D). This way we obtained a zoo of possible 3D morphologies. Real gene networks are not random, but a random search allows a relatively unbiased exploration of what is needed to develop complex robust morphologies. Compared to the networks leading to simple morphologies, the networks leading to complex morphologies have the following in common: 1) They are rarer; 2) They need to be finely tuned; 3) Mutations in them tend to decrease morphological complexity; 4) They are less robust to noise; and 5) They have more complex GPMs. These results imply that, when complexity evolves, it does so at a progressively decreasing rate over generations. This is because as morphological complexity increases, the likelihood of mutations increasing complexity decreases, morphologies become less robust to noise, and the GPM becomes more complex. We find some properties in common, but also some important differences, with non-developmental GPM models (e.g. RNA, protein and gene networks in single cells).

Populations of genetic circuits are unable to find the fittest solution in a multilevel genotype-phenotype map

The evolution of gene regulatory networks (GRNs) is of great relevance for both evolutionary and synthetic biology. Understanding the relationship between GRN structure and its function can allow us to understand the selective pressures that have shaped a given circuit. This is especially relevant when considering spatio-temporal expression patterns, where GRN models have been shown to be extremely robust and evolvable. However, previous models that studied GRN evolution did not include the evolution of protein and genetic elements that underlie GRN architecture. Here we use toyLIFE, a multilevel genotype-phenotype map, to show that not all GRNs are equally likely in genotype space and that evolution is biased to find the most common GRNs. toyLIFE rules create Boolean GRNs that, embedded in a one-dimensional tissue, develop a variety of spatio-temporal gene expression patterns. Populations of toyLIFE organisms choose the most common GRN out of a set of equally fit alternatives and, most importantly, fail to find a target pattern when it is very rare in genotype space. Indeed, we show that the probability of finding the fittest phenotype increases dramatically with its abundance in genotype space. This phenotypic bias represents a mechanism that can prevent the fixation in the population of the fittest phenotype, one that is inherent to the structure of genotype space and the genotype-phenotype map.

Genotype Components as Predictors of Phenotype in Model Gene Regulatory Networks

Models of gene regulatory networks (GRN) have proven useful for understanding many aspects of the highly complex behavior of biological control networks. Randomly generated non-Boolean networks were used in experimental simulations to generate data on dynamic phenotypes as a function of several genotypic parameters. We found that predictive relationships between some phenotypes and quantitative genotypic parameters such as number of network genes, interaction density, and initial condition could be derived depending on the strength of the topological (positional) genotype on specific phenotypes. We quantitated the strength of the topological genotype effect (TGE) on a number of phenotypes in multi-gene networks. For phenotypes with a low influence of topological genotype, derived and empirical relationships using quantitative genotype parameters were accurate in phenotypic outcomes. We found a number of dynamic network properties, including oscillation behaviors, that were largely dependent on genotype topology, and for which no such general quantitative relationships were determinable. It remains to be determined if these results are applicable to biological gene regulatory networks.

Model genotype-phenotype mappings and the algorithmic structure of evolution

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.

Developmental bias in horned dung beetles and its contributions to innovation, adaptation, and resilience

Developmental processes transduce diverse influences during phenotype formation, thereby biasing and structuring amount and type of phenotypic variation available for evolutionary processes to act on. The causes, extent, and consequences of this bias are subject to significant debate. Here we explore the role of developmental bias in contributing to organisms' ability to innovate, to adapt to novel or stressful conditions, and to generate well integrated, resilient phenotypes in the face of perturbations. We focus our inquiry on one taxon, the horned dung beetle genus Onthophagus, and review the role developmental bias might play across several levels of biological organization: (a) gene regulatory networks that pattern specific body regions; (b) plastic developmental mechanisms that coordinate body wide responses to changing environments and; (c) developmental symbioses and niche construction that enable organisms to build teams and to actively modify their own selective environments. We posit that across all these levels developmental bias shapes the way living systems innovate, adapt, and withstand stress, in ways that can alternately limit, bias, or facilitate developmental evolution. We conclude that the structuring contribution of developmental bias in evolution deserves further study to better understand why and how developmental evolution unfolds the way it does.

Adding levels of complexity enhances robustness and evolvability in a multilevel genotype-phenotype map

Robustness and evolvability are the main properties that account for the stability and accessibility of phenotypes. They have been studied in a number of computational genotype-phenotype maps. In this paper, we study a metabolic genotype-phenotype map defined in toyLIFE, a multilevel computational model that represents a simplified cellular biology. toyLIFE includes several levels of phenotypic expression, from proteins to regulatory networks to metabolism. Our results show that toyLIFE shares many similarities with other seemingly unrelated computational genotype-phenotype maps. Thus, toyLIFE shows a high degeneracy in the mapping from genotypes to phenotypes, as well as a highly skewed distribution of phenotypic abundances. The neutral networks associated with abundant phenotypes are highly navigable, and common phenotypes are close to each other in genotype space. All of these properties are remarkable, as toyLIFE is built on a version of the HP protein-folding model that is neither robust nor evolvable: phenotypes cannot be mutually accessed through point mutations. In addition, both robustness and evolvability increase with the number of genes in a genotype. Therefore, our results suggest that adding levels of complexity to the mapping of genotypes to phenotypes and increasing genome size enhances both these properties.

Layers of Cryptic Genetic Variation Underlie a Yeast Complex Trait

To better understand cryptic genetic variation, Lee et al. comprehensively map the genetic basis of a trait that is typically suppressed in a yeast cross. By determining how three different genetic perturbations give rise...

Cryptic genetic variation may be an important contributor to heritable traits, but its extent and regulation are not fully understood. Here, we investigate the cryptic genetic variation underlying a Saccharomyces cerevisiae colony phenotype that is typically suppressed in a cross of the laboratory strain BY4716 (BY) and a derivative of the clinical isolate 322134S (3S). To do this, we comprehensively dissect the trait’s genetic basis in the BYx3S cross in the presence of three different genetic perturbations that enable its expression. This allows us to detect and compare the specific loci that interact with each perturbation to produce the trait. In total, we identify 21 loci, all but one of which interact with just a subset of the perturbations. Beyond impacting which loci contribute to the trait, the genetic perturbations also alter the extent of additivity, epistasis, and genotype–environment interaction among the detected loci. Additionally, we show that the single locus interacting with all three perturbations corresponds to the coding region of the cell surface gene FLO11. While nearly all of the other remaining loci influence FLO11 transcription in cis or trans, the perturbations tend to interact with loci in different pathways and subpathways. Our work shows how layers of cryptic genetic variation can influence complex traits. Here, these layers mainly represent different regulatory inputs into the transcription of a single key gene.

Developmental Bias and Evolution: A Regulatory Network Perspective

Phenotypic variation is generated by the processes of development, with some variants arising more readily than others-a phenomenon known as "developmental bias." Developmental bias and natural selection have often been portrayed as alternative explanations, but this is a false dichotomy: developmental bias can evolve through natural selection, and bias and selection jointly influence phenotypic evolution. Here, we briefly review the evidence for developmental bias and illustrate how it is studied empirically. We describe recent theory on regulatory networks that explains why the influence of genetic and environmental perturbation on phenotypes is typically not uniform, and may even be biased toward adaptive phenotypic variation. We show how bias produced by developmental processes constitutes an evolving property able to impose direction on adaptive evolution and influence patterns of taxonomic and phenotypic diversity. Taking these considerations together, we argue that it is not sufficient to accommodate developmental bias into evolutionary theory merely as a constraint on evolutionary adaptation. The influence of natural selection in shaping developmental bias, and conversely, the influence of developmental bias in shaping subsequent opportunities for adaptation, requires mechanistic models of development to be expanded and incorporated into evolutionary theory. A regulatory network perspective on phenotypic evolution thus helps to integrate the generation of phenotypic variation with natural selection, leaving evolutionary biology better placed to explain how organisms adapt and diversify.

On the networked architecture of genotype spaces and its critical effects on molecular evolution

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

Structural properties of genotype-phenotype maps

The map between genotype and phenotype is fundamental to biology. Biological information is stored and passed on in the form of genotypes, and expressed in the form of phenotypes. A growing body of literature has examined a wide range of genotype-phenotype (GP) maps and has established a number of properties that appear to be shared by many GP maps. These properties are 'structural' in the sense that they are properties of the distribution of phenotypes across the point-mutation network of genotypes. They include: a redundancy of genotypes, meaning that many genotypes map to the same phenotypes, a highly non-uniform distribution of the number of genotypes per phenotype, a high robustness of phenotypes and the ability to reach a large number of new phenotypes within a small number of mutational steps. A further important property is that the robustness and evolvability of phenotypes are positively correlated. In this review, I give an overview of the study of GP maps with particular emphasis on these structural properties, and discuss a model that attempts to explain why these properties arise, as well as some of the fundamental ways in which the structure of GP maps can affect evolutionary outcomes.

Robustness versus evolvability analysis for regulatory feed-forward loops

From the definition, it appears that phenotypic robustness and evolvability of an organism are inversely related to each other. However, a number of studies exploring this question have found conflicting evidences in this regard. This question motivated the current work where we explore the relationship between robustness and evolvability. As a model system, we pick the Feed Forward Loops (FFLs), and develop a framework to characterize their performance in terms of their ability to resist changes to steady state expression (robustness), and their ability to evolve towards novel phenotypes (evolvability). We demonstrate that robustness and evolvability are positively correlated in some FFL topologies. We compare this against other small regulatory topologies, and show that the same trend does not hold among them. We postulate that the ability to positively link robustness and evolvability could be an additional reason for over-representation of FFLs in living organisms, as compared to other regulatory topologies.

Human Sex Determination at the Edge of Ambiguity: INHERITED XY SEX REVERSAL DUE TO ENHANCED UBIQUITINATION AND PROTEASOMAL DEGRADATION OF A MASTER TRANSCRIPTION FACTOR

A general problem is posed by analysis of transcriptional thresholds governing cell fate decisions in metazoan development. A model is provided by testis determination in therian mammals. Its key step, Sertoli cell differentiation in the embryonic gonadal ridge, is initiated by SRY, a Y-encoded architectural transcription factor. Mutations in human SRY cause gonadal dysgenesis leading to XY female development (Swyer syndrome). Here, we have characterized an inherited mutation compatible with either male or female somatic phenotypes as observed in an XY father and XY daughter, respectively. The mutation (a crevice-forming substitution at a conserved back surface of the SRY high mobility group box) markedly destabilizes the domain but preserves specific DNA affinity and induced DNA bend angle. On transient transfection of diverse human and rodent cell lines, the variant SRY exhibited accelerated proteasomal degradation (relative to wild type) associated with increased ubiquitination; in vitro susceptibility to ubiquitin-independent ("default") cleavage by the 20S core proteasome was unchanged. The variant's gene regulatory activity (as assessed in a cellular model of the rat embryonic XY gonadal ridge) was reduced by 2-fold relative to wild-type SRY at similar levels of mRNA expression. Chemical proteasome inhibition restored native-like SRY expression and transcriptional activity in association with restored occupancy of a sex-specific enhancer element in principal downstream gene Sox9, demonstrating that the variant SRY exhibits essentially native activity on a per molecule basis. Our findings define a novel mechanism of impaired organogenesis, accelerated ubiquitin-directed proteasomal degradation of a master transcription factor leading to a developmental decision poised at the edge of ambiguity.

Evolution of mammalian sound localization circuits: A developmental perspective

Localization of sound sources is a central aspect of auditory processing. A unique feature of mammals is the smooth, tonotopically organized extension of the hearing range to high frequencies (HF) above 10kHz, which likely induced positive selection for novel mechanisms of sound localization. How this change in the auditory periphery is accompanied by changes in the central auditory system is unresolved. I will argue that the major VGlut2(+) excitatory projection neurons of sound localization circuits (dorsal cochlear nucleus (DCN), lateral and medial superior olive (LSO and MSO)) represent serial homologs with modifications, thus being paramorphs. This assumption is based on common embryonic origin from an Atoh1(+)/Wnt1(+) cell lineage in the rhombic lip of r5, same cell birth, a fusiform cell morphology, shared genetic components such as Lhx2 and Lhx9 transcription factors, and similar projection patterns. Such a parsimonious evolutionary mechanism likely accelerated the emergence of neurons for sound localization in all three dimensions. Genetic analyses indicate that auditory nuclei in fish, birds, and mammals receive contributions from the same progenitor lineages. Anatomical and physiological differences and the independent evolution of tympanic ears in vertebrate groups, however, argue for convergent evolution of sound localization circuits in tetrapods (amphibians, reptiles, birds, and mammals). These disparate findings are discussed in the context of the genetic architecture of the developing hindbrain, which facilitates convergent evolution. Yet, it will be critical to decipher the gene regulatory networks underlying development of auditory neurons across vertebrates to explore the possibility of homologous neuronal populations.

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.

toyLIFE: a computational framework to study the multi-level organisation of the genotype-phenotype map

The genotype-phenotype map is an essential object to understand organismal complexity and adaptability. However, its experimental characterisation is a daunting task. Thus, simple models have been proposed and investigated. They have revealed that genotypes differ in their robustness to mutations; phenotypes are represented by a broadly varying number of genotypes, and simple point mutations suffice to navigate the space of genotypes while maintaining a phenotype. Nonetheless, most current models focus only on one level of the map (folded molecules, gene regulatory networks, or networks of metabolic reactions), so that many relevant questions cannot be addressed. Here we introduce toyLIFE, a multi-level model for the genotype-phenotype map based on simple genomes and interaction rules from which a complex behaviour at upper levels emerges -remarkably plastic gene regulatory networks and metabolism. toyLIFE is a tool that permits the investigation of how different levels are coupled, in particular how and where mutations affect phenotype or how the presence of certain metabolites determines the dynamics of toyLIFE gene regulatory networks. The model can easily incorporate evolution through more complex mutations, recombination, or gene duplication and deletion, thus opening an avenue to explore extended genotype-phenotype maps.

Phenotypic robustness and the assortativity signature of human transcription factor networks

Many developmental, physiological, and behavioral processes depend on the precise expression of genes in space and time. Such spatiotemporal gene expression phenotypes arise from the binding of sequence-specific transcription factors (TFs) to DNA, and from the regulation of nearby genes that such binding causes. These nearby genes may themselves encode TFs, giving rise to a transcription factor network (TFN), wherein nodes represent TFs and directed edges denote regulatory interactions between TFs. Computational studies have linked several topological properties of TFNs — such as their degree distribution — with the robustness of a TFN's gene expression phenotype to genetic and environmental perturbation. Another important topological property is assortativity, which measures the tendency of nodes with similar numbers of edges to connect. In directed networks, assortativity comprises four distinct components that collectively form an assortativity signature. We know very little about how a TFN's assortativity signature affects the robustness of its gene expression phenotype to perturbation. While recent theoretical results suggest that increasing one specific component of a TFN's assortativity signature leads to increased phenotypic robustness, the biological context of this finding is currently limited because the assortativity signatures of real-world TFNs have not been characterized. It is therefore unclear whether these earlier theoretical findings are biologically relevant. Moreover, it is not known how the other three components of the assortativity signature contribute to the phenotypic robustness of TFNs. Here, we use publicly available DNaseI-seq data to measure the assortativity signatures of genome-wide TFNs in 41 distinct human cell and tissue types. We find that all TFNs share a common assortativity signature and that this signature confers phenotypic robustness to model TFNs. Lastly, we determine the extent to which each of the four components of the assortativity signature contributes to this robustness.

The cells of living organisms do not concurrently express their entire complement of genes. Instead, they regulate their gene expression, and one consequence of this is the potential for different cells to adopt different stable gene expression patterns. For example, the development of an embryo necessitates that cells alter their gene expression patterns in order to differentiate. These gene expression phenotypes are largely robust to genetic mutation, and one source of this robustness may reside in the network structure of interacting molecules that underlie genetic regulation. Theoretical studies of regulatory networks have linked network structure to robustness; however, it is also necessary to more extensively characterize real-world regulatory networks in order to understand which structural properties may be biologically meaningful. We recently used theoretical models to show that a particular structural property, degree assortativity, is linked to robustness. Here, we measure the assortativity of human regulatory networks in 41 distinct cell and tissue types. We then develop a theoretical framework to explore how this structural property affects robustness, and we find that the gene expression phenotypes of human regulatory networks are more robust than expected by chance alone.

Latent phenotypes pervade gene regulatory circuits

BACKGROUND

Latent phenotypes are non-adaptive byproducts of adaptive phenotypes. They exist in biological systems as different as promiscuous enzymes and genome-scale metabolic reaction networks, and can give rise to evolutionary adaptations and innovations. We know little about their prevalence in the gene expression phenotypes of regulatory circuits, important sources of evolutionary innovations.

RESULTS

Here, we study a space of more than sixteen million three-gene model regulatory circuits, where each circuit is represented by a genotype, and has one or more functions embodied in one or more gene expression phenotypes. We find that the majority of circuits with single functions have latent expression phenotypes. Moreover, the set of circuits with a given spectrum of functions has a repertoire of latent phenotypes that is much larger than that of any one circuit. Most of this latent repertoire can be easily accessed through a series of small genetic changes that preserve a circuit's main functions. Both circuits and gene expression phenotypes that are robust to genetic change are associated with a greater number of latent phenotypes.

CONCLUSIONS

Our observations suggest that latent phenotypes are pervasive in regulatory circuits, and may thus be an important source of evolutionary adaptations and innovations involving gene regulation.

Modeling the evolution of molecular systems from a mechanistic perspective

Systems biology-inspired genotype-phenotype mapping models are increasingly being used to study the evolutionary properties of molecular biological systems, in particular the general emergent properties of evolving systems, such as modularity, robustness, and evolvability. However, the level of abstraction at which many of these models operate might not be sufficient to capture all relevant intricacies of biological evolution in sufficient detail. Here, we argue that in particular gene and genome duplications, both evolutionary mechanisms of potentially major importance for the evolution of molecular systems and of special relevance to plant evolution, are not adequately accounted for in most GPM modeling frameworks, and that more fine-grained mechanistic models may significantly advance understanding of how gen(om)e duplication impacts molecular systems evolution.