Robustness and evolvability: a paradox resolved

Understanding species-specific and conserved RNA-protein interactions in vivo and in vitro

While evolution is often considered from a DNA- and protein-centric view, RNA-based regulation can also impact gene expression and protein sequences. Here we examine interspecies differences in RNA-protein interactions using the conserved neuronal RNA-binding protein, Unkempt (UNK) as model. We find that roughly half of mRNAs bound in human are also bound in mouse. Unexpectedly, even when transcript-level binding was conserved across species differential motif usage was prevalent. To understand the biochemical basis of UNK-RNA interactions, we reconstitute the human and mouse UNK-RNA interactomes using a high-throughput biochemical assay. We uncover detailed features driving binding, show that in vivo patterns are captured in vitro, find that highly conserved sites are the strongest bound, and associate binding strength with downstream regulation. Furthermore, subtle sequence differences surrounding motifs are key determinants of species-specific binding. We highlight the complex features driving protein-RNA interactions and how these evolve to confer species-specific regulation.

Mitochondria facilitate neuronal differentiation by metabolising nuclear-encoded RNA

Mitochondrial activity directs neuronal differentiation dynamics during brain development. In this context, the long-established metabolic coupling of mitochondria and the eukaryotic host falls short of a satisfactory mechanistic explanation, hinting at an undisclosed facet of mitochondrial function. Here, we reveal an RNA-based inter-organellar communication mode that complements metabolic coupling of host-mitochondria and underpins neuronal differentiation. We show that within minutes of exposure to differentiation cues and activation of the electron transport chain, the mitochondrial outer membrane transiently fuses with the nuclear membrane of neural progenitors, leading to efflux of nuclear-encoded RNAs (neRNA) into the positively charged mitochondrial intermembrane space. Subsequent degradation of mitochondrial neRNAs by Polynucleotide phosphorylase 1 (PNPase) located in the intermembrane space curbs the transcriptomic memory of progenitor cells. Further, acquisition of neRNA by mitochondria leads to a collapse of proton motive force, suppression of ATP production, and a resultant amplification of autophagic flux that attenuates proteomic memory. Collectively, these events force the progenitor cells towards a "tipping point" characterised by emergence of a competing neuronal differentiation program. It appears that neuronal differentiation is a consequence of reprogrammed coupling of metabolomic and transcriptomic landscapes of progenitor cells, with mitochondria emerging as key "reprogrammers" that operate by acquiring and metabolising neRNAs. However, the documented role of mitochondria as "reprogrammers" of differentiation remains to be validated in other neuronal lineages and in vivo.

Robustness and variability in Caenorhabditis elegans dauer gene expression

Both plasticity and robustness are pervasive features of developmental programs. The dauer in Caenorhabditis elegans is an arrested, hypometabolic alternative to the third larval stage of the nematode. Dauers undergo dramatic tissue remodeling and extensive physiological, metabolic, behavioral, and gene expression changes compared to conspecifics that continue development and can be induced by several adverse environments or genetic mutations that act as independent and parallel inputs into the larval developmental program. Therefore, dauer induction is an example of phenotypic plasticity. However, whether gene expression in dauer larvae induced to arrest development by different genetic or environmental triggers is invariant or varies depending on their route into dauer has not been examined. By using RNA-sequencing to characterize gene expression in different types of dauer larvae and computing the variance and concordance within Gene Ontologies (GO) and gene expression networks, we find that the expression patterns within most pathways are strongly correlated between dauer larvae, suggestive of transcriptional robustness. However, gene expression within specific defense pathways, pathways regulating some morphological traits, and several metabolic pathways differ between the dauer larvae. We speculate that the transcriptional robustness of core dauer pathways allows for the buffering of variation in the expression of genes involved in adaptation, allowing the dauers induced by different stimuli to survive in and exploit different niches.

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.

Robustness and evolvability: Revisited, redefined and applied

Building on and extending existing definitions of robustness and evolvability, we propose and utilize new formal definitions, with matching measures, of robustness and evolvability of systems with genotypes and corresponding phenotypes. We explain and show how these measures are more general and more representative of the concepts they stand for, than the commonly used/referenced measures originally proposed by Wagner. Further, a versatile digital modeling approach (BNK) is proposed that is inspired by NK systems. However, unlike NK systems, BNK incorporates a genotype and a phenotype, in addition to fitness. We develop and apply an Evolutionary Algorithm to a BNK-modeled system to find different types of perfect oscillators. We then map the resulting oscillating systems to possible genetic circuit realizations. Continuing with the synthetic biology theme, we also investigate the effect of noise in DNA synthesis on the predicted functionality of a DNA-based biosensor (i.e., its robustness), and we carry out a theoretical assessment of the evolvability of different types of ribozymes, undergoing directed evolution.

Emergence of phenotypic plasticity through epigenetic mechanisms

Plasticity is found in all domains of life and is particularly relevant when populations experience variable environmental conditions. Traditionally, evolutionary models of plasticity are non-mechanistic: they typically view reactions norms as the target of selection, without considering the underlying genetics explicitly. Consequently, there have been difficulties in understanding the emergence of plasticity, and in explaining its limits and costs. In this paper, we offer a novel mechanistic approximation for the emergence and evolution of plasticity. We simulate random "epigenetic mutations" in the genotype-phenotype mapping, of the kind enabled by DNA-methylations/demethylations. The frequency of epigenetic mutations at loci affecting the phenotype is sensitive to organism stress (trait-environment mismatch), but is also genetically determined and evolvable. Thus, the "random motion" of epigenetic markers enables developmental learning-like behaviors that can improve adaptation within the limits imposed by the genotypes. However, with random motion being "goal-less," this mechanism is also vulnerable to developmental noise leading to maladaptation. Our individual-based simulations show that epigenetic mutations can hide alleles that are temporarily unfavorable, thus enabling cryptic genetic variation. These alleles can be advantageous at later times, under regimes of environmental change, in spite of the accumulation of genetic loads. Simulations also demonstrate that plasticity is favored by natural selection in constant environments, but more under periodic environmental change. Plasticity also evolves under directional environmental change as long as the pace of change is not too fast and costs are low.

Evolvability: filling the explanatory gap between adaptedness and the long-term mathematical conception of fitness

The new foundation for the propensity interpretation of fitness (PIF), developed by Pence and Ramsey (Br J Philos Sci 64:851-881, 2013), describes fitness as a probability distribution that encompasses all possible daughter populations to which the organism may give rise, including daughter populations in which traits might change and the possible environments that members of the daughter populations might encounter. This long-term definition of fitness is general enough to avoid counterexamples faced by previous mathematical conceptions of PIF. However, there seem to be downsides to its generality: the ecological role of fitness involves describing the degree of adaptedness between an organism and the specific environment it inhabits. When all possible changes in traits and all possible environments that a daughter population may encounter are included in the concept, it becomes difficult to see how fitness can fulfill this role. In this paper, we argue that this is a feature of Pence and Ramsey's view rather than a bug: long-term fitness accommodates evolvability considerations, which concern the role that variation plays in evolutionary processes. Building on the foundations, we show that Pence and Ramsey's fitness-F-can be partitioned into fourths: adaptedness, robustness of adaptedness, and two facets of evolvability. Conceptualizing these last three components forces us to consider the role played by grains of description of both organisms and the environment when thinking about long-term fitness. They track the possibility that there could be a change in type in a daughter population as a way of responding to environmental challenges, or that the type persists in the face of novel environments. We argue that these components are just as salient as adaptedness for long-term fitness. Together, this decomposition of F provides a more accurate picture of the factors involved in long-term evolutionary success.

The role of promiscuous molecular recognition in the evolution of RNase-based self-incompatibility in plants

How do biological networks evolve and expand? We study these questions in the context of the plant collaborative-non-self recognition self-incompatibility system. Self-incompatibility evolved to avoid self-fertilization among hermaphroditic plants. It relies on specific molecular recognition between highly diverse proteins of two families: female and male determinants, such that the combination of genes an individual possesses determines its mating partners. Though highly polymorphic, previous models struggled to pinpoint the evolutionary trajectories by which new specificities evolved. Here, we construct a novel theoretical framework, that crucially affords interaction promiscuity and multiple distinct partners per protein, as is seen in empirical findings disregarded by previous models. We demonstrate spontaneous self-organization of the population into distinct "classes" with full between-class compatibility and a dynamic long-term balance between class emergence and decay. Our work highlights the importance of molecular recognition promiscuity to network evolvability. Promiscuity was found in additional systems suggesting that our framework could be more broadly applicable.

Body plan evolvability: The role of variability in gene regulatory networks

Recent computational modeling of early fruit fly (Drosophila) development has characterized the degree to which gene regulation networks can be robust to natural variability. In the first few hours of development, broad spatial gradients of maternally derived transcription factors activate embryonic gap genes. These gap patterns determine the subsequent segmented insect body plan through pair-rule gene expression. Gap genes are expressed with greater spatial precision than the maternal patterns. Computational modeling of the gap-gap regulatory interactions provides a mechanistic understanding for this robustness to maternal variability in wild-type (WT) patterning. A long-standing question in evolutionary biology has been how a system which is robust, such as the developmental program creating any particular species' body plan, is also evolvable, i.e. how can a system evolve or speciate, if the WT form is strongly buffered and protected? In the present work, we use the WT model to explore the breakdown of such Waddington-type 'canalization'. What levels of variability will push the system out of the WT form; are there particular pathways in the gene regulatory mechanism which are more susceptible to losing the WT form; and when robustness is lost, what types of forms are most likely to occur (i.e. what forms lie near the WT)? Manipulating maternal effects in several different pathways, we find a common gap 'peak-to-step' pattern transition in the loss of WT. We discuss these results in terms of the evolvability of insect segmentation, and in terms of experimental perturbations and mutations which could test the model predictions. We conclude by discussing the prospects for using continuum models of pattern dynamics to investigate a wider range of evo-devo problems.

Mutational robustness and the role of buffer genes in evolvability

Organisms rely on mutations to fuel adaptive evolution. However, many mutations impose a negative effect on fitness. Cells may have therefore evolved mechanisms that affect the phenotypic effects of mutations, thus conferring mutational robustness. Specifically, so-called buffer genes are hypothesized to interact directly or indirectly with genetic variation and reduce its effect on fitness. Environmental or genetic perturbations can change the interaction between buffer genes and genetic variation, thereby unmasking the genetic variation's phenotypic effects and thus providing a source of variation for natural selection to act on. This review provides an overview of our understanding of mutational robustness and buffer genes, with the chaperone gene HSP90 as a key example. It discusses whether buffer genes merely affect standing variation or also interact with de novo mutations, how mutational robustness could influence evolution, and whether mutational robustness might be an evolved trait or rather a mere side-effect of complex genetic interactions.

Non-Poissonian Bursts in the Arrival of Phenotypic Variation Can Strongly Affect the Dynamics of Adaptation

Modeling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modeled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype-phenotype maps to show that the introduction of novel phenotypes can be "bursty" or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for "monomorphic" populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype-phenotype map for RNA secondary structure, but find similar behavior in a lattice protein model and in Richard Dawkins's biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

Mechanistic interactions as the origin of modularity in biological networks

Biological networks are often modular. Explanations for this peculiarity either assume an adaptive advantage of a modular design such as higher robustness, or attribute it to neutral factors such as constraints underlying network assembly. Interestingly, most insights on the origin of modularity stem from models in which interactions are either determined by highly simplistic mechanisms, or have no mechanistic basis at all. Yet, empirical knowledge suggests that biological interactions are often mediated by complex structural or behavioural traits. Here, we investigate the origins of modularity using a model in which interactions are determined by potentially complex traits. Specifically, we model system elements-such as the species in an ecosystem-as finite-state machines (FSMs), and determine their interactions by means of communication between the corresponding FSMs. Using this model, we show that modularity probably emerges for free. We further find that the more modular an interaction network is, the less complex are the traits that mediate the interactions. Altogether, our results suggest that the conditions for modularity to evolve may be much broader than previously thought.

A mammalian tripartite enhancer cluster controls hypothalamic Pomc expression, food intake, and body weight

Food intake and energy balance are tightly regulated by a group of hypothalamic arcuate neurons expressing the proopiomelanocortin (POMC) gene. In mammals, arcuate-specific POMC expression is driven by two cis-acting transcriptional enhancers known as nPE1 and nPE2. Because mutant mice lacking these two enhancers still showed hypothalamic Pomc mRNA, we searched for additional elements contributing to arcuate Pomc expression. By combining molecular evolution with reporter gene expression in transgenic zebrafish and mice, here, we identified a mammalian arcuate-specific Pomc enhancer that we named nPE3, carrying several binding sites also present in nPE1 and nPE2 for transcription factors known to activate neuronal Pomc expression, such as ISL1, NKX2.1, and ERα. We found that nPE3 originated in the lineage leading to placental mammals and remained under purifying selection in all mammalian orders, although it was lost in Simiiformes (monkeys, apes, and humans) following a unique segmental deletion event. Interestingly, ablation of nPE3 from the mouse genome led to a drastic reduction (>70%) in hypothalamic Pomc mRNA during development and only moderate (<33%) in adult mice. Comparison between double (nPE1 and nPE2) and triple (nPE1, nPE2, and nPE3) enhancer mutants revealed the relative contribution of nPE3 to hypothalamic Pomc expression and its importance in the control of food intake and adiposity in male and female mice. Altogether, these results demonstrate that nPE3 integrates a tripartite cluster of partially redundant enhancers that originated upon a triple convergent evolutionary process in mammals and that is critical for hypothalamic Pomc expression and body weight homeostasis.

Adaptive Capacity of a DNA Polymerase Clamp-loader ATPase Complex

The ability of mutations to facilitate adaptation is central to evolution. To understand how mutations can lead to functional adaptation in a complex molecular machine, we created a defective version of the T4 clamp-loader complex, which is essential for DNA replication. This variant, which is ∼5,000-fold less active than the wild type, was made by replacing the catalytic domains with those from another phage. A directed-evolution experiment revealed that multiple substitutions to a single negatively charged residue in the chimeric clamp loader-Asp 86-restore fitness to within ∼20-fold of wild type. These mutations remove an adventitious electrostatic repulsive interaction between Asp 86 and the sliding clamp. Thus, the fitness decrease of the chimeric clamp loader is caused by a reduction in affinity between the clamp loader and the clamp. Deep mutagenesis shows that the reduced fitness of the chimeric clamp loader is also compensated for by lysine and arginine substitutions of several DNA-proximal residues in the clamp loader or the sliding clamp. Our results demonstrate that there is a latent capacity for increasing the affinity of the clamp loader for DNA and the sliding clamp, such that even single-point mutations can readily compensate for the loss of function due to suboptimal interactions elsewhere.

Understanding species-specific and conserved RNA-protein interactions in vivo and in vitro

While evolution is often considered from a DNA- and protein-centric view, RNA-based regulation can also impact gene expression and protein sequences. Here we examined interspecies differences in RNA-protein interactions using the conserved neuronal RNA binding protein, Unkempt (UNK) as model. We find that roughly half of mRNAs bound in human are also bound in mouse. Unexpectedly, even when transcript-level binding was conserved across species differential motif usage was prevalent. To understand the biochemical basis of UNK-RNA interactions, we reconstituted the human and mouse UNK-RNA interactomes using a high-throughput biochemical assay. We uncover detailed features driving binding, show that in vivo patterns are captured in vitro, find that highly conserved sites are the strongest bound, and associate binding strength with downstream regulation. Furthermore, subtle sequence differences surrounding motifs are key determinants of species-specific binding. We highlight the complex features driving protein-RNA interactions and how these evolve to confer species-specific regulation.

Genetic drift promotes and recombination hinders speciation on holey fitness landscapes

Dobzhansky and Muller proposed a general mechanism through which microevolution, the substitution of alleles within populations, can cause the evolution of reproductive isolation between populations and, therefore, macroevolution. As allopatric populations diverge, many combinations of alleles differing between them have not been tested by natural selection and may thus be incompatible. Such genetic incompatibilities often cause low fitness in hybrids between species. Furthermore, the number of incompatibilities grows with the genetic distance between diverging populations. However, what determines the rate and pattern of accumulation of incompatibilities remains unclear. We investigate this question by simulating evolution on holey fitness landscapes on which genetic incompatibilities can be identified unambiguously. We find that genetic incompatibilities accumulate more slowly among genetically robust populations and identify two determinants of the accumulation rate: recombination rate and population size. In large populations with abundant genetic variation, recombination selects for increased genetic robustness and, consequently, incompatibilities accumulate more slowly. In small populations, genetic drift interferes with this process and promotes the accumulation of genetic incompatibilities. Our results suggest a novel mechanism by which genetic drift promotes and recombination hinders speciation.

The evolutionary consequences of epigenesis and neutral change: A conceptual approach at the organismal level

Living beings are autopoietic systems with highly context-dependent structural dynamics and interactions, that determine whether a disturbance in the genotype or environment will lead or not to phenotypic change. The concept of epigenesis entails how a change in the phenotype may not correspond to a change in the structure of an earlier developmental stage, including the genome. Disturbances of embryonic structure may fail to change the phenotype, as in regulated development, or when different genotypes are associated to a single phenotype. Likewise, the same genotype or early embryonic structure may develop different phenotypes, as in phenotypic plasticity. Disturbances that fail to trigger phenotypic change are considered neutral, but even so, they can alter unexpressed developmental potential. Here, we present conceptual diagrams of the "epigenic field": similar to Waddington's epigenetic landscapes, but including the ontogenic niche (organism/environment interactional dynamics during ontogeny) as a factor in defining epigenic fields, rather than just selecting among possible pathways. Our diagrams illustrate transgenerational changes of genotype, ontogenic niche, and their correspondence (or lack thereof) with changes of phenotype. Epigenic fields provide a simple way to understand developmental constraints on evolution, for instance: how constraints evolve as a result of developmental system drift; how neutral changes can be involved in genetic assimilation and de-assimilation; and how constraints can evolve as a result of neutral changes in the ontogenic niche (not only the genotype). We argue that evolutionary thinking can benefit from a framework for evolution with conceptual foundations at the organismal level.

Co-expression of distinct L1 retrotransposon coiled coils can lead to their entanglement

L1 (LINE1) non-LTR retrotransposons are ubiquitous genomic parasites and the dominant transposable element in humans having generated about 40% of their genomic DNA during their ~ 100 million years (Myr) of activity in primates. L1 replicates in germ line cells and early embryos, causing genetic diversity and defects, but can be active in some somatic stem cells, tumors and during aging. L1 encodes two proteins essential for retrotransposition: ORF2p, a reverse transcriptase that contains an endonuclease domain, and ORF1p, a coiled coil mediated homo trimer, which functions as a nucleic acid chaperone. Both proteins contain highly conserved domains and preferentially bind their encoding transcript to form an L1 ribonucleoprotein (RNP), which mediates retrotransposition. However, the coiled coil has periodically undergone episodes of substantial amino acid replacement to the extent that a given L1 family can concurrently express multiple ORF1s that differ in the sequence of their coiled coils. Here we show that such distinct ORF1p sequences can become entangled forming heterotrimers when co-expressed from separate vectors and speculate on how coiled coil entanglement could affect coiled coil evolution.

Molecular determinants of protein evolvability

The plethora of biological functions that sustain life is rooted in the remarkable evolvability of proteins. An emerging view highlights the importance of a protein's initial state in dictating evolutionary success. A deeper comprehension of the mechanisms that govern the evolvability of these initial states can provide invaluable insights into protein evolution. In this review, we describe several molecular determinants of protein evolvability, unveiled by experimental evolution and ancestral sequence reconstruction studies. We further discuss how genetic variation and epistasis can promote or constrain functional innovation and suggest putative underlying mechanisms. By establishing a clear framework for these determinants, we provide potential indicators enabling the forecast of suitable evolutionary starting points and delineate molecular mechanisms in need of deeper exploration.

The non-deterministic genotype-phenotype map of RNA secondary structure

Selection and variation are both key aspects in the evolutionary process. Previous research on the mapping between molecular sequence (genotype) and molecular fold (phenotype) has shown the presence of several structural properties in different biological contexts, implying that these might be universal in evolutionary spaces. The deterministic genotype-phenotype (GP) map that links short RNA sequences to minimum free energy secondary structures has been studied extensively because of its computational tractability and biologically realistic nature. However, this mapping ignores the phenotypic plasticity of RNA. We define a GP map that incorporates non-deterministic (ND) phenotypes, and take RNA as a case study; we use the Boltzmann probability distribution of folded structures and examine the structural properties of ND GP maps for RNA sequences of length 12 and coarse-grained RNA structures of length 30 (RNAshapes30). A framework is presented to study robustness, evolvability and neutral spaces in the ND map. This framework is validated by demonstrating close correspondence between the ND quantities and sample averages of their deterministic counterparts. When using the ND framework we observe the same structural properties as in the deterministic GP map, such as bias, negative correlation between genotypic robustness and evolvability, and positive correlation between phenotypic robustness and evolvability.

Learning to learn by using nonequilibrium training protocols for adaptable materials

Evolution in time-varying environments naturally leads to adaptable biological systems that can easily switch functionalities. Advances in the synthesis of environmentally responsive materials therefore open up the possibility of creating a wide range of synthetic materials which can also be trained for adaptability. We consider high-dimensional inverse problems for materials where any particular functionality can be realized by numerous equivalent choices of design parameters. By periodically switching targets in a given design algorithm, we can teach a material to perform incompatible functionalities with minimal changes in design parameters. We exhibit this learning strategy for adaptability in two simulated settings: elastic networks that are designed to switch deformation modes with minimal bond changes and heteropolymers whose folding pathway selections are controlled by a minimal set of monomer affinities. The resulting designs can reveal physical principles, such as nucleation-controlled folding, that enable such adaptability.

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.

The effect of mutational robustness on the evolvability of multicellular organisms and eukaryotic cells

Canalization involves mutational robustness, the lack of phenotypic change as a result of genetic mutations. Given the large divergence in phenotype across species, understanding the relationship between high robustness and evolvability has been of interest to both theorists and experimentalists. Although canalization was originally proposed in the context of multicellular organisms, the effect of multicellularity and other classes of hierarchical organization on evolvability has not been considered by theoreticians. We address this issue using a Boolean population model with explicit representation of an environment in which individuals with explicit genotype and a hierarchical phenotype representing multicellularity evolve. Robustness is described by a single real number between zero and one which emerges from the genotype-phenotype map. We find that high robustness is favoured in constant environments, and lower robustness is favoured after environmental change. Multicellularity and hierarchical organization severely constrain robustness: peak evolvability occurs at an absolute level of robustness of about 0.99 compared with values of about 0.5 in a classical neutral network model. These constraints result in a sharp peak of evolvability in which the maximum is set by the fact that the fixation of adaptive mutations becomes more improbable as robustness decreases. When robustness is put under genetic control, robustness levels leading to maximum evolvability are selected for, but maximal relative fitness appears to require recombination.

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.

A shark-inspired general model of tooth morphogenesis unveils developmental asymmetries in phenotype transitions

Developmental complexity stemming from the dynamic interplay between genetic and biomechanic factors canalizes the ways genotypes and phenotypes can change in evolution. As a paradigmatic system, we explore how changes in developmental factors generate typical tooth shape transitions. Since tooth development has mainly been researched in mammals, we contribute to a more general understanding by studying the development of tooth diversity in sharks. To this end, we build a general, but realistic, mathematical model of odontogenesis. We show that it reproduces key shark-specific features of tooth development as well as real tooth shape variation in small-spotted catsharks Scyliorhinus canicula. We validate our model by comparison with experiments in vivo. Strikingly, we observe that developmental transitions between tooth shapes tend to be highly degenerate, even for complex phenotypes. We also discover that the sets of developmental parameters involved in tooth shape transitions tend to depend asymmetrically on the direction of that transition. Together, our findings provide a valuable base for furthering our understanding of how developmental changes can lead to both adaptive phenotypic change and trait convergence in complex, phenotypically highly diverse, structures.

The evolution of gastrulation morphologies

During gastrulation, early embryos specify and reorganise the topology of their germ layers. Surprisingly, this fundamental and early process does not appear to be rigidly constrained by evolutionary pressures; instead, the morphology of gastrulation is highly variable throughout the animal kingdom. Recent experimental results demonstrate that it is possible to generate different alternative gastrulation modes in single organisms, such as in early cnidarian, arthropod and vertebrate embryos. Here, we review the mechanisms that underlie the plasticity of vertebrate gastrulation both when experimentally manipulated and during evolution. Using the insights obtained from these experiments we discuss the effects of the increase in yolk volume on the morphology of gastrulation and provide new insights into two crucial innovations during amniote gastrulation: the transition from a ring-shaped mesoderm domain in anamniotes to a crescent-shaped domain in amniotes, and the evolution of the reptilian blastoporal plate/canal into the avian primitive streak.

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.

The ensemble of gene regulatory networks at mutation-selection balance

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

Rebuilding ships while at sea-Character individuality, homology, and evolutionary innovation

How novel traits originate in evolution is still one of the most perplexing questions in Evolutionary Biology. Building on a previous account of evolutionary innovation, I here propose that evolutionary novelties are those individualized characters that are not homologous to any characters in the ancestor. To clarify this definition, I here provide a detailed analysis of the concepts of "character individuality" and "homology" first, before addressing their role for our understanding of evolutionary innovation. I will argue (1) that functional as well as structural considerations are important for character individualization; and (2) that compositional (structural) and positional homology need to be clearly distinguished to properly describe the evolutionary transformations of hierarchically structured characters. My account will therefore integrate functional and structural perspectives and put forward a new multi-level view of character identity and transformation.

Exploring the expanse between theoretical questions and experimental approaches in the modern study of evolvability

Despite several decades of computational and experimental work across many systems, evolvability remains on the periphery with regards to its status as a widely accepted and regularly applied theoretical concept. Here we propose that its marginal status is partly a result of large gaps between the diverse but disconnected theoretical treatments of evolvability and the relatively narrower range of studies that have tested it empirically. To make this case, we draw on a range of examples-from experimental evolution in microbes, to molecular evolution in proteins-where attempts have been made to mend this disconnect. We highlight some examples of progress that has been made and point to areas where synthesis and translation of existing theory can lead to further progress in the still-new field of empirical measurements of evolvability.

Adaptive evolvability through direct selection instead of indirect, second-order selection

Can evolvability itself be the product of adaptive evolution? To answer this question is challenging, because any DNA mutation that alters only evolvability is subject to indirect, "second order" selection on the future effects of this mutation. Such indirect selection is weaker than "first-order" selection on mutations that alter fitness, in the sense that it can operate only under restrictive conditions. Here I discuss a route to adaptive evolvability that overcomes this challenge. Specifically, a recent evolution experiment showed that some mutations can enhance both fitness and evolvability through a combination of direct and indirect selection. Unrelated evidence from gene duplication and the evolution of gene regulation suggests that mutations with such dual effects may not be rare. Through such mutations, evolvability may increase at least in part because it provides an adaptive advantage. These observations suggest a research program on the adaptive evolution of evolvability, which aims to identify such mutations and to disentangle their direct fitness effects from their indirect effects on evolvability. If evolvability is itself adaptive, Darwinian evolution may have created more than life's diversity. It may also have helped create the very conditions that made the success of Darwinian evolution possible.

Organelle bottlenecks facilitate evolvability by traversing heteroplasmic fitness valleys

Bioenergetic organelles-mitochondria and plastids-retain their own genomes (mtDNA and ptDNA), and these organelle DNA (oDNA) molecules are vital for eukaryotic life. Like all genomes, oDNA must be able to evolve to suit new environmental challenges. However, mixed oDNA populations in cells can challenge cellular bioenergetics, providing a penalty to the appearance and adaptation of new mutations. Here we show that organelle "bottlenecks," mechanisms increasing cell-to-cell oDNA variability during development, can overcome this mixture penalty and facilitate the adaptation of beneficial mutations. We show that oDNA heteroplasmy and bottlenecks naturally emerge in evolutionary simulations subjected to fluctuating environments, demonstrating that this evolvability is itself evolvable. Usually thought of as a mechanism to clear damaging mutations, organelle bottlenecks therefore also resolve the tension between intracellular selection for pure cellular oDNA populations and the "bet-hedging" need for evolvability and adaptation to new environments. This general theory suggests a reason for the maintenance of organelle heteroplasmy in cells, and may explain some of the observed diversity in organelle maintenance and inheritance across taxa.

L’impact des mutations neutres sur l’évolvabilité et l’évolution des génomes

Les mutations bénéfiques à forts effets sont rares et les mutations délétères sont éliminées par la sélection naturelle. La majorité des mutations qui s’accumulent dans les génomes ont donc des effets sélectifs très faibles, voire nuls ; elles sont alors appelées mutations neutres. Au cours des deux dernières décennies, il a été montré que les mutations, même en l’absence d’effet sur la valeur sélective des organismes, affectent leur évolvabilité, en donnant accès à de nouveaux phénotypes par le biais de mutations apparaissant ultérieurement, et qui n’auraient pas été disponibles autrement. En plus de cet effet, de nombreuses mutations neutres – indépendamment de leurs effets sélectifs – peuvent affecter la mutabilité de séquences d’ADN voisines, et moduler l’efficacité de la recombinaison homologue. De telles mutations ne modifient pas le spectre des phénotypes accessibles, mais plutôt la vitesse à laquelle de nouveaux phénotypes seront produits, un processus qui a des conséquences à long terme mais aussi potentiellement à court terme, en lien avec l’émergence de cancers.

A Trait-Based Approach to Predicting Viral Host-Range Evolvability

Predicting the evolution of virus host range has proven to be extremely difficult, in part because of the sheer diversity of viruses, each with unique biology and ecological interactions. We have not solved this problem, but to make the problem more tractable, we narrowed our focus to three traits intrinsic to all viruses that may play a role in host-range evolvability: mutation rate, recombination rate, and phenotypic heterogeneity. Although each trait should increase evolvability, they cannot do so unbounded because fitness trade-offs limit the ability of all three traits to maximize evolvability. By examining these constraints, we can begin to identify groups of viruses with suites of traits that make them especially concerning, as well as ecological and environmental conditions that might push evolution toward accelerating host-range expansion.

The structure of genotype-phenotype maps makes fitness landscapes navigable

Fitness landscapes are often described in terms of 'peaks' and 'valleys', indicating an intuitive low-dimensional landscape of the kind encountered in everyday experience. The space of genotypes, however, is extremely high dimensional, which results in counter-intuitive structural properties of genotype-phenotype maps. Here we show that these properties, such as the presence of pervasive neutral networks, make fitness landscapes navigable. For three biologically realistic genotype-phenotype map models-RNA secondary structure, protein tertiary structure and protein complexes-we find that, even under random fitness assignment, fitness maxima can be reached from almost any other phenotype without passing through fitness valleys. This in turn indicates that true fitness valleys are very rare. By considering evolutionary simulations between pairs of real examples of functional RNA sequences, we show that accessible paths are also likely to be used under evolutionary dynamics. Our findings have broad implications for the prediction of natural evolutionary outcomes and for directed evolution.

Orthology-based analysis helps map evolutionary diversification and predict substrate class use of BAHD acyltransferases

Large enzyme families catalyze metabolic diversification by virtue of their ability to use diverse chemical scaffolds. How enzyme families attain such functional diversity is not clear. Furthermore, duplication and promiscuity in such enzyme families limits their functional prediction, which has produced a burgeoning set of incompletely annotated genes in plant genomes. Here, we address these challenges using BAHD acyltransferases as a model. This fast-evolving family expanded drastically in land plants, increasing from one to five copies in algae to approximately 100 copies in diploid angiosperm genomes. Compilation of >160 published activities helped visualize the chemical space occupied by this family and define eight different classes based on structural similarities between acceptor substrates. Using orthologous groups (OGs) across 52 sequenced plant genomes, we developed a method to predict BAHD acceptor substrate class utilization as well as origins of individual BAHD OGs in plant evolution. This method was validated using six novel and 28 previously characterized enzymes and helped improve putative substrate class predictions for BAHDs in the tomato genome. Our results also revealed that while cuticular wax and lignin biosynthetic activities were more ancient, anthocyanin acylation activity was fixed in BAHDs later near the origin of angiosperms. The OG-based analysis enabled identification of signature motifs in anthocyanin-acylating BAHDs, whose importance was validated via molecular dynamic simulations, site-directed mutagenesis and kinetic assays. Our results not only describe how BAHDs contributed to evolution of multiple chemical phenotypes in the plant world but also propose a biocuration-enabled approach for improved functional annotation of plant enzyme families.

Beyond genotype-phenotype maps: Toward a phenotype-centered perspective on evolution

Evolutionary biology is paying increasing attention to the mechanisms that enable phenotypic plasticity, evolvability, and extra-genetic inheritance. Yet, there is a concern that these phenomena remain insufficiently integrated within evolutionary theory. Understanding their evolutionary implications would require focusing on phenotypes and their variation, but this does not always fit well with the prevalent genetic representation of evolution that screens off developmental mechanisms. Here, we instead use development as a starting point, and represent it in a way that allows genetic, environmental and epigenetic sources of phenotypic variation to be independent. We show why this representation helps to understand the evolutionary consequences of both genetic and non-genetic phenotype determinants, and discuss how this approach can instigate future areas of empirical and theoretical research.

Fast free-energy-based neutral set size estimates for the RNA genotype-phenotype map

The genotype-phenotype (GP) map of RNA secondary structure links each RNA sequence to its corresponding secondary structure. Previous research has shown that the large-scale structural properties of GP maps, such as the size of neutral sets in genotype space, can influence evolutionary outcomes. In order to use neutral set sizes, efficient and accurate computational methods are needed to compute them. Here, we propose a new method, which is based on free energy estimates and is much faster than existing sample-based methods. Moreover, this approach can give insight into the reasons behind neutral set size variations, for example, why structures with fewer stacks tend to have larger neutral set sizes. In addition, we generalize neutral set size calculations from the previously studied many-to-one framework, where each sequence folds into a single energetically preferred structure, to a fuller many-to-many framework, where several low-energy structures are included. We find that structures with high neutral sets in one framework also tend to have large neutral sets in the other framework for a range of parameters and thus the choice of GP map does not fundamentally affect which structures have the largest neutral set sizes.

The historical nature of biological complexity and the ineffectiveness of the mathematical approach to it

Contemporary scientific knowledge is built on both methodological and epistemological reductionism. The discovery of the limitations of the reductionist paradigm in the mathematical treatment of certain physical phenomena originated the notion of complexity, both as a pattern and process. After clarifying some very general terms and ideas on biological evolution and biological complexity, the article will tackle to seek to summarize the debate on biological complexity and discuss the difference between complexities of living and inert matter. Some examples of the major successes of mathematics applied to biological problems will follow; the notion of an intrinsic limitation in the application of mathematics to biological complexity as a global, relational, and historical phenomenon at the individual and species level will also be advanced.

Elucidating multi-input processing 3-node gene regulatory network topologies capable of generating striped gene expression patterns

A central problem in developmental and synthetic biology is understanding the mechanisms by which cells in a tissue or a Petri dish process external cues and transform such information into a coherent response, e.g., a terminal differentiation state. It was long believed that this type of positional information could be entirely attributed to a gradient of concentration of a specific signaling molecule (i.e., a morphogen). However, advances in experimental methodologies and computer modeling have demonstrated the crucial role of the dynamics of a cell’s gene regulatory network (GRN) in decoding the information carried by the morphogen, which is eventually translated into a spatial pattern. This morphogen interpretation mechanism has gained much attention in systems biology as a tractable system to investigate the emergent properties of complex genotype-phenotype maps. In this study, we apply a Markov chain Monte Carlo (MCMC)-like algorithm to probe the design space of three-node GRNs with the ability to generate a band-like expression pattern (target phenotype) in the middle of an arrangement of 30 cells, which resemble a simple (1-D) morphogenetic field in a developing embryo. Unlike most modeling studies published so far, here we explore the space of GRN topologies with nodes having the potential to perceive the same input signal differently. This allows for a lot more flexibility during the search space process, and thus enables us to identify a larger set of potentially interesting and realizable morphogen interpretation mechanisms. Out of 2061 GRNs selected using the search space algorithm, we found 714 classes of network topologies that could correctly interpret the morphogen. Notably, the main network motif that generated the target phenotype in response to the input signal was the type 3 Incoherent Feed-Forward Loop (I3-FFL), which agrees with previous theoretical expectations and experimental observations. Particularly, compared to a previously reported pattern forming GRN topologies, we have uncovered a great variety of novel network designs, some of which might be worth inquiring through synthetic biology methodologies to test for the ability of network design with minimal regulatory complexity to interpret a developmental cue robustly.

Systems biology is a fast growing field largely powered by advances in high-performance computing and sophisticated mathematical modeling of biological systems. Based on these advances, we are now in a position to mechanistically understand and accurately predict the behavior of complex biological processes, including cell differentiation and spatial pattern formation during embryogenesis. In this article, we use an in silico approach to probe the design space of multi-input, three-node Gene Regulatory Networks (GRNs) capable of generating a striped gene expression pattern in the context of a simplified 1-D morphogenetic field.

Heterogeneity of the GFP fitness landscape and data-driven protein design

Studies of protein fitness landscapes reveal biophysical constraints guiding protein evolution and empower prediction of functional proteins. However, generalisation of these findings is limited due to scarceness of systematic data on fitness landscapes of proteins with a defined evolutionary relationship. We characterized the fitness peaks of four orthologous fluorescent proteins with a broad range of sequence divergence. While two of the four studied fitness peaks were sharp, the other two were considerably flatter, being almost entirely free of epistatic interactions. Mutationally robust proteins, characterized by a flat fitness peak, were not optimal templates for machine-learning-driven protein design - instead, predictions were more accurate for fragile proteins with epistatic landscapes. Our work paves insights for practical application of fitness landscape heterogeneity in protein engineering.

A computational exploration of resilience and evolvability of protein-protein interaction networks

Protein-protein interaction (PPI) networks represent complex intra-cellular protein interactions, and the presence or absence of such interactions can lead to biological changes in an organism. Recent network-based approaches have shown that a phenotype's PPI network's resilience to environmental perturbations is related to its placement in the tree of life; though we still do not know how or why certain intra-cellular factors can bring about this resilience. Here, we explore the influence of gene expression and network properties on PPI networks' resilience. We use publicly available data of PPIs for E. coli, S. cerevisiae, and H. sapiens, where we compute changes in network resilience as new nodes (proteins) are added to the networks under three node addition mechanisms-random, degree-based, and gene-expression-based attachments. By calculating the resilience of the resulting networks, we estimate the effectiveness of these node addition mechanisms. We demonstrate that adding nodes with gene-expression-based preferential attachment (as opposed to random or degree-based) preserves and can increase the original resilience of PPI network in all three species, regardless of gene expression distribution or network structure. These findings introduce a general notion of prospective resilience, which highlights the key role of network structures in understanding the evolvability of phenotypic traits.

A small, computationally flexible network produces the phenotypic diversity of song recognition in crickets

How neural networks evolved to generate the diversity of species-specific communication signals is unknown. For receivers of the signals, one hypothesis is that novel recognition phenotypes arise from parameter variation in computationally flexible feature detection networks. We test this hypothesis in crickets, where males generate and females recognize the mating songs with a species-specific pulse pattern, by investigating whether the song recognition network in the cricket brain has the computational flexibility to recognize different temporal features. Using electrophysiological recordings from the network that recognizes crucial properties of the pulse pattern on the short timescale in the cricket Gryllus bimaculatus, we built a computational model that reproduces the neuronal and behavioral tuning of that species. An analysis of the model's parameter space reveals that the network can provide all recognition phenotypes for pulse duration and pause known in crickets and even other insects. Phenotypic diversity in the model is consistent with known preference types in crickets and other insects, and arises from computations that likely evolved to increase energy efficiency and robustness of pattern recognition. The model's parameter to phenotype mapping is degenerate - different network parameters can create similar changes in the phenotype - which likely supports evolutionary plasticity. Our study suggests that computationally flexible networks underlie the diverse pattern recognition phenotypes, and we reveal network properties that constrain and support behavioral diversity.

Insertions and deletions in the RNA sequence-structure map

Genotype-phenotype maps link genetic changes to their fitness effect and are thus an essential component of evolutionary models. The map between RNA sequences and their secondary structures is a key example and has applications in functional RNA evolution. For this map, the structural effect of substitutions is well understood, but models usually assume a constant sequence length and do not consider insertions or deletions. Here, we expand the sequence-structure map to include single nucleotide insertions and deletions by using the RNAshapes concept. To quantify the structural effect of insertions and deletions, we generalize existing definitions for robustness and non-neutral mutation probabilities. We find striking similarities between substitutions, deletions and insertions: robustness to substitutions is correlated with robustness to insertions and, for most structures, to deletions. In addition, frequent structural changes after substitutions also tend to be common for insertions and deletions. This is consistent with the connection between energetically suboptimal folds and possible structural transitions. The similarities observed hold both for genotypic and phenotypic robustness and mutation probabilities, i.e. for individual sequences and for averages over sequences with the same structure. Our results could have implications for the rate of neutral and non-neutral evolution.

Heightened among-individual variation in life history but not morphology is related to developmental temperature in reptiles

Increases in phenotypic variation under extreme (e.g. novel or stressful) environmental conditions are emerging as a crucial process through which evolutionary adaptation can occur. Lack of prior stabilizing selection, as well as potential instability of developmental processes in these environments, may lead to a release of phenotypic variation that can have important evolutionary consequences. Although such patterns have been shown in model study organisms, we know little about the generality of trait variance across environments for non-model organisms. Here, we test whether extreme developmental temperatures increase the phenotypic variation across diverse reptile taxa. We find that the among-individual variation in a key life-history trait (post-hatching growth) increases at extreme cold and hot temperatures. However, variations in two measures of hatchling morphology and in hatchling performance were not related to developmental temperature. Although extreme developmental temperatures may increase the variation in growth, our results suggest that plastic responses to stressful incubation conditions do not generally make more extreme phenotypes available to selection. We discuss the reasons for the general lack of increased variability at extreme incubation temperatures and the implications this has for local adaptation in hatchling morphology and physiology.

Studying evolution of the primary body axis in vivo and in vitro

The metazoan body plan is established during early embryogenesis via collective cell rearrangements and evolutionarily conserved gene networks, as part of a process commonly referred to as gastrulation. While substantial progress has been achieved in terms of characterizing the embryonic development of several model organisms, underlying principles of many early patterning processes nevertheless remain enigmatic. Despite the diversity of (pre-)gastrulating embryo and adult body shapes across the animal kingdom, the body axes, which are arguably the most fundamental features, generally remain identical between phyla. Recently there has been a renewed appreciation of ex vivo and in vitro embryo-like systems to model early embryonic patterning events. Here, we briefly review key examples and propose that similarities in morphogenesis and associated gene expression dynamics may reveal an evolutionarily conserved developmental mode as well as provide further insights into the role of external or extraembryonic cues in shaping the early embryo. In summary, we argue that embryo-like systems can be employed to inform previously uncharted aspects of animal body plan evolution as well as associated patterning rules.