Dynamics of gene circuits shapes evolvability

To what extent does the dynamical mechanism producing a specific biological phenotype bias the ability to evolve into novel phenotypes? We use the interpretation of a morphogen gradient into a single stripe of gene expression as a model phenotype. Although there are thousands of three-gene circuit topologies that can robustly develop a stripe of gene expression, the vast majority of these circuits use one of just six fundamentally different dynamical mechanisms. Here we explore the potential for gene circuits that use each of these six mechanisms to evolve novel phenotypes such as multiple stripes, inverted stripes, and gradients of gene expression. Through a comprehensive and systematic analysis, we find that circuits that use alternative mechanisms differ in the likelihood of reaching novel phenotypes through mutation. We characterize the phenotypic transitions and identify key ingredients of the evolutionary potential, such as sensitive interactions and phenotypic hubs. Finally, we provide an intuitive understanding on how the modular design of a particular mechanism favors the access to novel phenotypes. Our work illustrates how the dynamical mechanism by which an organism develops constrains how it can evolve. It is striking that these dynamical mechanisms and their impact on evolvability can be observed even for such an apparently simple patterning task, performed by just three-node circuits.Evolution occurs through mutations on existing genotypes, potentially transforming the original phenotype or trait into a novel one, with latent beneficial consequences. It is a fundamental problem in biology to understand the relationship between a genotype and the associated phenotypes accessible through mutations, in other words, its evolvability. From the many definitions of evolvability (1, 2), we refer here to the ability of genotypes to access novel phenotypes, irrespective of the subsequent process of natural selection.To understand how a phenotype evolves we need to consider that a huge number of distinct genotypes can achieve that same phenotype. For example, hundreds of distinct RNA sequences fold in the same secondary structure (3), as do proteins in their 3D structure (4). Similarly, distinct gene regulatory architectures can produce the same gene expression pattern (5, 6) or temporal behavior (7, 8). However, among these genotypes, some are more evolvable than others. The existing studies have targeted two key drivers of evolvability: a genotype’s design and a genotype’s location within a neutral space.A first class of studies focuses on a circuit’s general architectural features, such as feed-back or feed-forward loops, revealing that these distinct families of designs or motifs differ in their evolvability (9, 10). The second class of studies centers not on single designs but on the whole collection of genotypes capable of producing the same phenotype. These genotypes with a common phenotype form a region in genotype space termed a neutral space or neutral network (3), as mutations within this region produce no change in the phenotype.As revealed by many studies, the existence of neutral spaces has two major consequences to the evolutionary process. First, these neutral spaces often appear as fully connected and dense regions (11–13). Therefore, although genotypes internal to the neutral space are highly robust to mutations (i.e., not evolvable), only genotypes close to the edges of the neutral space might access novel phenotypes. From this perspective, neutral mutations and thus the process of neutral drift can generate cryptic genetic variation (14) by moving a species closer to the edges of the neutral space into a more evolvable state (12, 15). Second, different positions in genotype space give access to distinct novel phenotypes. Large neutral spaces percolate through genotype space, providing access to a diversity of novel phenotypes from different genotypes (11–13). In a nutshell, the accessible innovations are critically determined by a genotype’s position in genotype space (16) (Fig. 1).Open in a separate windowFig. 1.Phenotype-based view on evolvability. (A) Evolvability accounts for the accessible novel phenotypes, whereas developmental constraints imply that certain hypothetical forms are not possible: phenotype 2 (purple) is not available by gradual mutation. (B) Innovations accessible from a given genotype constitute its phenotypic neighborhood. The arrangement and diversity of this neighborhood is a measure of the genotype’s evolvability (16). Genotype space is high dimensional, but we schematically represent it here in 2D for illustrative purposes.Although the abovementioned features of genotype-phenotype maps have been much studied, another important aspect of the system has thus far been neglected. None of the existing studies addressed the impact of the underlying dynamical mechanism of a gene circuit on its evolvability. By mechanism, we mean the causal dynamics responsible for the trajectory of the system (i.e., the spatiotemporal course of gene expression) resulting in the final phenotype. In addition to the increasing awareness that dynamics itself is a decisive property of gene circuits (17), several specific observations led us to hypothesize that dynamics does impact on evolvability.First, to achieve a given biological function, a gene circuit uses one of few fundamental solutions referred to as dynamical mechanisms (5–7, 18–20). More specifically, circuits with the same underlying dynamical mechanism share a common arrangement of phase portraits (20, 21). Second, Cotterell and Sharpe (6) revealed that, for a simple patterning function, it is not possible to smoothly and functionally transition from one mechanism to another. That is, in contrast to the common view (11–13), this particular neutral space does not form a single fully connected region when the underlying mechanism is taken into account. Instead, the neutral space for the simple patterning function studied by Cotterell and Sharpe (6) breaks up into scattered islands of genotypes characterized by distinct underlying mechanisms. These observations suggest that evolvability may be constrained specifically by the dynamical mechanism of the gene circuit. As neutral spaces can be broken up into a discrete collection of separated islands, the process of neutral drift may be limited to these mechanism-specific regions.To assess the impact of dynamical mechanisms, we chose to study circuits that control spatial (multicellular) gene expression patterns. It is well established in developmental biology that the spatial organization of gene expression orchestrates cell differentiation. Their diversification causes evolution of both modest morphological traits, such as novel pigmentation patterns (22), and major evolutionary breakthroughs, such as new body structures (23). Here we chose to address the interpretation of a morphogen gradient by a field of cells into different cell fates (5–7, 18, 24–27) (Fig. 2A), a critical patterning event in embryo’s morphogenesis (28). We build on the work of Cotterell and Sharpe (6), who extracted six fundamental mechanisms for this patterning task: Bistable, Incoherent feed-forward, Mutual Inhibition, Overlapping Domains, Classical, and Frozen Oscillator (Fig. 2B and SI Appendix, Fig. S1).Open in a separate windowFig. 2.Alternative mechanisms to achieve a single phenotype. (A) Within the French Flag conceptual framework, a preestablished fixed concentration gradient (input) is interpreted by a one-dimensional row of cells into different cell fates through a threshold-dependent mechanism. Additionally, cells communicate to one another through diffusive gene products (dashed arrows). We exhaustively enumerate all possible three-gene circuit topologies and sample large numbers of genotypes (i.e., parameter values; SI Appendix, Methods). Solutions of our search are genotypes able to interpret the morphogen gradient into a band of gene expression (6). Similar exhaustive approaches have being adopted for exploring a variety of biological functions, such as temporal behaviors (7, 25) or other spatial patterning functions (5, 18). (B) A stripe-forming circuit uses one of six distinct mechanisms (6), each mechanism uses a distinct gene expression dynamics in space and time to reach the same phenotype. Importantly, Mutual Inhibition (bicoid-hunchback-knirps), Incoherent feed-forward (caudal-knirps-giant), and Classical (hunchback-krüppel-knirps) are involved in Drosophila anterior-posterior patterning (26), whereas Incoherent feed-forward controls the mesoderm inducer Xenopus Brachyury (27).For the current study, we analyzed each of these six mechanisms independently and obtained a mechanism-specific measure of evolvability. We found that, indeed, the likelihood of accessing distinct phenotypic innovations is different for each dynamical mechanism, despite the fact that they all produce the same phenotype. Our analysis uncovers key features of the mechanistic neutral spaces and provides useful insight into how phenotypic transitions and thus innovations occur.