Mechanistic Explanations for Restricted Evolutionary Paths That Emerge from Gene Regulatory Networks

The extent and the nature of the constraints to evolutionary trajectories are central issues in biology. Constraints can be the result of systems dynamics causing a non-linear mapping between genotype and phenotype. How prevalent are these developmental constraints and what is their mechanistic basis? Although this has been extensively explored at the level of epistatic interactions between nucleotides within a gene, or amino acids within a protein, selection acts at the level of the whole organism, and therefore epistasis between disparate genes in the genome is expected due to their functional interactions within gene regulatory networks (GRNs) which are responsible for many aspects of organismal phenotype. Here we explore epistasis within GRNs capable of performing a common developmental function – converting a continuous morphogen input into discrete spatial domains. By exploring the full complement of GRN wiring designs that are able to perform this function, we analyzed all possible mutational routes between functional GRNs. Through this study we demonstrate that mechanistic constraints are common for GRNs that perform even a simple function. We demonstrate a common mechanistic cause for such a constraint involving complementation between counter-balanced gene-gene interactions. Furthermore we show how such constraints can be bypassed by means of “permissive” mutations that buffer changes in a direct route between two GRN topologies that would normally be unviable. We show that such bypasses are common and thus we suggest that unlike what was observed in protein sequence-function relationships, the “tape of life” is less reproducible when one considers higher levels of biological organization.     

Mutation Rules and the Evolution of Sparseness and Modularity in Biological Systems

Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity – the near decomposability of the system into modules with distinct functionality. Recent work suggests that modularity can evolve in a variety of circumstances, including goals that vary in time such that they share the same subgoals (modularly varying goals), or when connections are costly. Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than on connection cost or variations in the goal. We use simulations of evolution with different mutation rules. We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations. In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers – a better model for the effects of biological mutations – led to sparseness naturally. When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they tend to reduce interactions, and to keep small interaction terms small.     

Pruning and model-selecting algorithms in the RBF frameworks constructed by support vector learning

This paper presents the pruning and model-selecting algorithms to the support vector learning for sample classification and function regression. When constructing RBF network by support vector learning we occasionally obtain redundant support vectors which do not significantly affect the final classification and function approximation results. The pruning algorithms primarily based on the sensitivity measure and the penalty term. The kernel function parameters and the position of each support vector are updated in order to have minimal increase in error, and this makes the structure of SVM network more flexible. We illustrate this approach with synthetic data simulation and face detection problem in order to demonstrate the pruning effectiveness.     

Positive aspects of negative design: simultaneous selection of specificity and interaction stability

The energetic determinants that drive specific protein-protein interactions are not entirely understood. We describe simultaneous in vivo selection of specific and stable interactions using homologous peptides which compete with protein libraries for an interaction with a target molecule. Library members binding to their target, and promoting cell growth, must outcompete competitor interactions with the target (i.e., competition) and evade binding to the competitors (i.e., negative design). We term this a competitive and negative design initiative (CANDI). We combined CANDI with a protein-fragment complementation assay (PCA) and observed major specificity improvements, by driving selection of winning library members that bind their target with maximum efficacy, ensuring that otherwise energetically accessible alternatives are inaccessible. CANDI-PCA has been used with libraries targeted at coiled coil regions of oncogenic AP-1 components cJun and cFos. We demonstrate that comparable hydrophobic and electrostatic contributions in desired species are compromised in nondesired species when CANDI is executed, demonstrating that both core and electrostatic residues are required to direct specific interactions. Major energetic differences (>or=5.6 kcal/mol) are observed between desired and nondesired interaction stabilities for a CANDI-PCA derived peptide relative to a conventional PCA derived helix, with significantly more stability (3.2 kcal/mol) than the wild-type cJun-cFos complex. As a negative control, a library lacking a residue repertoire able to generate a specific and stable helix was tested. Negative protein design has broad implications in generating specific and therapeutically relevant peptide-based drugs, proteins able to act with minimal cross-talk to homologues or analogues, and in nanobiotechnological design.     

Stochasticity Versus Determinism: Consequences for Realistic Gene Regulatory Network Modelling and Evolution

Gene regulation is one important mechanism in producing observed phenotypes and heterogeneity. Consequently, the study of gene regulatory network (GRN) architecture, function and evolution now forms a major part of modern biology. However, it is impossible to experimentally observe the evolution of GRNs on the timescales on which living species evolve. In silico evolution provides an approach to studying the long-term evolution of GRNs, but many models have either considered network architecture from non-adaptive evolution, or evolution to non-biological objectives. Here, we address a number of important modelling and biological questions about the evolution of GRNs to the realistic goal of biomass production. Can different commonly used simulation paradigms, in particular deterministic and stochastic Boolean networks, with and without basal gene expression, be used to compare adaptive with non-adaptive evolution of GRNs? Are these paradigms together with this goal sufficient to generate a range of solutions? Will the interaction between a biological goal and evolutionary dynamics produce trade-offs between growth and mutational robustness? We show that stochastic basal gene expression forces shrinkage of genomes due to energetic constraints and is a prerequisite for some solutions. In systems that are able to evolve rates of basal expression, two optima, one with and one without basal expression, are observed. Simulation paradigms without basal expression generate bloated networks with non-functional elements. Further, a range of functional solutions was observed under identical conditions only in stochastic networks. Moreover, there are trade-offs between efficiency and yield, indicating an inherent intertwining of fitness and evolutionary dynamics.     

Evolution of Gene Regulatory Networks by Fluctuating Selection and Intrinsic Constraints

Various characteristics of complex gene regulatory networks (GRNs) have been discovered during the last decade, e.g., redundancy, exponential indegree distributions, scale-free outdegree distributions, mutational robustness, and evolvability. Although progress has been made in this field, it is not well understood whether these characteristics are the direct products of selection or those of other evolutionary forces such as mutational biases and biophysical constraints. To elucidate the causal factors that promoted the evolution of complex GRNs, we examined the effect of fluctuating environmental selection and some intrinsic constraining factors on GRN evolution by using an individual-based model. We found that the evolution of complex GRNs is remarkably promoted by fixation of beneficial gene duplications under unpredictably fluctuating environmental conditions and that some internal factors inherent in organisms, such as mutational bias, gene expression costs, and constraints on expression dynamics, are also important for the evolution of GRNs. The results indicate that various biological properties observed in GRNs could evolve as a result of not only adaptation to unpredictable environmental changes but also non-adaptive processes owing to the properties of the organisms themselves. Our study emphasizes that evolutionary models considering such intrinsic constraining factors should be used as null models to analyze the effect of selection on GRN evolution.     

Seed‐dispersal interactions in fragmented landscapes – a metanetwork approach

Mutualistic interactions repeatedly preserved across fragmented landscapes can scale‐up to form a spatial metanetwork describing the distribution of interactions across patches. We explored the structure of a bird seed‐dispersal (BSD) metanetwork in 16 Neotropical forest fragments to test whether a distinct subset of BSD‐interactions may mediate landscape functional connectivity. The metanetwork is interaction‐rich, modular and poorly connected, showing high beta‐diversity and turnover of species and interactions. Interactions involving large‐sized species were lost in fragments < 10 000 ha, indicating a strong filtering by habitat fragmentation on the functional diversity of BSD‐interactions. Persistent interactions were performed by small‐seeded, fast growing plant species and by generalist, small‐bodied bird species able to cross the fragmented landscape. This reduced subset of interactions forms the metanetwork components persisting to defaunation and fragmentation, and may generate long‐term deficits of carbon storage while delaying forest regeneration at the landscape level.     

Networks of Causal Linkage Between Eigenmodes Characterize Behavioral Dynamics of Caenorhabditis elegans

Behavioral phenotyping of model organisms has played an important role in unravelling the complexities of animal behavior. Techniques for classifying behavior often rely on easily identified changes in posture and motion. However, such approaches are likely to miss complex behaviors that cannot be readily distinguished by eye (e.g., behaviors produced by high dimensional dynamics). To explore this issue, we focus on the model organism Caenorhabditis elegans, where behaviors have been extensively recorded and classified. Using a dynamical systems lens, we identify high dimensional, nonlinear causal relationships between four basic shapes that describe worm motion (eigenmodes, also called “eigenworms”). We find relationships between all pairs of eigenmodes, but the timescales of the interactions vary between pairs and across individuals. Using these varying timescales, we create “interaction profiles” to represent an individual’s behavioral dynamics. As desired, these profiles are able to distinguish well-known behavioral states: i.e., the profiles for foraging individuals are distinct from those of individuals exhibiting an escape response. More importantly, we find that interaction profiles can distinguish high dimensional behaviors among divergent mutant strains that were previously classified as phenotypically similar. Specifically, we find it is able to detect phenotypic behavioral differences not previously identified in strains related to dysfunction of hermaphrodite-specific neurons.     

Positive epistasis between co-infecting plasmids promotes plasmid survival in bacterial populations

Plasmids have a key role in the horizontal transfer of genes among bacteria. Although plasmids are catalysts for bacterial evolution, it is challenging to understand how they can persist in bacterial populations over the long term because of the burden they impose on their hosts (the ‘plasmid paradox''). This paradox is especially perplexing in the case of ‘small'' plasmids, which are unable to self-transfer by conjugation. Here, for the first time, we investigate how interactions between co-infecting plasmids influence plasmid persistence. Using an experimental model system based on interactions between a diverse assemblage of ‘large'' plasmids and a single small plasmid, pNI105, in the pathogenic bacterium Pseudomonas aeruginosa, we demonstrate that positive epistasis minimizes the cost associated with carrying multiple plasmids over the short term and increases the stability of the small plasmid over a longer time scale. In support of these experimental data, bioinformatic analysis showed that associations between small and large plasmids are more common than would be expected owing to chance alone across a range of families of bacteria; more generally, we find that co-infection with multiple plasmids is more common than would be expected owing to chance across a wide range of bacterial phyla. Collectively, these results suggest that positive epistasis promotes plasmid stability in bacterial populations. These findings pave the way for future mechanistic studies aimed at elucidating the molecular mechanisms of plasmid–plasmid interaction, and evolutionary studies aimed at understanding how the coevolution of plasmids drives the spread of plasmid-encoded traits.     

Evolution and spatial structure interact to influence plant–herbivore population and community dynamics

An individual-based model of plant–herbivore interactions was developed to test the potentially interactive effects of explicit space and coevolution on population and community dynamics. Individual plants and herbivores resided in cells on a lattice and carried linked interaction genes. Interaction strength between individual plants and herbivores depended on concordance between these genes (gene-for-gene coevolution). Mating and dispersal among individuals were controlled spatially within variably sized neighbourhoods. Without evolution we observed high-frequency plant–herbivore oscillations (blue spectra) with small individual neighbourhoods, and stochastic fluctuations (white spectra) with large neighbourhoods. Evolution resulted in decreased interaction strength, decreased herbivore-induced plant mortality, increased population sizes, and longer-term fluctuations (reddened spectra). Small herbivore neighbourhoods led to herbivore extinction only with evolution. To explore the increased population size response to evolution we ran simulations without evolution while tuning plant–herbivore interaction strength from high to none. We found that herbivore populations were maximized at intermediate levels of interaction strength that coincided with the interaction strength achieved when the system tuned itself through evolution. Overall, our model shows that the small-scale details of phenotypically variable individual-level interactions, leading to evolutionary dynamics, affect large-scale population and community dynamics.     

The Modular Organization of Domain Structures: Insights into Protein–Protein Binding

Domains are the building blocks of proteins and play a crucial role in protein–protein interactions. Here, we propose a new approach for the analysis and prediction of domain–domain interfaces. Our method, which relies on the representation of domains as residue-interacting networks, finds an optimal decomposition of domain structures into modules. The resulting modules comprise highly cooperative residues, which exhibit few connections with other modules. We found that non-overlapping binding sites in a domain, involved in different domain–domain interactions, are generally contained in different modules. This observation indicates that our modular decomposition is able to separate protein domains into regions with specialized functions. Our results show that modules with high modularity values identify binding site regions, demonstrating the predictive character of modularity. Furthermore, the combination of modularity with other characteristics, such as sequence conservation or surface patches, was found to improve our predictions. In an attempt to give a physical interpretation to the modular architecture of domains, we analyzed in detail six examples of protein domains with available experimental binding data. The modular configuration of the TEM1-β-lactamase binding site illustrates the energetic independence of hotspots located in different modules and the cooperativity of those sited within the same modules. The energetic and structural cooperativity between intramodular residues is also clearly shown in the example of the chymotrypsin inhibitor, where non–binding site residues have a synergistic effect on binding. Interestingly, the binding site of the T cell receptor β chain variable domain 2.1 is contained in one module, which includes structurally distant hot regions displaying positive cooperativity. These findings support the idea that modules possess certain functional and energetic independence. A modular organization of binding sites confers robustness and flexibility to the performance of the functional activity, and facilitates the evolution of protein interactions.     

Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties

In this paper, the design problem of state estimator for genetic regulatory networks with time delays and randomly occurring uncertainties has been addressed by a delay decomposition approach. The norm-bounded uncertainties enter into the genetic regulatory networks (GRNs) in random ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the uncertain GRNs. Delay-dependent stability criteria are obtained in terms of linear matrix inequalities by constructing a Lyapunov–Krasovskii functional and using some inequality techniques (LMIs). Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs. Finally, a numerical example is provided to demonstrate the feasibility of the proposed estimation schemes.     

Modular prophage interactions driven by capsule serotype select for capsule loss under phage predation

Klebsiella species are able to colonize a wide range of environments and include worrisome nosocomial pathogens. Here, we sought to determine the abundance and infectivity of prophages of Klebsiella to understand how the interactions between induced prophages and bacteria affect population dynamics and evolution. We identified many prophages in the species, placing these taxa among the top 5% of the most polylysogenic bacteria. We selected 35 representative strains of the Klebsiella pneumoniae species complex to establish a network of induced phage–bacteria interactions. This revealed that many prophages are able to enter the lytic cycle, and subsequently kill or lysogenize closely related Klebsiella strains. Although 60% of the tested strains could produce phages that infect at least one other strain, the interaction network of all pairwise cross-infections is very sparse and mostly organized in modules corresponding to the strains’ capsule serotypes. Accordingly, capsule mutants remain uninfected showing that the capsule is a key factor for successful infections. Surprisingly, experiments in which bacteria are predated by their own prophages result in accelerated loss of the capsule. Our results show that phage infectiousness defines interaction modules between small subsets of phages and bacteria in function of capsule serotype. This limits the role of prophages as competitive weapons because they can infect very few strains of the species complex. This should also restrict phage-driven gene flow across the species. Finally, the accelerated loss of the capsule in bacteria being predated by their own phages, suggests that phages drive serotype switch in nature.Subject terms: Bacteriophages, Microbial ecology, Environmental microbiology     

Architecture of basic building blocks in protein and domain structural interaction networks

MOTIVATION: The structural interaction of proteins and their domains in networks is one of the most basic molecular mechanisms for biological cells. Topological analysis of such networks can provide an understanding of and solutions for predicting properties of proteins and their evolution in terms of domains. A single paradigm for the analysis of interactions at different layers, such as domain and protein layers, is needed. RESULTS: Applying a colored vertex graph model, we integrated two basic interaction layers under a unified model: (1) structural domains and (2) their protein/complex networks. We identified four basic and distinct elements in the model that explains protein interactions at the domain level. We searched for motifs in the networks to detect their topological characteristics using a pruning strategy and a hash table for rapid detection. We obtained the following results: first, compared with a random distribution, a substantial part of the protein interactions could be explained by domain-level structural interaction information. Second, there were distinct kinds of protein interaction patterns classified by specific and distinguishable numbers of domains. The intermolecular domain interaction was the most dominant protein interaction pattern. Third, despite the coverage of the protein interaction information differing among species, the similarity of their networks indicated shared architectures of protein interaction network in living organisms. Remarkably, there were only a few basic architectures in the model (>10 for a 4-node network topology), and we propose that most biological combinations of domains into proteins and complexes can be explained by a small number of key topological motifs. CONTACT: doheon@kaist.ac.kr.     

Linear Motif-Mediated Interactions Have Contributed to the Evolution of Modularity in Complex Protein Interaction Networks

The modular architecture of protein-protein interaction (PPI) networks is evident in diverse species with a wide range of complexity. However, the molecular components that lead to the evolution of modularity in PPI networks have not been clearly identified. Here, we show that weak domain-linear motif interactions (DLIs) are more likely to connect different biological modules than strong domain-domain interactions (DDIs). This molecular division of labor is essential for the evolution of modularity in the complex PPI networks of diverse eukaryotic species. In particular, DLIs may compensate for the reduction in module boundaries that originate from increased connections between different modules in complex PPI networks. In addition, we show that the identification of biological modules can be greatly improved by including molecular characteristics of protein interactions. Our findings suggest that transient interactions have played a unique role in shaping the architecture and modularity of biological networks over the course of evolution.     

GeNESiS: gene network evolution simulation software

Background  

There has been a lot of interest in recent years focusing on the modeling and simulation of Gene Regulatory Networks (GRNs). However, the evolutionary mechanisms that give rise to GRNs in the first place are still largely unknown. In an earlier work, we developed a framework to analyze the effect of objective functions, input types and starting populations on the evolution of GRNs with a specific emphasis on the robustness of evolved GRNs.