Robustness can evolve gradually in complex regulatory gene networks with varying topology

Historical contingency and the gradual evolution of metabolic properties in central carbon and genome-scale metabolisms

BACKGROUND

A metabolism can evolve through changes in its biochemical reactions that are caused by processes such as horizontal gene transfer and gene deletion. While such changes need to preserve an organism's viability in its environment, they can modify other important properties, such as a metabolism's maximal biomass synthesis rate and its robustness to genetic and environmental change. Whether such properties can be modulated in evolution depends on whether all or most viable metabolisms - those that can synthesize all essential biomass precursors - are connected in a space of all possible metabolisms. Connectedness means that any two viable metabolisms can be converted into one another through a sequence of single reaction changes that leave viability intact. If the set of viable metabolisms is disconnected and highly fragmented, then historical contingency becomes important and restricts the alteration of metabolic properties, as well as the number of novel metabolic phenotypes accessible in evolution.

RESULTS

We here computationally explore two vast spaces of possible metabolisms to ask whether viable metabolisms are connected. We find that for all but the simplest metabolisms, most viable metabolisms can be transformed into one another by single viability-preserving reaction changes. Where this is not the case, alternative essential metabolic pathways consisting of multiple reactions are responsible, but such pathways are not common.

CONCLUSIONS

Metabolism is thus highly evolvable, in the sense that its properties could be fine-tuned by successively altering individual reactions. Historical contingency does not strongly restrict the origin of novel metabolic phenotypes.

A tractable genotype-phenotype map modelling the self-assembly of protein quaternary structure

The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype–phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.

Analysis of gene network robustness based on saturated fixed point attractors

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.

Epigenetics decouples mutational from environmental robustness. Did it also facilitate multicellularity?

The evolution of ever increasing complex life forms has required innovations at the molecular level in order to overcome existing barriers. For example, evolving processes for cell differentiation, such as epigenetic mechanisms, facilitated the transition to multicellularity. At the same time, studies using gene regulatory network models, and corroborated in single-celled model organisms, have shown that mutational robustness and environmental robustness are correlated. Such correlation may constitute a barrier to the evolution of multicellularity since cell differentiation requires sensitivity to cues in the internal environment during development. To investigate how this barrier might be overcome, we used a gene regulatory network model which includes epigenetic control based on the mechanism of histone modification via Polycomb Group Proteins, which evolved in tandem with the transition to multicellularity. Incorporating the Polycomb mechanism allowed decoupling of mutational and environmental robustness, thus allowing the system to be simultaneously robust to mutations while increasing sensitivity to the environment. In turn, this decoupling facilitated cell differentiation which we tested by evaluating the capacity of the system for producing novel output states in response to altered initial conditions. In the absence of the Polycomb mechanism, the system was frequently incapable of adding new states, whereas with the Polycomb mechanism successful addition of new states was nearly certain. The Polycomb mechanism, which dynamically reshapes the network structure during development as a function of expression dynamics, decouples mutational and environmental robustness, thus providing a necessary step in the evolution of multicellularity.

Robustness, evolvability, and the logic of genetic regulation

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

Trans-acting small interfering RNA4: key to nutraceutical synthesis in grape development?

The facility and versatility of microRNAs (miRNAs) to evolve and change likely underlies how they have become dominant constituents of eukaryotic genomes. In this opinion article I propose that trans-acting small interfering RNA gene 4 (TAS4) evolution may be important for biosynthesis of polyphenolics, arbuscular symbiosis, and bacterial pathogen etiologies. Expression-based and phylogenetic evidence shows that TAS4 targets two novel grape (Vitis vinifera L.) MYB transcription factors (VvMYBA6, VvMYBA7) that spawn phased small interfering RNAs (siRNAs) which probably function in nutraceutical bioflavonoid biosynthesis and fruit development. Characterization of the molecular mechanisms of TAS4 control of plant development and integration into biotic and abiotic stress- and nutrient-signaling regulatory networks has applicability to molecular breeding and the development of strategies for engineering healthier foods.

A computational pipeline for identifying kinetic motifs to aid in the design and improvement of synthetic gene circuits

BACKGROUND

An increasing number of genetic components are available in several depositories of such components to facilitate synthetic biology research, but picking out those that will allow a designed circuit to achieve the specified function still requires multiple cycles of testing. Here, we addressed this problem by developing a computational pipeline to mathematically simulate a gene circuit for a comprehensive range and combination of the kinetic parameters of the biological components that constitute the gene circuit.

RESULTS

We showed that, using a well-studied transcriptional repression cascade as an example, the sets of kinetic parameters that could produce the specified system dynamics of the gene circuit formed clusters of recurrent combinations, referred to as kinetic motifs, which appear to be associated with both the specific topology and specified dynamics of the circuit. Furthermore, the use of the resulting "handbook" of performance-ranked kinetic motifs in finding suitable circuit components was illustrated in two application scenarios.

CONCLUSIONS

These results show that the computational pipeline developed here can provide a rational-based guide to aid in the design and improvement of synthetic gene circuits.

The relationship between modularity and robustness in signalling networks

Many biological networks tend to have a high modularity structural property and the dynamic characteristic of high robustness against perturbations. However, the relationship between modularity and robustness is not well understood. To investigate this relationship, we examined real signalling networks and conducted simulations using a random Boolean network model. As a result, we first observed that the network robustness is negatively correlated with the network modularity. In particular, this negative correlation becomes more apparent as the network density becomes sparser. Even more interesting is that, the negative relationship between the network robustness and the network modularity occurs mainly because nodes in the same module with the perturbed node tend to be more sensitive to the perturbation than those in other modules. This result implies that dynamically similar nodes tend to be located in the same module of a network. To support this, we show that a pair of genes associated with the same disease or a pair of functionally similar genes is likely to belong to the same module in a human signalling network.

Topology of molecular interaction networks

Molecular interactions are often represented as network models which have become the common language of many areas of biology. Graphs serve as convenient mathematical representations of network models and have themselves become objects of study. Their topology has been intensively researched over the last decade after evidence was found that they share underlying design principles with many other types of networks.Initial studies suggested that molecular interaction network topology is related to biological function and evolution. However, further whole-network analyses did not lead to a unified view on what this relation may look like, with conclusions highly dependent on the type of molecular interactions considered and the metrics used to study them. It is unclear whether global network topology drives function, as suggested by some researchers, or whether it is simply a byproduct of evolution or even an artefact of representing complex molecular interaction networks as graphs.Nevertheless, network biology has progressed significantly over the last years. We review the literature, focusing on two major developments. First, realizing that molecular interaction networks can be naturally decomposed into subsystems (such as modules and pathways), topology is increasingly studied locally rather than globally. Second, there is a move from a descriptive approach to a predictive one: rather than correlating biological network topology to generic properties such as robustness, it is used to predict specific functions or phenotypes.Taken together, this change in focus from globally descriptive to locally predictive points to new avenues of research. In particular, multi-scale approaches are developments promising to drive the study of molecular interaction networks further.

The influence of assortativity on the robustness and evolvability of gene regulatory networks upon gene birth

Gene regulatory networks (GRNs) represent the interactions between genes and gene products, which drive the gene expression patterns that produce cellular phenotypes. GRNs display a number of characteristics that are beneficial for the development and evolution of organisms. For example, they are often robust to genetic perturbation, such as mutations in regulatory regions or loss of gene function. Simultaneously, GRNs are often evolvable as these genetic perturbations are occasionally exploited to innovate novel regulatory programs. Several topological properties, such as degree distribution, are known to influence the robustness and evolvability of GRNs. Assortativity, which measures the propensity of nodes of similar connectivity to connect to one another, is a separate topological property that has recently been shown to influence the robustness of GRNs to point mutations in cis-regulatory regions. However, it remains to be seen how assortativity may influence the robustness and evolvability of GRNs to other forms of genetic perturbation, such as gene birth via duplication or de novo origination. Here, we employ a computational model of genetic regulation to investigate whether the assortativity of a GRN influences its robustness and evolvability upon gene birth. We find that the robustness of a GRN generally increases with increasing assortativity, while its evolvability generally decreases. However, the rate of change in robustness outpaces that of evolvability, resulting in an increased proportion of assortative GRNs that are simultaneously robust and evolvable. By providing a mechanistic explanation for these observations, this work extends our understanding of how the assortativity of a GRN influences its robustness and evolvability upon gene birth.

Constraint and contingency in multifunctional gene regulatory circuits

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

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

Using evolutionary computations to understand the design and evolution of gene and cell regulatory networks

This paper surveys modeling approaches for studying the evolution of gene regulatory networks (GRNs). Modeling of the design or 'wiring' of GRNs has become increasingly common in developmental and medical biology, as a means of quantifying gene-gene interactions, the response to perturbations, and the overall dynamic motifs of networks. Drawing from developments in GRN 'design' modeling, a number of groups are now using simulations to study how GRNs evolve, both for comparative genomics and to uncover general principles of evolutionary processes. Such work can generally be termed evolution in silico. Complementary to these biologically-focused approaches, a now well-established field of computer science is Evolutionary Computations (ECs), in which highly efficient optimization techniques are inspired from evolutionary principles. In surveying biological simulation approaches, we discuss the considerations that must be taken with respect to: (a) the precision and completeness of the data (e.g. are the simulations for very close matches to anatomical data, or are they for more general exploration of evolutionary principles); (b) the level of detail to model (we proceed from 'coarse-grained' evolution of simple gene-gene interactions to 'fine-grained' evolution at the DNA sequence level); (c) to what degree is it important to include the genome's cellular context; and (d) the efficiency of computation. With respect to the latter, we argue that developments in computer science EC offer the means to perform more complete simulation searches, and will lead to more comprehensive biological predictions.

Genetic and environmental factors affecting cryptic variations in gene regulatory networks

BACKGROUND

Cryptic genetic variation (CGV) is considered to facilitate phenotypic evolution by producing visible variations in response to changes in the internal and/or external environment. Several mechanisms enabling the accumulation and release of CGVs have been proposed. In this study, we focused on gene regulatory networks (GRNs) as an important mechanism for producing CGVs, and examined how interactions between GRNs and the environment influence the number of CGVs by using individual-based simulations.

RESULTS

Populations of GRNs were allowed to evolve under various stabilizing selections, and we then measured the number of genetic and phenotypic variations that had arisen. Our results showed that CGVs were not depleted irrespective of the strength of the stabilizing selection for each phenotype, whereas the visible fraction of genetic variation in a population decreased with increasing strength of selection. On the other hand, increasing the number of different environments that individuals encountered within their lifetime (i.e., entailing plastic responses to multiple environments) suppressed the accumulation of CGVs, whereas the GRNs with more genes and interactions were favored in such heterogeneous environments.

CONCLUSIONS

Given the findings that the number of CGVs in a population was largely determined by the size (order) of GRNs, we propose that expansion of GRNs and adaptation to novel environments are mutually facilitating and sustainable sources of evolvability and hence the origins of biological diversity and complexity.

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.

Female mating preferences determine system-level evolution in a gene network model

Environmental patterns of directional, stabilizing and fluctuating selection can influence the evolution of system-level properties like evolvability and mutational robustness. Intersexual selection produces strong phenotypic selection and these dynamics may also affect the response to mutation and the potential for future adaptation. In order to to assess the influence of mating preferences on these evolutionary properties, I modeled a male trait and female preference determined by separate gene regulatory networks. I studied three sexual selection scenarios: sexual conflict, a Gaussian model of the Fisher process described in Lande (in Proc Natl Acad Sci 78(6):3721-3725, 1981) and a good genes model in which the male trait signalled his mutational condition. I measured the effects these mating preferences had on the potential for traits and preferences to evolve towards new states, and mutational robustness of both the phenotype and the individual's overall viability. All types of sexual selection increased male phenotypic robustness relative to a randomly mating population. The Fisher model also reduced male evolvability and mutational robustness for viability. Under good genes sexual selection, males evolved an increased mutational robustness for viability. Females choosing their mates is a scenario that is sufficient to create selective forces that impact genetic evolution and shape the evolutionary response to mutation and environmental selection. These dynamics will inevitably develop in any population where sexual selection is operating, and affect the potential for future adaptation.

Visualizing time-related data in biology, a review

Time is of the essence in biology as in so much else. For example, monitoring disease progression or the timing of developmental defects is important for the processes of drug discovery and therapy trials. Furthermore, an understanding of the basic dynamics of biological phenomena that are often strictly time regulated (e.g. circadian rhythms) is needed to make accurate inferences about the evolution of biological processes. Recent advances in technologies have enabled us to measure timing effects more accurately and in more detail. This has driven related advances in visualization and analysis tools that try to effectively exploit this data. Beyond timeline plots, notable attempts at more involved temporal interpretation have been made in recent years, but awareness of the available resources is still limited within the scientific community. Here, we review some advances in biological visualization of time-driven processes and consider how they aid data analysis and interpretation.

In silico evolution of gene cooption in pattern-forming gene networks

Gene recruitment or cooption occurs when a gene, which may be part of an existing gene regulatory network (GRN), comes under the control of a new regulatory system. Such re-arrangement of pre-existing networks is likely more common for increasing genomic complexity than the creation of new genes. Using evolutionary computations (EC), we investigate how cooption affects the evolvability, outgrowth and robustness of GRNs. We use a data-driven model of insect segmentation, for the fruit fly Drosophila, and evaluate fitness by robustness to maternal variability—a major constraint in biological development. We compare two mechanisms of gene cooption: a simpler one with gene Introduction and Withdrawal operators; and one in which GRN elements can be altered by transposon infection. Starting from a minimal 2-gene network, insufficient for fitting the Drosophila gene expression patterns, we find a general trend of coopting available genes into the GRN, in order to better fit the data. With the transposon mechanism, we find co-evolutionary oscillations between genes and their transposons. These oscillations may offer a new technique in EC for overcoming premature convergence. Finally, we comment on how a differential equations (in contrast to Boolean) approach is necessary for addressing realistic continuous variation in biochemical parameters.

Environmental noise, genetic diversity and the evolution of evolvability and robustness in model gene networks

The ability of organisms to adapt and persist in the face of environmental change is accepted as a fundamental feature of natural systems. More contentious is whether the capacity of organisms to adapt (or “evolvability”) can itself evolve and the mechanisms underlying such responses. Using model gene networks, I provide evidence that evolvability emerges more readily when populations experience positively autocorrelated environmental noise (red noise) compared to populations in stable or randomly varying (white noise) environments. Evolvability was correlated with increasing genetic robustness to effects on network viability and decreasing robustness to effects on phenotypic expression; populations whose networks displayed greater viability robustness and lower phenotypic robustness produced more additive genetic variation and adapted more rapidly in novel environments. Patterns of selection for robustness varied antagonistically with epistatic effects of mutations on viability and phenotypic expression, suggesting that trade-offs between these properties may constrain their evolutionary responses. Evolution of evolvability and robustness was stronger in sexual populations compared to asexual populations indicating that enhanced genetic variation under fluctuating selection combined with recombination load is a primary driver of the emergence of evolvability. These results provide insight into the mechanisms potentially underlying rapid adaptation as well as the environmental conditions that drive the evolution of genetic interactions.

Simulated evolution of signal transduction networks

Signal transduction is the process of routing information inside cells when receiving stimuli from their environment that modulate the behavior and function. In such biological processes, the receptors, after receiving the corresponding signals, activate a number of biomolecules which eventually transduce the signal to the nucleus. The main objective of our work is to develop a theoretical approach which will help to better understand the behavior of signal transduction networks due to changes in kinetic parameters and network topology. By using an evolutionary algorithm, we designed a mathematical model which performs basic signaling tasks similar to the signaling process of living cells. We use a simple dynamical model of signaling networks of interacting proteins and their complexes. We study the evolution of signaling networks described by mass-action kinetics. The fitness of the networks is determined by the number of signals detected out of a series of signals with varying strength. The mutations include changes in the reaction rate and network topology. We found that stronger interactions and addition of new nodes lead to improved evolved responses. The strength of the signal does not play any role in determining the response type. This model will help to understand the dynamic behavior of the proteins involved in signaling pathways. It will also help to understand the robustness of the kinetics of the output response upon changes in the rate of reactions and the topology of the network.

On the contributions of topological features to transcriptional regulatory network robustness

BACKGROUND

Because biological networks exhibit a high-degree of robustness, a systemic understanding of their architecture and function requires an appraisal of the network design principles that confer robustness. In this project, we conduct a computational study of the contribution of three degree-based topological properties (transcription factor-target ratio, degree distribution, cross-talk suppression) and their combinations on the robustness of transcriptional regulatory networks. We seek to quantify the relative degree of robustness conferred by each property (and combination) and also to determine the extent to which these properties alone can explain the robustness observed in transcriptional networks.

RESULTS

To study individual properties and their combinations, we generated synthetic, random networks that retained one or more of the three properties with values derived from either the yeast or E. coli gene regulatory networks. Robustness of these networks were estimated through simulation. Our results indicate that the combination of the three properties we considered explains the majority of the structural robustness observed in the real transcriptional networks. Surprisingly, scale-free degree distribution is, overall, a minor contributor to robustness. Instead, most robustness is gained through topological features that limit the complexity of the overall network and increase the transcription factor subnetwork sparsity.

CONCLUSIONS

Our work demonstrates that (i) different types of robustness are implemented by different topological aspects of the network and (ii) size and sparsity of the transcription factor subnetwork play an important role for robustness induction. Our results are conserved across yeast and E Coli, which suggests that the design principles examined are present within an array of living systems.

Functional analysis of metabolic channeling and regulation in lignin biosynthesis: a computational approach

Lignin is a polymer in secondary cell walls of plants that is known to have negative impacts on forage digestibility, pulping efficiency, and sugar release from cellulosic biomass. While targeted modifications of different lignin biosynthetic enzymes have permitted the generation of transgenic plants with desirable traits, such as improved digestibility or reduced recalcitrance to saccharification, some of the engineered plants exhibit monomer compositions that are clearly at odds with the expected outcomes when the biosynthetic pathway is perturbed. In Medicago, such discrepancies were partly reconciled by the recent finding that certain biosynthetic enzymes may be spatially organized into two independent channels for the synthesis of guaiacyl (G) and syringyl (S) lignin monomers. Nevertheless, the mechanistic details, as well as the biological function of these interactions, remain unclear. To decipher the working principles of this and similar control mechanisms, we propose and employ here a novel computational approach that permits an expedient and exhaustive assessment of hundreds of minimal designs that could arise in vivo. Interestingly, this comparative analysis not only helps distinguish two most parsimonious mechanisms of crosstalk between the two channels by formulating a targeted and readily testable hypothesis, but also suggests that the G lignin-specific channel is more important for proper functioning than the S lignin-specific channel. While the proposed strategy of analysis in this article is tightly focused on lignin synthesis, it is likely to be of similar utility in extracting unbiased information in a variety of situations, where the spatial organization of molecular components is critical for coordinating the flow of cellular information, and where initially various control designs seem equally valid.

The inheritance of process: a dynamical systems approach

A central unresolved problem of evolutionary biology concerns the way in which evolution at the genotypic level relates to the evolution of phenotypes. This genotype-phenotype map involves developmental and physiological processes, which are complex and not well understood. These processes co-determine the rate and direction of adaptive change by shaping the distribution of phenotypic variability on which selection can act. In this study, we argue-expanding on earlier ideas by Goodwin, Oster, and Alberch-that an explicit treatment of this map in terms of dynamical systems theory can provide an integrated understanding of evolution and development. We describe a conceptual framework, which demonstrates how development determines the probability of possible phenotypic transitions-and hence the evolvability of a biological system. We use a simple conceptual model to illustrate how the regulatory dynamics of the genotype-phenotype map can be passed on from generation to generation, and how heredity itself can be treated as a dynamic process. Our model yields explanations for punctuated evolutionary dynamics, the difference between micro- and macroevolution, and for the role of the environment in major phenotypic transitions. We propose a quantitative research program in evolutionary developmental systems biology-combining experimental methods with mathematical modeling-which aims at elaborating our conceptual framework by applying it to a wide range of evolving developmental systems. This requires a large and sustained effort, which we believe is justified by the significant potential benefits of an extended evolutionary theory that uses dynamic molecular genetic data to reintegrate development and evolution.

Criticality is an emergent property of genetic networks that exhibit evolvability

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.

Dynamically critical systems are those which operate at the border of a phase transition between two behavioral regimes often present in complex systems: order and disorder. Critical systems exhibit remarkable properties such as fast information processing, collective response to perturbations or the ability to integrate a wide range of external stimuli without saturation. Recent evidence indicates that the genetic networks of living cells are dynamically critical. This has far reaching consequences, for it is at criticality that living organisms can tolerate a wide range of external fluctuations without changing the functionality of their phenotypes. Therefore, it is necessary to know how genetic criticality emerged through evolution. Here we show that dynamical criticality naturally emerges from the delicate balance between two fundamental forces of natural selection that make organisms evolve: (i) the existing phenotypes must be resilient to random mutations, and (ii) new phenotypes must emerge for the organisms to adapt to new environmental challenges. The joint effect of these two forces, which are essential for evolvability, is sufficient in our computational models to generate populations of genetic networks operating at criticality. Thus, natural selection acting as a tinkerer of evolvable systems naturally generates critical dynamics.

Design constraints on a synthetic metabolism

A metabolism is a complex network of chemical reactions that converts sources of energy and chemical elements into biomass and other molecules. To design a metabolism from scratch and to implement it in a synthetic genome is almost within technological reach. Ideally, a synthetic metabolism should be able to synthesize a desired spectrum of molecules at a high rate, from multiple different nutrients, while using few chemical reactions, and producing little or no waste. Not all of these properties are achievable simultaneously. We here use a recently developed technique to create random metabolic networks with pre-specified properties to quantify trade-offs between these and other properties. We find that for every additional molecule to be synthesized a network needs on average three additional reactions. For every additional carbon source to be utilized, it needs on average two additional reactions. Networks able to synthesize 20 biomass molecules from each of 20 alternative sole carbon sources need to have at least 260 reactions. This number increases to 518 reactions for networks that can synthesize more than 60 molecules from each of 80 carbon sources. The maximally achievable rate of biosynthesis decreases by approximately 5 percent for every additional molecule to be synthesized. Biochemically related molecules can be synthesized at higher rates, because their synthesis produces less waste. Overall, the variables we study can explain 87 percent of variation in network size and 84 percent of the variation in synthesis rate. The constraints we identify prescribe broad boundary conditions that can help to guide synthetic metabolism design.

Limitations of gene duplication models: evolution of modules in protein interaction networks

It has been generally acknowledged that the module structure of protein interaction networks plays a crucial role with respect to the functional understanding of these networks. In this paper, we study evolutionary aspects of the module structure of protein interaction networks, which forms a mesoscopic level of description with respect to the architectural principles of networks. The purpose of this paper is to investigate limitations of well known gene duplication models by showing that these models are lacking crucial structural features present in protein interaction networks on a mesoscopic scale. This observation reveals our incomplete understanding of the structural evolution of protein networks on the module level.

Most networks in Wagner's model are cycling

In this paper we study a model of gene networks introduced by Andreas Wagner in the 1990s that has been used extensively to study the evolution of mutational robustness. We investigate a range of model features and parameters and evaluate the extent to which they influence the probability that a random gene network will produce a fixed point steady state expression pattern. There are many different types of models used in the literature, (discrete/continuous, sparse/dense, small/large network) and we attempt to put some order into this diversity, motivated by the fact that many properties are qualitatively the same in all the models. Our main result is that random networks in all models give rise to cyclic behavior more often than fixed points. And although periodic orbits seem to dominate network dynamics, they are usually considered unstable and not allowed to survive in previous evolutionary studies. Defining stability as the probability of fixed points, we show that the stability distribution of these networks is highly robust to changes in its parameters. We also find sparser networks to be more stable, which may help to explain why they seem to be favored by evolution. We have unified several disconnected previous studies of this class of models under the framework of stability, in a way that had not been systematically explored before.

The influence of assortativity on the robustness of signal-integration logic in gene regulatory networks

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

Mutational robustness of gene regulatory networks

Mutational robustness of gene regulatory networks refers to their ability to generate constant biological output upon mutations that change network structure. Such networks contain regulatory interactions (transcription factor – target gene interactions) but often also protein-protein interactions between transcription factors. Using computational modeling, we study factors that influence robustness and we infer several network properties governing it. These include the type of mutation, i.e. whether a regulatory interaction or a protein-protein interaction is mutated, and in the case of mutation of a regulatory interaction, the sign of the interaction (activating vs. repressive). In addition, we analyze the effect of combinations of mutations and we compare networks containing monomeric with those containing dimeric transcription factors. Our results are consistent with available data on biological networks, for example based on evolutionary conservation of network features. As a novel and remarkable property, we predict that networks are more robust against mutations in monomer than in dimer transcription factors, a prediction for which analysis of conservation of DNA binding residues in monomeric vs. dimeric transcription factors provides indirect evidence.

Virtual genomes in flux: an interplay of neutrality and adaptability explains genome expansion and streamlining

The picture that emerges from phylogenetic gene content reconstructions is that genomes evolve in a dynamic pattern of rapid expansion and gradual streamlining. Ancestral organisms have been estimated to possess remarkably rich gene complements, although gene loss is a driving force in subsequent lineage adaptation and diversification. Here, we study genome dynamics in a model of virtual cells evolving to maintain homeostasis. We observe a pattern of an initial rapid expansion of the genome and a prolonged phase of mutational load reduction. Generally, load reduction is achieved by the deletion of redundant genes, generating a streamlining pattern. Load reduction can also occur as a result of the generation of highly neutral genomic regions. These regions can expand and contract in a neutral fashion. Our study suggests that genome expansion and streamlining are generic patterns of evolving systems. We propose that the complex genotype to phenotype mapping in virtual cells as well as in their biological counterparts drives genome size dynamics, due to an emerging interplay between adaptation, neutrality, and evolvability.

The role of robustness in phenotypic adaptation and innovation

Phenotypes that vary in response to DNA mutations are essential for evolutionary adaptation and innovation. Therefore, it seems that robustness, a lack of phenotypic variability, must hinder adaptation. The main purpose of this review is to show why this is not necessarily correct. There are two reasons. The first is that robustness causes the existence of genotype networks--large connected sets of genotypes with the same phenotype. I discuss why genotype networks facilitate phenotypic variability. The second reason emerges from the evolutionary dynamics of evolving populations on genotype networks. I discuss how these dynamics can render highly robust phenotypes more variable, using examples from protein and RNA macromolecules. In addition, robustness can help avoid an important evolutionary conflict between the interests of individuals and populations-a conflict that can impede evolutionary adaptation.

Evolutionary systems biology: historical and philosophical perspectives on an emerging synthesis

Systems biology (SB) is at least a decade old now and maturing rapidly. A more recent field, evolutionary systems biology (ESB), is in the process of further developing system-level approaches through the expansion of their explanatory and potentially predictive scope. This chapter will outline the varieties of ESB existing today by tracing the diverse roots and fusions that make up this integrative project. My approach is philosophical and historical. As well as examining the recent origins of ESB, I will reflect on its central features and the different clusters of research it comprises. In its broadest interpretation, ESB consists of five overlapping approaches: comparative and correlational ESB; network architecture ESB; network property ESB; population genetics ESB; and finally, standard evolutionary questions answered with SB methods. After outlining each approach with examples, I will examine some strong general claims about ESB, particularly that it can be viewed as the next step toward a fuller modern synthesis of evolutionary biology (EB), and that it is also the way forward for evolutionary and systems medicine. I will conclude with a discussion of whether the emerging field of ESB has the capacity to combine an even broader scope of research aims and efforts than it presently does.

Phenotypic plasticity and robustness: evolutionary stability theory, gene expression dynamics model, and laboratory experiments

Plasticity and robustness, which are two basic concepts in the evolution of developmental dynamics, are characterized in terms of the variance of phenotype distribution. Plasticity concerns the response of a phenotype against environmental and genetic changes, whereas robustness is the degree of insensitivity against such changes. Note that the sensitivity increases with the variance, and the inverse of the variance works as a measure of the robustness. First, it is found that the response ratio is proportional to the phenotype variance, as described by extending the fluctuation-response relationship in statistical physics. Next, it is shown that through the course of robust evolution, the phenotype variance caused by genetic change decreases in proportion to that by noise during the developmental process. This evolution, resulting in increased robustness, is achieved only when the noise in the developmental process is sufficiently large; in other words, robustness to noise leads to robustness to mutation. For a system that achieves robustness in the phenotype, it is also found that the proportionality between the two variances also holds across different phenotypic traits. These general relationships for plasticity and robustness in terms of fluctuations are demonstrated using macroscopic phenomenological theory, simulations of gene-expression dynamics models with regulation networks, and laboratory selection experiments. It is also shown that an optimal noise level compatibility between robustness and plasticity is achieved to cope with a fluctuating environment.

Life's attractors : understanding developmental systems through reverse engineering and in silico evolution

We propose an approach to evolutionary systems biology which is based on reverse engineering of gene regulatory networks and in silico evolutionary simulations. We infer regulatory parameters for gene networks by fitting computational models to quantitative expression data. This allows us to characterize the regulatory structure and dynamical repertoire of evolving gene regulatory networks with a reasonable amount of experimental and computational effort. We use the resulting network models to identify those regulatory interactions that are conserved, and those that have diverged between different species. Moreover, we use the models obtained by data fitting as starting points for simulations of evolutionary transitions between species. These simulations enable us to investigate whether such transitions are random, or whether they show stereotypical series of regulatory changes which depend on the structure and dynamical repertoire of an evolving network. Finally, we present a case study-the gap gene network in dipterans (flies, midges, and mosquitoes)-to illustrate the practical application of the proposed methodology, and to highlight the kind of biological insights that can be gained by this approach.

Gene regulatory network reconstruction using Bayesian networks, the Dantzig Selector, the Lasso and their meta-analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth "Dialogue for Reverse Engineering Assessments and Methods" (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on "Systems Genetics" proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the 16 teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics.

Model transcriptional networks with continuously varying expression levels

BACKGROUND

At a time when genomes are being sequenced by the hundreds, much attention has shifted from identifying genes and phenotypes to understanding the networks of interactions among genes. We developed a gene network developmental model expanding on previous models of transcription regulatory networks. In our model, each network is described by a matrix representing the interactions between transcription factors, and a vector of continuous values representing the transcription factor expression in an individual.

RESULTS

In this work we used the gene network model to look at the impact of mating as well as insertions and deletions of genes in the evolution of complexity of these networks. We found that the natural process of diploid mating increases the likelihood of maintaining complexity, especially in higher order networks (more than 10 genes). We also show that gene insertion is a very efficient way to add more genes to a network as it provides a much higher chance of developmental stability.

CONCLUSIONS

The continuous model affords a more complete view of the evolution of interacting genes. The notion of a continuous output vector also incorporates the reality of gene networks and graded concentrations of gene products.

Algorithms in nature: the convergence of systems biology and computational thinking

Biologists rely on computational methods to analyze and integrate large data sets, while several computational methods were inspired by the high-level design principles of biological systems. This Perspectives discusses the recent convergence of these two ways of thinking.

Computer science and biology have enjoyed a long and fruitful relationship for decades. Biologists rely on computational methods to analyze and integrate large data sets, while several computational methods were inspired by the high-level design principles of biological systems. Recently, these two directions have been converging. In this review, we argue that thinking computationally about biological processes may lead to more accurate models, which in turn can be used to improve the design of algorithms. We discuss the similar mechanisms and requirements shared by computational and biological processes and then present several recent studies that apply this joint analysis strategy to problems related to coordination, network analysis, and tracking and vision. We also discuss additional biological processes that can be studied in a similar manner and link them to potential computational problems. With the rapid accumulation of data detailing the inner workings of biological systems, we expect this direction of coupling biological and computational studies to greatly expand in the future.

Motifs emerge from function in model gene regulatory networks

Gene regulatory networks allow the control of gene expression patterns in living cells. The study of network topology has revealed that certain subgraphs of interactions or "motifs" appear at anomalously high frequencies. We ask here whether this phenomenon may emerge because of the functions carried out by these networks. Given a framework for describing regulatory interactions and dynamics, we consider in the space of all regulatory networks those that have prescribed functional capabilities. Markov Chain Monte Carlo sampling is then used to determine how these functional networks lead to specific motif statistics in the interactions. In the case where the regulatory networks are constrained to exhibit multistability, we find a high frequency of gene pairs that are mutually inhibitory and self-activating. In contrast, networks constrained to have periodic gene expression patterns (mimicking for instance the cell cycle) have a high frequency of bifan-like motifs involving four genes with at least one activating and one inhibitory interaction.

Conserved regulation of p53 network dosage by microRNA-125b occurs through evolving miRNA-target gene pairs

MicroRNAs regulate networks of genes to orchestrate cellular functions. MiR-125b, the vertebrate homologue of the Caenorhabditis elegans microRNA lin-4, has been implicated in the regulation of neural and hematopoietic stem cell homeostasis, analogous to how lin-4 regulates stem cells in C. elegans. Depending on the cell context, miR-125b has been proposed to regulate both apoptosis and proliferation. Because the p53 network is a central regulator of both apoptosis and proliferation, the dual roles of miR-125b raise the question of what genes in the p53 network might be regulated by miR-125b. By using a gain- and loss-of-function screen for miR-125b targets in humans, mice, and zebrafish and by validating these targets with the luciferase assay and a novel miRNA pull-down assay, we demonstrate that miR-125b directly represses 20 novel targets in the p53 network. These targets include both apoptosis regulators like Bak1, Igfbp3, Itch, Puma, Prkra, Tp53inp1, Tp53, Zac1, and also cell-cycle regulators like cyclin C, Cdc25c, Cdkn2c, Edn1, Ppp1ca, Sel1l, in the p53 network. We found that, although each miRNA-target pair was seldom conserved, miR-125b regulation of the p53 pathway is conserved at the network level. Our results lead us to propose that miR-125b buffers and fine-tunes p53 network activity by regulating the dose of both proliferative and apoptotic regulators, with implications for tissue stem cell homeostasis and oncogenesis.

The molecular origins of evolutionary innovations

The history of life is a history of evolutionary innovations, qualitatively new phenotypic traits that endow their bearers with new, often game-changing abilities. We know many individual examples of innovations and their natural history, but we know little about the fundamental principles of phenotypic variability that permit new phenotypes to arise. Most phenotypic innovations result from changes in three classes of systems: metabolic networks, regulatory circuits, and macromolecules. I here highlight two important features that these classes of systems share. The first is the ubiquity of vast genotype networks - connected sets of genotypes with the same phenotype. The second is the great phenotypic diversity of small neighborhoods around different genotypes in genotype space. I here explain that both features are essential for the phenotypic variability that can bring forth qualitatively new phenotypes. Both features emerge from a common cause, the robustness of phenotypes to perturbations, whose origins are linked to life in changing environments.

Environmental versatility promotes modularity in genome-scale metabolic networks

BACKGROUND

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new arrangements that may benefit their carrier. Conversely, modularity may emerge as a by-product of some trait. We here ask whether this last scenario may play a role in genome-scale metabolic networks that need to sustain life in one or more chemical environments. For such networks, we define a network module as a maximal set of reactions that are fully coupled, i.e., whose fluxes can only vary in fixed proportions. This definition overcomes limitations of purely graph based analyses of metabolism by exploiting the functional links between reactions. We call a metabolic network viable in a given chemical environment if it can synthesize all of an organism's biomass compounds from nutrients in this environment. An organism's metabolism is highly versatile if it can sustain life in many different chemical environments. We here ask whether versatility affects the modularity of metabolic networks.

RESULTS

Using recently developed techniques to randomly sample large numbers of viable metabolic networks from a vast space of metabolic networks, we use flux balance analysis to study in silico metabolic networks that differ in their versatility. We find that highly versatile networks are also highly modular. They contain more modules and more reactions that are organized into modules. Most or all reactions in a module are associated with the same biochemical pathways. Modules that arise in highly versatile networks generally involve reactions that process nutrients or closely related chemicals. We also observe that the metabolism of E. coli is significantly more modular than even our most versatile networks.

CONCLUSIONS

Our work shows that modularity in metabolic networks can be a by-product of functional constraints, e.g., the need to sustain life in multiple environments. This organizational principle is insensitive to the environments we consider and to the number of reactions in a metabolic network. Because we observe this principle not just in one or few biological networks, but in large random samples of networks, we propose that it may be a generic principle of metabolic network organization.

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.

Impact of selection on genes involved in regulatory network: a modelling study

Complex phenotypes are often controlled by many interacting genes. One question emerging from such organization is how selection, acting at the phenotypic level, shapes the evolution of genes involved in regulatory networks controlling the phenotypes. We studied this issue through a matrix model of such networks. In a population submitted to selection, we simulated the evolution of a quantitative trait controlled by a set of loci that regulate each other through positive or negative interactions. Investigating several levels of selection intensity on the trait, we studied the evolution of regulation intensity between the genes and the evolution of the genetic diversity of those genes as an indirect measure of the strength of selection acting on them. We show that an increasing intensity of selection on the phenotype leads to an increased level of regulation between the loci. Moreover, we found that the genes responding more strongly to selection within the network were those evolving towards stronger regulatory action on the other genes and/or those that are the less regulated by the other genes. This observation is strongest for an intermediate level of selection. This may explain why several experimental studies have shown evidence of selection on regulatory genes inside gene networks.