In silico evolution of functional modules in biochemical networks

Cesium: A public database of evolved oscillatory reaction networks

New tools and software in systems biology require testing and validation on reaction networks with desired characteristics such as number of reactions or oscillating behaviors. Often, there is only a modest number of published models that are suitable, so researchers must generate reaction networks with the desired characteristics, a process that can be computationally expensive. To reduce these computational costs, we developed a data base of synthetic reaction networks to facilitate reuse. The current database contains thousands of networks generated using directed evolution. The network are of two types: (1) those with oscillations in species concentrations and (2) those for which no oscillation was found using directed evolution. To facilitate access to networks of interest, the database is queryable by the number of species and reactants, the presence or absence of autocatalytic and degradation reactions, and the network behavior. Our analysis of the data revealed some interesting insights, such as the population of oscillating networks possess more autocatalytic reactions compared to random control networks. In the future, this database will be expanded to include other network behaviors.

Are There Biomimetic Lessons from Genetic Regulatory Networks for Developing a Lunar Industrial Ecology?

We examine the prospect for employing a bio-inspired architecture for a lunar industrial ecology based on genetic regulatory networks. The lunar industrial ecology resembles a metabolic system in that it comprises multiple chemical processes interlinked through waste recycling. Initially, we examine lessons from factory organisation which have evolved into a bio-inspired concept, the reconfigurable holonic architecture. We then examine genetic regulatory networks and their application in the biological cell cycle. There are numerous subtleties that would be challenging to implement in a lunar industrial ecology but much of the essence of biological circuitry (as implemented in synthetic biology, for example) is captured by traditional electrical engineering design with emphasis on feedforward and feedback loops to implement robustness.

Designing synthetic networks in silico: a generalised evolutionary algorithm approach

Background

Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes).

Results

The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction.

Conclusions

In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0499-9) contains supplementary material, which is available to authorized users.

Combining in silico evolution and nonlinear dimensionality reduction to redesign responses of signaling networks

The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.

Consistent scaling of population structure across landscapes despite intraspecific variation in movement and connectivity

Understanding the spatial scale of population structure is fundamental to long-standing tenets of population biology, landscape ecology and conservation. Nonetheless, identifying such scales has been challenging because a key factor that influences scaling - movement among patches or local populations - is a multicausal process with substantial phenotypic and temporal variation. We resolve this problem via a novel application of network modularity. When applied to movements, modularity provides a formal description of the functional aggregation of populations and identifies potentially critical scales for ecological and evolutionary dynamics. We first test for modularity using several different types of biologically relevant movements across the entire geographic range of an endangered bird, the snail kite (Rostrhamus sociabilis plumbeus). We then ask whether variation in movement based on (i) age, (ii) sex and (iii) time (annual, seasonal and within-season movements) influences spatial population structure (i.e. modularity) in snail kites. We identified significant modularity in annual dispersal of snail kites (all adults, males only, females only, and juveniles only) and in within-breeding season movements of adults, yet no evidence of modularity in seasonal (non-breeding) movements. For those movements with observed modular structure, we found striking similarities in the spatial configuration of population structure, even though movement properties varied considerably among these different types of movements. Our results suggest that the emergence of modularity in population networks can be robust despite movement heterogeneity and differences in patch-based measures of connectivity. Furthermore, our comparison of the population structure and connectivity across multiple movement phases helps to identify wetland patches most critical to population connectivity at multiple spatiotemporal scales. We argue that understanding modularity in populations may provide a robust complement to existing measures of population structure and connectivity and will help to clarify the limiting roles of movement for populations. Such information is increasingly needed for interpreting population persistence and guiding effective conservation strategies with ongoing environmental change.

Enzyme Sequestration as a Tuning Point in Controlling Response Dynamics of Signalling Networks

Signalling networks result from combinatorial interactions among many enzymes and scaffolding proteins. These complex systems generate response dynamics that are often essential for correct decision-making in cells. Uncovering biochemical design principles that underpin such response dynamics is a prerequisite to understand evolved signalling networks and to design synthetic ones. Here, we use in silico evolution to explore the possible biochemical design space for signalling networks displaying ultrasensitive and adaptive response dynamics. By running evolutionary simulations mimicking different biochemical scenarios, we find that enzyme sequestration emerges as a key mechanism for enabling such dynamics. Inspired by these findings, and to test the role of sequestration, we design a generic, minimalist model of a signalling cycle, featuring two enzymes and a single scaffolding protein. We show that this simple system is capable of displaying both ultrasensitive and adaptive response dynamics. Furthermore, we find that tuning the concentration or kinetics of the sequestering protein can shift system dynamics between these two response types. These empirical results suggest that enzyme sequestration through scaffolding proteins is exploited by evolution to generate diverse response dynamics in signalling networks and could provide an engineering point in synthetic biology applications.

Selection Shapes Transcriptional Logic and Regulatory Specialization in Genetic Networks

Background

Living organisms need to regulate their gene expression in response to environmental signals and internal cues. This is a computational task where genes act as logic gates that connect to form transcriptional networks, which are shaped at all scales by evolution. Large-scale mutations such as gene duplications and deletions add and remove network components, whereas smaller mutations alter the connections between them. Selection determines what mutations are accepted, but its importance for shaping the resulting networks has been debated.

Methodology

To investigate the effects of selection in the shaping of transcriptional networks, we derive transcriptional logic from a combinatorially powerful yet tractable model of the binding between DNA and transcription factors. By evolving the resulting networks based on their ability to function as either a simple decision system or a circadian clock, we obtain information on the regulation and logic rules encoded in functional transcriptional networks. Comparisons are made between networks evolved for different functions, as well as with structurally equivalent but non-functional (neutrally evolved) networks, and predictions are validated against the transcriptional network of E. coli.

Principal Findings

We find that the logic rules governing gene expression depend on the function performed by the network. Unlike the decision systems, the circadian clocks show strong cooperative binding and negative regulation, which achieves tight temporal control of gene expression. Furthermore, we find that transcription factors act preferentially as either activators or repressors, both when binding multiple sites for a single target gene and globally in the transcriptional networks. This separation into positive and negative regulators requires gene duplications, which highlights the interplay between mutation and selection in shaping the transcriptional networks.

BioJazz: in silico evolution of cellular networks with unbounded complexity using rule-based modeling

Systems biologists aim to decipher the structure and dynamics of signaling and regulatory networks underpinning cellular responses; synthetic biologists can use this insight to alter existing networks or engineer de novo ones. Both tasks will benefit from an understanding of which structural and dynamic features of networks can emerge from evolutionary processes, through which intermediary steps these arise, and whether they embody general design principles. As natural evolution at the level of network dynamics is difficult to study, in silico evolution of network models can provide important insights. However, current tools used for in silico evolution of network dynamics are limited to ad hoc computer simulations and models. Here we introduce BioJazz, an extendable, user-friendly tool for simulating the evolution of dynamic biochemical networks. Unlike previous tools for in silico evolution, BioJazz allows for the evolution of cellular networks with unbounded complexity by combining rule-based modeling with an encoding of networks that is akin to a genome. We show that BioJazz can be used to implement biologically realistic selective pressures and allows exploration of the space of network architectures and dynamics that implement prescribed physiological functions. BioJazz is provided as an open-source tool to facilitate its further development and use. Source code and user manuals are available at: http://oss-lab.github.io/biojazz and http://osslab.lifesci.warwick.ac.uk/BioJazz.aspx.

Evolving robust gene regulatory networks

Design and implementation of robust network modules is essential for construction of complex biological systems through hierarchical assembly of 'parts' and 'devices'. The robustness of gene regulatory networks (GRNs) is ascribed chiefly to the underlying topology. The automatic designing capability of GRN topology that can exhibit robust behavior can dramatically change the current practice in synthetic biology. A recent study shows that Darwinian evolution can gradually develop higher topological robustness. Subsequently, this work presents an evolutionary algorithm that simulates natural evolution in silico, for identifying network topologies that are robust to perturbations. We present a Monte Carlo based method for quantifying topological robustness and designed a fitness approximation approach for efficient calculation of topological robustness which is computationally very intensive. The proposed framework was verified using two classic GRN behaviors: oscillation and bistability, although the framework is generalized for evolving other types of responses. The algorithm identified robust GRN architectures which were verified using different analysis and comparison. Analysis of the results also shed light on the relationship among robustness, cooperativity and complexity. This study also shows that nature has already evolved very robust architectures for its crucial systems; hence simulation of this natural process can be very valuable for designing robust biological systems.

Elucidating the adaptation and temporal coordination of metabolic pathways using in-silico evolution

Cellular metabolism, the interconversion of small molecules by chemical reactions, is a tightly coordinated process that requires integration of diverse environmental and intracellular cues. While for many organisms the topology of the network of metabolic reactions is increasingly known, the regulatory principles that shape the network's adaptation to diverse and changing environments remain largely elusive. To investigate the principles of metabolic adaptation and regulation in metabolic pathways, we propose a computational approach based on in-silico evolution. Rather than analyzing existing regulatory schemes, we let a population of minimal, prototypical metabolic cells evolve rate constants and appropriate regulatory schemes that allow for optimal growth in static and fluctuating environments. Applying our approach to a small, but already sufficiently complex, minimal system reveals intricate transitions between metabolic modes. These results have implications for trade-offs in resource allocation. Going from static to varying environments, we show that for fluctuating nutrient availability, active metabolic regulation results in a significantly increased overall rate of metabolism.

Generation of oscillating gene regulatory network motifs

Using an improved version of an evolutionary algorithm originally proposed by François and Hakim [Proc. Natl. Acad. Sci. USA 101, 580 (2004)], we generated small gene regulatory networks in which the concentration of a target protein oscillates in time. These networks may serve as candidates for oscillatory modules to be found in larger regulatory networks and protein interaction networks. The algorithm was run for 10(5) times to produce a large set of oscillating modules, which were systematically classified and analyzed. The robustness of the oscillations against variations of the kinetic rates was also determined, to filter out the least robust cases. Furthermore, we show that the set of evolved networks can serve as a database of models whose behavior can be compared to experimentally observed oscillations. The algorithm found three smallest (core) oscillators in which nonlinearities and number of components are minimal. Two of those are two-gene modules: the mixed feedback loop, already discussed in the literature, and an autorepressed gene coupled with a heterodimer. The third one is a single gene module which is competitively regulated by a monomer and a dimer. The evolutionary algorithm also generated larger oscillating networks, which are in part extensions of the three core modules and in part genuinely new modules. The latter includes oscillators which do not rely on feedback induced by transcription factors, but are purely of post-transcriptional type. Analysis of post-transcriptional mechanisms of oscillation may provide useful information for circadian clock research, as recent experiments showed that circadian rhythms are maintained even in the absence of transcription.

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.

AutoBioCAD: full biodesign automation of genetic circuits

Synthetic regulatory networks with prescribed functions are engineered by assembling a reduced set of functional elements. We could also assemble them computationally if the mathematical models of those functional elements were predictive enough in different genetic contexts. Only after achieving this will we have libraries of models of biological parts able to provide predictive dynamical behaviors for most circuits constructed with them. We thus need tools that can automatically explore different genetic contexts, in addition to being able to use such libraries to design novel circuits with targeted dynamics. We have implemented a new tool, AutoBioCAD, aimed at the automated design of gene regulatory circuits. AutoBioCAD loads a library of models of genetic elements and implements evolutionary design strategies to produce (i) nucleotide sequences encoding circuits with targeted dynamics that can then be tested experimentally and (ii) circuit models for testing regulation principles in natural systems, providing a new tool for synthetic biology. AutoBioCAD can be used to model and design genetic circuits with dynamic behavior, thanks to the incorporation of stochastic effects, robustness, qualitative dynamics, multiobjective optimization, or degenerate nucleotide sequences, all facilitating the link with biological part/circuit engineering.

Modeling the evolution of gene regulatory networks for spatial patterning in embryo development

A central question in evolutionary biology concerns the transition between discrete numbers of units (e.g. vertebrate digits, arthropod segments). How do particular numbers of units, robust and characteristic for one species, evolve into another number for another species? Intermediate phases with a diversity of forms have long been theorized, but these leave little fossil or genomic data. We use evolutionary computations (EC) of a gene regulatory network (GRN) model to investigate how embryonic development is altered to create new forms. The trajectories are epochal and non-smooth, in accord with both the observed stability of species and the evolvability between forms.

Gene network requirements for regulation of metabolic gene expression to a desired state

Gene circuits that control metabolism should restore metabolic functions upon environmental changes. Whether gene networks are capable of steering metabolism to optimal states is an open question. Here we present a method to identify such optimal gene networks. We show that metabolic network optimisation over a range of environments results in an input-output relationship for the gene network that guarantees optimal metabolic states. Optimal control is possible if the gene network can achieve this input-output relationship. We illustrate our approach with the best-studied regulatory network in yeast, the galactose network. We find that over the entire range of external galactose concentrations, the regulatory network is able to optimally steer galactose metabolism. Only a few gene network parameters affect this optimal regulation. The other parameters can be tuned independently for optimisation of other functions, such as fast and low-noise gene expression. This study highlights gene network plasticity, evolvability, and modular functionality.

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.

Evolution of associative learning in chemical networks

Organisms that can learn about their environment and modify their behaviour appropriately during their lifetime are more likely to survive and reproduce than organisms that do not. While associative learning - the ability to detect correlated features of the environment - has been studied extensively in nervous systems, where the underlying mechanisms are reasonably well understood, mechanisms within single cells that could allow associative learning have received little attention. Here, using in silico evolution of chemical networks, we show that there exists a diversity of remarkably simple and plausible chemical solutions to the associative learning problem, the simplest of which uses only one core chemical reaction. We then asked to what extent a linear combination of chemical concentrations in the network could approximate the ideal Bayesian posterior of an environment given the stimulus history so far? This Bayesian analysis revealed the 'memory traces' of the chemical network. The implication of this paper is that there is little reason to believe that a lack of suitable phenotypic variation would prevent associative learning from evolving in cell signalling, metabolic, gene regulatory, or a mixture of these networks in cells.

Perspectives on the automatic design of regulatory systems for synthetic biology

Automatic design is based on computational modeling and optimization methods to provide prototype designs to targeted problems in an unsupervised manner. For biological circuits, we need to produce quantitative predictions of cell behavior for a given genotype as consequence of the different molecular interactions. Automatic design techniques aim at solving the inverse problem of finding the sequences of nucleotides that better fit a targeted behavior. In the post-genomic era, our molecular knowledge and modeling capabilities have allowed to start using such methodologies with success. Herein, we describe how the emergence of this new type of tools could enable novel synthetic biology applications. We highlight the essential elements to develop automatic design procedures for synthetic biology pointing out their advantages and bottlenecks. We discuss in detail the experimental difficulties to overcome in the in vivo implementation of designed networks. The use of automatic design to engineer biological networks is starting to emerge as a new technique to perform synthetic biology, which should not be neglected in the future.

In silico implementation of synthetic gene networks

Computational synthetic biology has borrowed methods, concepts, and techniques from systems biology and electrical engineering. Features of tools for the analysis of biochemical networks and the design of electric circuits have been combined to develop new software, where Standard Biological Parts (physically stored at the MIT Registry) have a mathematical description, based on mass action or Hill kinetics, and can be assembled into genetic networks in a visual, "drag & drop" fashion. Recent tools provide the user with databases, simulation environments, formal languages, and even algorithms for circuit automatic design to refine and speed up gene network construction. Moreover, advances in automation of DNA assembly indicate that synthetic biology software soon will drive the wet-lab implementation of DNA sequences.

Computational design of synthetic regulatory networks from a genetic library to characterize the designability of dynamical behaviors

The engineering of synthetic gene networks has mostly relied on the assembly of few characterized regulatory elements using rational design principles. It is of outmost importance to analyze the scalability and limits of such a design workflow. To analyze the design capabilities of libraries of regulatory elements, we have developed the first automated design approach that combines such elements to search the genotype space associated to a given phenotypic behavior. Herein, we calculated the designability of dynamical functions obtained from circuits assembled with a given genetic library. By designing circuits working as amplitude filters, pulse counters and oscillators, we could infer new mechanisms for such behaviors. We also highlighted the hierarchical design and the optimization of the interface between devices. We dissected the functional diversity of a constrained library and we found that even such libraries can provide a rich variety of behaviors. We also found that intrinsic noise slightly reduces the designability of digital circuits, but it increases the designability of oscillators. Finally, we analyzed the robust design as a strategy to counteract the evolvability and noise in gene expression of the engineered circuits within a cellular background, obtaining mechanisms for robustness through non-linear negative feedback loops.

Evolutionary computation for the design of a stochastic switch for synthetic genetic circuits

Biological systems are inherently stochastic, a fact which is often ignored when simulating genetic circuits. Synthetic biology aims to design genetic circuits de novo, and cannot therefore afford to ignore the effects of stochastic behavior. Since computational design tools will be essential for large-scale synthetic biology, it is important to develop an understanding of the role of stochasticity in molecular biology, and incorporate this understanding into computational tools for genetic circuit design. We report upon an investigation into the combination of evolutionary algorithms and stochastic simulation for genetic circuit design, to design regulatory systems based on the Bacillus subtilis sin operon.

The contributions of interlocking loops and extensive nonlinearity to the properties of circadian clock models

BACKGROUND

Sensitivity and robustness are essential properties of circadian clock systems, enabling them to respond to the environment but resist noisy variations. These properties should be recapitulated in computational models of the circadian clock. Highly nonlinear kinetics and multiple loops are often incorporated into models to match experimental time-series data, but these also impact on model properties for clock models.

METHODOLOGY/PRINCIPAL FINDINGS

Here, we study the consequences of complicated structure and nonlinearity using simple Goodwin-type oscillators and the complex Arabidopsis circadian clock models. Sensitivity analysis of the simple oscillators implies that an interlocked multi-loop structure reinforces sensitivity/robustness properties, enhancing the response to external and internal variations. Furthermore, we found that reducing the degree of nonlinearity could sometimes enhance the robustness of models, implying that ad hoc incorporation of nonlinearity could be detrimental to a model's perceived credibility.

CONCLUSION

The correct multi-loop structure and degree of nonlinearity are therefore critical in contributing to the desired properties of a model as well as its capacity to match experimental data.

Avoiding transcription factor competition at promoter level increases the chances of obtaining oscillation

Background

The ultimate goal of synthetic biology is the conception and construction of genetic circuits that are reliable with respect to their designed function (e.g. oscillators, switches). This task remains still to be attained due to the inherent synergy of the biological building blocks and to an insufficient feedback between experiments and mathematical models. Nevertheless, the progress in these directions has been substantial.

Results

It has been emphasized in the literature that the architecture of a genetic oscillator must include positive (activating) and negative (inhibiting) genetic interactions in order to yield robust oscillations. Our results point out that the oscillatory capacity is not only affected by the interaction polarity but by how it is implemented at promoter level. For a chosen oscillator architecture, we show by means of numerical simulations that the existence or lack of competition between activator and inhibitor at promoter level affects the probability of producing oscillations and also leaves characteristic fingerprints on the associated period/amplitude features.

Conclusions

In comparison with non-competitive binding at promoters, competition drastically reduces the region of the parameters space characterized by oscillatory solutions. Moreover, while competition leads to pulse-like oscillations with long-tail distribution in period and amplitude for various parameters or noisy conditions, the non-competitive scenario shows a characteristic frequency and confined amplitude values. Our study also situates the competition mechanism in the context of existing genetic oscillators, with emphasis on the Atkinson oscillator.

Evolving enhanced topologies for the synchronization of dynamical complex networks

Enhancing the synchronization of dynamical networks is of great interest to those designing and analyzing many man-made and natural systems. In this work, we investigate how network topology can be evolved to improve this property through the rewiring of edges. A computational tool called NETEVO performs this task using a simulated annealing metaheuristic. In contrast to other work which considers topological attributes when assessing current performance, we instead take a dynamical approach using simulated output from the system to direct the evolution of the network. Resultant topologies are analyzed using standard network measures, B matrices, and motif distributions. These uncover the convergence of many similar features for all our networks, highlighting also significant differences between those evolved using topological rather than dynamical performance measures.

Design of a dynamic model of genes with multiple autonomous regulatory modules by evolutionary computations

A new approach to design a dynamic model of genes with multiple autonomous regulatory modules by evolutionary computations is proposed. The approach is based on Genetic Algorithms (GA), with new crossover operators especially designed for these purposes. The new operators use local homology between parental strings to preserve building blocks found by the algorithm. The approach exploits the subbasin-portal architecture of the fitness functions suitable for this kind of evolutionary modeling. This architecture is significant for Royal Road class fitness functions. Two real-life Systems Biology problems with such fitness functions are implemented here: evolution of the bacterial promoter rrnPl and of the enhancer of the Drosophila even-skipped gene. The effectiveness of the approach compared to standard GA is demonstrated on several benchmark and real-life tasks.

Towards the automated engineering of a synthetic genome

The development of the technology to synthesize new genomes and to introduce them into hosts with inactivated wild-type chromosome opens the door to new horizons in synthetic biology. Here it is of outmost importance to harness the ability of using computational design to predict and optimize a synthetic genome before attempting its synthesis. The methodology to computationally design a genome is based on an optimization that computationally mimics genome evolution. The biggest bottleneck lies on the use of an appropriate fitness function. This fitness function, usually cell growth, relies on the ability to quantitatively model the biochemical networks of the cell at the genome scale using parameters inferred from high-throughput data. Computational methods integrating such models in a common multilayer design platform can be used to automatically engineer synthetic genomes under physiological specifications. We describe the current state-of-the-art on automated methods for engineering or re-engineering synthetic genomes. We restrict ourselves to global models of metabolism, transcription and DNA structure. Although we are still far from the de novo computational genome design, it is important to collect all relevant work towards this goal. Finally, we discuss future perspectives about the practicability of an automated methodology for such computational design of synthetic genomes.

Computing algebraic functions with biochemical reaction networks

In biological organisms, networks of chemical reactions control the processing of information in a cell. A general approach to study the behavior of these networks is to analyze common modules. Instead of this analytical approach to study signaling networks, we construct functional motifs from the bottom up. We formulate conceptual networks of biochemical reactions that implement elementary algebraic operations over the domain and range of positive real numbers. We discuss how the steady state behavior relates to algebraic functions, and study the stability of the networks' fixed points. The primitive networks are then combined in feed-forward networks, allowing us to compute a diverse range of algebraic functions, such as polynomials. With this systematic approach, we explore the range of mathematical functions that can be constructed with these networks.

Network dynamics

Probably one of the most characteristic features of a living system is its continual propensity to change as it juggles the demands of survival with the need to replicate. Internally these adjustments are manifest as changes in metabolite, protein, and gene activities. Such changes have become increasingly obvious to experimentalists, with the advent of high-throughput technologies. In this chapter we highlight some of the quantitative approaches used to rationalize the study of cellular dynamics. The chapter focuses attention on the analysis of quantitative models based on differential equations using biochemical control theory. Basic pathway motifs are discussed, including straight chain, branched, and cyclic systems. In addition, some of the properties conferred by positive and negative feedback loops are discussed, particularly in relation to bistability and oscillatory dynamics.

Memory switches in chemical reaction space

Just as complex electronic circuits are built from simple Boolean gates, diverse biological functions, including signal transduction, differentiation, and stress response, frequently use biochemical switches as a functional module. A relatively small number of such switches have been described in the literature, and these exhibit considerable diversity in chemical topology. We asked if biochemical switches are indeed rare and if there are common chemical motifs and family relationships among such switches. We performed a systematic exploration of chemical reaction space by generating all possible stoichiometrically valid chemical configurations up to 3 molecules and 6 reactions and up to 4 molecules and 3 reactions. We used Monte Carlo sampling of parameter space for each such configuration to generate specific models and checked each model for switching properties. We found nearly 4,500 reaction topologies, or about 10% of our tested configurations, that demonstrate switching behavior. Commonly accepted topological features such as feedback were poor predictors of bistability, and we identified new reaction motifs that were likely to be found in switches. Furthermore, the discovered switches were related in that most of the larger configurations were derived from smaller ones by addition of one or more reactions. To explore even larger configurations, we developed two tools: the “bistabilizer,” which converts almost-bistable systems into bistable ones, and frequent motif mining, which helps rank untested configurations. Both of these tools increased the coverage of our library of bistable systems. Thus, our systematic exploration of chemical reaction space has produced a valuable resource for investigating the key signaling motif of bistability.

How does a cell know what type of cell it is supposed to become? How do external chemical signals change the underlying “state” of the cell? How are response pathways triggered on the application of a stress? Such questions of differentiation, signal transduction, and stress response, while seemingly diverse, all pertain to the storage of state information, or “memory,” by biochemical switches. Just as a computer memory unit can store a bit of 0 or 1 through electrical signals, a biochemical switch can be in one of two states, where chemical signals are on or off. This lets the cell record the presence/absence of an environmental stimulus, the level of a signaling molecule, or the result of a cell fate decision. There are a small number of published ways by which a group of chemical reactions come together to realize a switch. We undertook an exhaustive computational exploration to see if chemical switches are indeed rare and found, surprisingly, that they are actually abundant, highly diverse, but related to one another. Our catalog of switches opens up new bioinformatics approaches to understanding cellular decision making and cellular memory.

Evolution of evolvability in gene regulatory networks

Gene regulatory networks are perhaps the most important organizational level in the cell where signals from the cell state and the outside environment are integrated in terms of activation and inhibition of genes. For the last decade, the study of such networks has been fueled by large-scale experiments and renewed attention from the theoretical field. Different models have been proposed to, for instance, investigate expression dynamics, explain the network topology we observe in bacteria and yeast, and for the analysis of evolvability and robustness of such networks. Yet how these gene regulatory networks evolve and become evolvable remains an open question.

An individual-oriented evolutionary model is used to shed light on this matter. Each individual has a genome from which its gene regulatory network is derived. Mutations, such as gene duplications and deletions, alter the genome, while the resulting network determines the gene expression pattern and hence fitness. With this protocol we let a population of individuals evolve under Darwinian selection in an environment that changes through time.

Our work demonstrates that long-term evolution of complex gene regulatory networks in a changing environment can lead to a striking increase in the efficiency of generating beneficial mutations. We show that the population evolves towards genotype-phenotype mappings that allow for an orchestrated network-wide change in the gene expression pattern, requiring only a few specific gene indels. The genes involved are hubs of the networks, or directly influencing the hubs. Moreover, throughout the evolutionary trajectory the networks maintain their mutational robustness. In other words, evolution in an alternating environment leads to a network that is sensitive to a small class of beneficial mutations, while the majority of mutations remain neutral: an example of evolution of evolvability.

A cell receives signals both from its internal and external environment and responds by changing the expression of genes. In this manner the cell adjusts to heat, osmotic pressures and other circumstances during its lifetime. Over long timescales, the network of interacting genes and its regulatory actions also undergo evolutionary adaptation. Yet how do such networks evolve and become adapted?

In this paper we describe the study of a simple model of gene regulatory networks, focusing solely on evolutionary adaptation. We let a population of individuals evolve, while the external environment changes through time. To ensure evolution is the only source of adaptation, we do not provide the individuals with a sensor to the environment. We show that the interplay between the long-term process of evolution and short-term gene regulation dynamics leads to a striking increase in the efficiency of creating well-adapted offspring. Beneficial mutations become more frequent, nevertheless robustness to the majority of mutations is maintained. Thus we demonstrate a clear example of the evolution of evolvability.

Computational design of digital and memory biological devices

The use of combinatorial optimization techniques with computational design allows the development of automated methods to design biological systems. Automatic design integrates design principles in an unsupervised algorithm to sample a larger region of the biological network space, at the topology and parameter levels. The design of novel synthetic transcriptional networks with targeted behaviors will be key to understand the design principles underlying biological networks. In this work, we evolve transcriptional networks towards a targeted dynamics, by using a library of promoters and coding sequences, to design a complex biological memory device. The designed sequential transcription network implements a JK-Latch, which is fully predictable and richer than other memory devices. Furthermore, we present designs of transcriptional devices behaving as logic gates, and we show how to create digital behavior from analog promoters. Our procedure allows us to propose a scenario for the evolution of multi-functional genetic networks. In addition, we discuss the decomposability of regulatory networks in terms of genetic modules to develop a given cellular function. Summary. We show how to use an automated procedure to design logic and sequential transcription circuits. This methodology will allow advancing the rational design of biological devices to more complex systems, and we propose the first design of a biological JK-latch memory device.

Evolution of complex modular biological networks

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their modularity of function, with modules defined as sets of genes that are strongly interconnected but whose function is separable from those of other modules. Here, we investigate the in silico evolution of modularity and robustness in complex artificial metabolic networks that encode an increasing amount of information about their environment while acquiring ubiquitous features of biological, social, and engineering networks, such as scale-free edge distribution, small-world property, and fault-tolerance. These networks evolve in environments that differ in their predictability, and allow us to study modularity from topological, information-theoretic, and gene-epistatic points of view using new tools that do not depend on any preconceived notion of modularity. We find that for our evolved complex networks as well as for the yeast protein–protein interaction network, synthetic lethal gene pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor gene pairs are farther apart and often straddle modules, suggesting that knockdown rescue is mediated by alternative pathways or modules. The combination of network modularity tools together with genetic interaction data constitutes a powerful approach to study and dissect the role of modularity in the evolution and function of biological networks.

The modular organization of cells is not immediately obvious from the network of interacting genes, proteins, and molecules. A new window into cellular modularity is opened up by genetic data that identifies pairs of genes that interact either directly or indirectly to provide robustness to cellular function. Such pairs can map out the modular nature of a network if we understand how they relate to established mathematical clustering methods applied to networks to identify putative modules. We can test the relationship between genetically interacting pairs and modules on artificial data: large networks of interacting proteins and molecules that were evolved within an artificial chemistry and genetics, and that pass the standard tests for biological networks. Modularity evolves in these networks in order to deal with a multitude of functional goals, with a degree depending on environmental variability. Relationships between genetically interacting pairs and modules similar to those displayed by the artificial gene networks are found in the protein–protein interaction network of baker's yeast. The evolution of complex functional biological networks in silico provides an opportunity to develop and test new methods and tools to understand the complexity of biological systems at the network level.