The inheritance of process: a dynamical systems approach

Naturalizing relevance realization: why agency and cognition are fundamentally not computational

The way organismic agents come to know the world, and the way algorithms solve problems, are fundamentally different. The most sensible course of action for an organism does not simply follow from logical rules of inference. Before it can even use such rules, the organism must tackle the problem of relevance. It must turn ill-defined problems into well-defined ones, turn semantics into syntax. This ability to realize relevance is present in all organisms, from bacteria to humans. It lies at the root of organismic agency, cognition, and consciousness, arising from the particular autopoietic, anticipatory, and adaptive organization of living beings. In this article, we show that the process of relevance realization is beyond formalization. It cannot be captured completely by algorithmic approaches. This implies that organismic agency (and hence cognition as well as consciousness) are at heart not computational in nature. Instead, we show how the process of relevance is realized by an adaptive and emergent triadic dialectic (a trialectic), which manifests as a metabolic and ecological-evolutionary co-constructive dynamic. This results in a meliorative process that enables an agent to continuously keep a grip on its arena, its reality. To be alive means to make sense of one's world. This kind of embodied ecological rationality is a fundamental aspect of life, and a key characteristic that sets it apart from non-living matter.

The origin of RNA interference: Adaptive or neutral evolution?

The origin of RNA interference (RNAi) is usually explained by a defense-based hypothesis, in which RNAi evolved as a defense against transposable elements (TEs) and RNA viruses and was already present in the last eukaryotic common ancestor (LECA). However, since RNA antisense regulation and double-stranded RNAs (dsRNAs) are ancient and widespread phenomena, the origin of defensive RNAi should have occurred in parallel with its regulative functions to avoid imbalances in gene regulation. Thus, we propose a neutral evolutionary hypothesis for the origin of RNAi in which qualitative system drift from a prokaryotic antisense RNA gene regulation mechanism leads to the formation of RNAi through constructive neutral evolution (CNE). We argue that RNAi was already present in the ancestor of LECA before the need for a new defense system arose and that its presence helped to shape eukaryotic genomic architecture and stability.

Where does RNA interference come from? This Essay describes a new step-by-step evolutionary model of how RNA interference might have originated in early eukaryotes through neutral events from the molecular machinery present in prokaryotes.

Trade-offs predicted by metabolic network structure give rise to evolutionary specialization and phenotypic diversification

Mitigating trade-offs between different resource-utilization functions is key to an organism's ecological and evolutionary success. These trade-offs often reflect metabolic constraints with a complex molecular underpinning; therefore, their consequences for evolutionary processes have remained elusive. Here, we investigate how metabolic architecture induces resource utilization constraints and how these constraints, in turn, elicit evolutionary specialization and diversification. Guided by the metabolic network structure of the bacterium Lactococcus cremoris, we selected two carbon sources (fructose and galactose) with predicted co-utilization constraints. By evolving L. cremoris on either fructose, galactose or a mix of both sugars, we imposed selection favoring divergent metabolic specializations or co-utilization of both resources, respectively. Phenotypic characterization revealed the evolution of either fructose or galactose specialists in the single-sugar treatments. In the mixed sugar regime, we observed adaptive diversification: both specialists coexisted, and no generalist evolved. Divergence from the ancestral phenotype occurred at key pathway junctions in the central carbon metabolism. Fructose specialists evolved mutations in the fbp and pfk genes that appear to balance anabolic and catabolic carbon fluxes. Galactose specialists evolved increased expression of pgmA (the primary metabolic bottleneck of galactose metabolism) and silencing of ptnABCD (the main glucose transporter) and ldh (regulator/enzyme of downstream carbon metabolism). Overall, our study shows how metabolic network architecture and historical contingency serve to predict targets of selection and inform the functional interpretation of evolved mutations. The elucidation of the relationship between molecular constraints and phenotypic trade-offs contributes to an integrative understanding of evolutionary specialization and diversification.

Genetic Causation in Complex Regulatory Systems: An Integrative Dynamic Perspective

The logic of genetic discovery has changed little over time, but the focus of biology is shifting from simple genotype-phenotype relationships to complex metabolic, physiological, developmental, and behavioral traits. In light of this, the traditional reductionist view of individual genes as privileged difference-making causes of phenotypes is re-examined. The scope and nature of genetic effects in complex regulatory systems, in which dynamics are driven by regulatory feedback and hierarchical interactions across levels of organization are considered. This review argues that it is appropriate to treat genes as specific actual difference-makers for the molecular regulation of gene expression. However, they are often neither stable, proportional, nor specific as causes of the overall dynamic behavior of regulatory networks. Dynamical models, properly formulated and validated, provide the tools to probe cause-and-effect relationships in complex biological systems, allowing to go beyond the limitations of genetic reductionism to gain an integrative understanding of the causal processes underlying complex phenotypes.

Homology of process: developmental dynamics in comparative biology

Comparative biology builds up systematic knowledge of the diversity of life, across evolutionary lineages and levels of organization, starting with evidence from a sparse sample of model organisms. In developmental biology, a key obstacle to the growth of comparative approaches is that the concept of homology is not very well defined for levels of organization that are intermediate between individual genes and morphological characters. In this paper, we investigate what it means for ontogenetic processes to be homologous, focusing specifically on the examples of insect segmentation and vertebrate somitogenesis. These processes can be homologous without homology of the underlying genes or gene networks, since the latter can diverge over evolutionary time, while the dynamics of the process remain the same. Ontogenetic processes like these therefore constitute a dissociable level and distinctive unit of comparison requiring their own specific criteria of homology. In addition, such processes are typically complex and nonlinear, such that their rigorous description and comparison requires not only observation and experimentation, but also dynamical modelling. We propose six criteria of process homology, combining recognized indicators (sameness of parts, morphological outcome and topological position) with novel ones derived from dynamical systems modelling (sameness of dynamical properties, dynamical complexity and evidence for transitional forms). We show how these criteria apply to animal segmentation and other ontogenetic processes. We conclude by situating our proposed dynamical framework for homology of process in relation to similar research programmes, such as process structuralism and developmental approaches to morphological homology.

Dynamical modules in metabolism, cell and developmental biology

Modularity is an essential feature of any adaptive complex system. Phenotypic traits are modules in the sense that they have a distinguishable structure or function, which can vary (quasi-)independently from its context. Since all phenotypic traits are the product of some underlying regulatory dynamics, the generative processes that constitute the genotype-phenotype map must also be functionally modular. Traditionally, modular processes have been identified as structural modules in regulatory networks. However, structure only constrains, but does not determine, the dynamics of a process. Here, we propose an alternative approach that decomposes the behaviour of a complex regulatory system into elementary activity-functions. Modular activities can occur in networks that show no structural modularity, making dynamical modularity more widely applicable than structural decomposition. Furthermore, the behaviour of a regulatory system closely mirrors its functional contribution to the outcome of a process, which makes dynamical modularity particularly suited for functional decomposition. We illustrate our approach with numerous examples from the study of metabolism, cellular processes, as well as development and pattern formation. We argue that dynamical modules provide a shared conceptual foundation for developmental and evolutionary biology, and serve as the foundation for a new account of process homology, which is presented in a separate contribution by DiFrisco and Jaeger to this focus issue.

The omnistat: A flexible continuous-culture system for prolonged experimental evolution

Microbial evolution experiments provide a powerful tool to unravel the molecular basis of adaptive evolution but their outcomes can be difficult to interpret, unless the selective forces that are applied during the experiment are carefully controlled. In this respect, experimental evolution in continuous cultures provides advantages over commonly used sequential batch-culture protocols because continuous cultures allow for more accurate control over the induced selective environment. However, commercial continuous-culture systems are large and expensive, while available DIY continuous-culture systems are not versatile enough to allow for multiple sensors and rigorous stirring.We present a modular continuous-culture system that adopts the commonly used GL45 glass laboratory bottle as a bioreactor vessel. Our design offers three advantages: first, it is equipped with a large head plate, fitting two sensors and seven input/output ports, enabling the customization of the system for many running modes (chemostat, auxostat, etc.). Second, the bioreactor is small (25-250 ml), which makes it feasible to run many replicates in parallel. Third, bioreactor modules can be coupled by uni- or bi-directional flows to induce spatiotemporal variation in selection. These features result in a particularly flexible culturing platform that facilitates the investigation of a broad range of evolutionary and ecological questions.To illustrate the versatility of our culturing system, we outline two evolution experiments that impose a temporally or spatially variable regime of selection. The first experiment illustrates how controlled temporal variation in resource availability can be utilized to select for anticipatory switching. The second experiment illustrates a spatially structured morbidostat setup that is designed to probe epistatic interactions between adaptive mutations. Furthermore, we demonstrate how sensor data can be used to stabilize selection pressures or track evolutionary adaptation.Evolution experiments in which populations are exposed to controlled spatiotemporal variation, are essential to gain insight into the process of adaptation and the mechanisms that constrain evolution. Continuous-culture systems, like the one presented here, offer control over key environmental parameters and establish a well-defined regime of selection. As such, they create the opportunity to expose evolutionary constraints in the form of phenotypic trade-offs, contributing to a mechanistic understanding of adaptive evolution.

Modularity, criticality, and evolvability of a developmental gene regulatory network

The existence of discrete phenotypic traits suggests that the complex regulatory processes which produce them are functionally modular. These processes are usually represented by networks. Only modular networks can be partitioned into intelligible subcircuits able to evolve relatively independently. Traditionally, functional modularity is approximated by detection of modularity in network structure. However, the correlation between structure and function is loose. Many regulatory networks exhibit modular behaviour without structural modularity. Here we partition an experimentally tractable regulatory network-the gap gene system of dipteran insects-using an alternative approach. We show that this system, although not structurally modular, is composed of dynamical modules driving different aspects of whole-network behaviour. All these subcircuits share the same regulatory structure, but differ in components and sensitivity to regulatory interactions. Some subcircuits are in a state of criticality, while others are not, which explains the observed differential evolvability of the various expression features in the system.

A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila

Insects determine their body segments in two different ways. Short-germband insects, such as the flour beetle Tribolium castaneum, use a molecular clock to establish segments sequentially. In contrast, long-germband insects, such as the vinegar fly Drosophila melanogaster, determine all segments simultaneously through a hierarchical cascade of gene regulation. Gap genes constitute the first layer of the Drosophila segmentation gene hierarchy, downstream of maternal gradients such as that of Caudal (Cad). We use data-driven mathematical modelling and phase space analysis to show that shifting gap domains in the posterior half of the Drosophila embryo are an emergent property of a robust damped oscillator mechanism, suggesting that the regulatory dynamics underlying long- and short-germband segmentation are much more similar than previously thought. In Tribolium, Cad has been proposed to modulate the frequency of the segmentation oscillator. Surprisingly, our simulations and experiments show that the shift rate of posterior gap domains is independent of maternal Cad levels in Drosophila. Our results suggest a novel evolutionary scenario for the short- to long-germband transition and help explain why this transition occurred convergently multiple times during the radiation of the holometabolan insects.

Different insect species exhibit one of two distinct modes of determining their body segments (known as segmentation) during development: they either use a molecular oscillator to position segments sequentially, or they generate segments simultaneously through a hierarchical gene-regulatory cascade. The sequential mode is ancestral, while the simultaneous mode has been derived from it independently several times during evolution. In this paper, we present evidence suggesting that simultaneous segmentation also involves an oscillator in the posterior end of the embryo of the vinegar fly, Drosophila melanogaster. This surprising result indicates that both modes of segment determination are much more similar than previously thought. Such similarity provides an important step towards our understanding of the frequent evolutionary transitions observed between sequential and simultaneous segmentation.

Why an extended evolutionary synthesis is necessary

Since the last major theoretical integration in evolutionary biology—the modern synthesis (MS) of the 1940s—the biosciences have made significant advances. The rise of molecular biology and evolutionary developmental biology, the recognition of ecological development, niche construction and multiple inheritance systems, the ‘-omics’ revolution and the science of systems biology, among other developments, have provided a wealth of new knowledge about the factors responsible for evolutionary change. Some of these results are in agreement with the standard theory and others reveal different properties of the evolutionary process. A renewed and extended theoretical synthesis, advocated by several authors in this issue, aims to unite pertinent concepts that emerge from the novel fields with elements of the standard theory. The resulting theoretical framework differs from the latter in its core logic and predictive capacities. Whereas the MS theory and its various amendments concentrate on genetic and adaptive variation in populations, the extended framework emphasizes the role of constructive processes, ecological interactions and systems dynamics in the evolution of organismal complexity as well as its social and cultural conditions. Single-level and unilinear causation is replaced by multilevel and reciprocal causation. Among other consequences, the extended framework overcomes many of the limitations of traditional gene-centric explanation and entails a revised understanding of the role of natural selection in the evolutionary process. All these features stimulate research into new areas of evolutionary biology.

Phenotypic Novelty in EvoDevo: The Distinction Between Continuous and Discontinuous Variation and Its Importance in Evolutionary Theory

The introduction of novel phenotypic structures is one of the most significant aspects of organismal evolution. Yet the concept of evolutionary novelty is used with drastically different connotations in various fields of research, and debate exists about whether novelties represent features that are distinct from standard forms of phenotypic variation. This article contrasts four separate uses for novelty in genetics, population genetics, morphology, and behavioral science, before establishing how novelties are used in evolutionary developmental biology (EvoDevo). In particular, it is detailed how an EvoDevo-specific research approach to novelty produces insight distinct from other fields, gives the concept explanatory power with predictive capacities, and brings new consequences to evolutionary theory. This includes the outlining of research strategies that draw attention to productive areas of inquiry, such as threshold dynamics in development. It is argued that an EvoDevo-based approach to novelty is inherently mechanistic, treats the phenotype as an agent with generative potential, and prompts a distinction between continuous and discontinuous variation in evolutionary theory.

Gap Gene Regulatory Dynamics Evolve along a Genotype Network

Developmental gene networks implement the dynamic regulatory mechanisms that pattern and shape the organism. Over evolutionary time, the wiring of these networks changes, yet the patterning outcome is often preserved, a phenomenon known as “system drift.” System drift is illustrated by the gap gene network—involved in segmental patterning—in dipteran insects. In the classic model organism Drosophila melanogaster and the nonmodel scuttle fly Megaselia abdita, early activation and placement of gap gene expression domains show significant quantitative differences, yet the final patterning output of the system is essentially identical in both species. In this detailed modeling analysis of system drift, we use gene circuits which are fit to quantitative gap gene expression data in M. abdita and compare them with an equivalent set of models from D. melanogaster. The results of this comparative analysis show precisely how compensatory regulatory mechanisms achieve equivalent final patterns in both species. We discuss the larger implications of the work in terms of “genotype networks” and the ways in which the structure of regulatory networks can influence patterns of evolutionary change (evolvability).

Evolution-development congruence in pattern formation dynamics: Bifurcations in gene expression and regulation of networks structures

Search for possible relationships between phylogeny and ontogeny is important in evolutionary-developmental biology. Here we uncover such relationships by numerical evolution and unveil their origin in terms of dynamical systems theory. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, gene regulation networks are evolved under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Both in the evolution and development pattern changes consist of several epochs where stripes are formed in a short time, while for other temporal regimes, pattern hardly changes. In evolution, these quasi-stationary regimes are generations needed to hit relevant mutations, while in development, they are due to some gene expression that varies slowly and controls the pattern change. The morphogenesis is regulated by combinations of feedback or feedforward regulations, where the upstream feedforward network reads the external morphogen gradient, and generates a pattern used as a boundary condition for the later patterns. The ordering from up to downstream is common in evolution and development, while the successive epochal changes in development and evolution are represented as common bifurcations in dynamical-systems theory, which lead to the evolution-development congruence. Mechanism of exceptional violation of the congruence is also unveiled. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis.

Can biological complexity be reverse engineered?

Concerns with the use of engineering approaches in biology have recently been raised. I examine two related challenges to biological research that I call the synchronic and diachronic underdetermination problem. The former refers to challenges associated with the inference of design principles underlying system capacities when the synchronic relations between lower-level processes and higher-level systems capacities are degenerate (many-to-many). The diachronic underdetermination problem regards the problem of reverse engineering a system where the non-linear relations between system capacities and lower-level mechanisms are changing over time. Braun and Marom argue that recent insights to biological complexity leave the aim of reverse engineering hopeless - in principle as well as in practice. While I support their call for systemic approaches to capture the dynamic nature of living systems, I take issue with the conflation of reverse engineering with naïve reductionism. I clarify how the notion of design principles can be more broadly conceived and argue that reverse engineering is compatible with a dynamic view of organisms. It may even help to facilitate an integrated account that bridges the gap between mechanistic and systems approaches.

Reshaping the epigenetic landscape during early flower development: induction of attractor transitions by relative differences in gene decay rates

BACKGROUND

Gene regulatory network (GRN) dynamical models are standard systems biology tools for the mechanistic understanding of developmental processes and are enabling the formalization of the epigenetic landscape (EL) model.

METHODS

In this work we propose a modeling framework which integrates standard mathematical analyses to extend the simple GRN Boolean model in order to address questions regarding the impact of gene specific perturbations in cell-fate decisions during development.

RESULTS

We systematically tested the propensity of individual genes to produce qualitative changes to the EL induced by modification of gene characteristic decay rates reflecting the temporal dynamics of differentiation stimuli. By applying this approach to the flower specification GRN (FOS-GRN) we uncovered differences in the functional (dynamical) role of their genes. The observed dynamical behavior correlates with biological observables. We found a relationship between the propensity of undergoing attractor transitions between attraction basins in the EL and the direction of differentiation during early flower development - being less likely to induce up-stream attractor transitions as the course of development progresses. Our model also uncovered a potential mechanism at play during the transition from EL basins defining inflorescence meristem to those associated to flower organs meristem. Additionally, our analysis provided a mechanistic interpretation of the homeotic property of the ABC genes, being more likely to produce both an induced inter-attractor transition and to specify a novel attractor. Finally, we found that there is a close relationship between a gene's topological features and its propensity to produce attractor transitions.

CONCLUSIONS

The study of how the state-space associated with a dynamical model of a GRN can be restructured by modulation of genes' characteristic expression times is an important aid for understanding underlying mechanisms occurring during development. Our contribution offers a simple framework to approach such problem, as exemplified here by the case of flower development. Different GRN models and the effect of diverse inductive signals can be explored within the same framework. We speculate that the dynamical role of specific genes within a GRN, as uncovered here, might give information about which genes are more likely to link a module to other regulatory circuits and signaling transduction pathways.

Phenotype accessibility and noise in random threshold gene regulatory networks

Evolution requires phenotypic variation in a population of organisms for selection to function. Gene regulatory processes involved in organismal development affect the phenotypic diversity of organisms. Since only a fraction of all possible phenotypes are predicted to be accessed by the end of development, organisms may evolve strategies to use environmental cues and noise-like fluctuations to produce additional phenotypic diversity, and hence to enhance the speed of adaptation. We used a generic model of organismal development --gene regulatory networks-- to investigate how different levels of noise on gene expression states (i.e. phenotypes) may affect access to new, unique phenotypes, thereby affecting phenotypic diversity. We studied additional strategies that organisms might adopt to attain larger phenotypic diversity: either by augmenting their genome or the number of gene expression states. This was done for different types of gene regulatory networks that allow for distinct levels of regulatory influence on gene expression or are more likely to give rise to stable phenotypes. We found that if gene expression is binary, increasing noise levels generally decreases phenotype accessibility for all network types studied. If more gene expression states are considered, noise can moderately enhance the speed of discovery if three or four gene expression states are allowed, and if there are enough distinct regulatory networks in the population. These results were independent of the network types analyzed, and were robust to different implementations of noise. Hence, for noise to increase the number of accessible phenotypes in gene regulatory networks, very specific conditions need to be satisfied. If the number of distinct regulatory networks involved in organismal development is large enough, and the acquisition of more genes or fine tuning of their expression states proves costly to the organism, noise can be useful in allowing access to more unique phenotypes.

A Philosophical Perspective on Evolutionary Systems Biology

Evolutionary systems biology (ESB) is an emerging hybrid approach that integrates methods, models, and data from evolutionary and systems biology. Drawing on themes that arose at a cross-disciplinary meeting on ESB in 2013, we discuss in detail some of the explanatory friction that arises in the interaction between evolutionary and systems biology. These tensions appear because of different modeling approaches, diverse explanatory aims and strategies, and divergent views about the scope of the evolutionary synthesis. We locate these discussions in the context of long-running philosophical deliberations on explanation, modeling, and theoretical synthesis. We show how many of the issues central to ESB's progress can be understood as general philosophical problems. The benefits of addressing these philosophical issues feed back into philosophy too, because ESB provides excellent examples of scientific practice for the development of philosophy of science and philosophy of biology.

The Comet Cometh: Evolving Developmental Systems

In a recent opinion piece, Denis Duboule has claimed that the increasing shift towards systems biology is driving evolutionary and developmental biology apart, and that a true reunification of these two disciplines within the framework of evolutionary developmental biology (EvoDevo) may easily take another 100 years. He identifies methodological, epistemological, and social differences as causes for this supposed separation. Our article provides a contrasting view. We argue that Duboule’s prediction is based on a one-sided understanding of systems biology as a science that is only interested in functional, not evolutionary, aspects of biological processes. Instead, we propose a research program for an evolutionary systems biology, which is based on local exploration of the configuration space in evolving developmental systems. We call this approach—which is based on reverse engineering, simulation, and mathematical analysis—the natural history of configuration space. We discuss a number of illustrative examples that demonstrate the past success of local exploration, as opposed to global mapping, in different biological contexts. We argue that this pragmatic mode of inquiry can be extended and applied to the mathematical analysis of the developmental repertoire and evolutionary potential of evolving developmental mechanisms and that evolutionary systems biology so conceived provides a pragmatic epistemological framework for the EvoDevo synthesis.

Bioattractors: dynamical systems theory and the evolution of regulatory processes

In this paper, we illustrate how dynamical systems theory can provide a unifying conceptual framework for evolution of biological regulatory systems. Our argument is that the genotype-phenotype map can be characterized by the phase portrait of the underlying regulatory process. The features of this portrait--such as attractors with associated basins and their bifurcations--define the regulatory and evolutionary potential of a system. We show how the geometric analysis of phase space connects Waddington's epigenetic landscape to recent computational approaches for the study of robustness and evolvability in network evolution. We discuss how the geometry of phase space determines the probability of possible phenotypic transitions. Finally, we demonstrate how the active, self-organizing role of the environment in phenotypic evolution can be understood in terms of dynamical systems concepts. This approach yields mechanistic explanations that go beyond insights based on the simulation of evolving regulatory networks alone. Its predictions can now be tested by studying specific, experimentally tractable regulatory systems using the tools of modern systems biology. A systematic exploration of such systems will enable us to understand better the nature and origin of the phenotypic variability, which provides the substrate for evolution by natural selection.

The genome as a developmental organ

This paper applies the conceptual toolkit of Evolutionary Developmental Biology (evo-devo) to the evolution of the genome and the role of the genome in organism development. This challenges both the Modern Evolutionary Synthesis, the dominant view in evolutionary theory for much of the 20th century, and the typically unreflective analysis of heredity by evo-devo. First, the history of the marginalization of applying system-thinking to the genome is described. Next, the suggested framework is presented. Finally, its application to the evolution of genome modularity, the evolution of induced mutations, the junk DNA versus ENCODE debate, the role of drift in genome evolution, and the relationship between genome dynamics and symbiosis with microorganisms are briefly discussed.

Gradual and contingent evolutionary emergence of leaf mimicry in butterfly wing patterns

Background

Special resemblance of animals to natural objects such as leaves provides a representative example of evolutionary adaptation. The existence of such sophisticated features challenges our understanding of how complex adaptive phenotypes evolved. Leaf mimicry typically consists of several pattern elements, the spatial arrangement of which generates the leaf venation-like appearance. However, the process by which leaf patterns evolved remains unclear.

Results

In this study we show the evolutionary origin and process for the leaf pattern in Kallima (Nymphalidae) butterflies. Using comparative morphological analyses, we reveal that the wing patterns of Kallima and 45 closely related species share the same ground plan, suggesting that the pattern elements of leaf mimicry have been inherited across species with lineage-specific changes of their character states. On the basis of these analyses, phylogenetic comparative methods estimated past states of the pattern elements and enabled reconstruction of the wing patterns of the most recent common ancestor. This analysis shows that the leaf pattern has evolved through several intermediate patterns. Further, we use Bayesian statistical methods to estimate the temporal order of character-state changes in the pattern elements by which leaf mimesis evolved, and show that the pattern elements changed their spatial arrangement (e.g., from a curved line to a straight line) in a stepwise manner and finally establish a close resemblance to a leaf venation-like appearance.

Conclusions

Our study provides the first evidence for stepwise and contingent evolution of leaf mimicry.　 Leaf mimicry patterns evolved in a gradual, rather than a sudden, manner from a non-mimetic ancestor. Through a lineage of Kallima butterflies, the leaf patterns evolutionarily originated through temporal accumulation of orchestrated changes in multiple pattern elements.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-014-0229-5) contains supplementary material, which is available to authorized users.

Ernest Everett Just: Egg and embryo as excitable systems

Ernest Everett Just (1883-1941) was an African American embryologist of international standing whose research interests lay in the area of fertilization and early development in marine invertebrates. Perhaps best known for his discovery of the dynamical and structural blocks to polyspermy that sweep over the egg upon fertilization, E. E. Just also was the first to associate cell surface changes with stages of embryonic development. He was deeply familiar with the natural history of the animals whose eggs he studied, and his knowledge of natural settings led him to emphasize the importance of using laboratory conditions that closely match those in nature. Based on more than 30 years of work, he came to believe that it was the cell surface that played the most critical role in development, heredity, and evolution. He promoted a holistic view of cells and organisms in opposition to the gene-centric view that was becoming more prevalent with the rise of genetics, but rejected the vitalism espoused by some biologists of his era, calling instead for "a physics and chemistry in a new dimension …superimposed upon the now known physics and chemistry" to account for biological phenomena. Just's incisive critique of genetic reductionism finds echoes in contemporary multiscale, systems approaches in biology. His speculations on the relationship between developmental and evolutionary mechanisms resonate with today's evolutionary developmental biology. After a brief biographical sketch, this paper outlines and discusses some of Just's scientific contributions, and shows how his ideas remain relevant today.

Modeling the evolution of molecular systems from a mechanistic perspective

Systems biology-inspired genotype-phenotype mapping models are increasingly being used to study the evolutionary properties of molecular biological systems, in particular the general emergent properties of evolving systems, such as modularity, robustness, and evolvability. However, the level of abstraction at which many of these models operate might not be sufficient to capture all relevant intricacies of biological evolution in sufficient detail. Here, we argue that in particular gene and genome duplications, both evolutionary mechanisms of potentially major importance for the evolution of molecular systems and of special relevance to plant evolution, are not adequately accounted for in most GPM modeling frameworks, and that more fine-grained mechanistic models may significantly advance understanding of how gen(om)e duplication impacts molecular systems evolution.

Classification of transient behaviours in a time-dependent toggle switch model

BACKGROUND

Waddington's epigenetic landscape is an intuitive metaphor for the developmental and evolutionary potential of biological regulatory processes. It emphasises time-dependence and transient behaviour. Nowadays, we can derive this landscape by modelling a specific regulatory network as a dynamical system and calculating its so-called potential surface. In this sense, potential surfaces are the mathematical equivalent of the Waddingtonian landscape metaphor. In order to fully capture the time-dependent (non-autonomous) transient behaviour of biological processes, we must be able to characterise potential landscapes and how they change over time. However, currently available mathematical tools focus on the asymptotic (steady-state) behaviour of autonomous dynamical systems, which restricts how biological systems are studied.

RESULTS

We present a pragmatic first step towards a methodology for dealing with transient behaviours in non-autonomous systems. We propose a classification scheme for different kinds of such dynamics based on the simulation of a simple genetic toggle-switch model with time-variable parameters. For this low-dimensional system, we can calculate and explicitly visualise numerical approximations to the potential landscape. Focussing on transient dynamics in non-autonomous systems reveals a range of interesting and biologically relevant behaviours that would be missed in steady-state analyses of autonomous systems. Our simulation-based approach allows us to identify four qualitatively different kinds of dynamics: transitions, pursuits, and two kinds of captures. We describe these in detail, and illustrate the usefulness of our classification scheme by providing a number of examples that demonstrate how it can be employed to gain specific mechanistic insights into the dynamics of gene regulation.

CONCLUSIONS

The practical aim of our proposed classification scheme is to make the analysis of explicitly time-dependent transient behaviour tractable, and to encourage the wider use of non-autonomous models in systems biology. Our method is applicable to a large class of biological processes.

A quantitative atlas of Even-skipped and Hunchback expression in Clogmia albipunctata (Diptera: Psychodidae) blastoderm embryos

Background

Comparative studies of developmental processes are one of the main approaches to evolutionary developmental biology (evo-devo). Over recent years, there has been a shift of focus from the comparative study of particular regulatory genes to the level of whole gene networks. Reverse-engineering methods can be used to computationally reconstitute and analyze the function and dynamics of such networks. These methods require quantitative spatio-temporal expression data for model fitting. Obtaining such data in non-model organisms remains a major technical challenge, impeding the wider application of data-driven mathematical modeling to evo-devo.

Results

We have raised antibodies against four segmentation gene products in the moth midge Clogmia albipunctata, a non-drosophilid dipteran species. We have used these antibodies to create a quantitative atlas of protein expression patterns for the gap gene hunchback (hb), and the pair-rule gene even-skipped (eve). Our data reveal differences in the dynamics of Hb boundary positioning and Eve stripe formation between C. albipunctata and Drosophila melanogaster. Despite these differences, the overall relative spatial arrangement of Hb and Eve domains is remarkably conserved between these two distantly related dipteran species.

Conclusions

We provide a proof of principle that it is possible to acquire quantitative gene expression data at high accuracy and spatio-temporal resolution in non-model organisms. Our quantitative data extend earlier qualitative studies of segmentation gene expression in C. albipunctata, and provide a starting point for comparative reverse-engineering studies of the evolutionary and developmental dynamics of the segmentation gene system.

Pattern formation in individual-based systems with time-varying parameters

We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models. Similar to the well-known Kibble-Zurek scenario of defect formation, large-scale patterns are generated when model parameters are varied slowly, whereas fast sweeps produce a large number of small domains. The symmetry breaking is triggered by intrinsic noise, originating from the discrete dynamics at the microlevel. Based on a linear-noise approximation, we calculate the characteristic length scale of these patterns. We demonstrate the applicability of this approach in a simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and a model of cell differentiation. Our theoretical estimates are confirmed in simulations. In further numerical work, we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.

Monotonicity is a key feature of genotype-phenotype maps

It was recently shown that monotone gene action, i.e., order-preservation between allele content and corresponding genotypic values in the mapping from genotypes to phenotypes, is a prerequisite for achieving a predictable parent-offspring relationship across the whole allele frequency spectrum. Here we test the consequential prediction that the design principles underlying gene regulatory networks are likely to generate highly monotone genotype-phenotype maps. To this end we present two measures of the monotonicity of a genotype-phenotype map, one based on allele substitution effects, and the other based on isotonic regression. We apply these measures to genotype-phenotype maps emerging from simulations of 1881 different 3-gene regulatory networks. We confirm that in general, genotype-phenotype maps are indeed highly monotonic across network types. However, regulatory motifs involving incoherent feedforward or positive feedback, as well as pleiotropy in the mapping between genotypes and gene regulatory parameters, are clearly predisposed for generating non-monotonicity. We present analytical results confirming these deep connections between molecular regulatory architecture and monotonicity properties of the genotype-phenotype map. These connections seem to be beyond reach by the classical distinction between additive and non-additive gene action.

Reverse-engineering post-transcriptional regulation of gap genes in Drosophila melanogaster

Systems biology proceeds through repeated cycles of experiment and modeling. One way to implement this is reverse engineering, where models are fit to data to infer and analyse regulatory mechanisms. This requires rigorous methods to determine whether model parameters can be properly identified. Applying such methods in a complex biological context remains challenging. We use reverse engineering to study post-transcriptional regulation in pattern formation. As a case study, we analyse expression of the gap genes Krüppel, knirps, and giant in Drosophila melanogaster. We use detailed, quantitative datasets of gap gene mRNA and protein expression to solve and fit a model of post-transcriptional regulation, and establish its structural and practical identifiability. Our results demonstrate that post-transcriptional regulation is not required for patterning in this system, but is necessary for proper control of protein levels. Our work demonstrates that the uniqueness and specificity of a fitted model can be rigorously determined in the context of spatio-temporal pattern formation. This greatly increases the potential of reverse engineering for the study of development and other, similarly complex, biological processes.

The analysis of pattern-forming gene networks is largely focussed on transcriptional regulation. However, post-transcriptional events, such as translation and regulation of protein stability also play important roles in the establishment of protein expression patterns and levels. In this study, we use a reverse-engineering approach—fitting mathematical models to quantitative expression data—to analyse post-transcriptional regulation of the Drosophila gap genes Krüppel, knirps and giant, involved in segment determination during early embryogenesis. Rigorous fitting requires us to establish whether our models provide a robust and unique solution. We demonstrate, for the first time, that this can be done in the context of a complex spatio-temporal regulatory system. This is an important methodological advance for reverse-engineering developmental processes. Our results indicate that post-transcriptional regulation is not required for pattern formation, but is necessary for proper regulation of gap protein levels. Specifically, we predict that translation rates must be tuned for rapid early accumulation, and protein stability must be increased for persistence of high protein levels at late stages of gap gene expression.

What is evolutionary novelty? Process versus character based definitions

With the rise of EvoDevo, the topic of evolutionary novelty has received renewed attention. Indeed, it has been argued that one of the major contributions of EvoDevo to evolutionary theory is the explanation of phenotypic novelty. Despite such assertions, dispute continues over what exactly a novelty is and whether the term applies to a unique type of evolutionary phenomenon or whether it merely has informal meaning. In a recent special issue of J. Exp. Zool. (Mol. Dev. Evol.) dedicated to novelty, a new definition was introduced, linking novelty exclusively with adaptation and developmental constraint. In our commentary, we discuss how defining novelty in this process oriented manner leads to heightened difficulties with the application of the term and the identification of novelties. At the same time it conceals important implications for evolutionary studies. In contrast, we argue for a character based definition that is independent from adaptive necessities and promotes the integration of evolutionary factors not included in the standard theory. The implications of approaching novelty in this manner take the issue beyond definitional debates.

Evolutionary systems biology: what it is and why it matters

Evolutionary systems biology (ESB) is a rapidly growing integrative approach that has the core aim of generating mechanistic and evolutionary understanding of genotype-phenotype relationships at multiple levels. ESB's more specific objectives include extending knowledge gained from model organisms to non-model organisms, predicting the effects of mutations, and defining the core network structures and dynamics that have evolved to cause particular intracellular and intercellular responses. By combining mathematical, molecular, and cellular approaches to evolution, ESB adds new insights and methods to the modern evolutionary synthesis, and offers ways in which to enhance its explanatory and predictive capacities. This combination of prediction and explanation marks ESB out as a research manifesto that goes further than its two contributing fields. Here, we summarize ESB via an analysis of characteristic research examples and exploratory questions, while also making a case for why these integrative efforts are worth pursuing.

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.