Anton Crombach

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.

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.

Life’s Attractors

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

BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology.

BackgroundDynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions.ResultsHere we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker’s yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation.ConclusionsThis suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/.

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

BackgroundWaddington’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.ResultsWe 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.ConclusionsThe 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.

Quantitative system drift compensates for altered maternal inputs to the gap gene network of the Scuttle Fly Megaselia abdita

The segmentation gene network in insects can produce equivalent phenotypic outputs despite differences in upstream regulatory inputs between species. We investigate the mechanistic basis of this phenomenon through a systems-level analysis of the gap gene network in the scuttle fly Megaselia abdita (Phoridae). It combines quantification of gene expression at high spatio-temporal resolution with systematic knock-downs by RNA interference (RNAi). Initiation and dynamics of gap gene expression differ markedly between M. abdita and Drosophila melanogaster, while the output of the system converges to equivalent patterns at the end of the blastoderm stage. Although the qualitative structure of the gap gene network is conserved, there are differences in the strength of regulatory interactions between species. We term such network rewiring ‘quantitative system drift’. It provides a mechanistic explanation for the developmental hourglass model in the dipteran lineage. Quantitative system drift is likely to be a widespread mechanism for developmental evolution. DOI: http://dx.doi.org/10.7554/eLife.04785.001

Evolution of early development in dipterans: reverse-engineering the gap gene network in the moth midge Clogmia albipunctata (Psychodidae).

Understanding the developmental and evolutionary dynamics of regulatory networks is essential if we are to explain the non-random distribution of phenotypes among the diversity of organismic forms. Here, we present a comparative analysis of one of the best understood developmental gene regulatory networks today: the gap gene network involved in early patterning of insect embryos. We use gene circuit models, which are fitted to quantitative spatio-temporal gene expression data for the four trunk gap genes hunchback (hb), Krüppel (Kr), giant (gt), and knirps (kni)/knirps-like (knl) in the moth midge Clogmia albipunctata, and compare them to equivalent reverse-engineered circuits from our reference species, the vinegar fly Drosophila melanogaster. In contrast to the single network structure we find for D. melanogaster, our models predict four alternative networks for C. albipunctata. These networks share a core structure, which includes the central regulatory feedback between hb and knl. Other interactions are only partially determined, as they differ between our four network structures. Nevertheless, our models make testable predictions and enable us to gain specific insights into gap gene regulation in C. albipunctata. They suggest a less central role for Kr in C. albipunctata than in D. melanogaster, and show that the mechanisms causing an anterior shift of gap domains over time are largely conserved between the two species, although shift dynamics differ. The set of C. albipunctata gene circuit models presented here will be used as the starting point for data-constrained in silico evolutionary simulations to study patterning transitions in the early development of dipteran species.

Medium-Throughput Processing of Whole Mount In Situ Hybridisation Experiments into Gene Expression Domains

Understanding the function and evolution of developmental regulatory networks requires the characterisation and quantification of spatio-temporal gene expression patterns across a range of systems and species. However, most high-throughput methods to measure the dynamics of gene expression do not preserve the detailed spatial information needed in this context. For this reason, quantification methods based on image bioinformatics have become increasingly important over the past few years. Most available approaches in this field either focus on the detailed and accurate quantification of a small set of gene expression patterns, or attempt high-throughput analysis of spatial expression through binary pattern extraction and large-scale analysis of the resulting datasets. Here we present a robust, “medium-throughput” pipeline to process in situ hybridisation patterns from embryos of different species of flies. It bridges the gap between high-resolution, and high-throughput image processing methods, enabling us to quantify graded expression patterns along the antero-posterior axis of the embryo in an efficient and straightforward manner. Our method is based on a robust enzymatic (colorimetric) in situ hybridisation protocol and rapid data acquisition through wide-field microscopy. Data processing consists of image segmentation, profile extraction, and determination of expression domain boundary positions using a spline approximation. It results in sets of measured boundaries sorted by gene and developmental time point, which are analysed in terms of expression variability or spatio-temporal dynamics. Our method yields integrated time series of spatial gene expression, which can be used to reverse-engineer developmental gene regulatory networks across species. It is easily adaptable to other processes and species, enabling the in silico reconstitution of gene regulatory networks in a wide range of developmental contexts.

Lack of tailless leads to an increase in expression variability in Drosophila embryos

Developmental processes are robust, or canalised: dynamic patterns of gene expression across space and time are regulated reliably and precisely in the presence of genetic and environmental perturbations. It remains unclear whether canalisation relies on specific regulatory factors (such as heat-shock proteins), or whether it is based on more general redundancy and distributed robustness at the network level. The latter explanation implies that mutations in many regulatory factors should exhibit loss of canalisation. Here, we present a quantitative characterisation of segmentation gene expression patterns in mutants of the terminal gap gene tailless (tll) in Drosophila melanogaster. Our analysis provides new insights into the dynamic mechanisms underlying gap gene regulation, and reveals significantly increased variability of gene expression in the mutant compared to the wild-type background. We show that both position and timing of posterior segmentation gene expression domains vary strongly from embryo-to-embryo in tll mutants. This variability must be caused by a vulnerability in the regulatory system which is hidden or buffered in the wild-type, but becomes uncovered by the deletion of tll. Our analysis provides evidence that loss of canalisation in mutants could be more widespread than previously thought.

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).