Evolution of form and function in a model of differentiated multicellular organisms with gene regulatory networks

Abstract

The emergence of novelties, as a generator of diversity, in the form and function of the organisms have long puzzled biologists. The study of the developmental process and the anatomical properties of an organism provides scarce information into the means by which its morphology evolved. Some have argued that the very nature of novelty is believed to be linked to the evolution of gene regulation, rather than to the emergence of new structural genes. In order to gain further insight into the evolution of novelty and diversity, we describe a simple computational model of gene regulation that controls the development of locomotive multicellular organisms through a fixed set of simple structural genes. Organisms, modeled as two-dimensional spring networks, are simulated in a virtual environment to evaluate their steering skills for path-following. Proposed as a behavior-finding problem, this fitness function guides an evolutionary algorithm that produces structures whose function is well-adapted to the environment (i.e., good path-followers). We show that, despite the fixed simple set of structural genes, the evolution of gene regulation yields a rich variety of body plans, including symmetries, body segments, and modularity, resulting in a diversity of original behaviors to follow a simple path. These results suggest that the sole variation in the regulation of gene expression is a sufficient condition for the emergence of novelty and diversity.

Introduction

Nowadays, our planet is populated by some 1–20 million animal species. Quite remarkably, they represent less than 1% of the total number of animal species that have ever existed (Carroll et al., 2004). This astonishing diversity of forms and behaviors has emerged by the evolution of novel features among animal species, a process not fully understood yet, which remains as a fascinating and challenging topic of research (Carroll et al., 2004, Moczek, 2008). Biological evidence suggests that the sources of novelty might have to do with a complexification in the regulation of gene expression (Levine and Tjian, 2003). In this sense, it has been pointed out that evolutionary change in body plans devolves from change in the architecture of developmental regulatory programs (Davidson, 2006), suggesting that diversity can be better explained by variation in the regulation of gene expression than by variation in the structural genes (Davidson and Erwin, 2006). Moreover, the developmental process seems to be a key component in the evolution of diversity (Borenstein and Krakauer, 2008). However, due to the limitations to perform experiments in biological evolutionary processes, it has not been demonstrated yet that the reason for evolutionary emergence of developmental novel features and diversity is in fact the variation in the regulation of gene expression, rather than the variation in the structural genes.

On the other hand, theoretical models of biological phenomena are a valid alternative to experimentation, and have been extensively used to prompt new questions and research directions, especially in biological fields not suited to experimentation, such as evolutionary development. The work presented here subscribes to this approach. We show that a computer model, including genetic regulation of developmental processes, placed in a scenario of artificial evolution provides information about the evolutionary emergence of novelty and diversity.

Several theoretical models and formalisms have been proposed to describe genetic regulatory systems (see de Jong, 2002 for a review). Among them, the Boolean networks proposed by Kauffman (1969) have been extensively used, and allow the simulation of large regulatory networks (de Jong, 2002). Furthermore, a recent study (Davidich and Bornholdt, 2008) has demonstrated a good correspondence between Boolean networks and more realistic models based on differential equations of chemical kinetics. Similarly to Boolean networks, other network-level models focus on a statistical analysis of network properties and patterns. When these models are embedded in an evolutionary context, mutation is typically implemented as changes in the connectivity and in the nodal output functions. These transformations have little to do with the effects derived from biological mutations and impose limitations to the way networks, and hence phenotypes, do evolve (Watson et al., 2004). Thus, in order to apply realistic mutation operators in network-level models, an encoding of the network in a sequence-based genome is needed. Among such models, the Artificial Genome proposed by Reil (1999) has attracted much attention. An Artificial Genome encodes a regulatory network in a sequence of digits, being the dynamics of this regulatory network equivalent to a Boolean network that limits the possible Boolean functions in its nodes (Willadsen and Wiles, 2003).

Similarly, theoretical models have also been proposed to model biological development, experiencing a considerable growth as a subfield of evolutionary computation. The main reasons of such advances are the benefits brought about by these models in scalability, adaptability, and evolvability (Hornby and Pollack, 2002) in a wide range of problems (see Stanley and Miikkulainen, 2003 for a review). Within this emerging discipline, some models have been proposed at the network-level for developmental regulation. Fleischer and Barr (1993) presented a developmental model based on genetic encoding (hand-coded), chemical diffusion, and mechanical interactions, formalized by ordinary differential equations, which were coupled with if-clauses for cell differentiation. Unfortunately, evolutionary developmental properties could not be studied, since this model was not embedded in an evolutionary process. Dellaert and Beer (1994) proposed a model where organisms are made up of two-dimensional squares, which develop by square division and differentiation through regulation by a Boolean network. Although the model included complex regulation, the phenotypes based on square divisions were inadequate for the emergence of novelty. Sims (1994b) presented a system for the evolution of physically simulated virtual creatures made of articulated rigid parts, effectors, and sensors, and controlled by an extended neural network. Several tasks were optimized, resulting in a considerable variety of morphologies and behaviors. However, the morphology and the controller were encoded separately in two recurrent directed graphs, what does not really model biological development. Eggenberger (1997) described a growing phenotype made up of spherical modules, connected by articulated joints. A parametric regulatory network model was used, including diffusion concentration and diffusion sites of genes. The evolved forms presented limited variability, emerging only bilaterality. Bongard and Pfeifer (2003) extended that model by adding a neural controller, that was intended to evolve agents that developed directed locomotion and block pushing. The evolved agents managed to perform the assigned tasks, although with a limited variability in their characteristics. Hogeweg (2000) proposed a morphogenetic model of 2D multicellular organisms where cells behaved according to a multiscale cellular automaton. Although the phenotypes presented interesting developmental dynamics, the simplicity of the organisms made the results hard to use in studies of novelty. Kumar and Bentley (2003) proposed a computational model of development where a regulatory network controlled the synthesis of proteins, and embryos with spherical forms were evolved. Here, again, the simplicity of the evolved phenotypes is not enough for studies of novelty emergence. Roth et al. (2007) presented a model of developmental multicellular organisms based on an artificial genetic regulatory network and chemical diffusion of morphogens. In this work, squares in a lattice represent cells that can differentiate into motors and sensors, connected by a simple wiring strategy. However, the model lacks an evolutionary component. Watson et al. (2008) proposed a model of artificial development and evolution of early land plants in 3D. This model employs an artificial genome to regulate the timing of bifurcation events and its rotation angles, yet the evolved phenotypes are too simple for the emergence of appreciable novelties. Doursat (2008) proposed a model of growing multicellular development, where a 2D lattice of cells proliferates and self-patterns into differential domains orchestrated by a gene regulatory network. Although the model produced substantial results, the process was not studied in an evolutionary perspective. Chavoya and Duthen (2008) proposed a model for 2D cell pattern generation based on a gene regulatory network, which controls a cellular automaton. The phenotypes generated by the model represented simple flag-like patterns, which are not adequate for novelty studies. Andersen et al. (2009) proposed a model of developmental cellular systems in 3D based on signaling and gene regulatory networks. Evolved embryos showed particular stable shapes and high capacity for self-repairing; however, the shapes presented by the phenotypes were too simple, rectangular or spherical, for the emergence of novelty. Finally, Zhan et al. (2009) presented an evolutionary developmental system based on cell signalling and artificial genetic regulatory networks focused on engineering design: electronic circuits design. In summary, the theoretical developmental models based on genetic regulation presented in the literature are not completely adequate for the study of the emergence of evolutionary novelty and diversity.

In this paper, we propose and analyze the results obtained by a theoretical model intended to gain further insight into the evolution of novel features and diversity. More precisely, these results suggest that the evolution of genetic regulation could be a sufficient condition for the emergence of novelty and diversity. The model is based on an Artificial Genome that encodes a Boolean network. Regulating the expression of a fixed elementary set of structural genes, the network controls the development of locomotive multicellular organisms. Organisms develop form and function simultaneously during the developmental process, resulting in a phenotype that integrates seamless morphology and control. An evolutionary algorithm is implemented to evolve organisms that succeed in following a path. We show that, despite the simplicity and invariability of the structural genes, the evolution of gene regulation yields a rich variety of novel body plans, including symmetries, body segments, and modularity. Moreover, the morphological diversity obtained yields a diversity of path-following behaviors.

Section 2 describes in detail the proposed artificial development model, from the description of the genome to the evolutionary algorithm. The results of the evolution are presented in Section 3. Finally, in Section 4 the conclusions derived from the results are discussed.