In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.

motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.

A major challenge for evolutionary computation is to evolve phenotypes such as neural networks, sensory systems, or motor controllers at the same level of complexity as found in biological organisms. In order to meet this challenge, many researchers are proposing indirect encodings, that is, evolutionary mechanisms where the same genes are used multiple times in the process of building a phenotype. Such gene reuse allows compact representations of very complex phenotypes. Development is a natural choice for implementing indirect encodings, if only because nature itself uses this very process. Motivated by the development of embryos in nature, we define Artificial Embryogeny (AE) as the subdiscipline of evolutionary computation (EC) in which phenotypes undergo a developmental phase. An increasing number of AE systems are currently being developed, and a need has arisen for a principled approach to comparing and contrasting, and ultimately building, such systems. Thus, in this paper, we develop a principled taxonomy for AE. This taxonomy provides a unified context for long-term research in AE, so that implementation decisions can be compared and contrasted along known dimensions in the design space of embryogenic systems. It also allows predicting how the settings of various AE parameters affect the capacity to efficiently evolve complex phenotypes.

This paper presents a simulation framework and computational testbed for studying multicellular pattern formation. The approach combines several developmental mechanisms (chemical, mechanical, genetic and electrical) known to be important for biological pattern formation. The mechanisms are present in an environment containing discrete cells which are capable of independent movement (cell migration). Experience with the testbed indicates that the interactions between the developmental mechanisms are important in determining multicellular and developmental patterns. Each simulated cell has an artificial genome whose expression is dependent only upon its internal state and its local environment. The changes of each cell's state and of the environment are determined by piecewise continuous differential equations. The current two-dimensional simulation exhibits a variety of multicellular behaviors, including cell migration, cell differentiation, gradient following, clustering, lateral inhibition, and neurite outgrowth (see color plates). We plan to perform simulated evolution on developmental models as part of a long range goal to create artificial neural networks which solve problems in perception and control [Fleischer]. The testbed is a step on the path towards this goal. 1 Introduction

Biological cell networks exhibit complex combinations of both discrete and continuous behaviors: indeed, the dynamics that govern the spatial and temporal increase or decrease of protein concentration inside a single cell are continuous di#erential equations, while the activation or deactivation of these continuous dynamics are triggered by discrete switches which encode protein concentrations reaching given thresholds. In this paper, we model as a hybrid system a striking example of this behavior in a biological mechanism called Delta-Notch signaling, which is thought to be the primary mechanism of cell di#erentiation in a variety of cell networks. We present results in both simulation and reachability analysis of this hybrid system. We emphasize how the hybrid system model is computationally superior (for both simulation and analysis) to other nonlinear models in the literature, without compromising faithful modeling of the biological phenomena. 1

Development is an important, powerful and integral element of biological evolution. In this paper we present two models of development that can be used to evolve functional autonomous agents, complete with bodies and neural control systems. The first and most complex model is more biologically defensible in its details. It has been used to hand-design a genome for the development of complete agents capable of executing a simple avoidance task. These agents were then incrementally improved through evolution. The second model is simpler and uses a random Boolean network model for the genome and cell state that is somewhat more removed from the biological realm, making it easier to analyze and more amenable to artificial evolution. Using this model, we have successfully evolved complete agents from scratch that are capable of following curved lines.

This paper introduces a combined discrete/continuous model of plant development that integrates L-system-style productions and differential equations. The model is suitable for animating simulated developmental processes in a manner resembling time-lapse photography. The proposed technique is illustrated using several developmental models, including the flowering plants Campanula rapunculoides, Lychnis coronaria, and Hieracium umbellatum. CR categories: F.4.2 [Mathematical Logic and Formal Languages ]: Grammars and Other Rewriting Systems: Parallel rewriting systems, I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism: Animation, I.6.3 [Simulation and Modeling ]: Applications, J.3 [Life and Medical Sciences]: Biology Keywords: animation through simulation, realistic image synthesis, modeling of plants, combined discrete/continuous simulation, L-system, piecewise-continuous differential equation. 1 INTRODUCTION Time-lapse photography reveals the enormous visual appeal...

This thesis discusses a biologically defensible model of development for artificial organisms. It can be used in conjunction with genetic algorithms to design autonomous agents, complete with body and nervous system. It also has potential applications in the field of theoretical biology. The approach taken is one of exploration, i.e. the model is implemented simultaneously at three different levels of complexity: regulation of gene expression, development of body morphology and finally neural development. At each level the model's behavior under evolutionary pressure is addressed. The whole integrated model will be illustrated with a hand-designed artificial organism, that is capable of executing a simple avoidance behavior in a simulated world.

The origin of multicellular organisms and the mechanism of development in cell societies are studied by choosing a model with intracellular biochemical dynamics allowing for oscillations, cell--cell interaction through diffusive chemicals on a two-dimensional grid, and state-dependent cell adhesion. Cells differentiate due to a dynamical instability, as described by our "isologous diversi#cation" theory. A #xed spatial pattern of differentiated cells emerges, where spatial information is sustained by cell--cell interactions. This pattern is robust against perturbations. With an adequate cell adhesion force, active cells are released that form the seed of a new generation of multicellular organisms, accompanied by death of the original multicellular unit as a halting state. It is shown that the emergence of multicellular organisms with differentiation, regulation, and life cycle is not an accidental event, but a natural consequence in a system of replicating cells with growth.

The topology of cellular circuits (the who-interacts-with-whom) is key to understand their robustness to both mutations and noise. The reason is that many biochemical parameters driving circuit behavior vary extensively and are thus not fine-tuned. Existing work in this area asks to what extent the function of any one given circuit is robust. But is high robustness truly remarkable, or would it be expected for many circuits of similar topology? And how can high robustness come about through gradual Darwinian evolution that changes circuit topology gradually, one interaction at a time? We here ask these questions for a model of transcriptional regulation networks, in which we explore millions of different network topologies. Robustness to mutations and noise are correlated in these networks. They show a skewed distribution, with a very small number of networks being vastly more robust than the rest. All networks that attain a given gene expression state can be organized into a graph whose nodes are networks that differ in their topology. Remarkably, this graph is connected and can be easily traversed by gradual changes of network topologies. Thus, robustness is an evolvable property. This connectedness and evolvability of robust networks may be a general organizational principle of biological networks. In addition, it exists also for RNA and protein structures, and may thus be a general organizational principle of all biological systems.