Shapes in the Shadow: Evolutionary Dynamics of Morphogenesis

This article investigates the evolutionary dynamics of morphogenesis. In this study, morphogenesis arises as a side-effect of maximization of number of cell types. Thus, it investigates the evolutionary dynamics of side-effects. Morphogenesis is governed by the interplay between differential cell adhesion, gene-regulation, and intercellular signaling. Thus, it investigates the potential to generate complex behavior by entanglement of relatively "boring" processes, and the (automatic) coordination between these processes. The evolutionary dynamics shows all the hallmarks of evolutionary dynamics governed by nonlinear genotype phenotype mapping: for example, punctuated equilibria and diffusion on neutral paths. More striking is the result that interesting, complex morphogenesis occurs mainly in the "shadow" of neutral paths which preserve cell differentiation, that is, the interesting morphologies arise as mutants of the fittest individuals. Characteristics of the evolution of such side-effects in the shadow appear to be the following: (1) The speci?c complex morphologies are unique (or at least very rare) among the set of de novo initiated evolutionary histories. (2) Similar morphologies are reinvented at large temporal distances during one evolutionary history and also when evolution is restarted after the main cell differentiation pattern has been established. (3) A mosaic-like evolution at the morphological level, where different morphological features occur in many combinations, while at the genotypic level recombination is not implemented and genotypes diverge linearly and at a constant rate

On searching generic properties of non generic phenomena: an approach to bioinformatic theory formation

In this paper we first shortly review the current view of the evolution of complexity and novelty in biotic evo- lution. Next we show that the basic processes thereof do happen automatically and are generic properties of systems including the basic mechanisms of Darwini- an evolution plus local as opposed to global interac- tions. Thus we show that the so generated multilevel evolution can be studied within the paradigm 'simple rules lead to complex phenomena'. We derive some re- sults demonstrating the power of such multilevel evolu- tionary processes to integrate information at multiple space and time scales. Nevertheless we also point out shortcomings of such an approach which necessarily uses a priori chosen and preferentially relatively simple interaction schemes. However, straightforward extensions towards more complex interaction schemes generally leads to ad hoc- ness and over-determinedness, rather than fundamen- tally new behavior of the system, and often to less understanding of that behavior. Nevertheless biologi- cal theory formation needs a method to go beyond the generic behavior of simple interaction schemes. We propose to use evolutionary optimization of very trivial fitness functions which are obtainable in many different ways to push back the necessary a priori choic- es and to zoom in to interesting non generic phenom- ena and their general properties. . We thus derive insights in relationships between sets of derived prop- erties at several scales. We discuss how this approach can be used in biological theory formation, focusing on information accumulation and utilization in replicator systems and immune systems

Attractors and Spatial Patterns in Hypercycles with Negative Interactions

This study reports on the effect of adding negative interaction terms to the hypercycle equation. It is shown that there is a simple parameter condition at which the behaviour of the hypercycle switches from dominant catalysis to dominant suppression. In the suppression!dominated hypercycles the main attractor turns out to be different for cycles consisting of an even or odd number of species. In "odd" cycles there is typically a limit cycle attractor, whereas in "even" cycles there are two alternative stable attractors each containing half of the species. In a spatial domain, odd cycles create spiral waves. Even cycles create a "voting pattern", i.e. initial fluctuations are quickly frozen into patches of the alternative attractors and subsequently, very slowly, small patches will disappear and only one of the two attractors remains. In large cycles (both even and odd) there are additional limit cycle attractors[ In a spatial domain these limit cycles fail to form stable spiral waves, but they can form stable rotating waves around an obstacle. However, these waves are outcompeted by the dominant spatial pattern of the system[ In competition between even and odd cycles, the patches of even cycles are generally stronger than the spiral waves of odd cycles. If the growth parameters of the species vary a little, a patch will no longer contain only half of the species but will instead attract "predator" species from the other patch type. In such a system one of the patch types will slowly disappear and the final dynamics resembles that of a predator-prey system with multiple trophic levels. The conclusion is that adding negative interactions to a hypercycle tends to cause the cycle to break and thereafter the system attains an ecosystem type of dynamics

Modelling Morphogenesis: From Single Cells to Crawling Slugs

We present a three-dimensional hybrid cellular automata (CA)/partial differential equation (PDE) model that allows for the study of morphogenesis in simple cellular systems. We apply the model to the cellular slime mold Dictyostelium discoideum "from single cells to crawling slug". Using simple local interactions we can achieve the basic morphogenesis with only three processes: production of and chemotaxis to cAMP and cellular adhesion. The interplay of these processes causes the amoebae to spatially self-organize leading to the complex behaviour of stream and mound formation, cell sorting and slug migration all without any change of parameters during the complete morphogenetic process

Phototaxis during the slug stage of Dictyostelium discoideum: a model study

During the slug stage, the cellular slime mould Dictyostelium discoideum moves towards light sources. We have modelled this phototactic behaviour using a hybrid cellular automata/partial differential equation model. In our model, individual amoebae are not able to measure the direction from which the light comes, and differences in light intensity do not lead to differentiation in motion velocity among the amoebae. Nevertheless, the whole slug orientates itself towards the light. This behaviour is mediated by a modification of the cyclic AMP (cAMP) waves. As an explanation for phototaxis we propose the following mechanism, which is basically characterized by four processes: (i) light is focused on the distal side of the slug as a result of the so-called `lens-e¡ect'; (ii) differences in luminous intensity cause differences in NH3 concentration; (iii) NH3 alters the excitability of the cell, and thereby the shape of the cAMP wave; and (iv) chemotaxis towards cAMP causes the slug to turn.We show that this mechanism can account for a number of other behaviours that have been observed in experiments, such as bidirec- tional phototaxis and the cancellation of bidirectionality by a decrease in the light intensity or the addition of charcoal to the medium

Moving Forward Moving Backward: Directional Sorting of Chemotactic Cells due to Size and Adhesion Differences

Differential movement of individual cells within tissues is an important yet poorly understood process in biological development. Here we present a computational study of cell sorting caused by a combination of cell adhesion and chemotaxis, where we assume that all cells respond equally to the chemotactic signal. To capture in our model mesoscopic properties of biological cells, such as their size and deformability, we use the Cellular Potts Model, a multiscale, cell-based Monte Carlo model. We demonstrate a rich array of cell-sorting phenomena, which depend on a combination of mescoscopic cell properties and tissue level constraints. Under the conditions studied, cell sorting is a fast process, which scales linearly with tissue size. We demonstrate the occurrence of “absolute negative mobility”, which means that cells may move in the direction opposite to the applied force (here chemotaxis). Moreover, during the sorting, cells may even reverse the direction of motion. Another interesting phenomenon is “minority sorting”, where the direction of movement does not depend on cell type, but on the frequency of the cell type in the tissue. A special case is the cAMP-wave-driven chemotaxis of Dictyostelium cells, which generates pressure waves that guide the sorting. The mechanisms we describe can easily be overlooked in studies of differential cell movement, hence certain experimental observations may be misinterpreted

Metabolic Adaptation after Whole Genome Duplication

Whole genome duplications (WGDs) have been hypothesized to be responsible for major transitions in evolution. However, the effects of WGD and subsequent gene loss on cellular behavior and metabolism are still poorly understood. Here we develop a genome scale evolutionary model to study the dynamics of gene loss and metabolic adaptation after WGD. Using the metabolic network of Saccharomyces cerevisiae as an example, we primarily study the outcome of WGD on yeast as it currently is. However, similar results were obtained using a recontructed hypothetical metabolic network of the pre-WGD ancestor.We show that the retention of genes in duplicate in the model, corresponds nicely with those retained in duplicate after the ancestral WGD in S. cerevisiae. Also, we observe that transporter and glycolytic genes have a higher probability to be retained in duplicate after WGD and subsequent gene loss, both in the model as in S. cerevisiae, which leads to an increase in glycolytic flux after WGD. Furthermore, the model shows that WGD leads to better adaptation than small-scale duplications, in environments for which duplication of a whole pathway instead of single reactions is needed to increase fitness. This is indeed the case for adaptation to high glucose levels. Thus, our model confirms the hypothesis that WGD has been important in the adaptation of yeast to the new, glucose-rich environment that arose after the appearance of angiosperms. Moreover, the model shows that WGD is almost always detrimental on the short term in environments to which the lineage is preadapted, but can have immediate fitness benefits in “new” environments. This explains why WGD, while pivotal in the evolution of many lineages and an apparent “easy” genetic operator, occurs relatively rarely

Sequential Predation: A Multi-model Study

In many ecosystems food resources are available sequentially. The paper analyses a situation with two competing prey species both of which are consumed by a common predator species. Within a season the two prey species are available sequentially, although there may be an overlap. Three modelling methodologies are applied to this system] discrete dynamical systems (difference equations), individual-oriented event-driven simulations and cellular automata. The presence of the predator is shown to have a strong impact on the outcome of the prey species competition. The system of coexisting prey species changes to a system of founder-controlled competition. It appears that sequential predation can even have counterintuitive evolutionary consequences for the prey species. The species which appears later in the season will be more successful in its competition with the early species if it favours the predator; for example, by a high leaf palatability. Spatial structuring and topological issues are found to play a crucial role in both the ecological and evolutionary dynamics. The advantages of a multi!model approach are discussed

Local Orientation and the Evolution of Foraging: Changes in Decision Making Can Eliminate Evolutionary Trade-offs

Information processing is a major aspect of the evolution of animal behavior. In foraging, responsiveness to local feeding opportunities can generate patterns of behavior which reflect or “recognize patterns” in the environment beyond the perception of individuals. Theory on the evolution of behavior generally neglects such opportunity-based adaptation. Using a spatial individual-based model we study the role of opportunity-based adaptation in the evolution of foraging, and how it depends on local decision making. We compare two model variants which differ in the individual decision making that can evolve (restricted and extended model), and study the evolution of simple foraging behavior in environments where food is distributed either uniformly or in patches. We find that opportunity-based adaptation and the pattern recognition it generates, plays an important role in foraging success, particularly in patchy environments where one of the main challenges is “staying in patches”. In the restricted model this is achieved by genetic adaptation of move and search behavior, in light of a trade-off on within- and between-patch behavior. In the extended model this trade-off does not arise because decision making capabilities allow for differentiated behavioral patterns. As a consequence, it becomes possible for properties of movement to be specialized for detection of patches with more food, a larger scale information processing not present in the restricted model. Our results show that changes in decision making abilities can alter what kinds of pattern recognition are possible, eliminate an evolutionary trade-off and change the adaptive landscape

Spatial Pattern Formation During Aggregation of the Slime Mould Dictyostelium discoideum

Stream formation and spiral wave behaviour during the aggregation of Dictyostelium discoideum (Dd) are studied in a model based on the Martiel-Goldbeter equations for cAMP relay, combined with chemotactic motion of Dd cells. The results show that stream formation occurs if the turnover rate of intracellular cAMP is increased. This increase in the turnover rate of cAMP[in] leads to a dependence of the speed of the cAMP wave on the cell density. We propose that this dependence of wave speed on cell density is the underlying mechanism for stream formation. Besides stream formation, increasing the turnover rate of cAMP[in] also results in a spiral wave period that decreases during aggregation, a phenomenon that is commonly observed in situ. Furthermore, the dependence of wave speed on cell density is measured empirically[ The speed of the cAMP wave is found to decrease as the wave travels from high to low cell density. This indicates that in situ, wave speed does depend on cell density