Evolving homeostatic tissue using genetic algorithms

Multicellular organisms maintain form and function through a multitude of homeostatic mechanisms. The details of these mechanisms are in many cases unknown, and so are their evolutionary origin and their link to development. In order to illuminate these issues we have investigated the evolution of structural homeostasis in the simplest of cases, a tissue formed by a mono-layer of cells. To this end, we made use of a 3-dimensional hybrid cellular automaton, an individual-based model in which the behaviour of each cell depends on its local environment. Using an evolutionary algorithm (EA) we evolved cell signalling networks, both with a fixed and an incremental fitness evaluation, which give rise to and maintain a mono-layer tissue structure. Analysis of the solutions provided by the EA shows that the two evaluation methods gives rise to different types of solutions to the problem of homeostasis. The fixed method leads to almost optimal solutions, where the tissue relies on a high rate of cell turnover, while the solutions from the incremental scheme behave in a more conservative manner, only dividing when necessary. In order to test the robustness of the solutions we subjected them to environmental stress, by wounding the tissue, and to genetic stress, by introducing mutations. The results show that the robustness very much depends on the mechanism responsible for maintaining homeostasis. The two evolved cell types analysed present contrasting mechanisms by which tissue homeostasis can be maintained. This compares well to different tissue types found in multicellular organisms. For example the epithelial cells lining the colon in humans are shed at a considerable rate, while in other tissue types, which are not as exposed, the conservative type of homeostatic mechanism is normally found. These results will hopefully shed light on how multicellular organisms have evolved homeostatic mechanisms and what might occur when these mechanisms fail, as in the case of cancer.     

Mechanisms of developmental robustness

We present a review of noise buffering mechanisms responsible for developmental robustness. We focus on functions of chaperone Hsp90, miRNA, and cross-regulation of gap genes in Drosophila. The noise buffering mechanisms associated with these functions represent specific examples of the developmental canalization, reducing the phenotypical variability in presence of either genetic or environmental perturbations. We demonstrate that robustness often appears as a function of a network of interacting elements and that the system level approach is needed to understand the mechanisms of noise filtering.     

Structural robustness of metabolic networks with respect to multiple knockouts

We present a generalised framework for analysing structural robustness of metabolic networks, based on the concept of elementary flux modes (EFMs). Extending our earlier study on single knockouts [Wilhelm, T., Behre, J., Schuster, S., 2004. Analysis of structural robustness of metabolic networks. IEE Proc. Syst. Biol. 1(1), 114-120], we are now considering the general case of double and multiple knockouts. The robustness measures are based on the ratio of the number of remaining EFMs after knockout vs. the number of EFMs in the unperturbed situation, averaged over all combinations of knockouts. With the help of simple examples we demonstrate that consideration of multiple knockouts yields additional information going beyond single-knockout results. It is proven that the robustness score decreases as the knockout depth increases.We apply our extended framework to metabolic networks representing amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes. Moreover, in the E. coli model the two subnetworks synthesising amino acids that are essential and those that are non-essential for humans are studied separately. The results are discussed from an evolutionary viewpoint. We find that E. coli has the most robust metabolism of all the cell types studied here. Considering only the subnetwork of the synthesis of non-essential amino acids, E. coli and the human hepatocyte show about the same robustness.     

An agent-based model to investigate the roles of attractive and repellent pheromones in ant decision making during foraging

Pharaoh's ants organise their foraging system using three types of trail pheromone. All previous foraging models based on specific ant foraging systems have assumed that only a single attractive pheromone is used. Here we present an agent-based model based on trail choice at a trail bifurcation within the foraging trail network of a Pharaoh's ant colony which includes both attractive (positive) and repellent (negative) trail pheromones. Experiments have previously shown that Pharaoh's ants use both types of pheromone. We investigate how the repellent pheromone affects trail choice and foraging success in our simulated foraging system. We find that both the repellent and attractive pheromones have a role in trail choice, and that the repellent pheromone prevents random fluctuations which could otherwise lead to a positive feedback loop causing the colony to concentrate its foraging on the unrewarding trail. An emergent feature of the model is a high level of variability in the level of repellent pheromone on the unrewarding branch. This is caused by the repellent pheromone exerting negative feedback on its own deposition. We also investigate the dynamic situation where the location of the food is changed after foraging trails are established. We find that the repellent pheromone has a key role in enabling the colony to refocus the foraging effort to the new location. Our results show that having a repellent pheromone is adaptive, as it increases the robustness and flexibility of the colony's overall foraging response.     

Bayesian nonparametric meta-analysis using Polya tree mixture models

Summary .   A common goal in meta-analysis is estimation of a single effect measure using data from several studies that are each designed to address the same scientific inquiry. Because studies are typically conducted in geographically disperse locations, recent developments in the statistical analysis of meta-analytic data involve the use of random effects models that account for study-to-study variability attributable to differences in environments, demographics, genetics, and other sources that lead to heterogeneity in populations. Stemming from asymptotic theory, study-specific summary statistics are modeled according to normal distributions with means representing latent true effect measures. A parametric approach subsequently models these latent measures using a normal distribution, which is strictly a convenient modeling assumption absent of theoretical justification. To eliminate the influence of overly restrictive parametric models on inferences, we consider a broader class of random effects distributions. We develop a novel hierarchical Bayesian nonparametric Polya tree mixture (PTM) model. We present methodology for testing the PTM versus a normal random effects model. These methods provide researchers a straightforward approach for conducting a sensitivity analysis of the normality assumption for random effects. An application involving meta-analysis of epidemiologic studies designed to characterize the association between alcohol consumption and breast cancer is presented, which together with results from simulated data highlight the performance of PTMs in the presence of nonnormality of effect measures in the source population.     

Objective Bayesian analysis for the Student-t regression model

We develop a Bayesian analysis based on two different Jeffreyspriors for the Student-t regression model with unknown degreesof freedom. It is typically difficult to estimate the numberof degrees of freedom: improper prior distributions may leadto improper posterior distributions, whereas proper prior distributionsmay dominate the analysis. We show that Bayesian analysis witheither of the two considered Jeffreys priors provides a properposterior distribution. Finally, we show that Bayesian estimatorsbased on Jeffreys analysis compare favourably to other Bayesianestimators based on priors previously proposed in the literature.     

Evolution of Structural Shape in Bacterial Globin-Related Proteins

The globin family of proteins has a characteristic structural pattern of helix interactions that nonetheless exhibits some variation. A simplified model for globin structural evolution was developed in which protein shape evolved by random change of contacts between helices. A conserved globin domain of 15 bacterial proteins representing four structural families was studied. Using a parsimony approach ancestral structural states could be reconstructed. The distribution of number of contact changes per site for a fixed topology tree fit a gamma distribution. Homoplasy was high, with multiple changes per site and no support for an invariant class of residue-residue contacts. Contacts changed more slowly than sequence. A phylogenetic reconstruction using a distance measure based on the proportion of shared contacts was generally consistent with a sequence-based phylogeny but not highly resolved. Contact pattern convergence between members of different globin family proteins could not be detected. Simulation studies indicated the convergence test was sensitive enough to have detected convergence involving only 10% of the contacts, suggesting a limit on the extent of selection for a specific contact pattern. Contact site methods may provide additional approaches to study the relationship between protein structure and sequence evolution. [Reviewing Editior: Dr. Lauren Ancel Meyers]     

Design of a network with state stability

Designing a network with given functions or reconstruct a network based on its dynamical behavior is an important problem in the study of complex systems. In this paper, we put forward certain principles in constructing a network with state stability. We show that a necessary and sufficient condition to design networks with a global fixed point is that active nodes inhibit inactive nodes, while the latter activate the former directly or indirectly. We also designed networks based on basic modules, where each basic module consists a sub-network, they communicate through the inhibition link from each activator in lower module to the inhibitor of upper module. We found that long activation links, i.e. indirect activation links are important to the formation of convergence trajectory. We believe that these principles may help us to understand the topology of biological networks.     

Robustness: predicting the effects of life history perturbations on stage-structured population dynamics

Matrix-based models lie at the core of many applications across the physical, engineering and life sciences. In ecology, matrix models arise naturally via population projection matrices (PPM). The eigendata of PPMs provide detailed quantitative and qualitative information on the dynamic behaviour of model populations, especially their asymptotic rates of growth or decline. A fundamental task in modern ecology is to assess the effect that perturbations to life-cycle transition rates of individuals have on such eigendata. The prevailing assessment tools in ecological applications of PPMs are direct matrix simulations of eigendata and linearised extrapolations to the typically non-linear relationship between perturbation magnitude and the resulting matrix eigenvalues. In recent years, mathematical systems theory has developed an analytical framework, called 'Robustness Analysis and Robust Control', encompassing also algorithms and numerical tools. This framework provides a systematic and precise approach to studying perturbations and uncertainty in systems represented by matrices. Here we lay down the foundations and concepts for a 'robustness' inspired approach to predictive analyses in population ecology. We treat a number of application-specific perturbation problems and show how they can be formulated and analysed using these robustness methodologies.     

Extending Zelterman's approach for robust estimation of population size to zero-truncated clustered Data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency.