Mark Broom

Protein–RNA interactions: Structural analysis and functional classes

A data set of 89 protein–RNA complexes has been extracted from the Protein Data Bank, and the nucleic acid recognition sites characterized through direct contacts, accessible surface area, and secondary structure motifs. The differences between RNA recognition sites that bind to RNAs in functional classes has also been analyzed. Analysis of the complete data set revealed that van der Waals interactions are more numerous than hydrogen bonds and the contacts made to the nucleic acid backbone occur more frequently than specific contacts to nucleotide bases. Of the base‐specific contacts that were observed, contacts to guanine and adenine occurred most frequently. The most favored amino acid–nucleotide pairings observed were lysine–phosphate, tyrosine–uracil, arginine–phosphate, phenylalanine–adenine and tryptophan–guanine. The amino acid propensities showed that positively charged and polar residues were favored as expected, but also so were tryptophan and glycine. The propensities calculated for the functional classes showed trends similar to those observed for the complete data set. However, the analysis of hydrogen bond and van der Waal contacts showed that in general proteins complexed with messenger RNA, transfer RNA and viral RNA have more base specific contacts and less backbone contacts than expected, while proteins complexed with ribosomal RNA have less base‐specific contacts than the expected. Hence, whilst the types of amino acids involved in the interfaces are similar, the distribution of specific contacts is dependent upon the functional class of the RNA bound. Proteins 2007.

Game-theoretical models in biology

Introduction The history of evolutionary games The key mathematical developments The range of applications Reading this book What Is a Game? Key game elements Games in biological settings Two Approaches to Game Analysis The dynamical approach The static approach-evolutionarily stable strategies (ESSs) Dynamics versus statics Some Classical Games The hawk-dove game The prisoners dilemma The war of attrition The sex ratio game The Underlying Biology Darwin and natural selection Genetics Games involving genetics Fitness, strategies and players Selfish genes: how can non-beneficial genes propagate? The role of simple mathematical models Matrix Games Properties of ESSs ESSs in a 2 x 2 matrix game Haighs procedure to locate all ESSs ESSs in a 3 x 3 matrix game Patterns of ESSs Extensions to the hawk-dove game Nonlinear Games Overview and general theory Linearity in the focal player strategy and playing the field Nonlinearity due to non-constant interaction rates Nonlinearity in the strategy of the focal player Some differences between linear and nonlinear theory Asymmetric Games Seltens theorem for games with two roles Bimatrix games Uncorrelated asymmetry-the owner-intruder game Correlated asymmetry Multi-Player Games Multi-player matrix games The multi-player war of attrition Structures of dependent pairwise games Extensive Form Games and Other Concepts in Game Theory Games in extensive form Perfect, imperfect and incomplete information Repeated games State-Based Games State-based games A question of size Life history theory Games in Finite and Structured Populations Finite populations and stochastic games Evolution on graphs Spatial games and cellular automata Adaptive Dynamics Introduction and philosophy Fitness functions and the fitness landscape Pairwise invasibility and evolutionarily singular strategies Adaptive dynamics with multiple traits The assumptions of adaptive dynamics The Evolution of Cooperation Kin selection and inclusive fitness Greenbeard genes Direct reciprocity: developments of the prisoners dilemma Punishment Indirect reciprocity and reputation dynamics The evolution of cooperation on graphs Multi-level selection Group Living The costs and benefits of group living Dominance hierarchies: formation and maintenance The enemy without: responses to predators The enemy within: infanticide and other anti-social behavior Mating Games Introduction and overview Direct conflict Indirect conflict and sperm competition The battle of the sexes Selecting mates: signaling and the handicap principle Other signaling scenarios Food Competition Introduction Ideal free distribution for a single species Ideal free distribution for multiple species Distributions at and deviations from the ideal free distribution Compartmental models of kleptoparasitism Compartmental models of interference Producer-scrounger models Predator-Prey and Host-Parasite Interactions Game-theoretical predator-prey models The evolution of defense and signaling Brood parasitism Parasitic wasps and the asymmetric war of attrition Complex parasite lifecycles Epidemic Models SIS and SIR models The evolution of virulence Viruses and the prisoners dilemma Conclusions Types of evolutionary games used in biology What makes a good mathematical model? Future developments Appendix: Intro to MATLAB Bibliography Index MATLAB, Further Reading, and Exercises appear at the end of each chapter.

An analysis of the fixation probability of a mutant on special classes of non-directed graphs

There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312–316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations.

Multi-player matrix games

Game theory has had remarkable success as a framework for the discussion of animal behaviour and evolution. It suggested new interpretations and prompted new observational studies. Most of this work has been done with 2-player games. That is the individuals of a population compete in pairwise interactions. While this is often the case in nature, it is not exclusively so. Here we introduce a class of models for situations in which more than two (possibly very many) individuals compete simultaneously. It is shown that the solutions (i.e. the behaviour which may be expected to be observable for long periods) are more complex than for 2-player games. The concluding section lists some of the new phenomena which can occur.

Association patterns and shoal fidelity in the three-spined stickleback

We investigated pairwise association patterns and shoal fidelity in free–ranging, individual three–spine sticklebacks (Gasterosteus aculeatus) by capturing entire shoals of sticklebacks and tagging each shoal member with a unique individual mark before releasing the shoal at the point of capture. We recaptured tagged fishes in the study area on five subsequent days, noting their identity, their location and the individuals with which they were associated. Stable partner associations between fishes were observed which might provide the basis for shoal fidelity via social networks. These results suggest the potential for the kinds of inter–individual association patterns assumed by models of predator inspection and ‘tit–for–tat’ behaviours in free–ranging fishes.

Can epidemic models describe the diffusion of topics across disciplines

This paper introduces a new approach to describe the spread of research topics across disciplines using epidemic models. The approach is based on applying individual-based models from mathematical epidemiology to the diffusion of a research topic over a contact network that represents knowledge flows over the map of science—as obtained from citations between ISI Subject Categories. Using research publications on the protein class kinesin as a case study, we report a better fit between model and empirical data when using the citation-based contact network. Incubation periods on the order of 4–15.5 years support the view that, whilst research topics may grow very quickly, they face difficulties to overcome disciplinary boundaries.

Evolutionary games on graphs and the speed of the evolutionary process

In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example.

Evolutionary dynamics on small-order graphs

Abstract We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [E. Lieberman, C. Hauert and M. A. Nowak (2005), Evolutionary dynamics on graphs, Nature, Vol. 433, pp. 312–316]. We consider all possible connected undirected graphs of orders three through eight. For each graph, using the Monte Carlo Markov Chain simulations, we determine the fixation probability of a mutant introduced at every possible vertex. We show that the fixation probability depends on the vertex and on the graph. A randomly placed mutant has the highest chances of fixation in a star graph, closely followed by star-like graphs, and the fixation probability is lowest for regular and almost regular graphs. We also find that within a fixed graph, the fixation probability of a mutant has a negative correlation with the degree of the starting vertex.

Two results on evolutionary processes on general non-directed graphs

The paper [Broom & Rychtař (2008)][1] analytically investigated the probability for mutants to fixate in an otherwise uniform population on two types of heterogeneous graphs (lines and stars) by evolutionary dynamics. The main motivation for concentrating on those two types of graphs only was the

Evolutionary Dynamics on Graphs - the Effect of Graph Structure and Initial Placement on Mutant Spread

We study the stochastic birth-death process in a finite and structured population and analyze how the fixation probability of a mutant depends on its initial placement. In particular, we study how the fixation probability depends on the degree of the vertex where the mutant is introduced, and which vertices are its neighbours. We find that within a fixed graph, the fixation probability of a mutant has a negative correlation with the degree of the starting vertex. For a general mutant fitness r, we give approximations of relative fixation probabilities in terms of the fixation probabilities of neighbours which will be useful for considering graphs of relatively simple structure but many vertices, for instance of the small world network type, and compare our approximations to simulation results. Further, we explore which types of graphs are conducive to mutant fixation and which are not. We find a high positive correlation between a fixation probability of a randomly placed mutant and the variation of vertex degrees on that graph.