Robert M. Seymour

Computational challenges of systems biology

Progress in the study of biological systems such as the heart, brain, and liver will require computer scientists to work closely with life scientists and mathematicians. Computer science will play a key role in shaping the new discipline of systems biology and addressing the significant computational challenges it poses.

Augmented discounting: interaction between ageing and time–preference behaviour

Discounting occurs when an immediate benefit is systematically valued more highly than a delayed benefit of the same magnitude. It is manifested in physiological and behavioural strategies of organisms. This study brings together life–history theory and time–preference theory within a single modelling framework. We consider an animal encountering reproductive opportunities as a random process. Under an external hazard, optimal life–history strategy typically prioritizes immediate reproduction at the cost of declining fertility and increasing mortality with age. Given such ageing, an immediate reproductive reward should be preferred to a delayed reward because of both the risk of death and declining fertility. By this analysis, ageing is both a consequence of discounting by the body and a cause of behavioural discounting. A series of models is developed, making different assumptions about external hazards and biological ageing. With realistic ageing assumptions (increasing mortality and an accelerating rate of fertility decline) the time–preference rate increases in old age. Under an uncertain external hazard rate, young adults should also have relatively high time–preference rates because their (Bayesian) estimate of the external hazard is high. Middle–aged animals may therefore be the most long term in their outlook.

The Evolution of Continuous Variation in Ejaculate Expenditure Strategy

Sperm competition theory has largely focused on the evolution of ejaculate expenditure strategies across different species or populations or across discrete mating roles on which sperm competition operates differentially. Few studies have considered the extent to which male ejaculate expenditure is influenced by continuous change in male phenotype within a population. Here we model how optimal ejaculate expenditure responds to two sources of continuous variation: (1) the quantity of resources allocated by a male to mating within a breeding season and (2) the resource cost of obtaining a mate. We find that variation in the amount of resources available for mating does not alone produce selection for differing ejaculate investment strategies. However, when there is variation in the cost of obtaining a mate, males with a lower cost will be selected to invest fewer sperm per mating than males whose cost is higher. Any parameter decreasing this cost will also select for decreased ejaculate investment per mating. These results provide a novel insight into the evolution of male ejaculate expenditure strategies, revealing that individual constraints on the ability to secure matings can lead to variation in ejaculate expenditure even when the risk of sperm competition is the same for all males.

Regional-scale scenario modeling for coral reefs: a decision support tool to inform management of a complex system

The worldwide decline of coral reefs threatens the livelihoods of coastal communities and puts at risk valuable ecosystem services provided by reefs. There is a pressing need for robust predictions of potential futures of coral reef and associated human systems under alternative management scenarios. Understanding and predicting the dynamics of coral reef systems at regional scales of tens to hundreds of kilometers is imperative, because reef systems are connected by physical and socioeconomic processes across regions and often across international boundaries. We present a spatially explicit regional-scale model of ecological dynamics for a general coral reef system. In designing our model as a tool for decision support, we gave precedence to portability and accessibility; the model can be parameterized for dissimilar coral reef systems in different parts of the world, and the model components and outputs are understandable for nonexperts. The model simulates local-scale dynamics, which are coupled across regions through larval connectivity between reefs. We validate our model using an instantiation for the Meso-American Reef system. The model realistically captures local and regional ecological dynamics and responds to external forcings in the form of harvesting, pollution, and physical damage (e.g., hurricanes, coral bleaching) to produce trajectories that largely fall within limits observed in the real system. Moreover, the model demonstrates behaviors that have relevance for management considerations. In particular, differences in larval supply between reef localities drive spatial variability in modeled reef community structure. Reef tracts for which recruitment is low are more vulnerable to natural disturbance and synergistic effects of anthropogenic stressors. Our approach provides a framework for projecting the likelihood of different reef futures at local to regional scales, with important applications for the management of complex coral reef systems.

Costly but worthless gifts facilitate courtship

What are the characteristics of a good courtship gift? We address this question by modelling courtship as a sequential game. This is structured as follows: the male offers a gift to a female; after observing the gift, the female decides whether or not to accept it; she then chooses whether or not to mate with the male. In one version of the game, based on human courtship, the female is uncertain about whether the male intends to stay or desert after mating. In a second version, there is no paternal care but the female is uncertain about the males quality. The two versions of the game are shown to be mathematically equivalent. We find robust equilibrium solutions in which mating is predominantly facilitated by an ‘extravagant’ gift which is costly to the male but intrinsically worthless to the female. By being costly to the male, the gift acts as a credible signal of his intentions or quality. At the same time, its lack of intrinsic value to the female serves to deter a ‘gold-digger’, who has no intention of mating with the male, from accepting the gift. In this way, an economically inefficient gift enables mutually suitable partners to be matched.

Selection for mitonuclear co-adaptation could favour the evolution of two sexes

Mitochondria are descended from free-living bacteria that were engulfed by another cell between one and a half to two billion years ago. A redistribution of DNA led to most genetic information being lost or transferred to a large central genome in the nucleus, leaving a residual genome in each mitochondrion. Oxidative phosphorylation, the most critical function of mitochondria, depends on the functional compatibility of proteins encoded by both the nucleus and mitochondria. We investigate whether selection for adaptation between the nuclear and mitochondrial genomes (mitonuclear co-adaptation) could, in principle, have promoted uniparental inheritance of mitochondria and thereby the evolution of two mating types or sexes. Using a mathematical model, we explore the importance of the radical differences in ploidy levels, sexual and asexual modes of inheritance, and mutation rates of the nucleus and mitochondria. We show that the major features of mitochondrial inheritance, notably uniparental inheritance and bottlenecking, enhance the co-adaptation of mitochondrial and nuclear genes and therefore improve fitness. We conclude that, under a wide range of conditions, selection for mitonuclear co-adaptation favours the evolution of two distinct mating types or sexes in sexual species.

Evolution of the human ABO polymorphism by two complementary selective pressures

The best–known example of terminal–glycan variation is the ABO histo–blood group polymorphism in humans. We model two selective forces acting on histo–blood group antigens that may account for this polymorphism. The first is generated by the invasion of opportunistic bacterial or other pathogens that interact with the epithelial–mucosal surfaces. The bacteria adapt to the microenvironments of common host phenotypes and so create frequency–dependent selection for rarer host alleles. The second is generated by intracellular viruses, and accounts for the observed differentials between the ABO–phenotype frequencies. It is thought that viruses acquire histo–blood group structures as part of their envelope from their previous host. The presence of host antigens on the viral envelope causes differential transmission of the virus between host types owing to the asymmetric action of ABO natural antibodies. Our model simulations show that these two forces acting together can account for the major features of the ABO polymorphism in humans.

Dynamics of mitochondrial inheritance in the evolution of binary mating types and two sexes

The uniparental inheritance (UPI) of mitochondria is thought to explain the evolution of two mating types or even true sexes with anisogametes. However, the exact role of UPI is not clearly understood. Here, we develop a new model, which considers the spread of UPI mutants within a biparental inheritance (BPI) population. Our model explicitly considers mitochondrial mutation and selection in parallel with the spread of UPI mutants and self-incompatible mating types. In line with earlier work, we find that UPI improves fitness under mitochondrial mutation accumulation, selfish conflict and mitonuclear coadaptation. However, we find that as UPI increases in the population its relative fitness advantage diminishes in a frequency-dependent manner. The fitness benefits of UPI ‘leak’ into the biparentally reproducing part of the population through successive matings, limiting the spread of UPI. Critically, while this process favours some degree of UPI, it neither leads to the establishment of linked mating types nor the collapse of multiple mating types to two. Only when two mating types exist beforehand can associated UPI mutants spread to fixation under the pressure of high mitochondrial mutation rate, large mitochondrial population size and selfish mutants. Variation in these parameters could account for the range of UPI actually observed in nature, from strict UPI in some Chlamydomonas species to BPI in yeast. We conclude that UPI of mitochondria alone is unlikely to have driven the evolution of two mating types in unicellular eukaryotes.

Addressing the challenges of multiscale model management in systems biology

Mathematical and computational modelling are emerging as important techniques for studying the behaviour of complex biological systems. We argue that two advances are necessary to properly leverage these techniques: firstly, the ability to integrate models developed and executed on separate tools, without the need for substantial translation and secondly, a comprehensive system for storing and man-ageing not only the models themselves but also the parameters and tools used to execute those models and the results they produce. A framework for modelling with these features is described here. We have developed of a suite of XML-based services used for the storing and analysis of models, model parameters and results, and tools for model integration. We present these here, and evaluate their effectiveness using a worked example based on part of the hepatocyte glycogenolysis system.

Using large-scale perturbations in gene network reconstruction

BackgroundRecent analysis of the yeast gene network shows that most genes have few inputs, indicating that enumerative gene reconstruction methods are both useful and computationally feasible. A simple enumerative reconstruction method based on a discrete dynamical system model is used to study how microarray experiments involving modulated global perturbations can be designed to obtain reasonably accurate reconstructions. The method is tested on artificial gene networks with biologically realistic in/out degree characteristics.ResultsIt was found that a relatively small number of perturbations significantly improve inference accuracy, particularly for low-order inputs of one or two genes. The perturbations themselves should alter the expression level of approximately 50–60% of the genes in the network.ConclusionsTime-series obtained from perturbations are a common form of expression data. This study illustrates how gene networks can be significantly reconstructed from such time-series while requiring only a relatively small number of calibrated perturbations, even for large networks, thus reducing experimental costs.