SANDPIT: Multi-scale dynamics and gene communities

Evolution has mostly been studied in the context of the higher organisms, where the transfer of genetic material is almost always from parents to offspring. However some years ago it was discovered that bacteria, by contrast, are able to transfer genetic material directly between individuals. The first type of transfer is called vertical and the second type horizontal. So when we talk about bacteria evolving, we are referring to the genes which they contain, and horizontal transfer is a way of changing this content. From the point of view of the genes, the bacteria are habitats where the genes can reside, just like an ecosystem such as a forest or lake is a habitat where plants and animals can reside. So while the survival and reproduction of genes and the bacteria they live in are related, the fact that genes are not bound to a specific organism means that their interests are not identical. So genetic material transferred between bacteria can evolve strategies that can either help or hurt the bacteria. These are referred to as mutualism and parasitism respectively. This means that the mechanism of natural selection may take place at two levels: at the genetic level and at the level of the organism, and that these may be in conflict with each other. This conflict is played out in the ways that the genes interact with each other, and how these interactions determine the properties of the bacterium in which they are found. Evolution is a process which is random, and there is evidence that randomness is important in the horizontal transfer of genes. The analysis of systems made up of a large number of interacting objects, which have a degree of randomness, is an important area of applied mathematics. So far, however, progress in analysing these systems mathematically has lagged behind their study using computer simulations. We propose to develop an appropriate mathematical analysis of horizontal gene transfer in bacteria. We will be guided by computer simulations and also by databases of the distribution of genes in a wide range of different organisms. The final theory, although developed for a specific biological situation, can provide a model for mathematical treatments of other interacting random systems, which are found widely in physical, biological, and social contexts. It will also address an important theoretical problem in biology. We have already referred to the fact that selection can happen at the lower (genetic) level and the higher (organism) level. There could in principle be more than two levels, leading to what is called multi-level selection. In this case entities (genes, bacteria,...) at each level can reproduce, mutate and compete with each other. We will also gain greater understanding of the way that genes in bacteria move around, and so gain some insight into the current diversity of bacteria which is observed. This should allow for the monitoring and managing of new infections and antibiotic resistance.

One of the major challenges of the 21st century is to develop a more quantitative theory of the biological and social sciences. The physical sciences have been formulated in a mathematical way for centuries, but the nature of the biological and social sciences has made this process far more difficult. However, the development of computer simulations has pointed the way forward. The interaction of a large number of entities, interacting with each other at given rates - which is typical of problems in these fields - can be effectively simulated. This has yielded many useful insights, but in order to draw general conclusions, understand governing principles and generally make statements with some kind of universal applicability, the development of novel mathematical frameworks and calculational schemes is required. In fact, the majority of computer simulations can be reformulated in mathematical form: they are Markov processes (in a perhaps extended state space) in which a large number of agents interact according to specified reaction schemes. Thus a large class of problems may be reduced to the analysis of such systems. Of course, the generic problem is very complex and intractable, but the project we are putting forward covers a large sub-class of such problems, namely those where several levels or stages are involved. Typical of these systems are entities which cluster together in groups, with a dynamic assumed for both the individual entities and the groups. Moreover, there are feedbacks between the two levels. We believe that the work suggested in this project will enable us to develop mathematical techniques to study systems of this type, and thus lead to methods to analyse general multi-level systems. This should lead to insights, and have application to, a large number of biological and social systems that have a hierarchical structure. Evolution is at the heart of all biology, so improving our understanding of evolution has the potential to contribute to advancing almost every fundamental biological field: development, disease, immunity, healing, ageing, populations, ecosystems, etc. Many of the fundamental principles and theoretical constructs of evolution are based on studies of higher eukaryotes, where lineages and species are relatively well defined, and horizontal transfer is the exception, and representations of related families of organisms are appropriately represented by phylogenetic trees. Higher eukaryotes, however, represent only a miniscule fraction of life on earth. The tools and approaches that often are used to study the vast bulk of life may be inappropriate. For example, the observation that there are species of bacteria cannot be understood with eukaryotic approaches such as reproductive isolation. Unfortunately, we have not generated a sufficiently advanced alternative conceptual framework. This project is directed towards the aspects of bacterial evolution that are central to its difference from eukaryotic evolution. Insights that we draw from our study of these aspects will help to create this alternative framework. More specifically, the properties of biological systems are the result of the evolutionary process. Features can arise through many different mechanisms, including adaptation, neutral drift, hitchhiking, or as consequences of the evolutionary dynamics or of other evolutionary changes. Unravelling how and why these features emerged, and what that implies about the functional and physiological significance of these features, is often best addressed with models that capture the necessary salient aspects of this evolutionary process. Conversely, evolution occurs through the changes in assemblies of biological macromolecules. The nature of the evolutionary process cannot be understood without understanding the constraints imposed by the properties of these evolving systems, by the molecular processes available to the organisms.