Regional Meeting on Mathematics, Computation and Biology 2nd June 2009 University of Bristol

Abstracts

Presentations

Andrew Pomiankowski: Keynote Speaker

Stalk-eyed flies are a classic textbook example of exaggerated sexual ornaments evolving through the action of female mate preference. Putative genetic benefits are genes which confer condition or suppressors of meiotic drive. Female stalk-eyed flies also show low fertility. Males transfer very small ejaculates and very few sperm per mating. Females need to mate multiply in order to raise their fertility. Here we investigate whether preference for larger male eyespan (the sexual ornament) could confer fertility benefits on females. Theory suggests that the conditions under which this can occur are limited, and many of our findings support this view. However, the nature of the stalk-eyed fly mating system points to natural conditions under which females can gain fertility benefits. The contribution of fertility and genetic benefits to the evolution of mate preference will be compared.

Richard Brereton: "Pattern Recognition for Metabolomic Profiling"

Chemical constituents of secretions such as sweat, urine, saliva, mammal scent marks contain up to 500 identifiable chemicals. This chemosignal contains a wealth of information e.g. about genetics, age, sex, diet, disease state etc. Pattern Recognition approaches can be employed to unravel this complex signal. Case studies involving an isolated population in Carinthia (Southern Austria) and mice clones will be described in order to look at whether there are signals representative of sex (humans), diet (mice), genetics (mice). Also the chemosignal can be related to microbial communities, as microbes are likely to be responsible for some or most of the chemicals detected. A variety of pattern recognition approaches can be employed including exploratory methods (PCA and Self Organising Maps), Linear methods for discrimination (Partial Least Squares and Linear Discriminant Analysis), Neural Networks (Learning Vector Quantisation), Support Vector Machines and Multiblock Methods (Procrustes).

Elva Robinson: "Individual comparisons and collective decisions"

Collective decisions emerge from the individual-level behaviour of members of a group. Some individuals may be better informed than others, especially if only certain group members have had the opportunity to compare available options. Emigrating ant colonies (Temnothorax albipennis) show sophisticated nest-site choice, selecting superior sites even when they are nine times further away than the alternative. How do they do this? We used RFID (Radio-frequency Identification) tagged ants to monitor individual behaviour. Here we show for the first time that switching between nests during the decision process can influence nest choice without requiring direct comparison of nests. Ants finding the poor nest were likely to switch and find the good nest, whereas ants finding the good nest were more likely to stay committed to that nest. When ants switched quickly between the two nests, colonies chose the good nest. Switching by ants that had the opportunity to compare nests had little effect on nest choice. We suggest a new mechanism of collective nest choice: individuals respond to nest quality by the decision either to commit or to seek alternatives. Previously proposed mechanisms, recruitment latency and nest comparison, can be explained as side-effects of this simple rule. Colony-level comparison and choice can emerge, without direct comparison circuit. by individuals.

Tom Richardson: "Record dynamics and social feedback in ants"

The success of social animals (including ourselves) can be attributed to efficiencies that arise from a division of labour. Many animal societies have a communal nest which certain individuals must leave to forage. Staying at home to care for young or leaving to find food is one of the most fundamental divisions of labour. It is also often a choice between safety and danger. The nest offers safety in numbers and a sustaining microclimate. The outside world may team with natural enemies and deadly environmental risks. Here we explore the regulation of exits from ant nests. We consider the extreme situation in which no one returns and show experimentally that exiting decisions seem to be governed by record signals. A record signal is a new "high water mark" in the history of a system. Clearly, ants should hesitate to enter a dangerous outside world from which no one returns. Foraging triggered by record signals, perhaps because the ants in the nest are hungrier than ever before, could be a very effective mechanism to postpone, until the last possible moment, a potentially fatal decision. We also show that record dynamics seem to play a role for first exits by individually marked ants even when their nest mates are allowed to re-enter the nest. So record dynamics may play a role in ant social systems both in emergencies and in everyday life. The dynamics of certain physical systems seem to be based on record signals but this is the first time they have been shown in a biological system.

Marios Richards: "Compensating For Something - What's Missing From Epistasis?"

Models of epistasis are significant for several major problems in theoretical evolutionary biology (evolution of sex and mutational meltdown in asexual populations), but while previous work has highlighted the significance of compensatory mutations in biasing the average direction of epistasis current models neglect compensatory mutation. We present a generalised process-driven model, reformulate the assumptions of current models as predictions of the behaviour of the processes of deleterious and compensatory mutation and show them to be falsified by in silico studies of epistatic interactions in artificial gene networks. We also extend analysis from previous work positing that fitness landscape topology constrains the independence of terms in current epistasis models to predict specific relationships and show them to hold in the simulated systems. These results of are of particular significance for systems where the 'unmutated' reference sequence cannot be assumed to have the optimal fitness (cases where environmental change or coevolution are common).

Ana Sendova-Franks: "Movement patterns and social organisation: how ants move inside their nests"

Movement is the observable signature of behaviour. Excitingly, in recent years, studies of animal movement patterns have increased due, at least in part, to the development of tracking technologies. In a diverse species among the insects, fish, birds and mammals, movement is studied in relation to searching, foraging, defence, dispersal, migration, aggregation and segregation. In social insects, studying the movement of individuals within the confines of the colony nest is crucial for understanding their social organisation. In particular, movement patterns inside the nest are fundamental to, among others, task allocation and division of labour, brood sorting, building, the facilitation of the spread of resources, defence against the spread of disease. In Temnothorax ants and bumble bees, for example, individual workers have Spatial Fidelity Zones (SFZs) inside the nest. In Temnothorax the relative order of the SFZs is re-established after an emigration to a new nest site and is robust to the removal of the brood, the queen and a large proportion of the workers. Such spatial and social resilience facilitates an efficient division of labour because individuals can resume their tasks after a colony disturbance. An important question is how such worker sorting takes place. Furthermore, the building of the perimeter wall for the colony nest is episodic rather than continuous. Hence another important question is how the colony manages to cope with changing population density in its day-to-day division of labour. Here we show our first results from studying the movement patterns of individual workers within the nest when the complete colony is settled in it. We manipulated population density by offering each colony to occupy in a temporal sequence of nests with increasing or decreasing area. We found that the distribution of individual average moving velocity is continuous at both high and low population density. This is compatible with existing models of worker sorting. There is also evidence of some constraint on individual movement at high density. Instantaneous velocity is lower and flight length shorter when the nest area is smaller. Furthermore, at low density, a worker's average moving velocity is positively related to the fraction of time it was moving (a measure of its activity) while this relationship appears to be absent at high density. Yet there is no evidence that this impacts on the amount of work done. Our results also show that flight length follows a broad Levy-like distribution and that movement bout duration has a fractal character. These two signatures of a complex system pose the question whether the observed individual movement patterns are due to interactions or to individual ant behaviour.

David Gibson: "Computer Vision based Analysis of Moth Camouflage"

In this work we present the use of computational learning algorithms to provide potential analogues of human and bird visual systems for the study of the cryptic and disruptive camouflage of moths. Images of a background tree bark are treated with triangular foreground targets textured using a fully automated computational synthesis system in a similar style to that described in previous work (Cuthill et al, Nature 2005, and Fraser et al, Proc. R. Soc. B. 2007). Two learning algorithms are used: a Support Vector Machine (SVM), a single `strong' classifier and Adaptive Boosting (AdaBoost) a collection of many `weak' classifiers. Classification of grey level treated images is based on learning discriminative features generated by image responses to banks of log Gabor filters for foreground and background texture. A significant advantage of AdaBoost is that it enables a convenient insight into the importance of particular features in the very high dimensional feature space for recognition. In this work we show that the proposed computational model gives recognition results similar to those of human studies and indicate which features contribute to successful recognition. The combined application of computational synthesis, learning and classification is novel and the experimental results and analysis are providing new insights into animal camouflage.

Alejo Nevado: "Analytical and computational analysis of basal ganglia's oscillatory behaviour in Parkinson's disease"

The advance of Parkinson's disease is associated with the presence of abnormal oscillations within basal ganglia with frequencies including beta band. The question of the origin of these oscillations is still open, but some evidence suggests the oscillations observed in the basal ganglia originate from the network comprised of two nuclei: subthalamic nucleus (STN) and globus pallidus pars externa (GPe). We develop a computational model of the STN-GPe network based upon anatomical and electrophysiological studies. The simulations of the model demonstrate that as the parameters were changed to values corresponding to Parkinson's disease, the model started to produce beta band oscillations. Through mathematical analysis of the model we identified a simple set of necessary conditions on model parameters, which guarantees the existence of oscillatory behaviour in the beta band frequency. The validity of these conditions was confirmed in simulations. Importantly, these conditions describe changes in parameters that are consistent with those expected as a result of the development of Parkinon's disease, and predict manipulations that could inhibit the pathological oscillations.

Rafal Bogacz: "Do we have the Bayes theorem hardwired in our brains?"

Making fast and accurate decisions on the basis of noisy sensory information is critically important for survival of animals. One of the procedures that maximizes the speed of decisions (for a given accuracy), involves calculating the posterior probabilities of alternatives being correct (given sensory information), and making a choice as soon as the posterior probability for one of the alternatives exceeds a threshold. The posterior probabilities can be computed using the Bayes theorem, but does our brain support such computation? During this talk I will argue that the posterior probabilities are computed in a neural circuit involving cortex, basal ganglia and thalamus, and the Bayes equation can be mapped on the anatomy of this circuit.

Tom Gorochowski, Oliver Purcell, Petros Mina, and Stephen Reid : "Bacto-Builders"

Assembling particles at microscopic scales into desired patterns or structures is currently either extremely difficult, or in some cases impossible. This talk will introduce the BCCS iGEM 2008 project, "Bacto-Builders", which aims to help. As all construction projects require the manipulation of varying size components, in some cases much greater than any individual, it is necessary to work in teams towards a common goal. This idea forms the basis of the project which attempts to genetically engineer bacteria to physically move particles, through contact with a co-ordinated swarm. A stochastic agent based simulation environment is used to evaluate simple genetic programs (GRNs) that lead to favourable emergent behaviours. These are then evaluated and compared in silco to help guide biological experimentation. At the same time, results from the lab are feed back into the models, refining simulation accuracy. The talk will cover both modelling and wet-lab aspects of the project and briefly introduce some of the new ideas for the BCCS iGEM 2009 entry.

Konstantin Blyuss: "Mathematical modelling of immunological interaction of dengue serotypes"

Long-term epidemiological data reveal multi-annual fluctuations in the incidence of dengue fever and dengue haemorrhagic fever, as well as complex cyclical behaviour in the dynamics of the four serotypes of the dengue virus. It has previously been proposed that these patterns are due to the phenomenon of the so-called antibody-dependent enhancement (ADE) among dengue serotypes, whereby viral replication is increased during secondary infection with a heterologous serotype; however, recent studies have implied that this positive reinforcement cannot account for the temporal patterns of dengue and that some form f cross-immunity or external forcing is necessary. Here, we show that ADE alone can produce the observed periodicities and desynchronized oscillations of individual serotypes if its effects are decomposed into its two possible manifestations: enhancement of susceptibility to secondary infections and increased transmissibility from individuals suffering from secondary infections. This decomposition not only lowers the level of enhancement necessary for realistic disease patterns but also reduces the risk of stochastic extinction. Furthermore, our analyses reveal a time-lagged correlation between serotype dynamics and disease incidence rates, which could have important implications for understanding the irregular pattern of dengue epidemics.

Martin Madera: "Evolution of protein domain architectures"

Protein domains are the smallest units of protein structure that can function and evolve on their own. Most proteins contain more than one domain, and the number of domains per protein broadly increases with organismal complexity. The specific sequential order of domains on a protein chain is called the domain architecture. It is widely believed that most domain architectures arose only once in the course of evolution. However, the proportion of architectures that arose more than once has been debated. This is an important issue in a number of fields, including large-scale studies of horizontal gene transfer, recent approaches to phylogenetics based on genome content, and generally the study of evolution at the molecular level. Studies of domain architecture evolution are fraught with an unusually large number of confounding factors: horizontal transfer of genes among species, lineage-specific gene loss, errors in gene prediction, errors and inconsistencies in domain annotation, and handling of confidence estimates for phylogenetic trees. I will highlight the most interesting examples of each problem, and at the end of the talk provide my estimate of the proportion of architectures that evolved more than once.

Tom Cassey: "Optimal Sampling and Decision Making"

In this talk we consider how two techniques from statistical decision theory, namely hypothesis testing and bandit problems can be combined to provide a sequential decision making framework that, at each stage in the decision process, selects a source to be sampled such that the decision process terminates using the smallest number or samples whilst ensuring a specified expected error rate $\alpha$. We begin introducing a hypothesis testing technique known as the Likelihood Ratio Test (LRT) which uses a fixed sample size to make a decision between two hypotheses. Following this we show how the LRT can be extended to form a sequential test, known as the Sequential Probability Ratio Test (SPRT), that uses a variable sized sample to make a decision between two hypotheses. Next we discuss a resource allocation problem in which a a single resource (sampling instances) must be allocated between a set of consumers (sources) over a number of time intervals. Finally, we consider how these areas can be combined into a decision making technique that allocates sampling between a number of sources in order to minimise the number of samples needed before a decision.

Posters

Jane Hallett: "Predictive Life Sciences"

Predictive Life Sciences is a University of Bristol research theme at the interface between biological, mathematical and computational sciences. Rather than being a theme devoted to a single set of research questions, Predictive Life Sciences aims to promote a "Systems Biology" approach across the University, giving greater prominence and cohesion to researchers using mathematics and/or computational modelling as part of biological and biomedical research, and engaging others in new, exciting collaborations.

Frank Marten: "Theoretical descriptions of EEG activity: Application to absence seizures"

Absence seizures typically affect children and young adults. Electroencephalography (EEG) recordings of patients with absence seizures display 2-4 Hz rhythmic activity, the classically observed rhythm being spike-wave discharges. However, a systematic study of data from various subjects with absence seizures also revealed polyspike-wave, wave-spike or even no discernable spike-wave onset during seizure events. We present a unifying mathematical framework to study the mechanisms underlying these EEG signals. The model we introduce is a cortico-thalamic system, used to describe the brain's electrical activity as recorded via EEG. The bifurcation structure of this model has been analyzed with the software package MATCONT. The aim of our analysis was to identify parameters that are crucial for the onset of abnormal activity, and investigate mechanisms leading to (poly)spike-wave solutions. We identified regions in parameter-space where our model supports (poly)spike wave activity. Transitions into these regions occur through Hopf bifurcations, and also through bistability. Hence, our model incorporates two mechanisms to simulate the onset of seizures. Moreover, we investigate the onset of poly-spike wave oscillations; these solutions are created through inflection-points. By studying the transitions in a theoretical model for EEG, using bifurcation analysis, we have identified parameters and mechanisms leading to the onset of (poly)spike wave dynamics. Future work will include a comparison between model and data, by means of parameter fitting. In addition, we aim to enhance our modelling approach by including spatial extent, physiological effects such as neurotransmitter timescales and anatomical effects such as volume conduction.

Mohit Adhikari: "Characterization of cortical response to deep brain stimulation of a thalamic nucleus: Modelling and Experiment"

Motivated by its success as a therapeutic treatment in other neurological disorders, most notably Parkinson's disease, Deep Brain Stimulation (DBS) is currently being trialled in a number of patients with drug unresponsive epilepsies. However, the mechanisms by which DBS interferes with neuronal activity linked to the disorder are not well understood. Furthermore, there is a need to identify optimized values of parameters (for example in amplitude/frequency space) of the stimulation protocol with which one aims to achieve the desired outcome. This poster presents results of a study to characterize the system response to stimulation, to gain an understanding of the role different brain regions play in generating the output observed in EEG. Experiments are performed in healthy rats, where the ventral-lateral thalamic nucleus is stimulated using a train of square-waves with different frequencies and amplitudes. The response to stimulation in the motor cortex is recorded and the drive-response relationship over frequency/amplitude space is considered. The experimental data is in good agreement with simulations of a mean-field model --- both in the time and frequency domains --- when considering a transition to sustained oscillatory activity in the cortex as the frequency of stimulation is increased. Overall, our study characterises the drive-response relationship of DBS in healthy animals. In this way, it constitutes a first step towards the goals of developing a closed-loop feedback control protocol for suppressing epileptic activity, by adaptively adjusting the stimulation protocol in response to EEG activity.

Marios Richards: "Does Learning Accelerate Evolution?"

Why do some species learn more than others? Learning (or any form of phenotypic plasticity) has long been conjectured to have a significant impact on evolutionary dynamics (a Baldwin Effect). Baldwin Effects may range from simply preserving species in difficult environments long enough for genetic adaptation, to actively 'guiding' evolution towards (an 'Expediting' Effect) or away from complex genetic adaptations (a 'Halting' Effect). There have been substantial recent advances in both empirical and theoretical treatments, which have particular relevance to human evolution (where the interactions between evolution and learning may be particularly significant). Hinton and Nowlan's seminal paper, "How Learning Can Guide Evolution" (1987), was the first to present a clear computer simulation of an Expediting Effect, but subsequent simulations found both Halting and Expediting Effects. Paenke et al's (2006-8) Gain Function framework and Borenstein et al's (2006) Landscape Drawdown model predict the effect of any given individual learning algorithm operating on single- and multi-peaked fitness landscapes, respectively. The Gain Function framework shows that learning accelerates (decelerates) evolution insofar as it increases (reduces) the lifetime fitness difference between different genotypes undergoing directional selection. Drawdown reflects the depth of the deepest valley that must be crossed to reach the global optimum and places a lower bound on the average transit time - learning accelerates (decelerates) evolution insofar as it reduces (increases) the drawdown in a landscape.