Michael P. H. Stumpf

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

Evolution of pathogenicity and sexual reproduction in eight Candida genomes.

Candida species are the most common cause of opportunistic fungal infection worldwide. Here we report the genome sequences of six Candida species and compare these and related pathogens and non-pathogens. There are significant expansions of cell wall, secreted and transporter gene families in pathogenic species, suggesting adaptations associated with virulence. Large genomic tracts are homozygous in three diploid species, possibly resulting from recent recombination events. Surprisingly, key components of the mating and meiosis pathways are missing from several species. These include major differences at the mating-type loci (MTL); Lodderomyces elongisporus lacks MTL, and components of the a1/α2 cell identity determinant were lost in other species, raising questions about how mating and cell types are controlled. Analysis of the CUG leucine-to-serine genetic-code change reveals that 99% of ancestral CUG codons were erased and new ones arose elsewhere. Lastly, we revise the Candida albicans gene catalogue, identifying many new genes.

Estimating the size of the human interactome.

After the completion of the human and other genome projects it emerged that the number of genes in organisms as diverse as fruit flies, nematodes, and humans does not reflect our perception of their relative complexity. Here, we provide reliable evidence that the size of protein interaction networks in different organisms appears to correlate much better with their apparent biological complexity. We develop a stable and powerful, yet simple, statistical procedure to estimate the size of the whole network from subnet data. This approach is then applied to a range of eukaryotic organisms for which extensive protein interaction data have been collected and we estimate the number of interactions in humans to be ≈650,000. We find that the human interaction network is one order of magnitude bigger than the Drosophila melanogaster interactome and ≈3 times bigger than in Caenorhabditis elegans.

Critical Truths About Power Laws

Most reported power laws lack statistical support and mechanistic backing. The ability to summarize observations using explanatory and predictive theories is the greatest strength of modern science. A theoretical framework is perceived as particularly successful if it can explain very disparate facts. The observation that some apparently complex phenomena can exhibit startling similarities to dynamics generated with simple mathematical models (1) has led to empirical searches for fundamental laws by inspecting data for qualitative agreement with the behavior of such models. A striking feature that has attracted considerable attention is the apparent ubiquity of power-law relationships in empirical data. However, although power laws have been reported in areas ranging from finance and molecular biology to geophysics and the Internet, the data are typically insufficient and the mechanistic insights are almost always too limited for the identification of power-law behavior to be scientifically useful (see the figure). Indeed, even most statistically “successful” calculations of power laws offer little more than anecdotal value.

Network motifs: structure does not determine function

BackgroundA number of publications have recently examined the occurrence and properties of the feed-forward motif in a variety of networks, including those that are of interest in genome biology, such as gene networks. The present work looks in some detail at the dynamics of the bi-fan motif, using systems of ordinary differential equations to model the populations of transcription factors, mRNA and protein, with the aim of extending our understanding of what appear to be important building blocks of gene network structure.ResultsWe develop an ordinary differential equation model of the bi-fan motif and analyse variants of the motif corresponding to its behaviour under various conditions. In particular, we examine the effects of different steady and pulsed inputs to five variants of the bifan motif, based on evidence in the literature of bifan motifs found in Saccharomyces cerevisiae (commonly known as bakers yeast). Using this model, we characterize the dynamical behaviour of the bi-fan motif for a wide range of biologically plausible parameters and configurations. We find that there is no characteristic behaviour for the motif, and with the correct choice of parameters and of internal structure, very different, indeed even opposite behaviours may be obtained.ConclusionEven with this relatively simple model, the bi-fan motif can exhibit a wide range of dynamical responses. This suggests that it is difficult to gain significant insights into biological function simply by considering the connection architecture of a gene network, or its decomposition into simple structural motifs. It is necessary to supplement such structural information by kinetic parameters, or dynamic time series experimental data, both of which are currently difficult to obtain.

Estimating recombination rates from population-genetic data

Obtaining an accurate measure of how recombination rates vary across the genome has implications for understanding the molecular basis of recombination, its evolutionary significance and the distribution of linkage disequilibrium in natural populations. Although measuring the recombination rate is experimentally challenging, good estimates can be obtained by applying population-genetic methods to DNA sequences taken from natural populations. Statistical methods are now providing insights into the nature and scale of variation in the recombination rate, particularly in humans. Such knowledge will become increasingly important owing to the growing use of population-genetic methods in biomedical research.

Simulation-based model selection for dynamical systems in systems and population biology

Motivation: Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not straightforward. We therefore require suitable statistical tools that allow us to choose rationally between different mechanistic models of, e.g. signal transduction or gene regulation networks. This is particularly challenging in systems biology where only a small number of molecular species can be assayed at any given time and all measurements are subject to measurement uncertainty. Results: Here, we develop such a model selection framework based on approximate Bayesian computation and employing sequential Monte Carlo sampling. We show that our approach can be applied across a wide range of biological scenarios, and we illustrate its use on real data describing influenza dynamics and the JAK-STAT signalling pathway. Bayesian model selection strikes a balance between the complexity of the simulation models and their ability to describe observed data. The present approach enables us to employ the whole formal apparatus to any system that can be (efficiently) simulated, even when exact likelihoods are computationally intractable. Contact: ttoni@imperial.ac.uk; m.stumpf@imperial.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online.

Managing membrane stress: the phage shock protein (Psp) response, from molecular mechanisms to physiology.

The bacterial phage shock protein (Psp) response functions to help cells manage the impacts of agents impairing cell membrane function. The system has relevance to biotechnology and to medicine. Originally discovered in Escherichia coli, Psp proteins and homologues are found in Gram-positive and Gram-negative bacteria, in archaea and in plants. Study of the E. coli and Yersinia enterocolitica Psp systems provides insights into how membrane-associated sensory Psp proteins might perceive membrane stress, signal to the transcription apparatus and use an ATP-hydrolysing transcription activator to produce effector proteins to overcome the stress. Progress in understanding the mechanism of signal transduction by the membrane-bound Psp proteins, regulation of the psp gene-specific transcription activator and the cell biology of the system is presented and discussed. Many features of the action of the Psp system appear to be dominated by states of self-association of the master effector, PspA, and the transcription activator, PspF, alongside a signalling pathway that displays strong conditionality in its requirement.

A Y chromosome census of the British Isles

The degree of population replacement in the British Isles associated with cultural changes has been extensively debated. Recent work has demonstrated that comparisons of genetic variation in the British Isles and on the European Continent can illuminate specific demographic processes in the history of the British Isles. For example, Wilson et al. used the similarity of Basque and Celtic Y chromosomes to argue for genetic continuity from the Upper Palaeolithic to the present in the paternal history of these populations (see also ). Differences in the Y chromosome composition of these groups also suggested genetic signatures of Norwegian influence in the Orkney Islands north of the Scottish mainland, an important center of Viking activities between 800 and 1300 A.D. More recently, Weale et al. argued for substantial Anglo-Saxon male migration into central England based on the analysis of eight British sample sets collected on an east-west transect across England and Wales. To provide a more complete assessment of the paternal genetic history of the British Isles, we have compared the Y chromosome composition of multiple geographically distant British sample sets with collections from Norway (two sites), Denmark, and Germany and with collections from central Ireland, representing, respectively, the putative invading and the indigenous populations. By analyzing 1772 Y chromosomes from 25 predominantly small urban locations, we found that different parts of the British Isles have sharply different paternal histories; the degree of population replacement and genetic continuity shows systematic variation across the sampled areas.

A Predominantly Indigenous Paternal Heritage for the Austronesian-Speaking Peoples of Insular Southeast Asia and Oceania

Modern humans reached Southeast Asia and Oceania in one of the first dispersals out of Africa. The resulting temporal overlap of modern and archaic humans-and the apparent morphological continuity between them-has led to claims of gene flow between Homo sapiens and H. erectus. Much more recently, an agricultural technology from mainland Asia spread into the region, possibly in association with Austronesian languages. Using detailed genealogical study of Y chromosome variation, we show that the majority of current Austronesian speakers trace their paternal heritage to Pleistocene settlers in the region, as opposed to more-recent agricultural immigrants. A fraction of the paternal heritage, however, appears to be associated with more-recent immigrants from northern populations. We also show that the northern Neolithic component is very unevenly dispersed through the region, with a higher contribution in Southeast Asia and a nearly complete absence in Melanesia. Contrary to claims of gene flow (under regional continuity) between H. erectus and H. sapiens, we found no ancestral Y chromosome lineages in a set of 1,209 samples. The finding excludes the possibility that early hominids contributed significantly to the paternal heritage of the region.