Motivation: A common class of behaviour encountered in the biological sciences involves branching and recombination. During branching, a statistical process bifurcates resulting in two or more potentially correlated processes that may undergo further branching; the contrary is true during recombination, where two or more statistical processes converge. A key objective is to identify the time of this bifurcation (branch or recombination time) from time series measurements, e.g. by comparing a control time series with perturbed time series. Gaussian processes (GPs) represent an ideal framework for such analysis, allowing for nonlinear regression that includes a rigorous treatment of uncertainty. Currently, however, GP models only exist for two-branch systems. Here, we highlight how arbitrarily complex branching processes can be built using the correct composition of covariance functions within a GP framework, thus outlining a general framework for the treatment of branching and recombination in the form of branch-recombinant Gaussian processes (B-RGPs). Results: We first benchmark the performance of B-RGPs compared to a variety of existing regression approaches, and demonstrate robustness to model misspecification. B-RGPs are then used to investigate the branching patterns of Arabidopsis thaliana gene expression following inoculation with the hemibotrophic bacteria, Pseudomonas syringae DC3000, and a disarmed mutant strain, hrpA. By grouping genes according to the number of branches, we could naturally separate out genes involved in basal immune response from those subverted by the virulent strain, and show enrichment for targets of pathogen protein effectors. Finally, we identify two early branching genes WRKY11 and WRKY17, and show that genes that branched at similar times to WRKY11/17 were enriched for W-box binding motifs, and overrepresented for genes differentially expressed in WRKY11/17 knockouts, suggesting that branch time could be used for identifying direct and indirect binding targets of key transcription factors. Availability and implementation: https://github.com/cap76/BranchingGPs. Supplementary information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Time course data are often used to study the changes to a biological process after perturbation. Statistical methods have been developed to determine whether such a perturbation induces changes over time, e.g. comparing a perturbed and unperturbed time course dataset to uncover differences. However, existing methods do not provide a principled statistical approach to identify the specific time when the two time course datasets first begin to diverge after a perturbation; we call this the perturbation time. Estimation of the perturbation time for different variables in a biological process allows us to identify the sequence of events following a perturbation and therefore provides valuable insights into likely causal relationships. RESULTS: We propose a Bayesian method to infer the perturbation time given time course data from a wild-type and perturbed system. We use a non-parametric approach based on Gaussian Process regression. We derive a probabilistic model of noise-corrupted and replicated time course data coming from the same profile before the perturbation time and diverging after the perturbation time. The likelihood function can be worked out exactly for this model and the posterior distribution of the perturbation time is obtained by a simple histogram approach, without recourse to complex approximate inference algorithms. We validate the method on simulated data and apply it to study the transcriptional change occurring in Arabidopsis following inoculation with Pseudomonas syringae pv. tomato DC3000 versus the disarmed strain DC3000hrpA AVAILABILITY AND IMPLEMENTATION: : An R package, DEtime, implementing the method is available at https://github.com/ManchesterBioinference/DEtime along with the data and code required to reproduce all the results. CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The ability to jointly learn gene regulatory networks (GRNs) in, or leverage GRNs between related species would allow the vast amount of legacy data obtained in model organisms to inform the GRNs of more complex, or economically or medically relevant counterparts. Examples include transferring information from Arabidopsis thaliana into related crop species for food security purposes, or from mice into humans for medical applications. Here we develop two related Bayesian approaches to network inference that allow GRNs to be jointly inferred in, or leveraged between, several related species: in one framework, network information is directly propagated between species; in the second hierarchical approach, network information is propagated via an unobserved 'hypernetwork'. In both frameworks, information about network similarity is captured via graph kernels, with the networks additionally informed by species-specific time series gene expression data, when available, using Gaussian processes to model the dynamics of gene expression. RESULTS: Results on in silico benchmarks demonstrate that joint inference, and leveraging of known networks between species, offers better accuracy than standalone inference. The direct propagation of network information via the non-hierarchical framework is more appropriate when there are relatively few species, while the hierarchical approach is better suited when there are many species. Both methods are robust to small amounts of mislabelling of orthologues. Finally, the use of Saccharomyces cerevisiae data and networks to inform inference of networks in the budding yeast Schizosaccharomyces pombe predicts a novel role in cell cycle regulation for Gas1 (SPAC19B12.02c), a 1,3-beta-glucanosyltransferase. AVAILABILITY AND IMPLEMENTATION: MATLAB code is available from http://go.warwick.ac.uk/systemsbiology/software/.

MOTIVATION: There are a number of algorithms to infer causal regulatory networks from time series (gene expression) data. Here we analyse the phenomena of regulator interference, where regulators with similar dynamics mutually suppress both the probability of regulating a target and the associated link strength; for instance, interference between two identical strong regulators reduces link probabilities by ∼50%. RESULTS: We construct a robust method to define an interference-corrected causal network based on an analysis of the conditional link probabilities that recovers links lost through interference. On a large real network (Streptomyces coelicolor, phosphate depletion), we demonstrate that significant interference can occur between regulators with a correlation as low as 0.865, losing an estimated 34% of links by interference. However, levels of interference cannot be predicted from the correlation between regulators alone and are data specific. Validating against known networks, we show that high numbers of functional links are lost by regulator interference. Performance against other methods on DREAM4 data is excellent. AVAILABILITY AND IMPLEMENTATION: The method is implemented in R and is publicly available as the NIACS package at http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software.

MOTIVATION: The generation of time series transcriptomic datasets collected under multiple experimental conditions has proven to be a powerful approach for disentangling complex biological processes, allowing for the reverse engineering of gene regulatory networks (GRNs). Most methods for reverse engineering GRNs from multiple datasets assume that each of the time series were generated from networks with identical topology. In this study, we outline a hierarchical, non-parametric Bayesian approach for reverse engineering GRNs using multiple time series that can be applied in a number of novel situations including: (i) where different, but overlapping sets of transcription factors are expected to bind in the different experimental conditions; that is, where switching events could potentially arise under the different treatments and (ii) for inference in evolutionary related species in which orthologous GRNs exist. More generally, the method can be used to identify context-specific regulation by leveraging time series gene expression data alongside methods that can identify putative lists of transcription factors or transcription factor targets. RESULTS: The hierarchical inference outperforms related (but non-hierarchical) approaches when the networks used to generate the data were identical, and performs comparably even when the networks used to generate data were independent. The method was subsequently used alongside yeast one hybrid and microarray time series data to infer potential transcriptional switches in Arabidopsis thaliana response to stress. The results confirm previous biological studies and allow for additional insights into gene regulation under various abiotic stresses. AVAILABILITY: The methods outlined in this article have been implemented in Matlab and are available on request.

Meiosis is the cell division that halves the genetic component of diploid cells to form gametes or spores. To achieve this, meiotic cells undergo a radical spatial reorganisation of chromosomes. This reorganisation is a prerequisite for the pairing of parental homologous chromosomes and the reductional division, which halves the number of chromosomes in daughter cells. Of particular note is the change from a centromere clustered layout (Rabl configuration) to a telomere clustered conformation (bouquet stage). The contribution of the bouquet structure to homologous chromosome pairing is uncertain. We have developed a new in silico model to represent the chromosomes of Saccharomyces cerevisiae in space, based on a worm-like chain model constrained by attachment to the nuclear envelope and clustering forces. We have asked how these constraints could influence chromosome layout, with particular regard to the juxtaposition of homologous chromosomes and potential nonallelic, ectopic, interactions. The data support the view that the bouquet may be sufficient to bring short chromosomes together, but the contribution to long chromosomes is less. We also find that persistence length is critical to how much influence the bouquet structure could have, both on pairing of homologues and avoiding contacts with heterologues. This work represents an important development in computer modeling of chromosomes, and suggests new explanations for why elucidating the functional significance of the bouquet by genetics has been so difficult.