On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo

Approximate Bayesian computation (ABC) has gained popularity over the past few years for the analysis of complex models arising in population genetics, epidemiology and system biology. Sequential Monte Carlo (SMC) approaches have become work-horses in ABC. Here we discuss how to construct the perturbation kernels that are required in ABC SMC approaches, in order to construct a sequence of distributions that start out from a suitably defined prior and converge towards the unknown posterior. We derive optimality criteria for different kernels, which are based on the Kullback-Leibler divergence between a distribution and the distribution of the perturbed particles. We will show that for many complicated posterior distributions, locally adapted kernels tend to show the best performance. We find that the added moderate cost of adapting kernel functions is easily regained in terms of the higher acceptance rate. We demonstrate the computational efficiency gains in a range of toy examples which illustrate some of the challenges faced in real-world applications of ABC, before turning to two demanding parameter inference problems in molecular biology, which highlight the huge increases in efficiency that can be gained from choice of optimal kernels. We conclude with a general discussion of the rational choice of perturbation kernels in ABC SMC settings

Control mechanisms for stochastic biochemical systems via computation of reachable sets.

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters

Transition state characteristics during cell differentiation

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington’s epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes—change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions

Conditional random matrix ensembles and the stability of dynamical systems

There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either specific to a particular model (leading to results that were not general), or chosen for mathematical convenience, yielding results unlikely to be meaningful for any interesting realistic system. May's work, and its subsequent elaborations, relied upon results from random matrix theory, particularly the circular law and its extensions, which only apply when the strengths of interactions between entities in the system are assumed to be independent and identically distributed (i.i.d.). Other studies have optimistically generalised from the analysis of very specific systems, in a way that does not hold up to closer scrutiny. We show here that this debate can be put to rest, once these two contrasting views have been reconciled --- which is possible in the statistical framework developed here. Here we use a range of illustrative examples of dynamical systems to demonstrate that (i) stability probability cannot be summarily deduced from any single property of the system (e.g. its diversity), and (ii) our assessment of stability depends on adequately capturing the details of the systems analysed. Failing to condition on the structure of dynamical systems will skew our analysis and can, even for very small systems, result in an unnecessarily pessimistic diagnosis of their stability

Bayesian non-parametric approaches to reconstructing oscillatory systems and the Nyquist limit

Reconstructing continuous signals from discrete time-points is a challenging inverse problem encountered in many scientific and engineering applications. For oscillatory signals classical results due to Nyquist set the limit below which it becomes impossible to reliably reconstruct the oscillation dynamics. Here we revisit this problem for vector-valued outputs and apply Bayesian non-parametric approaches in order to solve the function estimation problem. The main aim of the current paper is to map how we can use of correlations among different outputs to reconstruct signals at a sampling rate that lies below the Nyquist rate. We show that it is possible to use multiple-output Gaussian processes to capture dependences between outputs which facilitate reconstruction of signals in situation where conventional Gaussian processes (i.e. this aimed at describing scalar signals) fail, and we delineate the phase and frequency dependence of the reliability of this type of approach. In addition to simple toy-models we also consider the dynamics of the tumour suppressor gene p53, which exhibits oscillations under physiological conditions, and which can be reconstructed more reliably in our new framework. © 2014 Published by Elsevier B.V

Inference of random walk models to describe leukocyte migration

While the majority of cells in an organism are static and remain relatively immobile in their tissue, migrating cells occur commonly during developmental processes and are crucial for a functioning immune response. The mode of migration has been described in terms of various types of random walks. To understand the details of the migratory behaviour we rely on mathematical models and their calibration to experimental data. Here we propose an approximate Bayesian inference scheme to calibrate a class of random walk models characterized by a specific, parametric particle re-orientation mechanism to observed trajectory data. We elaborate the concept of transition matrices (TMs) to detect random walk patterns and determine a statistic to quantify these TM to make them applicable for inference schemes. We apply the developed pipeline to in vivo trajectory data of macrophages and neutrophils, extracted from zebrafish that had undergone tail transection. We find that macrophage and neutrophils exhibit very distinct biased persistent random walk patterns, where the strengths of the persistence and bias are spatio-temporally regulated. Furthermore, the movement of macrophages is far less persistent than that of neutrophils in response to wounding

A large fraction of HLA class I ligands are proteasome-generated spliced peptides

The proteasome generates the epitopes presented on human leukocyte antigen (HLA) class I molecules that elicit CD8+ T cell responses. Reports of proteasome-generated spliced epitopes exist, but they have been regarded as rare events. Here, however, we show that the proteasome-generated spliced peptide pool accounts for one-third of the entire HLA class I immunopeptidome in terms of diversity and one-fourth in terms of abundance. This pool also represents a unique set of antigens, possessing particular and distinguishing features. We validated this observation using a range of complementary experimental and bioinformatics approaches, as well as multiple cell types. The widespread appearance and abundance of proteasome-catalyzed peptide splicing events has implications for immunobiology and autoimmunity theories and may provide a previously untapped source of epitopes for use in vaccines and cancer immunotherapy

Sequencing of the Hepatitis C Virus: A Systematic Review

Since the identification of hepatitis C virus (HCV), viral sequencing has been important in understanding HCV classification, epidemiology, evolution, transmission clustering, treatment response and natural history. The length and diversity of the HCV genome has resulted in analysis of certain regions of the virus, however there has been little standardisation of protocols. This systematic review was undertaken to map the location and frequency of sequencing on the HCV genome in peer reviewed publications, with the aim to produce a database of sequencing primers and amplicons to inform future research. Medline and Scopus databases were searched for English language publications based on keyword/MeSH terms related to sequence analysis (9 terms) or HCV (3 terms), plus "primer" as a general search term. Exclusion criteria included non-HCV research, review articles, duplicate records, and incomplete description of HCV sequencing methods. The PCR primer locations of accepted publications were noted, and purpose of sequencing was determined. A total of 450 studies were accepted from the 2099 identified, with 629 HCV sequencing amplicons identified and mapped on the HCV genome. The most commonly sequenced region was the HVR-1 region, often utilised for studies of natural history, clustering/transmission, evolution and treatment response. Studies related to genotyping/classification or epidemiology of HCV genotype generally targeted the 5'UTR, Core and NS5B regions, while treatment response/resistance was assessed mainly in the NS3-NS5B region with emphasis on the Interferon sensitivity determining region (ISDR) region of NS5A. While the sequencing of HCV is generally constricted to certain regions of the HCV genome there is little consistency in the positioning of sequencing primers, with the exception of a few highly referenced manuscripts. This study demonstrates the heterogeneity of HCV sequencing, providing a comprehensive database of previously published primer sets to be utilised in future sequencing studies

Emergence of scale-free close-knit friendship structure in online social networks

Despite the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properties. It is found that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. The degree correlation is very weak over a wide range of the degrees. We propose a simple directed network model that captures the observed properties. The model incorporates two mechanisms: reciprocation and preferential attachment. Through rate equation analysis of our model, the local-scale and mesoscale structural properties are derived. In the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear relationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlations. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only on one global parameter -- the mean in/outdegree, while both the mean in/outdegree and the reciprocity together determine the ratio of the reciprocal degree of a node to its in/outdegree.Comment: 48 pages, 34 figure

Protein Networks Reveal Detection Bias and Species Consistency When Analysed by Information-Theoretic Methods

We apply our recently developed information-theoretic measures for the characterisation and comparison of protein–protein interaction networks. These measures are used to quantify topological network features via macroscopic statistical properties. Network differences are assessed based on these macroscopic properties as opposed to microscopic overlap, homology information or motif occurrences. We present the results of a large–scale analysis of protein–protein interaction networks. Precise null models are used in our analyses, allowing for reliable interpretation of the results. By quantifying the methodological biases of the experimental data, we can define an information threshold above which networks may be deemed to comprise consistent macroscopic topological properties, despite their small microscopic overlaps. Based on this rationale, data from yeast–two–hybrid methods are sufficiently consistent to allow for intra–species comparisons (between different experiments) and inter–species comparisons, while data from affinity–purification mass–spectrometry methods show large differences even within intra–species comparisons