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

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives 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.Comment: 26 pages, 9 figure

Accurate Reconstruction of Cell and Particle Tracks from 3D Live Imaging Data

Spatial structures often constrain the 3D movement of cells or particles in vivo, yet this information is obscured when microscopy data are analyzed using standard approaches. Here, we present methods, called unwrapping and Riemannian manifold learning, for mapping particle-tracking data along unseen and irregularly curved surfaces onto appropriate 2D representations. This is conceptually similar to the problem of reconstructing accurate geography from conventional Mercator maps, but our methods do not require prior knowledge of the environments’ physical structure. Unwrapping and Riemannian manifold learning accurately recover the underlying 2D geometry from 3D imaging data without the need for fiducial marks. They outperform standard x-y projections, and unlike standard dimensionality reduction techniques, they also successfully detect both bias and persistence in cell migration modes. We demonstrate these features on simulated data and zebrafish and Drosophila in vivo immune cell trajectory datasets. Software packages that implement unwrapping and Riemannian manifold learning are provided

ABC-SysBio—approximate Bayesian computation in Python with GPU support

Motivation: The growing field of systems biology has driven demand for flexible tools to model and simulate biological systems. Two established problems in the modeling of biological processes are model selection and the estimation of associated parameters. A number of statistical approaches, both frequentist and Bayesian, have been proposed to answer these questions

Decomposing Noise in Biochemical Signaling Systems Highlights the Role of Protein Degradation

AbstractStochasticity is an essential aspect of biochemical processes at the cellular level. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others. Here we propose a method that allows us to calculate contributions of individual reactions to the total variability of a system’s output. We demonstrate that reactions differ significantly in their relative impact on the total noise and we illustrate the importance of protein degradation on the overall variability for a range of molecular processes and signaling systems. With our flexible and generally applicable noise decomposition method, we are able to shed new, to our knowledge, light on the sources and propagation of noise in biochemical reaction networks; in particular, we are able to show how regulated protein degradation can be employed to reduce the noise in biochemical systems

Systems Analysis of the Dynamic Inflammatory Response to Tissue Damage Reveals Spatiotemporal Properties of the Wound Attractant Gradient

In the acute inflammatory phase following tissue damage, cells of the innate immune system are rapidly recruited to sites of injury by pro-inflammatory mediators released at the wound site. Although advances in live imaging allow us to directly visualize this process in vivo, the precise identity and properties of the primary immune damage attractants remain unclear, as it is currently impossible to directly observe and accurately measure these signals in tissues. Here, we demonstrate that detailed information about the attractant signals can be extracted directly from the in vivo behavior of the responding immune cells. By applying inference-based computational approaches to analyze the in vivo dynamics of the Drosophila inflammatory response, we gain new detailed insight into the spatiotemporal properties of the attractant gradient. In particular, we show that the wound attractant is released by wound margin cells, rather than by the wounded tissue per se, and that it diffuses away from this source at rates far slower than those of previously implicated signals such as H2O2 and ATP, ruling out these fast mediators as the primary chemoattractant. We then predict, and experimentally test, how competing attractant signals might interact in space and time to regulate multi-step cell navigation in the complex environment of a healing wound, revealing a period of receptor desensitization after initial exposure to the damage attractant. Extending our analysis to model much larger wounds, we uncover a dynamic behavioral change in the responding immune cells in vivo that is prognostic of whether a wound will subsequently heal or not

Which species is it? Species-driven gene name disambiguation using random walks over a mixture of adjacency matrices.

The scientific literature contains a wealth of information about biological systems. Manual curation lacks the scalability to extract this information due to the ever-increasing numbers of papers being published. The development and application of text mining technologies has been proposed as a way of dealing with this problem. However, the inter-species ambiguity of the genomic nomenclature makes mapping of gene mentions identified in text to their corresponding Entrez gene identifiers an extremely difficult task. We propose a novel method, which transforms a MEDLINE record into a mixture of adjacency matrices; by performing a random walkover the resulting graph, we can perform multi-class supervised classification allowing the assignment of taxonomy identifiers to individual gene mentions. The ability to achieve good performance at this task has a direct impact on the performance of normalizing gene mentions to Entrez gene identifiers. Such graph mixtures add flexibility and allow us to generate probabilistic classification schemes that naturally reflect the uncertainties inherent, even in literature-derived data.Our method performs well in terms of both micro- and macro-averaged performance, achieving micro-F(1) of 0.76 and macro-F(1) of 0.36 on the publicly available DECA corpus. Re-curation of the DECA corpus was performed, with our method achieving 0.88 micro-F(1) and 0.51 macro-F(1). Our method improves over standard classification techniques [such as support vector machines (SVMs)] in a number of ways: flexibility, interpretability and its resistance to the effects of class bias in the training data. Good performance is achieved without the need for computationally expensive parse tree generation or 'bag of words classification'

Model selection in systems and synthetic biology

Developing mechanistic models has become an integral aspect of systems biology, as has the need to differentiate between alternative models. Parameterizing mathematical models has been widely perceived as a formidable challenge, which has spurred the development of statistical and optimisation routines for parameter inference. But now focus is increasingly shifting to problems that require us to choose from among a set of different models to determine which one offers the best description of a given biological system. We will here provide an overview of recent developments in the area of model selection. We will focus on approaches that are both practical as well as build on solid statistical principles and outline the conceptual foundations and the scope for application of such methods in systems biology

Gene Expression Profiles of Blumeria graminis Indicate Dynamic Changes to Primary Metabolism during Development of an Obligate Biotrophic Pathogen

cDNA microarrays of Blumeria graminis f sp hordei transcript profiles during the asexual development cycle reveal the dynamics of global gene expression as the fungus germinates, penetrates, feeds on its host, and produces masses of conidia for dispersal. The expression profiles of genes encoding enzymes involved in primary metabolism show that there is a striking degree of coordinate regulation of some of the genes in the same pathway. In one example, genes encoding several glycolytic enzymes are significantly upregulated as mature appressoria form and also in infected epidermis, which contain fungal haustoria. In another example, mRNAs for lipid degrading enzymes are initially expressed at high levels in the conidia and the early germination stages and decrease significantly later. We discuss these results and draw inferences on the metabolic status of this obligate biotrophic fungus as it infects its host and completes its life cycle

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