Tina Toni

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.

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.

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. Results: Here we present a Python package, ABC-SysBio, that implements parameter inference and model selection for dynamical systems in an approximate Bayesian computation (ABC) framework. ABC-SysBio combines three algorithms: ABC rejection sampler, ABC SMC for parameter inference and ABC SMC for model selection. It is designed to work with models written in Systems Biology Markup Language (SBML). Deterministic and stochastic models can be analyzed in ABC-SysBio. Availability: http://abc-sysbio.sourceforge.net Contact: christopher.barnes@imperial.ac.uk; ttoni@imperial.ac.uk

The Evolution of the Phage Shock Protein Response System: Interplay between Protein Function, Genomic Organization, and System Function

Sensing the environment and responding appropriately to it are key capabilities for the survival of an organism. All extant organisms must have evolved suitable sensors, signaling systems, and response mechanisms allowing them to survive under the conditions they are likely to encounter. Here, we investigate in detail the evolutionary history of one such system: The phage shock protein (Psp) stress response system is an important part of the stress response machinery in many bacteria, including Escherichia coli K12. Here, we use a systematic analysis of the genes that make up and regulate the Psp system in E. coli in order to elucidate the evolutionary history of the system. We compare gene sharing, sequence evolution, and conservation of protein-coding as well as noncoding DNA sequences and link these to comparative analyses of genome/operon organization across 698 bacterial genomes. Finally, we evaluate experimentally the biological advantage/disadvantage of a simplified version of the Psp system under different oxygen-related environments. Our results suggest that the Psp system evolved around a core response mechanism by gradually co-opting genes into the system to provide more nuanced sensory, signaling, and effector functionalities. We find that recruitment of new genes into the response machinery is closely linked to incorporation of these genes into a psp operon as is seen in E. coli, which contains the bulk of genes involved in the response. The organization of this operon allows for surprising levels of additional transcriptional control and flexibility. The results discussed here suggest that the components of such signaling systems will only be evolutionarily conserved if the overall functionality of the system can be maintained.

Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems.

Combined model of intrinsic and extrinsic variability for computational network design with application to synthetic biology.

Biological systems are inherently variable, with their dynamics influenced by intrinsic and extrinsic sources. These systems are often only partially characterized, with large uncertainties about specific sources of extrinsic variability and biochemical properties. Moreover, it is not yet well understood how different sources of variability combine and affect biological systems in concert. To successfully design biomedical therapies or synthetic circuits with robust performance, it is crucial to account for uncertainty and effects of variability. Here we introduce an efficient modeling and simulation framework to study systems that are simultaneously subject to multiple sources of variability, and apply it to make design decisions on small genetic networks that play a role of basic design elements of synthetic circuits. Specifically, the framework was used to explore the effect of transcriptional and post-transcriptional autoregulation on fluctuations in protein expression in simple genetic networks. We found that autoregulation could either suppress or increase the output variability, depending on specific noise sources and network parameters. We showed that transcriptional autoregulation was more successful than post-transcriptional in suppressing variability across a wide range of intrinsic and extrinsic magnitudes and sources. We derived the following design principles to guide the design of circuits that best suppress variability: (i) high protein cooperativity and low miRNA cooperativity, (ii) imperfect complementarity between miRNA and mRNA was preferred to perfect complementarity, and (iii) correlated expression of mRNA and miRNA – for example, on the same transcript – was best for suppression of protein variability. Results further showed that correlations in kinetic parameters between cells affected the ability to suppress variability, and that variability in transient states did not necessarily follow the same principles as variability in the steady state. Our model and findings provide a general framework to guide design principles in synthetic biology.

Model selection in systems biology depends on experimental design

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a models predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.

Elucidating the in vivo phosphorylation dynamics of the ERK MAP kinase using quantitative proteomics data and Bayesian model selection.

Ever since reversible protein phosphorylation was discovered, it has been clear that it plays a key role in the regulation of cellular processes. Proteins often undergo double phosphorylation, which can occur through two possible mechanisms: distributive or processive. Which phosphorylation mechanism is chosen for a particular cellular regulation bears biological significance, and it is therefore in our interest to understand these mechanisms. In this paper we study dynamics of the MEK/ERK phosphorylation. We employ a model selection algorithm based on approximate Bayesian computation to elucidate phosphorylation dynamics from quantitative time course data obtained from PC12 cells in vivo. The algorithm infers the posterior distribution over four proposed models for phosphorylation and dephosphorylation dynamics, and this distribution indicates the amount of support given to each model. We evaluate the robustness of our inferential framework by systematically exploring different ways of parameterizing the models and for different prior specifications. The models with the highest inferred posterior probability are the two models employing distributive dephosphorylation, whereas we are unable to choose decisively between the processive and distributive phosphorylation mechanisms.

Parameter Inference and Model Selection in Signaling Pathway Models

To support and guide an extensive experimental research into systems biology of signaling pathways, increasingly more mechanistic models are being developed with hopes of gaining further insight into biological processes. In order to analyze these models, computational and statistical techniques are needed to estimate the unknown kinetic parameters. This chapter reviews methods from frequentist and Bayesian statistics for estimation of parameters and for choosing which model is best for modeling the underlying system. Approximate Bayesian computation techniques are introduced and employed to explore different hypothesis about the JAK-STAT signaling pathway.