Robustness analysis of stochastic biochemical systems

Combining formal methods and Bayesian approach for inferring discrete-state stochastic models from steady-state data

Stochastic population models are widely used to model phenomena in different areas such as cyber-physical systems, chemical kinetics, collective animal behaviour, and beyond. Quantitative analysis of stochastic population models easily becomes challenging due to the combinatorial number of possible states of the population. Moreover, while the modeller easily hypothesises the mechanistic aspects of the model, the quantitative parameters associated to these mechanistic transitions are difficult or impossible to measure directly. In this paper, we investigate how formal verification methods can aid parameter inference for population discrete-time Markov chains in a scenario where only a limited sample of population-level data measurements-sample distributions among terminal states-are available. We first discuss the parameter identifiability and uncertainty quantification in this setup, as well as how the existing techniques of formal parameter synthesis and Bayesian inference apply. Then, we propose and implement four different methods, three of which incorporate formal parameter synthesis as a pre-computation step. We empirically evaluate the performance of the proposed methods over four representative case studies. We find that our proposed methods incorporating formal parameter synthesis as a pre-computation step allow us to significantly enhance the accuracy, precision, and scalability of inference. Specifically, in the case of unidentifiable parameters, we accurately capture the subspace of parameters which is data-compliant at a desired confidence level.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

The key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their non-linear dynamics. The model dynamics are crucially dependent on the parameter values which are often estimated from observations. Over the past decade, the interest in parameter and state estimation in models of (bio-) chemical reaction networks (BRNs) grew considerably. The related inference problems are also encountered in many other tasks including model calibration, discrimination, identifiability, and checking, and optimum experiment design, sensitivity analysis, and bifurcation analysis. The aim of this review paper is to examine the developments in literature to understand what BRN models are commonly used, and for what inference tasks and inference methods. The initial collection of about 700 documents concerning estimation problems in BRNs excluding books and textbooks in computational biology and chemistry were screened to select over 270 research papers and 20 graduate research theses. The paper selection was facilitated by text mining scripts to automate the search for relevant keywords and terms. The outcomes are presented in tables revealing the levels of interest in different inference tasks and methods for given models in the literature as well as the research trends are uncovered. Our findings indicate that many combinations of models, tasks and methods are still relatively unexplored, and there are many new research opportunities to explore combinations that have not been considered-perhaps for good reasons. The most common models of BRNs in literature involve differential equations, Markov processes, mass action kinetics, and state space representations whereas the most common tasks are the parameter inference and model identification. The most common methods in literature are Bayesian analysis, Monte Carlo sampling strategies, and model fitting to data using evolutionary algorithms. The new research problems which cannot be directly deduced from the text mining data are also discussed.

A Novel Method to Verify Multilevel Computational Models of Biological Systems Using Multiscale Spatio-Temporal Meta Model Checking

Insights gained from multilevel computational models of biological systems can be translated into real-life applications only if the model correctness has been verified first. One of the most frequently employed in silico techniques for computational model verification is model checking. Traditional model checking approaches only consider the evolution of numeric values, such as concentrations, over time and are appropriate for computational models of small scale systems (e.g. intracellular networks). However for gaining a systems level understanding of how biological organisms function it is essential to consider more complex large scale biological systems (e.g. organs). Verifying computational models of such systems requires capturing both how numeric values and properties of (emergent) spatial structures (e.g. area of multicellular population) change over time and across multiple levels of organization, which are not considered by existing model checking approaches. To address this limitation we have developed a novel approximate probabilistic multiscale spatio-temporal meta model checking methodology for verifying multilevel computational models relative to specifications describing the desired/expected system behaviour. The methodology is generic and supports computational models encoded using various high-level modelling formalisms because it is defined relative to time series data and not the models used to generate it. In addition, the methodology can be automatically adapted to case study specific types of spatial structures and properties using the spatio-temporal meta model checking concept. To automate the computational model verification process we have implemented the model checking approach in the software tool Mule (http://mule.modelchecking.org). Its applicability is illustrated against four systems biology computational models previously published in the literature encoding the rat cardiovascular system dynamics, the uterine contractions of labour, the Xenopus laevis cell cycle and the acute inflammation of the gut and lung. Our methodology and software will enable computational biologists to efficiently develop reliable multilevel computational models of biological systems.

Conditional robustness analysis for fragility discovery and target identification in biochemical networks and in cancer systems biology

Background

The study of cancer therapy is a key issue in the field of oncology research and the development of target therapies is one of the main problems currently under investigation. This is particularly relevant in different types of tumor where traditional chemotherapy approaches often fail, such as lung cancer.

Results

We started from the general definition of robustness introduced by Kitano and applied it to the analysis of dynamical biochemical networks, proposing a new algorithm based on moment independent analysis of input/output uncertainty. The framework utilizes novel computational methods which enable evaluating the model fragility with respect to quantitative performance measures and parameters such as reaction rate constants and initial conditions. The algorithm generates a small subset of parameters that can be used to act on complex networks and to obtain the desired behaviors. We have applied the proposed framework to the EGFR-IGF1R signal transduction network, a crucial pathway in lung cancer, as an example of Cancer Systems Biology application in drug discovery. Furthermore, we have tested our framework on a pulse generator network as an example of Synthetic Biology application, thus proving the suitability of our methodology to the characterization of the input/output synthetic circuits.

Conclusions

The achieved results are of immediate practical application in computational biology, and while we demonstrate their use in two specific examples, they can in fact be used to study a wider class of biological systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0216-5) contains supplementary material, which is available to authorized users.