Model Checking of Biological Systems

Verifiable biology

The formalization of biological systems using computational modelling approaches as an alternative to mathematical-based methods has recently received much interest because computational models provide a deeper mechanistic understanding of biological systems. In particular, formal verification, complementary approach to standard computational techniques such as simulation, is used to validate the system correctness and obtain critical information about system behaviour. In this study, we survey the most frequently used computational modelling approaches and formal verification techniques for computational biology. We compare a number of verification tools and software suites used to analyse biological systems and biochemical networks, and to verify a wide range of biological properties. For users who have no expertise in formal verification, we present a novel methodology that allows them to easily apply formal verification techniques to analyse their biological or biochemical system of interest.

Symbolic Coloured SCC Decomposition

Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.

We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(p\cdot n\cdot \log n)$$\end{document}O(p·n·logn) symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{48}$$\end{document}248) coloured graphs produced by models appearing in systems biology.

Validation of Modeling and Simulation Methods in Computational Biology

In recent years, a highly sophisticated array of modeling and simulation tools in all areas of biological and biomedical research has been developed. These tools have the potential to provide new insights into biological mechanisms integrating subcellular, cellular, tissue, organ, and potentially whole organism levels. Current research is focused on how to use these methods for translational medical research, such as for disease diagnosis and understanding, as well as drug discovery. In addition, these approaches enhance the ability to use human-derived data and to contribute to the refinement of high-cost experimental-based research. Additionally, the conflicting conceptual frameworks and conceptions of modeling and simulation methods from the broad public of users could have a significant impact on the successful implementation of aforementioned applications. This in turn could result in successful collaborations across academic, clinical, and industrial sectors. To that end, this study provides an overview of the frameworks and disciplines used for validation of computational methodologies in biomedical sciences.

Automatic validation of computational models using pseudo-3D spatio-temporal model checking

BACKGROUND

Computational models play an increasingly important role in systems biology for generating predictions and in synthetic biology as executable prototypes/designs. For real life (clinical) applications there is a need to scale up and build more complex spatio-temporal multiscale models; these could enable investigating how changes at small scales reflect at large scales and viceversa. Results generated by computational models can be applied to real life applications only if the models have been validated first. Traditional in silico model checking techniques only capture how non-dimensional properties (e.g. concentrations) evolve over time and are suitable for small scale systems (e.g. metabolic pathways). The validation of larger scale systems (e.g. multicellular populations) additionally requires capturing how spatial patterns and their properties change over time, which are not considered by traditional non-spatial approaches.

RESULTS

We developed and implemented a methodology for the automatic validation of computational models with respect to both their spatial and temporal properties. Stochastic biological systems are represented by abstract models which assume a linear structure of time and a pseudo-3D representation of space (2D space plus a density measure). Time series data generated by such models is provided as input to parameterised image processing modules which automatically detect and analyse spatial patterns (e.g. cell) and clusters of such patterns (e.g. cellular population). For capturing how spatial and numeric properties change over time the Probabilistic Bounded Linear Spatial Temporal Logic is introduced. Given a collection of time series data and a formal spatio-temporal specification the model checker Mudi ( http://mudi.modelchecking.org ) determines probabilistically if the formal specification holds for the computational model or not. Mudi is an approximate probabilistic model checking platform which enables users to choose between frequentist and Bayesian, estimate and statistical hypothesis testing based validation approaches. We illustrate the expressivity and efficiency of our approach based on two biological case studies namely phase variation patterning in bacterial colony growth and the chemotactic aggregation of cells.

CONCLUSIONS

The formal methodology implemented in Mudi enables the validation of computational models against spatio-temporal logic properties and is a precursor to the development and validation of more complex multidimensional and multiscale models.