A model checking approach to the parameter estimation of biochemical pathways

Model checking has historically been an important tool to verify models of a wide variety of systems. Typically a model has to exhibit certain properties to be classed ‘acceptable’. In this work we use model checking in a new setting; parameter estimation. We characterise the desired behaviour of a model in a temporal logic property and alter the model to make it conform to the property (determined through model checking). We have implemented a computational system called MC2(GA) which pairs a model checker with a genetic algorithm. To drive parameter estimation, the fitness of set of parameters in a model is the inverse of the distance between its actual behaviour and the desired behaviour. The model checker used is the simulation-based Monte Carlo Model Checker for Probabilistic Linear-time Temporal Logic with numerical constraints, MC2(PLTLc). Numerical constraints as well as the overall probability of the behaviour expressed in temporal logic are used to minimise the behavioural distance. We define the theory underlying our parameter estimation approach in both the stochastic and continuous worlds. We apply our approach to biochemical systems and present an illustrative example where we estimate the kinetic rate constants in a continuous model of a signalling pathway

Developmental appearance of factors that bind specifically to cis-regulatory sequences of a gene expressed in the sea urchin embryo

Previous gene-transfer experiments have identified a 2500-nucleotide 5' domain of the CyIIIa cytoskeletal actin gene, which contains cis-regulatory sequences that are necessary and sufficient for spatial and temporal control of CyIIIa gene expression during embryogenesis. This gene is activated in late cleavage, exclusively in aboral ectoderm cell lineages. In this study, we focus on interactions demonstrated in vitro between sequences of the regulatory domain and proteins present in crude extracts derived from sea urchin embryo nuclei and from unfertilized eggs. Quantitative gel-shift measurements are utilized to estimate minimum numbers of factor molecules per embryo at 24 hr postfertilization, when the CyIIIa gene is active, at 7 hr, when it is still silent, and in the unfertilized egg. We also estimate the binding affinity preferences (K_r) of the various factors for their respective sites, relative to their affinity for synthetic DNA competitors. At least 14 different specific interactions occur within the regulatory regions, some of which produce multiple DNA-protein complexes. Values of K_r range from approximately 2 x 10^4 to approximately 2 x 10^6 for these factors under the conditions applied. With one exception, the minimum factor prevalences that we measured in the 400-cell 24-hr embryo nuclear extracts fell within the range of 2 x 10^5 to 2 x 10^6 molecules per embryo, i.e., a few hundred to a few thousand molecules per nucleus. Three developmental patterns were observed with respect to factor prevalence: Factors reacting at one site were found in unfertilized egg cytoplasm at about the same level per egg or embryo as in 24-hr embryo nuclei; factors reacting with five other regions of the regulatory domain are not detectable in egg cytoplasm but in 7-hr mid-cleavage-stage embryo, nuclei are already at or close to their concentrations in the 24-hr embryo nuclei; and factors reacting with five additional regions are not detectable in egg cytoplasm and are low in 7-hr embryo nuclei, i.e., ⩽10% per embryo of the level they attain in 24-hr embryo nuclei. The rise in concentration of factors of the latter class could provide the proximal cause for the temporal activation of the CyIIIa gene at the early blastula stage

BioDiVinE: A Framework for Parallel Analysis of Biological Models

In this paper a novel tool BioDiVinEfor parallel analysis of biological models is presented. The tool allows analysis of biological models specified in terms of a set of chemical reactions. Chemical reactions are transformed into a system of multi-affine differential equations. BioDiVinE employs techniques for finite discrete abstraction of the continuous state space. At that level, parallel analysis algorithms based on model checking are provided. In the paper, the key tool features are described and their application is demonstrated by means of a case study

Modelling the Dynamics of an Aedes albopictus Population

We present a methodology for modelling population dynamics with formal means of computer science. This allows unambiguous description of systems and application of analysis tools such as simulators and model checkers. In particular, the dynamics of a population of Aedes albopictus (a species of mosquito) and its modelling with the Stochastic Calculus of Looping Sequences (Stochastic CLS) are considered. The use of Stochastic CLS to model population dynamics requires an extension which allows environmental events (such as changes in the temperature and rainfalls) to be taken into account. A simulator for the constructed model is developed via translation into the specification language Maude, and used to compare the dynamics obtained from the model with real data.Comment: In Proceedings AMCA-POP 2010, arXiv:1008.314

Efficient Parallel Statistical Model Checking of Biochemical Networks

We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estimate the likelihood that a property is satisfied by sampling executions out of the stochastic model. We propose a methodology for efficiently estimating the likelihood that a LTL property P holds of a stochastic model of a biochemical network. As with other statistical verification techniques, the methodology we propose uses a stochastic simulation algorithm for generating execution samples, however there are three key aspects that improve the efficiency: first, the sample generation is driven by on-the-fly verification of P which results in optimal overall simulation time. Second, the confidence interval estimation for the probability of P to hold is based on an efficient variant of the Wilson method which ensures a faster convergence. Third, the whole methodology is designed according to a parallel fashion and a prototype software tool has been implemented that performs the sampling/verification process in parallel over an HPC architecture

A critical review on modelling formalisms and simulation tools in computational biosystems

Integration of different kinds of biological processes is an ultimate goal for whole-cell modelling. We briefly review modelling formalisms that have been used in Systems Biology and identify the criteria that must be addressed by an integrating framework capable of modelling, analysing and simulating different biological networks. Aware that no formalism can fit all purposes we realize Petri nets as a suitable model for Metabolic Engineering and take a deeper perspective on the role of this formalism as an integrating framework for regulatory and metabolic networks.Research supported by PhD grant SFRH/BD/35215/2007 from the Fundacao para a Ciencia e a Tecnologia (FCT) and the MIT-Portugal program

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.National Institutes of Health (U.S.) (Grant P50-GM068762)National Institutes of Health (U.S.) (Grant R24-DK090963)United States. Army Research Office (Grant W911NF-09-0001)German Research Foundation (Grant GSC 111

Training Signaling Pathway Maps to Biochemical Data with Constrained Fuzzy Logic: Quantitative Analysis of Liver Cell Responses to Inflammatory Stimuli

Predictive understanding of cell signaling network operation based on general prior knowledge but consistent with empirical data in a specific environmental context is a current challenge in computational biology. Recent work has demonstrated that Boolean logic can be used to create context-specific network models by training proteomic pathway maps to dedicated biochemical data; however, the Boolean formalism is restricted to characterizing protein species as either fully active or inactive. To advance beyond this limitation, we propose a novel form of fuzzy logic sufficiently flexible to model quantitative data but also sufficiently simple to efficiently construct models by training pathway maps on dedicated experimental measurements. Our new approach, termed constrained fuzzy logic (cFL), converts a prior knowledge network (obtained from literature or interactome databases) into a computable model that describes graded values of protein activation across multiple pathways. We train a cFL-converted network to experimental data describing hepatocytic protein activation by inflammatory cytokines and demonstrate the application of the resultant trained models for three important purposes: (a) generating experimentally testable biological hypotheses concerning pathway crosstalk, (b) establishing capability for quantitative prediction of protein activity, and (c) prediction and understanding of the cytokine release phenotypic response. Our methodology systematically and quantitatively trains a protein pathway map summarizing curated literature to context-specific biochemical data. This process generates a computable model yielding successful prediction of new test data and offering biological insight into complex datasets that are difficult to fully analyze by intuition alone.National Institutes of Health (U.S.) (NIH grant P50-GM68762)National Institutes of Health (U.S.) (Grant U54-CA112967)United States. Dept. of Defense (Institute for Collaborative Biotechnologies