ABSTRACT. We describe a hybrid system based framework for modeling gene regulation and other biomolecular networks and a method for analysis of the dynamic behavior of such models. A particular feature of the proposed framework is the focus on qualitative experimentally testable properties of the system. With this goal in mind we introduce the notion of the frame of a hybrid system, which allows for the discretisation of the state space of the network. We propose two different methods for the analysis of this state space. The result of the analysis is a set of attractors (generalizations of attractors used in Boolean models) that characterise the underlying biological system.

Whilst in the general case the problem of finding attractors in the state space is algorithmically undecidable, we demonstrate that our methods work for comparatively complex gene regulatory network model of lambda-phage. For this model we are able to identify attractors corresponding to two known biological behaviors of lambda-phage: lysis and lysogeny and also to show that there are no other stable behavior regions in state space of lambda-phage model.

ABSTRACT. Synaptic plasticity depends on the interaction between electrical activity in neurons and the synaptic proteome, the collection of over 1000 proteins in the post-synaptic density (PSD) of synapses. To construct models of synaptic plasticity with realistic numbers of proteins, we aim to combine rule-based models of molecular interactions in the synaptic proteome with compartmental models of the electrical activity of neurons. Rule-based systems allow interactions between the combinatorially large number of protein complexes in the postsynaptic proteome to be expressed straightforwardly, and simulations of rule-based systems are stochastic and thus can deal with the small copy numbers of proteins and complexes in the PSD. Compartmental models of neurons are expressed as systems of coupled ordinary differential equations and solved deterministically. We present an algorithm which incorporates stochastic rule-based models into deterministic compartmental models and demonstrate an implementation of this hybrid system using the SpatialKappa and NEURON simulators.

ABSTRACT. Wet-lab experiments, in which the dynamics within living cells are observed, are usually costly and time consuming. This is particularly true if single-cell measurements are obtained using experimental techniques such as flow-cytometry or fluorescence microscopy. It is therefore important to optimize experimentswith respect to the information they provide about the system. In this paper we make a priori predictions of the amount of information that can be obtained from measurements. We focus on the case where the measurements are made to estimate parameters of a stochastic model of the underlying biochemical reactions. We propose a numerical scheme to approximate the Fisher information of future experiments at different observation time points and determine optimal observation time points. To illustrate the usefulness of our approach, we apply our method to two interesting case studies.

ABSTRACT. Reachability analysis has recently proved to be a useful technique for analyzing the behaviors of under-specified biological models. In this paper, we propose a method exploiting the eigenstructure of a linear continuous system to efficiently estimate a bound on the time the system can reach a target set from an initial set. This estimation can be then directly integrated in an existing algorithm for hybrid systems with linear continuous dynamics, to speed up reachability computations. Furthermore, it can also be used to improve time-efficiency of the hybridization technique that is based on a piecewise-linear approximation of non-linear continuous dynamics. The proposed method is illustrated on a number of examples including a biological model.

ABSTRACT. We present a novel approach to the automated design of large scale biological systems. Our model connects multiple levels of cellular organisation through a hybrid continuous/discrete and deterministic/stochastic approach. At the core of our model, a hybrid dynamical system represents interactions between gene expression and DNA topology. Gene expression then influences the metabolic level of the cell by affecting the flux distribution in a genome-scale metabolic model of {\it Escherichia coli}. We implement a Bayesian optimisation strategy to select optimal parameters which maximally satisfy a temporal logic formula specifying the desired behaviour of the system. Finally, we show preliminary results of a study on the interaction of the master regulator FIS with supercoiling.

ABSTRACT. We present RKappa, a framework for the development and analysis of rule-base models within a mature statistically empowered R environment. The infrastructure allows model editing, modification, parameter sampling, simulation, statistical analysis and visualisation without leaving the R environment. We demonstrate its effectiveness through its application to Global Sensitivity Analysis, exploring it in “parallel” and “concurrent” implementations. The pipeline was designed for high- performance computing platforms and aims to facilitate analysis the behaviour of the large-scale systems with limited knowledge of exact mechanisms and respectively sparse availability of parameter values, which we illustrate here with two biological model examples. Package is available on github: https://github.com/lptolik/R4Kappa

ABSTRACT. In this talk I argue that progress in Biology requires, among other things, a more modern approach to modeling and analysis of dynamical models. Such models should not be  restricted to classical dynamical systems but also involve concepts and ideas from discrete-event dynamical systems (automata) and hybrid (discrete-continuous) systems. I will present some recent techniques for exploring the dynamics of under-determined systems, that is, systems that admit uncertainty in initial conditions, parameters and  environmental conditions. These techniques, inspired by formal verification, can be used to assess the robustness of proposed models and increase our confidence in their plausibility.