Showing papers presented at "Computational Methods in Systems Biology in 2015"

Moment-Based Methods for Parameter Inference and Experiment Design for Stochastic Biochemical Reaction Networks

Abstract: Continuous-time Markov chains are commonly used in practice for modeling biochemical reaction networks in which the inherent randomness of the molecular interactions cannot be ignored. This has motivated recent research effort into methods for parameter inference and experiment design for such models. The major difficulty is that such methods usually require one to iteratively solve the chemical master equation that governs the time evolution of the probability distribution of the system. This, however, is rarely possible, and even approximation techniques remain limited to relatively small and simple systems. An alternative explored in this article is to base methods on only some low-order moments of the entire probability distribution. We summarize the theory behind such moment-based methods for parameter inference and experiment design and provide new case studies where we investigate their performance.

Model Reconstruction for Moment-Based Stochastic Chemical Kinetics

Abstract: Based on the theory of stochastic chemical kinetics, the inherent randomness of biochemical reaction networks can be described by discrete-state continuous-time Markov chains. However, the analysis of such processes is computationally expensive and sophisticated numerical methods are required. Here, we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a very efficient simulation of the time evolution of the process. To regain the state probabilities from the moment representation, we combine the fast moment-based simulation with a maximum entropy approach for the reconstruction of the underlying probability distribution. We investigate the usefulness of this combined approach in the setting of stochastic chemical kinetics and present numerical results for three reaction networks showing its efficiency and accuracy. Besides a simple dimerization system, we study a bistable switch system and a multiattractor network with complex dynamics.

Stochastic Analysis of Chemical Reaction Networks Using Linear Noise Approximation

Abstract: Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some molecules occur in low numbers. Unfortunately, both approaches become infeasible if the system is complex and/or it cannot be ensured that initial populations are small. We develop a probabilistic logic for CRNs that enables stochastic analysis of the evolution of populations of molecular species. We present an approximate model checking algorithm based on the Linear Noise Approximation (LNA) of the CME, whose computational complexity is independent of the population size of each species and polynomial in the number of different species. The algorithm requires the solution of first order polynomial differential equations. We prove that our approach is valid for any CRN close enough to the thermodynamical limit. However, we show on three case studies that it can still provide good approximation even for low molecule counts. Our approach enables rigorous analysis of CRNs that are not analyzable by solving the CME, but are far from the deterministic limit. Moreover, it can be used for a fast approximate stochastic characterization of a CRN.

SReach: A Probabilistic Bounded Delta-Reachability Analyzer for Stochastic Hybrid Systems

Abstract: In this paper, we present a new tool SReach, which solves probabilistic bounded reachability problems for two classes of models of stochastic hybrid systems. The first one is (nonlinear) hybrid automata with parametric uncertainty. The second one is probabilistic hybrid automata with additional randomness for both transition probabilities and variable resets. Standard approaches to reachability problems for linear hybrid systems require numerical solutions for large optimization problems, and become infeasible for systems involving both nonlinear dynamics over the reals and stochasticity. SReach encodes stochastic information by using a set of introduced random variables, and combines \(\delta \)-complete decision procedures and statistical tests to solve \(\delta \)-reachability problems in a sound manner. Compared to standard simulation-based methods, it supports non-deterministic branching, increases the coverage of simulation, and avoids the zero-crossing problem. We demonstrate SReach’s applicability by discussing three representative biological models and additional benchmarks for nonlinear hybrid systems with multiple probabilistic system parameters.

Spatial-Temporal Modelling and Analysis of Bacterial Colonies with Phase Variable Genes

Abstract: This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.

Efficient Stochastic Simulation of Systems with Multiple Time Scales via Statistical Abstraction

Abstract: Stiffness in chemical reaction systems is a frequently encountered computational problem, arising when different reactions in the system take place at different time-scales. Computational savings can be obtained under time-scale separation. Assuming that the system can be partitioned into slow- and fast- equilibrating subsystems, it is then possible to efficiently simulate the slow subsystem only, provided that the corresponding kinetic laws have been modified so that they reflect their dependency on the fast system. We show that the rate expectation with respect to the fast subsystem’s steady-state is a continuous function of the state of the slow system. We exploit this result to construct an analytic representation of the modified rate functions via statistical modelling, which can be used to simulate the slow system in isolation. The computational savings of our approach are demonstrated in a number of non-trivial examples of stiff systems.

Parameter Synthesis by Parallel Coloured CTL Model Checking

Abstract: We propose a new distributed-memory parallel algorithm for parameter synthesis from CTL hypotheses. The algorithm colours the state space transitions by different parameterisations and extends CTL model checking to identify the maximal set of parameters that guarantee the satisfaction of the given CTL property. We experimentally confirm good scalability of our approach and demonstrate its applicability in the case study of a genetic switch controlling decisions in the cell cycle.

Computing Cumulative Rewards Using Fast Adaptive Uniformization

Abstract: The computation of transient probabilities for continuous-time Markov chains often employs uniformization, also known as the Jensen method The fast adaptive uniformization method introduced by Mateescu et al approximates the probability by neglecting insignificant states and has proven to be effective for quantitative analysis of stochastic models arising in chemical and biological applications However, this method has only been formulated for the analysis of properties at a given point of time t In this article, we extend fast adaptive uniformization to handle expected reward properties that reason about the model behavior until time t, for example, the expected number of chemical reactions that have occurred until t To show the feasibility of the approach, we integrate the method into the probabilistic model checker PRISM and apply it to a range of biological models The performance of the method is enhanced by the use of interval splitting We compare our implementation to standard uniformization implemented in PRISM and to fast adaptive uniformization without support for cumulative rewards implemented in MARCIE, demonstrating superior performance

Estimation and Verification of Hybrid Heart Models for Personalised Medical and Wearable Devices

Abstract: We are witnessing a huge growth in popularity of wearable and implantable devices equipped with sensors that are capable of monitoring a range of physiological processes and communicating the data to smartphones or to medical monitoring devices. Applications include not only medical diagnosis and treatment, but also biometric identification and authentication systems. An important requirement is personalisation of the devices, namely, their ability to adapt to the physiology of the human wearer and to faithfully reproduce the characteristics in real-time for the purposes of authentication or optimisation of medical therapies. In view of the complexity of the embedded software that controls such devices, model-based frameworks have been advocated for their design, development, verification and testing. In this paper, we focus on applications that exploit the unique characteristics of the heart rhythm. We introduce a hybrid automata model of the electrical conduction system of a human heart, adapted from Lian et al. [8], and present a framework for the estimation of personalised parameters, including the generation of synthetic ECGs from the model. We demonstrate the usefulness of the framework on two applications, ensuring safety of a pacemaker against a personalised heart model and ECG-based user authentication.

BioPSy: An SMT-based Tool for Guaranteed Parameter Set Synthesis of Biological Models

Abstract: The parameter set synthesis problem consists of identifying sets of parameter values for which a given system model satisfies a desired behaviour. This paper presents BioPSy, a tool that performs guaranteed parameter set synthesis for ordinary differential equation (ODE) biological models expressed in the Systems Biology Markup Language (SBML) given a desired behaviour expressed by time-series data. Three key features of BioPSy are: (1) BioPSy computes parameter intervals, not just single values; (2) for the identified intervals the model is formally guaranteed to satisfy the desired behaviour; and (3) BioPSy can handle virtually any Lipschitz-continuous ODEs, including nonlinear ones. BioPSy is able to achieve guaranteed synthesis by utilising Satisfiability Modulo Theory (SMT) solvers to determine acceptable parameter intervals. We have successfully applied our tool to several biological models including a prostate cancer therapy model, a human starvation model, and a cell cycle model.

Symbolic Dynamics of Biochemical Pathways as Finite States Machines

Abstract: We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a number of states that is inferior to the number of biochemical species. For nonlinear pathways, we propose a general approach to approximate their dynamics by finite state machines working on the metastable states of the network (long life states where the system has slow dynamics). For networks with polynomial rate functions we propose to compute metastable states as solutions of the tropical equilibration problem. Tropical equilibrations are defined by the equality of at least two dominant monomials of opposite signs in the differential equations of each dynamic variable. In algebraic geometry, tropical equilibrations are tantamount to tropical prevarieties, that are finite intersections of tropical hypersurfaces.

Inferring Executable Models from Formalized Experimental Evidence

Abstract: Executable symbolic models have been successfully used to analyze networks of biological reactions. However, the process of building an executable model from published experimental findings is still carried out manually. The process is very time consuming and requires expert knowledge. As a first step in addressing this problem, this paper introduces an automated method for deriving executable models from formalized experimental findings called datums. We identify the relevant data in a collection of datums. We then translate the information contained in datums to logical assertions. Together with a logical theory formalizing the interpretation of datums, these assertions are used to infer a knowledge base of reaction rules. These rules can then be assembled into executable models semi-automatically using the Pathway Logic system. We applied our technique to the experimental evidence relevant to Hras activation in response to Egf available in our datum knowledge base. When compared to the Pathway Logic model (curated manually from the same datums by an expert), our model makes most of the same predictions regarding reachability and knockouts. Missing information is due to missing assertions that require reasoning about the effects of mutations and background knowledge to generate. This is being addressed in ongoing work.

Structural Simplification of Chemical Reaction Networks Preserving Deterministic Semantics

Abstract: We study the structural simplification of chemical reaction networks preserving the deterministic kinetics. We aim at finding simplification rules that can eliminate intermediate molecules while preserving the dynamics of all others. The rules should be valid even though the network is plugged into a bigger context. An example is Michaelis-Menten’s simplification rule for enzymatic reactions. In this paper, we present a large class of structural simplification rules for reaction networks that can eliminate intermediate molecules at equilibrium, without assuming that all molecules are at equilibrium, i.e. in a steady state. We prove the correctness of our simplification rules for all contexts that preserve the equilibrium of the eliminated molecules. Finally, we illustrate at a concrete example network from systems biology that our simplification rules may allow to drastically reduce the size of reaction networks in practice.

Analysing Cell Line Specific EGFR Signalling via Optimized Automata Based Model Checking

Abstract: Building models with a high degree of specificity, e.g. for particular cell lines, is becoming an important tool in the advancement towards personalised medicine. Constraint-based modelling approaches allow for utilizing general system knowledge to generate a set of possible models that can be further filtered with more specific data. Here, we exploit such an approach in a Boolean modelling framework to investigate EGFR signalling for different cancer cell lines, motivated by a study from Klinger et al. [8]. To optimize performance of the underlying model checking procedure, we present a number of constraint encodings tailored to describing common data types and experimental set-ups. This results in a significant increase in the performance of the approach.

Adaptive Moment Closure for Parameter Inference of Biochemical Reaction Networks

Abstract: Continuous-time Markov chain (CTMC) models have become a central tool for understanding the dynamics of complex reaction networks and the importance of stochasticity in the underlying biochemical processes. When such models are employed to answer questions in applications, in order to ensure that the model provides a sufficiently accurate representation of the real system, it is of vital importance that the model parameters are inferred from real measured data. This, however, is often a formidable task and all of the existing methods fail in one case or the other, usually because the underlying CTMC model is high-dimensional and computationally difficult to analyze. The parameter inference methods that tend to scale best in the dimension of the CTMC are based on so-called moment closure approximations. However, there exists a large number of different moment closure approximations and it is typically hard to say a priori which of the approximations is the most suitable for the inference procedure. Here, we propose a moment-based parameter inference method that automatically chooses the most appropriate moment closure method. Accordingly, contrary to existing methods, the user is not required to be experienced in moment closure techniques. In addition to that, our method adaptively changes the approximation during the parameter inference to ensure that always the best approximation is used, even in cases where different approximations are best in different regions of the parameter space.

Boolean Network Identification from Multiplex Time Series Data

Abstract: Boolean networks (and more general logic models) are useful frameworks to study signal transduction across multiple pathways. Logical models can be learned from a prior knowledge network structure and multiplex phosphoproteomics data. However, most efficient and scal-able training methods focus on the comparison of two time-points and assume that the system has reached an early steady state. In this paper, we generalize such a learning procedure to take into account the time series traces of phosphoproteomics data in order to discriminate Boolean networks according to their transient dynamics. To that goal, we exhibit a necessary condition that must be satisfied by a Boolean network dynamics to be consistent with a discretized time series trace. Based on this condition, we use a declarative programming approach (Answer Set Programming) to compute an over-approximation of the set of Boolean networks which fit best with experimental data. Combined with model-checking approaches, we end up with a global learning algorithm and compare it to learning approaches based on static data.

Approximate Bayesian Computation for Stochastic Single-Cell Time-Lapse Data Using Multivariate Test Statistics

Abstract: Stochastic dynamics of individual cells are mostly modeled with continuous time Markov chains (CTMCs). The parameters of CTMCs can be inferred using likelihood-based and likelihood-free methods. In this paper, we introduce a likelihood-free approximate Bayesian computation (ABC) approach for single-cell time-lapse data. This method uses multivariate statistics on the distribution of single-cell trajectories. We evaluated our method for samples of a bivariate normal distribution as well as for artificial equilibrium and non-equilibrium single-cell time-series of a one-stage model of gene expression. In addition, we assessed our method for parameter variability and for the case of tree-structured time-series data. A comparison with an existing method using univariate statistics revealed an improved parameter identifiability using multivariate test statistics.

Hybrid Simulations of Heterogeneous Biochemical Models in SBML

Abstract: Models of biochemical systems presented as a set of formal reaction rules can be interpreted in different formalisms, most notably as either deterministic Ordinary Differential Equations, stochastic continuous-time Markov Chains, Petri nets, or Boolean transition systems. While the formal composition of reaction systems can be syntactically defined as the (multiset) union of the reactions, the composition and simulation of models in different formalisms remain a largely open issue. In this article, we show that the combination of reaction rules and events, as already present in SBML, can be used in a nonstandard way to define stochastic and Boolean simulators and give meaning to the hybrid composition and simulation of heterogeneous models of biochemical processes. In particular, we show how two SBML reaction models can be composed into one hybrid continuous--stochastic SBML model through a high-level interface for composing reaction models and specifying their interpretation. Furthermore, we describe dynamic strategies for automatically partitioning reactions with stochastic or continuous interpretations according to dynamic criteria. The performances are then compared to static partitioning. The proposed approach is illustrated and evaluated on several examples, including the reconstructions of the hybrid model of the mammalian cell cycle regulation of Singhania et al. as the composition of a Boolean model of cell cycle phase transitions with a continuous model of cyclin activation, the hybrid stochastic--continuous models of bacteriophage T7 infection of Alfonsi et al., and the bacteriophage λ model of Goutsias, showing the gain in both accuracy and simulation time of the dynamic partitioning strategy.

Model-Based Investigation of the Effect of the Cell Cycle on the Circadian Clock Through Transcription Inhibition During Mitosis

Abstract: Experimental observations have put in evidence autonomous self-sustained circadian oscillators in most mammalian cells, and proved the existence of molecular links between the circadian clock and the cell cycle. Several models have been elaborated to assess conditions of control of the cell cycle by the circadian clock, in particular through the regulation by clock genes of Wee1, an inhibitor of the mitosis promoting factor, responsible for a circadian gating of mitosis and cell division period doubling phenomena. However, recent studies in individual NIH3T3 fibroblasts have shown an unexpected acceleration of the circadian clock together with the cell cycle when the milieu is enriched in FBS, the absence of such acceleration in confluent cells, and the absence of any period doubling phenomena. In this paper, we try to explain these observations by a possible entrainment of the circadian clock by the cell cycle through the inhibition of transcription during mitosis. We develop a differential model of that reverse coupling of the cell cycle and the circadian clock and investigate the conditions in which both cycles are mutually entrained. We use the mammalian circadian clock model of Relogio et al. and a simple model of the cell cycle by Qu et al. which focuses on the mitosis phase. We show that our coupled model is able to reproduce the main observations reported by Feillet et al. in individual fibroblast experiments and use it for making some predictions.

Constrained Community-Based Gene Regulatory Network Inference

Abstract: The problem of gene regulatory network inference is a major concern of systems biology. In recent years, a novel methodology has gained momentum, called community network approach. Community networks integrate predictions from individual methods in a “metapredictor,” in order to compose the advantages of different methods and soften individual limitations. This article proposes a novel methodology to integrate prediction ensembles using constraint programming, a declarative modeling and problem solving paradigm. Constraint programming naturally allows the modeling of dependencies among components of the problem as constraints, facilitating the integration and use of different forms of knowledge. The new paradigm, referred to as constrained community network, uses constraints to capture properties of the regulatory networks (e.g., topological properties) and to guide the integration of knowledge derived from different families of network predictions. The article experimentally shows the potential of this approach: The addition of biological constraints can offer significant improvements in prediction accuracy.

Simulating Organogenesis: Algorithms for the Image-Based Determination of Displacement Fields

Abstract: Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between consecutive image frames need to be determined. Here we develop and evaluate different landmark-free algorithms for the determination of such displacement fields from image data. In particular, we examine minimal distance, normal distance, diffusion-based, and uniform mapping algorithms and test these algorithms with both synthetic and real data in 2D and 3D. We conclude that in most cases, the normal distance algorithm is the method of choice and wherever it fails, diffusion-based mapping provides a good alternative.

Qualitative Reasoning for Reaction Networks with Partial Kinetic Information

Abstract: We propose a formal modeling language for reaction networks with partial kinetic information. The language has a graphical syntax reminiscent to Petri nets. The kinetics of reactions need to be described only partially, so that the language can be used to model the regulation of metabolic networks. We present a qualitative reasoning method based on abstract interpretation of the steady state semantics of reaction networks modeled in our language. In particular, we can predict changes of influxes that lead to expected changes of outfluxes.

Feature Learning Using Stacked Autoencoders to Predict the Activity of Antimicrobial Peptides

Abstract: In recent years, pattern recognition methods have been applied to determine the activity of biological molecules, including the prediction of antimicrobial activity of synthetic and natural peptides where Quantitative Structure-Activity Relationship methodologies are widely used. Traditionally, works focused on designing descriptors for sequences to yield better correlations with the biological activity and improve predictors performance. Albeit there have been remarkable results, the small size of available datasets leave large room for improvement. In this work, rather than hand-crafting new descriptors, our approach consists in automatically learning them from existing ones. We use stacked autoencoders (a class of unsupervised neural networks), and the descriptors learnt are fed to a support vector regression task to predict biological activity. This method improves results in existing literature by roughly 12 % simultaneously in different metrics, providing interesting insights into the nature of descriptors learnt and suggesting its applicability in other areas in protein properties prediction.

Experimental Design for Inference over the A. thaliana Circadian Clock Network

Abstract: Planning experiments is a crucial step in successful investigations, which can greatly benefit from computational modeling approaches. Here we consider the problem of designing informative experiments for elucidating the dynamics of biological networks. Our approach extends previously proposed methodologies to the important case where the structure of the network is also uncertain. We demonstrate our approach on a benchmark scenario in plant biology, the circadian clock network of Arabidopsis thaliana, and discuss the different value of three types of commonly used experiments in terms of aiding the reconstruction of the unknown network.

A Genetically Modified Hoare Logic that Identifies the Parameters of a Gene Network

Abstract: The main difficulty when modelling gene networks is the identification of the parameters that govern the dynamics. Here we present a new approach based on Hoare logic and weakest preconditions (a la Dijkstra) that generates constraints on the parameter values: Once proper specifications are extracted from biological traces, they play a role similar to programs in the classical Hoare logic. We firstly remind the discrete modelling for genetic networks defined by Rene Thomas. Then, we define the Hoare/Dijkstra method extended to gene networks, that extracts the weakest precondition on parameter values.

Automating the Development of Metabolic Network Models

Abstract: Although substantial progress has been made in the automation of many areas of systems biology, from data processing and model building to experimentation, comparatively little work has been done on integrated systems that combine all of these aspects. This paper presents an active learning system, “Huginn”, that integrates experiment design and model revision in order to automate scientific reasoning about Metabolic Network Models. We have validated our approach in a simulated environment using substantial test cases derived from a state-of-the-art model of yeast metabolism. We demonstrate that Huginn can not only improve metabolic models, but that it is able to both solve a wider range of biochemical problems than previous methods, and to utilise a wider range of experiment types. Also, we show how design of extended crucial experiments can be automated using Abductive Logic Programming for the first time.

Derivation of Qualitative Dynamical Models from Biochemical Networks

Abstract: As technological advances allow a better identification of cellular networks, more and more molecular data are produced allowing the construction of detailed molecular interaction maps. One strategy to get insights into the dynamical properties of such systems is to derive compact dynamical models from these maps, in order to ease the analysis of their dynamics. Starting from a case study, we present a methodology for the derivation of qualitative dynamical models from biochemical networks. Properties are formalised using abstract interpretation. We first abstract states and traces by quotienting the number of instances of chemical species by intervals. Since this abstraction is too coarse to reproduce the properties of interest, we refine it by introducing additional constraints. The resulting abstraction is able to identify the dynamical properties of interest in our case study.

SBMLDock: Docker Driven Systems Biology Tool Development and Usage

Abstract: A glut of Systems Biology tools and their lack of accessibility has significantly delayed bioscience advances that depend on the analysis of large scale systems with big datasets and High Performance Computing (HPC) resources. This work presents SBMLDock, the first Systems Biology Docker image that aims to advance scalability, usability and reproducibility in Systems Biology by making tools much more immediately available to the biological domain scientist, student, and educator, without requiring special training for use, and without losing the reproducibility aspect of their research. SBMLDock consists of one Docker image containing basic tools developed for Systems Biology Model manipulation (parallel model similarity analyzer, model checker, model splitter, model annotation, model extractor). The user can then pull up the Docker image, customize it and/or run each tool as service. Stored on the Docker hub, the image version is managed to assure research reproducibility. SBMLDock is available as a Docker file under CC licence at github https://github.com/USDBioinformatics/SBMLDock and the Docker image can be found in Docker hub at https://registry.hub.docker.com/u/usdbioinformatics/sbmldock/ with supplementary documents.

Analysis of a Post-translational Oscillator Using Process Algebra and Spatio-Temporal Logic

Abstract: We describe the modelling of a post-translational oscillator using a process algebra and the specification of complex properties of its dynamics using a spatio-temporal logic. We show that specifications in the Logic of Behaviour in Context can be seen as hypotheses about oscillations and other biochemical behaviours, to be tested automatically by model-checking software. By using these techniques we show that the theoretical model behaves in a manner in keeping with known properties of biological circadian oscillators.

Approximating the dynamics of the Hybrid Stochastic-Deterministic Apoptosis pathway

Abstract: 1 Motivation Modeling and analysis of the dynamics of biological systems while accounting for single cell fluctuations is important. In particular, Bertaux et.al [1] considered an improved hybrid stochastic-deterministic model of TRAIL induced apoptosis. TRAIL is a protein that is known to induce apoptosis in cancer cells and hence has been a target for several anti-cancer therapeutic strategies. Their model combines a deterministic signal transduction model (modeled as ordinary differential equations (ODEs)), as in the original model of [3], and a stochastic model for protein turnover (factoring cell-to cell variability). Using this low level biochemical model, they were able to explain fractional killing and predicted the time dependent evolution of cell resistance to TRAIL. While this model is extremely useful for analyzing TRAIL induced apoptosis by drawing simulations in a single cell setting, it can be limiting in cases when we want to analyse the system in a multi-scale setting (say modeling a spheroid of thousands of cells at a larger time horizon for clinical trials). In such cases, simulating the original model can become extremely time consuming due to the scale of the resultant system. Instead, one could directly approximate the dynamics of the underlying system as an intermediate level behavioral model and use this approximation. In this direction, Bing et.al [2] proposed a Dynamic Bayesian Network (DBN) model as a probabilistic approximation of ODE dynamics. They discretize the value space (∼ 5 values per variable) and time domain of the different species of a system of ODEs, sample a representative set of simulations of the system and use the structure of the pathway to store them as a DBN. Once the DBN is constructed, efficient Bayesian inference methods are used to analyze the system. Our work in this poster presents initial work on extending and improving the work of Bing et.al [2] for the hybrid stochastic-deterministic (HSD) models, and in particular the one of TRAIL induced apoptosis. 2 Results We extend the method of [2] to HSD model, and propose several improvements. First, the model describes a population of cells with non deterministic behavior (unlike [2] where outcomes are deterministic). Additionally, simulations in the current setting may be truncated due to cell death. Last, some molecular species interact with many (∼ 10) different species. The latter presents challenges pertaining to maintaining and working with large conditional probability tables. In [2], dummy intermediate variables are introduced, approximating the conditional probabilities by splitting the dependencies. Instead, we use an improved sparse matrix representation to encode these conditional probabilities (filling around 600 non null entries among ∼ 5 10), allowing us to scale the system even when a variable has many direct dependencies. We also improve the naive simulation based inference of DBNs which was inefficient for the current setting. First, 99% of the samples hit an empty conditional probability entry and hence these samples are discarded. Further, every working sample (1% of all samples) ends up simulating a cell that died (giving 0% survivors compared to ∼ 30% survivors of the original hybrid model)). We propose a new algorithm which simulates the underlying DBN by looking ahead one time step and factoring this information to avoid empty probability entries. This considerably improved the simulation based inference of DBNs with 80% effective samples and the expected ∼ 30% survivors. We produced several DBNs corresponding to a treatment with 250 ng/ml TRAIL by simulating the hybrid model. We found a very good agreement between the cell death distribution of the original model and the DBN, as well as for the marginal distributions of other variables. 3 Perspectives and future work