Showing papers presented at "Computational Methods in Systems Biology in 2009"

A Bayesian Approach to Model Checking Biological Systems

Abstract: Recently, there has been considerable interest in the use of Model Checking for Systems Biology. Unfortunately, the state space of stochastic biological models is often too large for classical Model Checking techniques. For these models, a statistical approach to Model Checking has been shown to be an effective alternative. Extending our earlier work, we present the first algorithm for performing statistical Model Checking using Bayesian Sequential Hypothesis Testing. We show that our Bayesian approach outperforms current statistical Model Checking techniques, which rely on tests from Classical (aka Frequentist) statistics, by requiring fewer system simulations. Another advantage of our approach is the ability to incorporate prior Biological knowledge about the model being verified. We demonstrate our algorithm on a variety of models from the Systems Biology literature and show that it enables faster verification than state-of-the-art techniques, even when no prior knowledge is available.

A Reduction of Logical Regulatory Graphs Preserving Essential Dynamical Properties

Abstract: To cope with the increasing complexity of regulatory networks, we define a reduction method for multi-valued logical models. Starting with a detailed model, this method enables the computation of a reduced model by iteratively "hiding" regulatory components. To keep a consistent behaviour, the logical rules associated with the targets of each hidden node are actualised to account for the (indirect) effects of its regulators. The construction of reduced models ensures the preservation of a number of dynamical properties of the original model. In particular, stable states and more complex attractors are conserved. More generally, we focus on the relationship between the attractor configuration of the original model and that of the reduced model, along with the issue of attractor reachability. The power of the reduction method is illustrated by its application to a multi-valued model of the segment-polarity network Controlling segmentation in the fly Drosophila melanogaster.

Computing Reachable States for Nonlinear Biological Models

Abstract: In this paper we describe reachability computation for continuous and hybrid systems and its potential contribution to the process of building and debugging biological models. We then develop a novel algorithm for computing reachable states for nonlinear systems and report experimental results obtained using a prototype implementation. We believe these results constitute a promising contribution to the analysis of complex models of biological systems.

CSL Model Checking of Biochemical Networks with Interval Decision Diagrams

Abstract: This paper presents an Interval Decision Diagram based approach to symbolic CSL model checking of Continuous Time Markov Chains which are derived from stochastic Petri nets. Matrix-vector and vector-matrix multiplication are the major tasks of exact analysis. We introduce a simple, but powerful algorithm which uses explicitly the Petri net structure and allows for parallelisation. We present results demonstrating the efficiency of our first prototype implementation when applied to biochemical network models, specifically with increasing token numbers. Our tool currently supports CSL model checking of time-bounded operators and the Next operator for ordinary stochastic Petri nets.

Dynamic Compartments in the Imperative Π-Calculus

Abstract: Dynamic compartments with mutable configurations and variable volumes are of basic interest for the stochastic modeling of biochemistry in cells. We propose a new language to express dynamic compartments that we call the imperative Π -calculus . It is obtained from the attributed Π -calculus by adding imperative assignment operations to a global store. Previous approaches to dynamic compartments are improved in flexibility or efficiency. This is illustrated by an appropriate model of osmosis and a correct encoding of bioambBioAmbients.

On the Use of Stochastic Petri Nets in the Analysis of Signal Transduction Pathways for Angiogenesis Process

Abstract: In this paper we consider the modeling of a selected portion of signal transduction events involved in the angiogenesis process. The detailed model of this process contains a large number of parameters and the data available from wet-lab experiments are not sufficient to obtain reliable estimates for all of them. To overcome this problem, we suggest ways to simplify the detailed representation that result in models with a smaller number of parameters still capturing the overall behaviour of the detailed one. Starting from a detailed stochastic Petri net (SPN) model that accounts for all the reactions of the signal transduction cascade, using structural properties combined with the knowledge of the biological phenomena, we propose a set of model reductions.

Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Abstract: Circadian clocks are biochemical networks, present in nearly all living organisms, whose function is to regulate the expression of specific mRNAs and proteins to synchronise rhythms of metabolism, physiology and behaviour to the 24 hour day/night cycle. Because of their experimental tractability and biological significance, circadian clocks have been the subject of a number of computational modelling studies. In this study we focus on the simple circadian clock of the fungus Neurospora crassa . We use the Bio-PEPA process algebra to develop both a stochastic and a deterministic model of the system. The light on/off mechanism responsible for entrainment to the day/night cycle is expressed using discrete time-dependent events in Bio-PEPA. In order to validate our model, we compare it against the results of previous work which demonstrated that the deterministic model is in agreement with experimental data. Here we investigate the effect of stochasticity on the robustness of the clock's function in biological timing. In particular, we focus on the variations in the phase and amplitude of oscillations in circadian proteins with respect to different factors such as the presence/absence of a positive feedback loop, and the presence/absence of light. The time-dependent sensitivity of the model with respect to some key kinetic parameters is also investigated.

Approximation of Event Probabilities in Noisy Cellular Processes

Abstract: Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete -state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.

The κ-Lattice: Decidability Boundaries for Qualitative Analysis in Biological Languages

Abstract: The κ -calculus is a formalism for modelling molecular biology where molecules are terms with internal state and sites, bonds are represented by shared names labelling sites, and reactions are represented by rewriting rules. Depending on the shape of the rewriting rules, a lattice of dialects of κ can be obtained. We analyze the expressive power of some of these dialects by focusing on the thin boundary between decidability and undecidability for problems like reachability and coverability.

On Coupling Models Using Model-Checking: Effects of Irinotecan Injections on the Mammalian Cell Cycle

Abstract: In systems biology, the number of models of cellular processes increases rapidly, but re-using models in different contexts or for different questions remains a challenging issue. In this paper, we show how the validation of a coupled model and the optimization of its parameters with respect to biological properties formalized in temporal logics, can be done automatically by model-checking. More specifically, we illustrate this approach with the coupling of existing models of the mammalian cell cycle, the p53-based DNA-damage repair network, and irinotecan metabolism, with respect to the biological properties of this anticancer drug.

Probabilistic Approximations of Signaling Pathway Dynamics

Abstract: Systems of ordinary differential equations (ODEs) are often used to model the dynamics of complex biological pathways. We construct a discrete state model as a probabilistic approximation of the ODE dynamics by discretizing the value space and the time domain. We then sample a representative set of trajectories and exploit the discretization and the structure of the signaling pathway to encode these trajectories compactly as a dynamic Bayesian network. As a result, many interesting pathway properties can be analyzed efficiently through standard Bayesian inference techniques. We have tested our method on a model of EGF-NGF signaling pathway [1] and the results are very promising in terms of both accuracy and efficiency.

BlenX4Bio --- BlenX for Biologists

Abstract: We introduce BlenX4Bio, a high-level interface for the programming language BlenX. BlenX4Bio allows biologists to write BlenX programs without having any programming skills. The main elements of a biological model are specified by filling in a number of tables. Such tables include descriptions of both static and dynamic aspects of the biological system at hand and can then be automatically mapped to BlenX programs for simulation and analysis by means of the CoSBi Lab software platform. In this paper we illustrate the main characteristics of BlenX4Bio through examples taken from biology textbooks.

Quantitative Pathway Logic for Computational Biology

Abstract: This paper presents an extension of Pathway Logic, called Quantitative Pathway Logic (QPL), which allows one to reason about quantitative aspects of biological processes, such as element concentrations and reactions kinetics. Besides, it supports the modeling of inhibitors, that is, chemicals which may block a given reaction whenever their concentration exceeds a certain threshold. QPL models can be specified and directly simulated using rewriting logic or can be translated into Discrete Functional Petri Nets (DFPN) which are a subclass of Hybrid Functional Petri Nets in which only discrete transitions are allowed. Under some constraints over the anonymous variables appearing in the QPL models, the transformation between the two computational models is shown to preserve computations. By using the DFPN representation our models can be graphically visualized and simulated by means of well known tools (e.g. Cell Illustrator); moreover standard Petri net analyses (e.g. topological analysis, forward/backward reachability, etc .) may be performed on the net model. An executable framework for QPL and for the translation of QPL models into DFPNs has been implemented using the rewriting-based language Maude. We have tested this system on several examples.

A Prize-Collecting Steiner Tree Approach for Transduction Network Inference

Abstract: Into the cell, information from the environment is mainly propagated via signaling pathways which form a transduction network. Here we propose a new algorithm to infer transduction networks from heterogeneous data, using both the protein interaction network and expression datasets. We formulate the inference problem as an optimization task, and develop a message-passing, probabilistic and distributed formalism to solve it. We apply our algorithm to the pheromone response in the baker's yeast S. cerevisiae . We are able to find the backbone of the known structure of the MAPK cascade of pheromone response, validating our algorithm. More importantly, we make biological predictions about some proteins whose role could be at the interface between pheromone response and other cellular functions.

Equivalence and Discretisation in Bio-PEPA

Abstract: Bio-PEPA is a process algebra for modelling biological systems. An important aspect of Bio-PEPA is the ability it provides to discretise concentrations resulting in a smaller, more manageable state space. The discretisation is based on a step size which determines the size of each discrete level and also the maximum number of levels. This paper considers the relationship between two discretisations of the same Bio-PEPA model that differ only in the step size and hence the maximum number of levels, by using the idea of equivalence from concurrency and process algebra. We present a novel behavioural semantic equivalence, compression bisimulation, that equates two discretisations of the same model and we show that this equivalence is a congruence with respect to the synchronisation operator.

Reverse-engineering transcriptional modules from gene expression data.

Abstract: "Module networks" are a framework to learn gene regulatory networks from expression data using a probabilistic model in which coregulated genes share the same parameters and conditional distributions. We present a method to infer ensembles of such networks and an averaging procedure to extract the statistically most significant modules and their regulators. We show that the inferred probabilistic models extend beyond the dataset used to learn the models.

The condition-dependent transcriptional network in Escherichia coli

Abstract: Thanks to the availability of high-throughput omics data, bioinformatics approaches are able to hypothesize thus-far undocumented genetic interactions. However, due to the amount of noise in these data, inferences based on a single data source are often unreliable. A popular approach to overcome this problem is to integrate different data sources. In this study, we describe DISTILLER, a novel framework for data integration that simultaneously analyzes microarray and motif information to find modules that consist of genes that are co-expressed in a subset of conditions, and their corresponding regulators. By applying our method on publicly available data, we evaluated the condition-specific transcriptional network of Escherichia coli. DISTILLER confirmed 62% of 736 interactions described in RegulonDB, and 278 novel interactions were predicted.

The Equivalence between Biology and Computation

Abstract: A major challenge in computational systems biology is the articulation of a biological process in a form which can be understood by the biologist yet is amenable to computational execution. Process calculi have proved to especially powerful computational tools for modelling and reasoning about biological processes and we have previously described, and implemented, a Narrative approach to describing biological models which is a biologically intuitive high level language that can be translated into executable process calculus programs. Here we discuss an extension to the narrative approach which attempts to directly link biological data with Narrative primitives by suggesting an equivalence relationship between a string (the amino acid sequence) and a process. We outline future challenges in applying this approach more generally.

Prediction of Protein-Protein Interacting Sites: How to Bridge Molecular Events to Large Scale Protein Interaction Networks

Abstract: Most of the cellular functions are the result of the concerted action of protein complexes forming pathways and networks For this reason, efforts were devoted to the study of protein-protein interactions Large-scale experiments on whole genomes allowed the identification of interacting protein pairs However residues involved in the interaction are generally not known and the majority of the interactions still lack a structural characterization A crucial step towards the deciphering of the interaction mechanism of proteins is the recognition of their interacting surfaces, particularly in those structures for which also the most recent interaction network resources do not contain information To this purpose, we developed a neural network-based method that is able to characterize protein complexes, by predicting amino acid residues that mediate the interactions All the Protein Data Bank (PDB) chains, both in the unbound and in the complexed form, are predicted and the results are stored in a database of interaction surfaces (http://gpcrbiocompuniboit/zenpatches) Finally, we performed a survey on the different computational methods for protein-protein interaction prediction and on their training/testing sets in order to highlight the most informative properties of protein interfaces

Control Strategies for the Regulation of the Eukaryotic Heat Shock Response

Abstract: Elevated temperatures cause proteins in living cells to misfold. They start forming larger and larger aggregates that can eventually lead to the cell's death. The heat shock response is an evolutionary well conserved cellular response to massive protein misfolding and it is driven by the need to keep the level of misfolded proteins under control. We consider in this paper a recently proposed new molecular model for the heat shock response in eukaryotes, consisting of a temperature-induced activation mechanism, chaperoning of misfolded proteins and self-regulation of the chaperon synthesis. We take in this paper a control driven approach to studying this regulatory network. We modularize the network by identifying its main functional modules. We distinguish three main feedback loops. The main question we are addressing is why is this level of complexity needed for implementing what could in principle also be achieved with an open-loop design. We answer the question by comparing the numerical behavior of various knockdown mutants where one or more feedback loops are missing. We also discuss a new approach for a biologically-unbiased model comparison.

Qualitative Transition Systems for the Abstraction and Comparison of Transient Behavior in Parametrized Dynamic Models

Abstract: Quantitative models in Systems Biology depend on a large number of free parameters, whose values completely determine behavior of models. These parameters are often estimated by fitting the system to observed experimental measurements and data. The response of a model to parameter variation defines qualitative changes of the system's behavior. The influence of a given parameter can be estimated by varying it in a certain range. Some of these ranges produce similar system dynamics, making it possible to define general trends for trajectories of the system (e.g. oscillating behavior) in such parameter ranges. Such trends can be seen as a qualitative description of the system's dynamics within a parameter range. In this work, we define an automata-based formalism to formally describe the qualitative behavior of systems' dynamics. Qualitative behaviors are represented by finite transition systems whose states contain predicate valuation and whose transitions are labeled by probabilistic delays. Biochemical system' dynamics are automatically abstracted in terms of these qualitative transition systems by a random sampling of trajectories. Furthermore, we use graph theoretic tools to compare the resulting qualitative behaviors and to estimate those parameter ranges that yield similar behaviors. We validate this approach on published biochemical models and show that it enables rapid exploration of models' behavior, that is estimation of parameter ranges with a given behavior of interest and identification of some bifurcation points.

Improved Parameter Estimation for Completely Observed Ordinary Differential Equations with Application to Biological Systems

Abstract: We consider parameter estimation in ordinary differential equations (ODEs) from completely observed systems, and describe an improved version of our previously reported heuristic algorithm (IET Syst. Biol. , 2007). Basically, in that method, estimation based on decomposing the problem to simulation of one ODE, is followed by estimation based on simulation of all ODEs of the system. The main algorithmic improvement compared to the original version, is that we decompose not only to single ODEs, but also to arbitrary subsets of ODEs, as a complementary intermediate step. The subsets are selected based on an analysis of the interaction between the variables and possible common parameters. We evaluate our algorithm on a number of well-known hard test problems from the biological literature. The results show that our approach is more accurate and considerably faster compared to other reported methods on these problems. Additionally, we find that the algorithm scales favourably with problem size.

Formal Analysis of the Genetic Toggle

Abstract: The formal analysis of the toggle switch, which is among the most common motifs of genetic networks, shows that along with the powerful development of mathematical modelling, formal methods can be of great help in investigating the properties of genetic networks. In particular, a general approach to modelling genetic networks through the language of higher-order logic is advanced and mechanised in the theorem prover Isabelle. An inductive definition provides a formal model for the genetic toggle as the set of all possible evolutions of such network. Gene polymerase and protein concentration are formalised as primitive recursive functions. The main properties of the genetic toggle are confirmed upon the model: it is possible that one protein exceeds a stated concentration threshold and the other protein does not; it is impossible that both proteins exceed their respective concentration thresholds at the same time. To the best of the authors' knowledge, this is the first contribution of theorem proving in the area of genetic network analysis, and as such may set the foundations for a new niche of research.