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The LNCS journal Transactions on Computational Systems Biology is devoted to inter- and multidisciplinary research in the fields of computer science and life sciences and supports a paradigmatic shift in the techniques from computer and information science to cope with the new challenges arising from the systems oriented point of view of biological phenomena. This, the 14th Transactions on Computational Systems Biology volume, guest edited by Ion Petre and Erik de Vink, focuses on Computational Models for Cell Processes and features a number of carefully selected and enhanced contributions, initially presented at the CompMod workshop, which took place in Aachen, Germany, in September 2011. The papers, written from different points of view and following various approaches, cover a wide range of topics within the field of modeling and analysis of biological systems. In addition, two regular submissions deal with models of self-assembling systems and metabolic constraints on the evolution of genetic codes.



Biological and Biologically-Inspired Communication

Trend-Based Analysis of a Population Model of the AKAP Scaffold Protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system.

Oana Andrei, Muffy Calder

Quasi Product Form Approximation for Markov Models of Reaction Networks

In cell processes, such as gene regulation or cell differentiation, stochasticity often plays a crucial role. Quantitative analysis of stochastic models of the underlying chemical reaction network can be obstructed by the size of the state space which grows exponentially with the number of considered species. In a recent paper [1] we showed that the space complexity of the analysis can be drastically decreased by assuming that the transient probabilities of the model are in

product form

. This assumption, however, leads to approximations that are satisfactory only for a limited range of models. In this paper we relax the product form assumption by introducing the

quasi product form

assumption. This leads to an algorithm whose memory complexity is still reasonably low and provides a good approximation of the transient probabilities for a wide range of models. We discuss the characteristics of this algorithm and illustrate its application on several reaction networks.

Alessio Angius, András Horváth, Verena Wolf

Multiple Verification in Complex Biological Systems: The Bone Remodelling Case Study

We present a set of formal techniques and a methodology for a composite formal analysis at the tissue and organ level, focusing on the verification of quantitative properties in the process of bone remodelling. Starting from a differential equation model, we derive a stochastic model and a piecewise multi-affine approximation in order to perform model checking of stabilisation properties for the biological tissue, and to assess the differences between a regular remodelling activity and a defective activity typical of pathologies like osteoporosis. The complex nonlinear dynamics of bone remodelling is analysed with a variety of techniques: sensitivity analysis for the differential equation model; quantitative probabilistic model checking for the stochastic model; and classical model checking and parameter synthesis on the piecewise multi-affine model. Such analyses allow us to extract a wealth of information that is not only useful for a deeper understanding of the biological process but also towards medical diagnoses.

Ezio Bartocci, Pietro Liò, Emanuela Merelli, Nicola Paoletti

On Approximative Reachability Analysis of Biochemical Dynamical Systems

This is an extended version of the workshop paper [1], in which a new computational technique called quantitative discrete approximation has been introduced. The technique provides finite discrete approximation of continuous dynamical systems which is suitable especially for a significant class of biochemical dynamical systems. With decreasing granularity the approximation of behaviour between a discrete state and its successor converges to the behaviour of the original continuous system in the respective part of the phase space.

This paper provides a detailed description of the method and algorithms solving the reachability problem in biochemical dynamical systems. The method is supplemented with heuristics for reducing the cardinality of the reachable state space. The algorithms are evaluated on six models (with numbers of variables ranging from 2 to 12).

L. Brim, J. Fabriková, S. Dražan, D. Šafránek

Minimal Reaction Systems

Reaction systems are a formal model for processes inspired by the functioning of the living cell. These processes are determined by the iteration of the state transition functions of reaction systems, also called rs functions. In this paper we provide mathematical characterisations of rs functions implemented/defined by “minimal reaction systems”, ı.e., reaction systems with reactions using the minimal number of reactants, or the minimal number of inhibitors, or the minimal number of resources (ı.e., reactants and inhibitors together).

Andrzej Ehrenfeucht, Jetty Kleijn, Maciej Koutny, Grzegorz Rozenberg

Complex Functional Rates in Rule-Based Languages for Biochemistry

Rule-based languages (like, for example, Kappa, BioNetGen, and BioCham) have emerged as successful models for the representation, analysis, and simulation of bio-chemical systems. In particular Kappa, although based on reactions, differs from traditional chemistry as it allows for a graph-like representation of complexes. It follows the

“don’t care, don’t write”

approach: a rule contains the description of only those parts of the complexes that are actually involved in a reaction. Hence, given any possible combination of complexes that contain the reactants, such complexes can give rise to the reaction. In this paper we address the problem of extending the

“don’t care, don’t write”

approach to cases in which the actual structure of the complexes involved in the reaction could affect it (for instance, the mass of the complexes could influence the rate). The solutions that we propose is



, an extension of the Kappa-calculus in which rates are defined as functions of the actually involved complexes.

Cristian Versari, Gianluigi Zavattaro

Probabilistic Model Checking of the PDGF Signaling Pathway

In this paper, we apply the probabilistic symbolic model checker PRISM to the analysis of a biological system – the Platelet-Derived Growth Factor (PDGF) signaling pathway, demonstrating in detail how this pathway can be analyzed in PRISM. Moreover, we compare the results from verification and ODE simulation on the PDGF pathway and demonstrate by examples the influence of model structure, parameter values and pathway length on the two analysis methods.

Qixia Yuan, Panuwat Trairatphisan, Jun Pang, Sjouke Mauw, Monique Wiesinger, Thomas Sauter

Self-assembly Models of Variable Resolution

Model refinement is an important aspect of the model-building process. It can be described as a procedure which, starting from an abstract model of a system, performs a number of refinement steps in result of which a more detailed model is obtained. At the same time, in order to be correct, the refinement mechanism has to be capable of preserving already proven systemic quantitative properties of the original model, e.g. model fit, stochastic semantics, etc. In this study we concentrate on the refinement in the case of self-assembly models. Self-assembly is a process in which a disordered ensemble of basic components forms an organized structure as a result of specific, local interactions among these components, without external guidance. We develop a generic formal model for this process and introduce a notion of model resolution capturing the maximum size up to which objects can be distinguished individually in the model. All bigger objects are treated homogenously in the model. We show how this self-assembly model can be systematically refined in such a way that its resolution can be increased and decreased while preserving the original model fit to experimental data, without the need for tedious, computationally expensive process of parameter refitting. We demonstrate how the introduced methodology can be applied to a previously published model: we consider the case-study of

in vitro

self-assembly of intermediate filaments.

Andrzej Mizera, Eugen Czeizler, Ion Petre

Metabolic Constraints on the Evolution of Genetic Codes: Did Multiple Preaerobic’ Ecosystem Transitions Entrain Richer Dialects via Serial Endosymbiosis?

A model derived from Tlusty’s elegant topological deconstruction suggests that multiple punctuated ecosystem resilience regime changes in metabolic free energy broadly similar to the aerobic transition enabled a punctuated sequence of increasingly complex genetic codes and protein translators. In a manner similar to the Serial Endosymbiosis effecting the Eukaryotic transition, codes and translators coevolved until the ancestor of the present narrow spectrum of protein machineries became locked-in by evolutionary path dependence at a relatively modest level of fitness reflecting a modest embedding metabolic free energy ecology. A search for evidence of a sequence of ‘preaerobic’ ecosystem shifts in metabolic free energy availability or efficiency of use might be surprisingly fruitful.

Rodrick Wallace


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