Modeling A Multi-Compartments Biological System with Membrane Computing

Problem statement: Membrane computing formalism has provided better modeling capabilities for biological systems in comparison to conventional mathematical models. Model checking could be used to reason about the biological system in detail and with precision by verifying formally whether membrane computing model meets the properties of the system. Approach: This study was carried to investigate the preservation of properties of two biological systems that had been modeled and simulated in membrane computing by a method of model checking using PRISM. The two biological systems were prey-predator population and signal processing in the legend-receptor networks of protein TGF-β. Results: The model checking of membrane computing model of the biological systems with five different properties showed that the properties of the biological systems could be preserved in the membrane computing model. Conclusion: Membrane computing model not only provides a better approach in representing and simulating a biological system but also able to sustain the basic properties of the system.

Model checking is an established method for verifying behavioral properties of system models. But model checkers tend to support low-level modeling languages that require intricate models to represent even the simplest systems. Modeling complexity arises in part from the need to encode domain knowledge at relatively low levels of abstraction. In this paper, we demonstrate that formalized domain knowledge can be reused to raise the abstraction level of model and property specifications, and hence the effectiveness of model checking. We describe a novel method for domain-specific model checking called cascading verification that uses composite reasoning over high-level system specifications and formalized domain knowledge to synthesize both low-level system models and their behavioral properties for verification. In particular, model builders use a high-level domain-specific language (DSL) based on YAML to express system specifications that can be verified with probabilistic model checking. Domain knowledge is encoded in the Web Ontology Language (OWL), the Semantic Web Rule Language (SWRL) and Prolog, which are used in combination to overcome their individual limitations. A compiler then synthesizes models and properties for verification by the probabilistic model checker PRISM. We illustrate cascading verification for the domain of uninhabited aerial vehicles (UAVs), for which we have constructed a prototype implementation. An evaluation of this prototype reveals nontrivial reductions in the size and complexity of input specifications compared to the artifacts synthesized for PRISM.

Modeling and analysis of complex systems are important aspects of understanding systemic behavior. In the lack of detailed knowledge about a system, we often choose modeling equations out of convenience and search the (high-dimensional) parameter space randomly to learn about model properties. Qualitative modeling sidesteps the issue of choosing specific modeling equations and frees the inference from specific properties of the equations. We consider classes of ordinary differential equation (ODE) models arising from interactions of species/entities, such as (bio)chemical reaction networks or ecosystems. A class is defined by imposing mild assumptions on the interaction rates. In this framework, we investigate whether there can be multiple positive steady states in some ODE models in a given class. We have developed and implemented a method to decide whether any ODE model in a given class cannot have multiple steady states. The method runs efficiently on models of moderate size. We tested the method on a large set of models for gene silencing by sRNA interference and on two publicly available databases of biological models, KEGG and Biomodels. We recommend that this method is used as (i) a pre-screening step for selecting an appropriate model and (ii) for investigating the robustness of non-existence of multiple steady state for a given ODE model with respect to variation in interaction rates. Scripts and examples in Maple are available in the Supplementary Information. wiuf@math.ku.dk Supplementary data are available at Bioinformatics online.

High-performance data streaming technologies are increasingly adopted in IT companies to support the integration of heterogeneous and possibly distributed applications. Compared with the traditional message queuing middleware, a streaming platform enables the implementation of event-streaming systems (ESS) which include not only complex queues but also pipelines that transform and react to the streams of data. By analysing the centralised data streams, one can evaluate the Quality-of-Service for other systems and components that produce or consume those streams. We consider the exploitation of <i>probabilistic model checking</i> as a performance monitoring technique for ESS systems. Probabilistic model checking is a mature, powerful verification technique with successful application in performance analysis. However, an ESS system may contain quantitative parameters that are determined by event streams observed in a certain period of time. In this paper, we present a novel theoretical framework called QV4M (meaning &#x201C;quantitative verification for monitoring&#x201D;) for monitoring ESS systems, which is based on two recent methods of probabilistic model checking. QV4M assumes the parameters in a probabilistic system model as random variables and infers the statistical significance for the probabilistic model checking output. We also present an empirical evaluation of computational time and data cost for QV4M.

This paper extends the graphical and formal language of UML-B to provide the ability to model probabilities. Discrete probabilities, interval probabilities, and stochastic delays are added to the UML-B's state-machine syntax, and their corresponding semantics are defined in Event-B. In addition, as a secondary contribution, UML-B (probabilistic) state-machine models are defined as MDP (Markov Decision Process) models in order to provide a means of quantitative verification in PRISM (Probabilistic Symbolic Model Checker). As an important feature of the proposed method, it does not change the Event-B syntax or semantics. To evaluate this work, as a case study, the Zeroconf protocol will be modeled in the extended UML-B using the Rodin tool, and its Event-B counterpart is converted to a PRISM model. The results of evaluations indicate that this study's additions provide the capability of modeling and verification of probabilistic and stochastic systems.

In this paper we describe PRISM, a tool being developed at the University of Birmingham for the analysis of probabilistic systems. PRISM supports three probabilistic models: discrete-time Markov chains, Markov decision processes and continuous-time Markov chains. Analysis is performed through model checking such systems against specifications written in the probabilistic temporal logics PCTL and CSL. The tool features three model checking engines: one symbolic, using BDDs (binary decision diagrams) and MTBDDs (multi-terminal BDDs); one based on sparse matrices; and one which combines both symbolic and sparse matrix methods. PRISM has been successfully used to analyse probabilistic termination, performance, and quality of service properties for a range of systems, including randomized distributed algorithms, manufacturing systems and workstation clusters.KeywordsModel CheckMarkov Decision ProcessBinary Decision DiagramSymbolic Model CheckerModel Check ToolThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Model checking epistemic–probabilistic logic using probabilistic interpreted systems

Experimental results have shown that anti-cancer therapies, such as radiotherapy and chemotherapy, can modulate the cell cycle and generate cell cycle phase-dependent responses. As a result, obtaining a detailed understanding of the cell cycle is one possible path towards improving the efficacy of many of these therapies. Here, we consider a basic structured partial differential equation (PDE) model for cell progression through the cell cycle, and derive expressions for key quantities, such as the population growth rate and cell phase proportions. These quantities are shown to be periodic and, as such, we compare the PDE model to a corresponding ordinary differential equation (ODE) model in which the parameters are linked by ensuring that the long-term ODE behaviour agrees with the average PDE behaviour. By design, we find that the ODE model does an excellent job of representing the mean dynamics of the PDE model within just a few cell cycles. However, by probing the parameter space we find cases in which this mean behaviour is not a good measure of the PDE population growth. Our analytical comparison of two caricature models (one PDE and one ODE system) provides insight into cases in which the simple ODE model is an appropriate approximation to the PDE model.

US high school (HS) students are lagging behind their foreign peers in math performance. It is thus necessary to design teaching modules that motivate US HS students to learn more math and to improve their math skills. Our study set out to test two different software programs designed for the development of such skills. MATLAB Simulink provides a friendly interface with which HS students can build ordinary differential equation (ODE) models. An alternative programming language, the R language is free and extensively used in the field of statistical learning and engineering. In this study, a group of HS students first got trained in both Simulink and R and then solved an ODE model of a microbial fuel cell (MFC), which can convert the organic compounds found in waste water into electricity, using both Simulink and R. Three anonymous surveys were conducted for: 1) students’ feedback on the module-based teaching approaches with R and Simulink training, 2) students’ self-evaluation in the improvement of their skills in solving ODE models following their training in R and Simulink, and 3) students’ comparison of R and Simulink in their learning and modeling experience. The instructor also evaluated students’ modeling skills with R and Simulink based on their performance in developing the MFC ODE model. Both students’ self-evaluation and the instructor’s direct evaluation indicate that students’ skills in solving ODE models with both R and Simulink were significantly improved after this R-Simulink modeling project. The surveys show that students generally enjoyed the module-based teaching format and that they would recommended this project to their peers. It was shown in the surveys that students preferred Simulink over R in solving ODE models and that they preferred learning Simulink first and then following up by learning R. Students’ comments for opening questions indicate that the major hurdle in this project was their limited background knowledge in biology and electrochemistry for microbial fuel cells.

The four papers in this special issue apply tools and techniques from computer performance evaluation in the very different domain of modelling biological systems. This might seem to be a very odd thing to do but the practice of analysing biological systems in this way is becoming increasing common. As data about the internal components of biological systems is becoming more readily available, biologists are increasingly asking questions about how systems function. In addition to conducting laboratory experiments, they are supported in this exploration by in silico experimentation based on models. The view taken of the biological processes focusses on the stimuli and responses, a view akin to that taken of engineered systems in systems engineering. Thus this new endeavour in biology is known as Systems Biology . Performance analysts have a long tradition of modelling systems in order to understand and predict their function. Their focus is particularly on the dynamic aspects of the system, the use of, and contention for, resources, and the impact of uncertainty or randomness. These issues are important in the biological setting also, and so it is perhaps inevitable that we see some people and techniques from performance modelling being applied in systems biology. In particular some of the high-level modelling formalisms which have supported Markovian performance modelling in the last few decades (stochastic Petri nets, stochastic process algebras, etc.) are being applied in the biological domain. Furthermore analysis techniques, such as Markovian analysis, Monte Carlo simulation and probabilistic model checking have also been adoped. In this volume we have sought to give a snapshot of a variety of work which is going on at this interface between systems biology and more traditional quantitative analysis techniques. It is by no means an exhaustive account of this exciting area, but rather a taster which will hopefully whet your appetite to find out more. To open the volume, the editors provide a survey paper describing the motivations and goals of the systems biology endeavour, summarising the existing modelling techniques and outlining some instances of cross-over between performance modelling and systems biology. This includes an account of the use of ordinary differential equations (ODE) and stochastic simulation to analyse biological systems, and the adoption of high-level modelling formalisms such as Petri nets and process algebras to drive these ODE models and simulations. In their paper Kwiatkowska, Norman and Parker show the application of logic and probabilistic model checking to the analysis of biological signalling pathways. They use the PRISM probabilistic model-checker to check formulae of the CSL logic against CTMC-based models of the MAPK cascade, a sequence of biochemical reactions which sends a message within a cell. The paper provides an introduction to the CSL logic as well as the reactive modules language implemented by the PRISM model checker. Performance measures of interest are described using reward structures and the analysis achieved by PRISM is able to show how the percentage of activated MAPK, a key component of the pathway, and the number of MAPK-MAPKK reactions, vary as a function of time, for different values of the initial number of MAPKs. The paper by Jeschke, Ewald, Park, Fujimoto and Uhrmacher addresses the drive for increased physical accuracy in simulation models which represent the spatial aspects of cell biology. Standard approaches to stochastic simulation of cellular systems assume that the cell is a homogeneous soup of biochemical components. The truth is far removed from this, as the cell has a lot of internal structure which can have a profound effect on the dynamics of reactions. Setting aside the assumption that the reacting chemical species are well-stirred, spatial approaches divide the volume into sub-volumes and apply a structured method which identifies the next reaction to occur in each subvolume. The cost of such an increase in accuracy in the simulation model is a much increased running time so the authors use a parallel and distributed approach to improve performance. To close this special issue we have a paper by DemattB, Priami and Romanel which uses the BlenX language and the Beta Workbench software to analyse the MAPK pathway considered also by Kwiatkowska, Norman and Parker. The BlenX language, and the Beta-binders process calculus which was its inspiration, are examples of a new generation of languages which have been designed specifically for the biological domain, as an alternative to using existing languages designed for modelling computer systems. The paper shows how a well-designed platform for modelling and simulation can lift the user's experience and make their use of process calculi more valuable, delivering insights which would not have been seen otherwise.

Ordinary differential equation (ODE) models are quite popular for modelling complex dynamic processes in many scientific fields, and the parameters in these models are usually unknown, and we need to estimate them using statistical methods. When some observations are contaminated, regular estimation methods, such as nonlinear least-square estimation, will bring large bias. In this paper, robust estimations of both constant and time-varying parameters in ODE models using M-estimators are proposed, and their asymptotic properties are obtained under some mild conditions. We focus on Huber M-estimator, and also provide a method to adjust the Huber parameter automatically to the observations. The proposed method is compared to existing methods in numerical simulations and CD8+ T cell data analysis. It is demonstrated that our method gain substantial efficiency as well as robust properties.

Vector-borne diseases provide unique challenges to public health because the epidemiology is so closely tied to external environmental factors such as climate, landscape, and population migration, as well as the complicated biology of vector-transmitted pathogens. In particular, this close link between the epidemiology, the environment, and pathogen biology means that the traditional view that many vector-borne diseases are relatively stable in numerous regions does not provide a complete picture of their complexity. In fact, several regions exist with low levels of endemicity most of the time, punctuated by severe, often explosive, epidemics. These regions are considered unstable transmission settings. Ordinary differential equation (ODE) models have thus far dominated the study of vector-borne disease and have provided considerable insight into our understanding of transmission and effective control in stable transmission settings. To address the short-­comings of autonomous ODE models, we present a class of models, differential-delay equation (DDE) models, that have the potential to better describe unstable endemic settings for vector-borne disease. These models develop naturally out of the biology of diseases transmitted by vectors because of the extrinsic and intrinsic incubation periods and vector maturation process necessary for successful transmission of vector-transmitted pathogens. In this chapter, we introduce five examples of vector-borne diseases that span the globe, and discuss the clinical implications of unstable transmission of these diseases. Next, we present the original ODE version of the Ross-Macdonald model for vector-borne diseases, modify this model by introducing different types of naturally occurring delays, then illustrate how these models can exhibit more complex behavior such as oscillations via Hopf bifurcation and chaos via period-doubling, that the ODE model cannot produce. Finally, we explore the possibility for delay-models to contribute to our understanding of unstable transmission settings, which in turn will inform the development of effective control strategies for these epidemic-prone regions.

For system identification, the ordinary differential equations (ODEs) model is popular for its accuracy and effectiveness. Consequently, the ODEs model is extended to the stochastic differential equations (SDEs) model to tackle the stochastic case intuitively. But the existence of stochastic integral is a rigid barrier. We simply transform the SDEs to their corresponding stochastic difference equations (SDCEs) to eliminate stochastic integrals and propose an easy but effective solution to stochastic system identification. In this solution, the maximum likelihood estimation can be applied and the evolutionary algorithms are used to determine structures and parameters of the unknown system.

A system of recurrent neural networks for modularising, parameterising and dynamic analysis of cell signalling networks

We find concrete evidence for a recently discovered form of intermittency, referred to as in–out intermittency, in both partial differential equation (PDE) and ordinary differential equation (ODE) models of mean field dynamos. This type of intermittency [introduced in P. Ashwin, E. Covas, and R. Tavakol, Nonlinearity 9, 563 (1999)] occurs in systems with invariant submanifolds and, as opposed to on–off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behavior may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in–out intermittency are axisymmetric mean-field dynamo models which are often used to study the observed large-scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.