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## Über dieses Buch

Membrane Computing was introduced as a computational paradigm in Natural Computing. The models introduced, called Membrane (or P) Systems, provide a coherent platform to describe and study living cells as computational systems. Membrane Systems have been investigated for their computational aspects and employed to model problems in other fields, like: Computer Science, Linguistics, Biology, Economy, Computer Graphics, Robotics, etc. Their inherent parallelism, heterogeneity and intrinsic versatility allow them to model a broad range of processes and phenomena, being also an efficient means to solve and analyze problems in a novel way.

Membrane Computing has been used to model biological systems, becoming with time a thorough modeling paradigm comparable, in its modeling and predicting capabilities, to more established models in this area. This book is the result of the need to collect, in an organic way, different facets of this paradigm.

The chapters of this book, together with the web pages accompanying them, present different applications of Membrane Systems to Biology. Deterministic, non-deterministic and stochastic systems paired with different algorithms and methodologies show the full potential of this framework.

The book is addressed to researchers interested in applications of discrete biological models and the interplay between Membrane Systems and other approaches to analyze complex systems.

## Inhaltsverzeichnis

### Chapter 1. Infobiotics Workbench: A P Systems Based Tool for Systems and Synthetic Biology

Abstract
This chapter gives an overview of an integrated software suite, the Infobiotics Workbench, which is based on a novel spatial discrete-stochastic P systems modelling framework. The Workbench incorporates three important features, simulation, model checking and optimisation. Its capability for building, analysing and optimising large spatially discrete and stochastic models of multicellular systems makes it a useful, coherent and comprehensive in silico tool in systems and synthetic biology research.
Jonathan Blakes, Jamie Twycross, Savas Konur, Francisco Jose Romero-Campero, Natalio Krasnogor, Marian Gheorghe

### Chapter 2. Statistical Model Checking of Membrane Systems with Peripheral Proteins: Quantifying the Role of Estrogen in Cellular Mitosis and DNA Damage

Abstract
Systems biology is a natural application of membrane systems, allowing the analysis of biological systems using the formal technique of model checking. To overcome the intractable model size of typical biological systems, statistical model checking may be used to efficiently estimate the probability of properties of interest with arbitrary levels of confidence. In this chapter we analyse a biological system linked to breast cancer, using statistical model checking (SMC) applied to membrane systems. To do this, we have constructed a computational platform that integrates an SMC library with a stochastic simulator of membrane systems with peripheral proteins. We present the methodology to investigate the role of estrogen in cellular mitosis and DNA damage and we use our statistical model checker to find the most appropriate time-dependent dosage of antagonist that should be used to minimize the uncontrolled replication of abnormal cells.
Matteo Cavaliere, Tommaso Mazza, Sean Sedwards

### Chapter 3. Molecular Diffusion and Compartmentalization in Signal Transduction Pathways: An Application of Membrane Systems to the Study of Bacterial Chemotaxis

Abstract
In this chapter we present an application of membrane systems to the study of intracellular diffusive processes. In particular, a class of membrane systems, called $$\tau$$-DPP, is used for the modeling, simulation and analysis of bacterial chemotaxis. Two different models of this signal transduction pathway are presented. The first is a single volume model used to investigate the properties of bacterial chemotaxis and to analyze the effects of different perturbations (deletion of chemotactic proteins, addition of distinct amounts of external ligand, effect of different methylation states of the receptors) on the system dynamics. The second model represents a multivolume extension of the former, and it is exploited for the analysis of the diffusive processes that give rise to the formation of concentration gradients throughout the bacterial cytoplasm. The outcome of stochastic simulations of both models are exploited to analyze the process of synchronization of flagella, in order to evaluate the running and tumbling time intervals of bacterial cells.
Paolo Cazzaniga, Daniela Besozzi, Dario Pescini, Giancarlo Mauri

### Chapter 4. Membrane System-Based Models for Specifying Dynamical Population Systems

Abstract
Population Dynamics P systems (PDP systems, in short) provide a new formal bio-inspired modelling framework, which has been successfully used for modelling population dynamics on real ecosystems. The semantics of these systems is captured by the Direct distribution based on Consistent Blocks Algorithm (DCBA), which has been engineered into software simulation tools. In particular, MeCoSim (Membrane Computing Simulator) is a GUI developed in the framework of P-Lingua that can be used as a simulation environment for running virtual experiments. The parameters of each scenario to be simulated can be easily adjusted in a visual way, as well as the settings for the desired output format, thus facilitating the validation of the designed models against real data. The simulation of PDP systems is data intensive for large models. Therefore, the development of efficient simulators for this field is needed. In fact, the computational power of GPUs is currently being used to accelerate simulations of PDP systems. We illustrate the modelling framework presented with a case study concerning pandemics.
M. A. Colomer-Cugat, M. García-Quismondo, L. F. Macías-Ramos, M. A. Martínez-del-Amor, I. Pérez-Hurtado, M. J. Pérez–Jiménez, A. Riscos-Núñez, L. Valencia-Cabrera

### Chapter 5. Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for Applications in Chronobiology

Abstract
This chapter addresses three coordinated chronobiological studies demonstrating the convergence of experimental observations, fine-grained spatio-temporal modelling, and predictive simulation. Due to the discrete manner of molecular assembly in cell signalling and gene regulation, we define a framework of membrane systems equipped with discretised forms of reaction kinetics in concert with variable intramolecular structures. Our first study is dedicated to circadian clocks inducing daily biological rhythms. As an inspiring example, the KaiABC core oscillator reaches its functionality by cyclically varying protein structures. Within our second study, we present a meta-model of an entire circadian clockwork able to adapt its oscillation to an external stimulus in terms of a frequency control system acting in a phase-locked loop. Substrate concentration courses resulting from gene expression reflect its oscillatory behaviour utilised in a periodical trigger for subsequent processes. In this context, our third study cytometrically quantifies the dynamical behaviour of a bistable toggle switch resulting from mutual gene regulation.
Thomas Hinze, Jörn Behre, Christian Bodenstein, Gabi Escuela, Gerd Grünert, Petra Hofstedt, Peter Sauer, Sikander Hayat, Peter Dittrich

### Chapter 6. Biochemical Networks Discrete Modeling Inspired by Membrane Systems

Abstract
The ideas expressed in this work pertain to biochemical modeling. We explore our technique, the Nondeterministic Waiting Time algorithm, for modeling molecular signaling cascades. The algorithm is presented with pseudocode along with an explanation of its implementation. We discuss several important extensions including: (i) a heap with special maintenance functions for sorting reaction waiting times, (ii) a nondeterminstic component for handling reaction competition, and (iii) a memory enhancement allowing slower reactions to compete with faster reactions. Several example systems are provided for comparisons between modeling with systems of ordinary differential equations, the Gillespie Algorithm, and our Nondeterministic Waiting Time Algorithm. Our algorithm has a unique ability to exhibit behavior similar to the solutions to systems of ordinary differential equations for certain models and parameter choices, but it also has the nondeterministic component which yields results similar stochastic methods (e.g., the Gillespie Algorithm). There are several extensions for the current work discussed at the end of the chapter.
John Jack, Andrei Păun, Mihaela Păun

### Chapter 7. MP Modelling for Systems Biology: Two Case Studies

Abstract
Metabolic P systems (MP systems), based on Păun’s P systems, were introduced for modelling metabolic systems by means of suitable multiset rewriting grammars. The initial modelling framework has been widely extended in last years and equipped with a new regression algorithm which derives MP models from the time series of observed dynamics. This has allowed us to dramatically extend the range of possible MP modelling applications from metabolic dynamics to more general kinds of dynamical systems. In this work two applications of MP systems are presented, for discovering the internal regulation logic of two phenomena relevant to systems biology. The first one is a metabolic dynamics related to glucose/insulin interactions during the Intravenous Glucose Tolerance Test. The second one deals with the definition of gene expression networks related to breast cancer under the inhibition of a growth factor.
Luca Marchetti, Vincenzo Manca, Roberto Pagliarini, Aliccia Bollig-Fischer

### Chapter 8. Modelling and Analysis of E. coli Respiratory Chain

Abstract
In this chapter we present some results obtained in the study of the bacterium E. coli related to its behavior at different level of oxygen in the environment. The biological model is expressed in terms of different molecules and their reactions. First, an agent-based model of E. coli is implemented in the FLAME framework for multi-agents and some simulation results are given. Each agent is represented by an X-machine and the model corresponds to communicating X-machines. Then this model is transformed into a kernel P system. This kernel P system is implemented in the Rodin platform and in Spin and some properties are verified using the associated model checkers. Formulated using the LTL formalism, the verified properties refer to the variation of the number of different molecules as a result of the occurring reactions. Our main contribution is a simplified model of E. coli that preserves the main properties of the initial model, and can be formally verified using a model checker.
Adrian Ţurcanu, Laurenţiu Mierlă, Florentin Ipate, Alin Stefanescu, Hao Bai, Mike Holcombe, Simon Coakley
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