Stochastic Calculus of Wrapped Compartments

The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems. The main simplification consists in the removal of the sequencing operator, thus lightening the formal treatment of the patterns to be matched in a term (whose complexity in CLS is strongly affected by the variables matching in the sequences). We define a stochastic semantics for this new calculus. As an application we model the interaction between macrophages and apoptotic neutrophils and a mechanism of gene regulation in E.Coli

Ecological Modelling with the Calculus of Wrapped Compartments

The Calculus of Wrapped Compartments is a framework based on stochastic multiset rewriting in a compartmentalised setting originally developed for the modelling and analysis of biological interactions. In this paper, we propose to use this calculus for the description of ecological systems and we provide the modelling guidelines to encode within the calculus some of the main interactions leading ecosystems evolution. As a case study, we model the distribution of height of Croton wagneri, a shrub constituting the endemic predominant species of the dry ecosystem in southern Ecuador. In particular, we consider the plant at different altitude gradients (i.e. at different temperature conditions), to study how it adapts under the effects of global climate change.Comment: A preliminary version of this paper has been presented in CMC13 (LNCS 7762, pp 358-377, 2013

A Calculus for Molecular Interaction Maps

Molecular Interaction Maps are a graphical formalism used by biologists to describe complex interactions between molecules. We provide a formal description of MIMs using process algebras and determine its computational power

Measurable stochastics for Brane Calculus

AbstractThe main aim of this work is to give a stochastic extension of the Brane Calculus, along the lines of recent work by Cardelli and Mardare (2010) [12]. In this approach, the semantics of a process is a measure of the stochastic distribution of possible derivations. To this end, we first introduce a compositional, finitely branching labelled transition system for Brane Calculus; interestingly, the associated strong bisimulation is a congruence. Then, we give a stochastic semantics to Brane systems by defining them as Markov processes over the measurable space generated by terms up-to syntactic congruence, and where the measures are indexed by the actions of this new LTS. Finally, we provide an SOS presentation of this stochastic semantics, which is compositional and syntax-driven, and moreover the induced rate bisimilarity is a congruence

Hybrid Modeling of Cancer Drug Resistance Mechanisms

Cancer is a multi-scale disease and its overwhelming complexity depends upon the multiple interwind events occurring at both molecular and cellular levels, making it very difficult for therapeutic advancements in cancer research. The resistance to cancer drugs is a significant challenge faced by scientists nowadays. The roots of the problem reside not only at the molecular level, due to multiple type of mutations in a single tumor, but also at the cellular level of drug interactions with the tumor. Tumor heterogeneity is the term used by oncologists for the involvement of multiple mutations in the development of a tumor at the sub-cellular level. The mechanisms for tumor heterogeneity are rigorously being explored as a reason for drug resistance in cancer patients. It is important to observe cell interactions not only at intra-tumoral level, but it is also essential to study the drug and tumor cell interactions at cellular level to have a complete picture of the mechanisms underlying drug resistance. The multi-scale nature of cancer drug resistance problem require modeling approaches that can capture all the multiple sub-cellular and cellular interaction factors with respect to dierent scales for time and space. Hybrid modeling offers a way to integrate both discrete and continuous dynamics to overcome this challenge. This research work is focused on the development of hybrid models to understand the drug resistance behaviors in colorectal and lung cancers. The common thing about the two types of cancer is that they both have dierent mutations at epidermal growth factor receptors (EGFRs) and they are normally treated with anti-EGFR drugs, to which they develop resistances with the passage of time. The acquiring of resistance is the sign of relapse in both kind of tumors. The most challenging task in colorectal cancer research nowadays is to understand the development of acquired resistance to anti-EGFR drugs. The key reason for this problem is the KRAS mutations appearance after the treatment with monoclonal antibodies (moAb). A hybrid model is proposed for the analysis of KRAS mutations behavior in colorectal cancer with respect to moAb treatments. The colorectal tumor hybrid model is represented as a single state automata, which shows tumor progression and evolution by means of mathematical equations for tumor sub-populations, immune system components and drugs for the treatment. The drug introduction is managed as a discrete step in this model. To evaluate the drug performance on a tumor, equations for two types of tumors cells are developed, i.e KRAS mutated and KRAS wild-type. Both tumor cell populations were treated with a combination of moAb and chemotherapy drugs. It is observed that even a minimal initial concentration of KRAS mutated cells before the treatment has the ability to make the tumor refractory to the treatment. Moreover, a small population of KRAS mutated cells has a strong influence on a large number of wild-type cells by making them resistant to chemotherapy. Patient's immune responses are specifically taken into considerations and it is found that, in case of KRAS mutations, the immune strength does not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy) drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated cells. Results show that this combined treatment could be only effective for patients with high immune strengths and it should not be recommended as first-line therapy for patients with moderate immune strengths or weak immune systems because of a potential risk of relapse, with KRAS mutant cells acquired resistance involved with them. Lung cancer is more complicated then colorectal cancer because of acquiring of multiple resistances to anti-EGFR drugs. The appearance of EGFR T790M and KRAS mutations makes tumor resistant to a geftinib and AZD9291 drugs, respectively. The hybrid model for lung cancer consists of two non-resistant and resistant states of tumor. The non-resistant state is treated with geftinib drug until resistance to this drug makes tumor regrowth leading towards the resistant state. The resistant state is treated with AZD9291 drug for recovery. In this model the complete resistant state due to KRAS mutations is ignored because of the unavailability of parameter information and patient data. Each tumor state is evaluated by mathematical differential equations for tumor growth and progression. The tumor model consists of four tumor sub-population equations depending upon the type of mutations. The drug administration in this model is also managed as a discrete step for exact scheduling and dosages. The parameter values for the model are obtained by experiments performed in the laboratory. The experimental data is only available for the tumor progression along with the geftinib drug. The model is then fine tuned for obtaining the exact tumor growth patterns as observed in clinic, only for the geftinib drug. The growth rate for EGFR T790M tumor sub-population is changed to obtain the same tumor progression patterns as observed in real patients. The growth rate of mutations largely depends upon the immune system strength and by manipulating the growth rates for different tumor populations, it is possible to capture the factor of immune strength of the patient. The fine tuned model is then used to analyze the effect of AZD9291 drug on geftinib resistant state of the tumor. It is observed that AZD9291 could be the best candidate for the treatment of the EGFR T790M tumor sub-population. Hybrid modeling helps to understand the tumor drug resistance along with tumor progression due to multiple mutations, in a more realistic way and it also provides a way for personalized therapy by managing the drug administration in a strict pattern that avoid the growth of resistant sub-populations as well as target other populations at the same time. The only key to avoid relapse in cancer is the personalized therapy and the proposed hybrid models promises to do that

Development of a stochastic simulator for biological systems based on Calculus of Looping Sequences.

Molecular Biology produces a huge amount of data concerning the behavior of the single constituents of living organisms. Nevertheless, this reductionism view is not sucient to gain a deep comprehension of how such components interact together at the system level, generating the set of complex behavior we observe in nature. This is the main motivation of the rising of one of the most interesting and recent applications of computer science: Computational Systems Biology, a new science integrating experimental activity and mathematical modeling in order to study the organization principles and the dynamic behavior of biological systems. Among the formalisms that either have been applied to or have been inspired by biological systems there are automata based models, rewrite systems, and process calculi. Here we consider a formalism based on term rewriting called Calculus of Looping Sequences (CLS) aimed to model chemical and biological systems. In order to quantitatively simulate biological systems a stochastic extension of CLS has been developed; it allows to express rule schemata with the simplicity of notation of term rewriting and has some semantic means which are common in process calculi. In this thesis we carry out the study of the implementation of a stochastic simulator for the CLS formalism. We propose an extension of Gillespie's stochastic simulation algorithm that handles rule schemata with rate functions, and we present an efficient bottom-up, pre-processing based, CLS pattern matching algorithm. A simulator implementing the ideas introduced in this thesis, has been developed in F#, a multi-paradigm programming language for .NET framework modeled on OCaml. Although F# is a research project, still under continuous development, it has a product quality performance. It merges seamlessly the object oriented, the functional and the imperative programming paradigms, allowing to exploit the performance, the portability and the tools of .NET framework

A formal semantics for Molecular Interaction Maps

In the present work, we describe a possible formal semantics for Molecular Interaction Maps (MIMs), which are standard diagrams, used by biologists to depict interactions at molecular level within a cell environment. First we describe MIM notation in details, then we describe the Calculi of Looping Sequences (CLS), a family of formal languages which models biological systems, whose semantics is a transition systems. Finally, we give a possible formal semantics in CLS for MIMs

QUALITATIVE AND QUANTITATIVE FORMAL MODELING OF BIOLOGICAL SYSTEMS

Nella tesi si sviluppa un formalismo basato su riscrittura di termini e lo si propone come strumento per la descrizione di sistemi biologici. Tale formalismo, chiamato calculus of looping sequences (cls) consente di descrivere proteine, dna e membrane come termini, e interazioni tra questi elementi come regole di riscrittura. Diverse varianti di cls sono studiate al fine di descrivere diversi aspetti dei sistemi biologici, inoltre vengono definite equivalenze sul comportamento dei sistemi (bisimulazioni) e una versione stocastica del formalismo che consente di sviluppare strumenti di simulazione

A Practical Hardware Implementation of Systemic Computation

It is widely accepted that natural computation, such as brain computation, is far superior to typical computational approaches addressing tasks such as learning and parallel processing. As conventional silicon-based technologies are about to reach their physical limits, researchers have drawn inspiration from nature to found new computational paradigms. Such a newly-conceived paradigm is Systemic Computation (SC). SC is a bio-inspired model of computation. It incorporates natural characteristics and defines a massively parallel non-von Neumann computer architecture that can model natural systems efficiently. This thesis investigates the viability and utility of a Systemic Computation hardware implementation, since prior software-based approaches have proved inadequate in terms of performance and flexibility. This is achieved by addressing three main research challenges regarding the level of support for the natural properties of SC, the design of its implied architecture and methods to make the implementation practical and efficient. Various hardware-based approaches to Natural Computation are reviewed and their compatibility and suitability, with respect to the SC paradigm, is investigated. FPGAs are identified as the most appropriate implementation platform through critical evaluation and the first prototype Hardware Architecture of Systemic computation (HAoS) is presented. HAoS is a novel custom digital design, which takes advantage of the inbuilt parallelism of an FPGA and the highly efficient matching capability of a Ternary Content Addressable Memory. It provides basic processing capabilities in order to minimize time-demanding data transfers, while the optional use of a CPU provides high-level processing support. It is optimized and extended to a practical hardware platform accompanied by a software framework to provide an efficient SC programming solution. The suggested platform is evaluated using three bio-inspired models and analysis shows that it satisfies the research challenges and provides an effective solution in terms of efficiency versus flexibility trade-off