Spatial-temporal modelling and analysis of bacterial colonies with phase variable genes

2015 Copyright is held by the owner/author(s). This article defines a novel spatial-temporal modelling and analysis methodology applied to a systems biology case study, namely phase variation patterning in bacterial colony growth. We employ coloured stochastic Petri nets to construct the model and run stochastic simulations to record the development of the circular colonies over time and space. The simulation output is visualised in 2D, and sector-like patterns are automatically detected and analysed. Space is modelled using 2.5 dimensions considering both a rectangular and circular geometry, and the effects of imposing different geometries on space are measured. We close by outlining an interpretation of the Petri net model in terms of finite difference approximations of partial differential equations (PDEs). One result is the derivation of the “best” nine-point diffusion model. Our multidimensional modelling and analysis approach is a precursor to potential future work on more complex multiscale modelling.EPSRC Research Grant EP I036168/1; German BMBF Research Grant 0315449H

Spatial quorum sensing modelling using coloured hybrid Petri nets and simulative model checking

From The 2017 Network Tools and Applications in Biology (NETTAB) Workshop Palermo, Italy. 16–18 October 2017Background: Quorum sensing drives biofilm formation in bacteria in order to ensure that biofilm formation only occurs when colonies are of a sufficient size and density. This spatial behaviour is achieved by the broadcast communication of an autoinducer in a diffusion scenario. This is of interest, for example, when considering the role of gut microbiota in gut health. This behaviour occurs within the context of the four phases of bacterial growth, specifically in the exponential stage (phase 2) for autoinducer production and the stationary stage (phase 3) for biofilm formation. Results: We have used coloured hybrid Petri nets to step-wise develop a flexible computational model for E.coli biofilm formation driven by Autoinducer 2 (AI-2) which is easy to configure for different notions of space. The model describes the essential components of gene transcription, signal transduction, extra and intra cellular transport, as well as the two-phase nature of the system. We build on a previously published non-spatial stochastic Petri net model of AI-2 production, keeping the assumptions of a limited nutritional environment, and our spatial hybrid Petri net model of biofilm formation, first presented at the NETTAB 2017 workshop. First we consider the two models separately without space, and then combined, and finally we add space. We describe in detail our step-wise model development and validation. Our simulation results support the expected behaviour that biofilm formation is increased in areas of higher bacterial colony size and density. Our analysis techniques include behaviour checking based on linear time temporal logic. Conclusions: The advantages of our modelling and analysis approach are the description of quorum sensing and associated biofilm formation over two phases of bacterial growth, taking into account bacterial spatial distribution using a flexible and easy to maintain computational model. All computational results are reproducible.The open access fee has been covered by Brunel University Londo

Desarrollo de un enfoque de trabajo para el análisis y diseño de sistemas discretos y dinámicos : Aplicación a la simulación de la demanda eléctrica de la ciudad de Salta

La reunión de las disciplinas orientadas a los problemas y las soluciones puede llevar a importantes avances en ambas áreas. Las redes de Petri (RdP) proporcionan un medio excelente para modelar aspectos concurrentes y se han extendido de muchas maneras para hacer frente a muchos problemas. Las RdP se han aplicado con éxito muchas veces a varios problemas de ingeniería de software. Sin embargo, las dos disciplinas no pasan por un período de fertilización cruzada particularmente fuerte. Este trabajo trata de analizar algunos aspectos de la ingeniería de software, señalando aspectos en los que las RdP se han propuesto o se pueden proponer como soluciones a problemas críticos. En esta tesis, se propone el desarrollo de un enfoque de trabajo para realizar el análisis y diseño de sistemas discretos, dinámicos y estocásticos. Estos sistemas, se caracterizan por estar íntimamente relacionados con restricciones temporales y concurrentes, que por las características de los modelos desarrollados por UML, no pueden ser representadas; con lo cual es necesario complementar las herramientas con otras, que permitan modelar las características antes mencionadas; una de estas, son las RdP. Una RdP es un lenguaje útil para analizar y modelar formalmente varios sistemas. Recientemente, muchas RdP dedican sus esfuerzos a mejorar y extender el poder expresivo de las RdP. Uno de estos esfuerzos es extender las RdP con conceptos orientados a objetos. Un paradigma orientado a objetos proporciona conceptos excelentes para modelar problemas del mundo real. Los conceptos orientados a objetos nos permiten construir sistemas de software de forma fácil, intuitiva y natural. Se sugieren varias RdP de alto nivel con el concepto de objetos. Estas redes no son totalmente compatibles con el concepto orientado a objetos, por lo que no pueden llamarse RdP orientadas a objetos. La sintaxis formal y la semántica del enfoque propuesto se explican en detalle, adoptando una amplia gama de características del análisis y diseño orientados a objetos. Además, este enfoque es compatible con una variedad de mecanismos de análisis, como los métodos de descomposición, red e incrementales de los sistemas en evolución, el despliegue, a un nivel más bajo de la RdP y el análisis de accesibilidad incremental para los modelos desarrollado. Por último, se demuestra la eficiencia y la utilidad del enfoque desarrollado, a partir de la aplicación del mismo al caso de estudio, esto es, la simulación que explica el comportamiento y la demanda eléctrica residencial de la Ciudad de Salta, a partir de la cantidad y tipo de artefactos presentes en cada vivienda y el comportamiento humano para el encendido y apagado de los mismos.Facultad de Informátic

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

Biomodelkit - a framework for modular biomodel-engineering

Otto-von-Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Dissertation, 2017von Dipl.-Ing. Mary-Ann BlätkeLiteraturverzeichnis: Seite [177]-18

Programming Languages and Systems

This open access book constitutes the proceedings of the 28th European Symposium on Programming, ESOP 2019, which took place in Prague, Czech Republic, in April 2019, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019