Agent-based model of diffusion of N-acyl homoserine lactones in a multicellular environment of Pseudomonas aeruginosa and Candida albicans

Experimental incapacity to track microbemicrobe interactions in structures like biofilms, and the complexity inherent to the mathematical modelling of those interactions, raises the need for feasible, alternative modelling approaches. This work proposes an agent-based representation of the diffusion of N-acyl homoserine lactones (AHL) in a multicellular environment formed by Pseudomonas aeruginosa and Candida albicans. Depending on the spatial location, C. albicans cells were variably exposed to AHLs, an observation that might help explain why phenotypic switching of individual cells in biofilms occurred at different time points. The simulation and algebraic results were similar for simpler scenarios, although some statistical differences could be observed (p<0.05). The model was also successfully applied to a more complex scenario representing a small multicellular environment containing C. albicans and P. aeruginosa cells encased in a 3-D matrix. Further development of this model may help create a predictive tool to depict biofilm heterogeneity at the single-cell level.This work has been funded by a Research Grant 2014 by the European Society of Clinical Microbiology and Infectious Diseases (ESCMID) to AL; the Portuguese Foundation for Science and Technology (FCT) [grant numbers UID/ BIO/04469/2013, UID/EQU/00511/2013] units and COMPETE 2020 [grant numbers POCI-01-0145-FEDER-006684, POCI-01-0145-FEDER-006939]; North Portugal Regional Operational Programme (NORTE 2020) [grant number NORTE‐01‐0145‐FEDER‐000005 – LEPABE-2-ECO-INNOVATION] under the Portugal 2020 Partnership Agreement, through the European Regional Development Fund (ERDF).info:eu-repo/semantics/publishedVersio

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

Engineering a genetic circuit for Turing patterns in E. coli with a Synthetic Biology approach

Genetic circuits that can form spatial patterns have been a major topic of interest within Synthetic Biology. Turing patterns are self-organising spatial wave, spot or labyrinthine patterns that are formed in some reaction-diffusion circuits. The simplest Turing circuit involves a slow-diffusing activator and a fast-diffusing inhibitor, interacting to regulate their own and each other’s rates of production. An unambiguous implementation of Turing patterns with a genetic circuit is still lacking because of their exquisitely fine-tuned nature. This study aims to address this shortcoming and sets out to engineer a genetic circuit for Turing patterning in E. coli from first principles. Two genetic circuits were studied. Firstly, a phage circuit was designed according to the minimal self-activation, lateral inhibition Turing topology and involves a slow-diffusing M13 filamentous phage and a fast-diffusing 3OC6HSL quorum sensing signal. This circuit was abandoned because of the many complexities of phage biology, which were working against its successful implementation as a Turing generator. The focus was shifted to circuit ‘3954’, which was designed according to a more robust three-node topology and implemented with two small molecule diffusors; this could be done because the circuit allows for equal diffusivity of the two diffusing signals. All the components of circuit ‘3954’ were tested in reduced subcircuits and were shown to be functioning as expected. Growing bacterial colonies bearing the circuit were then visualised for pattern formation using confocal microscopy. Even though no Turing patterns were detected, the colonies consistently showed a centre-surround expression pattern of the fluorescence reporters, where GFP was expressed at the colony centre, whereas mCherry was predominantly expressed at the periphery. The obtained reaction-diffusion patterns are a good foundation for further tuning and exploration.Open Acces

Probabilistic modelling of noise as a driving force in biological systems

Systems biology takes a mechanistic, relational approach to the study of biological processes, commonly finding expression in mathematical models. Hypotheses about systems can be tested when formulated as models, and promising avenues for further study identified. A model sufficiently faithful to the system under study can be used to guide experiments, to probe the system in silico, and to learn about emergent features not evident from the static picture of the system. In this work, three contributions to the modelling community are proffered. First, a computational package is presented that implements an algorithm for the validation and parametrisation of a model. In validation, we are asking how likely we were to make some observation, given the model, or, equivalently, how able the model is to explain the data. The subsequent two contributions concern noise in biological systems. Biological systems display inherent variability, or noise, due to the stochastic mechanisms through which biochemical processes occur. This variability can be critical to the behaviour of a system and to the fates of individual cells. With this in mind, the second contribution is the development of a methodology to model protein-dependent population dynamics. The idea is to model cell population dynamics that result of noisy intracellular protein dynamics. The method's application is demonstrated in population-level models of a protein-dependent cell cycle and yeast antibiotic resistance. Given an appreciation of the pivotal effects of noise, the third and final contribution is a study of the mechanism of noise propagation. I present an analysis of the contributions of biochemical reaction motifs to the creation and transmission of noise that ultimately manifest in observations of biological systems. This study points to specific processes that enhance or attenuate noise, with the aim of beginning to unravel the flow of noise through a system.Open Acces

A novel theoretical and experimental approach permits a systems view on stochastic intracellular Ca 2+ signalling

Ca(2+)-Ionen sind ein universeller sekundärer Botenstoff in eukaryotischen Zellen und übertragen Information durch wiederholte, kurzzeitige Erhöhungen der cytosolischen Ca(2+)-Konzentration (Ca(2+) Spikes). Ein bekannter Mechanismus, der solche Ca(2+)-Signale erzeugt, beinhaltet die Freisetzung von Ca(2+)-Ionen aus dem endoplasmatischen Retikulum durch IP3-sensitive Kanäle. Puffs sind elementare Ereignisse der Ca(2+)-Freisetzung durch einzelne Cluster von Ca(2+)-Kanälen. Intrazelluläre Ca(2+)-Dynamik ist ein stochastisches System, allerdings konnte bisher keine vollständige stochastische Theorie entwickelt werden. Die vorliegende Dissertation formuliert die Theorie mit Hilfe von Interpuffintervallen und Pufflängen, da diese Größen im Gegensatz zu den Eigenschaften der Einzelkanäle direkt messbar sind. Die Theorie reproduziert das typische Spektrum bekannter Ca(2+)-Signale. Die Signalform und das durchschnittliche Interspikeinterval (ISI) hängen sensitiv von den genauen Eigenschaften und der räumlichen Anordnung der Cluster ab. Im Gegensatz dazu hängt die Beziehung zwischen Mittelwert und Standardabweichung der ISI weder von den Clustereigenschaften noch von der räumlichen Anordnung ab, sondern wird lediglich von globalen Feedbackprozessen im Ca(2+)-Signalweg reguliert. Diese Beziehung ist essentiell für die Funktion des Signalwegs, da sie trotz der Zufälligkeit der ISI eine Frequenzkodierung ermöglicht und den maximalen Informationsgehalt der Spikesequenzen bestimmt. Neben der theoretischen Analyse enthält die vorliegende Arbeit auch experimentelle Puff- und Spikemessungen an lebenden HEK-Zellen, die wichtige Ergebnisse verifizieren. Insgesamt wird durch die integrierte theoretische und experimentelle Untersuchung auf verschiedenen Stufen molekularer Organisation gezeigt, dass stochastische Ca(2+)-Signale verlässliche Informationsträger sind, und dass der Mechanismus durch globalen Feedback an die spezifischen Anforderungen eines Signalpfads angepasst werden kann.Ca(2+) is a universal second messenger in eukaryotic cells transmitting information through sequences of concentration spikes. A prominent mechanism to generate these spikes involves Ca(2+) release from the endoplasmic reticulum Ca(2+) store via IP3-sensitive channels. Puffs are elemental events of IP3-induced Ca(2+) release through single clusters of channels. Intracellular Ca(2+) dynamics are a stochastic system, but a complete stochastic theory has not been developed yet. As a new concept, this thesis formulates the theory in terms of interpuff interval and puff duration distributions, since unlike the properties of individual channels, they can be measured in vivo. This leads to a non-Markovian description of system dynamics, for which analytical solutions and efficient stochastic simulation techniques are derived. The theory reproduces the typical spectrum of Ca(2+) signals. Signal form and average interspike interval (ISI) depend sensitively on detailed properties and spatial arrangement of clusters. In difference to that, the relation between the average and the standard deviation of ISIs does not depend on cluster properties and cluster arrangement, and it is robust with respect to cell variability. It can only be regulated by global feedback processes in the Ca(2+) signalling pathway. That relation is essential for pathway function, since it ensures frequency encoding despite the randomness of ISIs and determines the maximal spike train information content. Apart from the theoretical investigation, this thesis verifies key results by live cell imaging of Ca(2+) spikes and puffs in HEK cells. Hence, this work comprises a systems level investigation of Ca(2+) signals, integrating data and theory from different levels of molecular organisation. It demonstrates that stochastic Ca(2+) signals can transmit information reliably, and that the mechanism can be adapted to the specific needs of a pathway by global feedback