On Quantitative Comparison of Chemical Reaction Network Models

Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations. Their dynamic behaviours are then analysed, often by using deterministic methods based on differential equations with a focus on the steady states. Here, we propose a method for comparing CRNs with respect to their behaviour in stochastic simulations. Our method is based on using the flux graphs that are delivered by stochastic simulations as abstract representations of their dynamic behaviour. This allows us to compare the behaviour of any two CRNs for any time interval, and define a notion of equivalence on them that overlaps with graph isomorphism at the lowest level of representation. The similarity between the compared CRNs can be quantified in terms of their distance. The results can then be used to refine the models or to replace a larger model with a smaller one that produces the same behaviour or vice versa.Comment: In Proceedings HCVS/PERR 2019, arXiv:1907.0352

How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks

With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, we explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of starting node degree in determining these indices, commonly used to describe epidemic spread.Comment: 22 pages, 9 figure

An Intuitive Automated Modelling Interface for Systems Biology

We introduce a natural language interface for building stochastic pi calculus models of biological systems. In this language, complex constructs describing biochemical events are built from basic primitives of association, dissociation and transformation. This language thus allows us to model biochemical systems modularly by describing their dynamics in a narrative-style language, while making amendments, refinements and extensions on the models easy. We demonstrate the language on a model of Fc-gamma receptor phosphorylation during phagocytosis. We provide a tool implementation of the translation into a stochastic pi calculus language, Microsoft Research's SPiM

Biophysical mechanism for Ras-nanocluster formation and signaling in plasma membrane

Ras GTPases are lipid-anchored G proteins which play a fundamental role in cell signaling processes. Electron micrographs of immunogold-labeled Ras have shown that membrane-bound Ras molecules segregate into nanocluster domains. Several models have been developed in attempts to obtain quantitative descriptions of nanocluster formation, but all have relied on assumptions such as a constant, expression-level independent ratio of Ras in clusters to Ras monomers (cluster/monomer ratio). However, this assumption is inconsistent with the law of mass action. Here, we present a biophysical model of Ras clustering based on short-range attraction and long-range repulsion between Ras molecules in the membrane. To test this model, we performed Monte Carlo simulations and compared statistical clustering properties with experimental data. We find that we can recover the experimentally-observed clustering across a range of Ras expression levels, without assuming a constant cluster/monomer ratio or the existence of lipid rafts. In addition, our model makes predictions about the signaling properties of Ras nanoclusters in support of the idea that Ras nanoclusters act as an analog-digital-analog converter for high fidelity signaling.Comment: 8 figures. PLoS ONE, in pres

Early stages of development in Mediterranean red coral (Corallium rubrum): The key role of sclerites

Corals are ecosystem engineers whose tree-like structures give three-dimensional complexity to the habitat. Their population dynamics are affected by recruitment and juvenile survival. Therefore, several defense strategies, such as the formation of hard skeletons and/or spicules, have evolved to protect these vulnerable stages. The family Coralliidae, to which “precious corals” belong, represent an exception in the order Scleralcyonacea, as they form hard CaCO3 skeletons and small CaCO3 structures, the sclerites. The skeletogenesis of Corallium species is relatively well documented in adult colonies but remains poorly known in the early stages of the development of new colonies. To shed light on the timing of Corallium rubrum’s early skeleton formation and the role of sclerites, we focused on the first 4-years of life, applying different techniques, from scanning electron microscopy to synchrotron tomography and laser ablation inductively coupled plasma-mass spectrometry. Our results show that: 1) the first visible sclerites in the primary polyp appear at least 12 days after larval settlement, which is associated with a high CaCO3 production rate (4.5 ± 2.3 μg of CaCO3 per day). Furthermore, growth rings are visible in the sclerites, showing that fully matured sclerites grow fast, probably in 3 to 4 days. 2) Sclerites are the only biomineral product in the first year of life of C. rubrum’s colonies. 3) The evidence of a consolidated axial skeleton, intended as the inner part of the skeleton characteristic of the adult red coral (the medullary zone, MZ), is recorded for the first time in 2-year-old colonies. 4) The annular zone (AZ) around the medullary zone starts forming not before four years after settlement. Thus, primary polyp builds a deformable armor made of only sclerites during the first year. This shelter provides mechanical protection from abrasion and predation to early settled colonies. After two years, settlers are firmly and mineralogically attached to the substratum, which makes them less vulnerable to predation than younger recruits that are not anchored by the skeleton

Stochastic simulations as a tool for assessing signal fidelity in gene expression in synthetic promoter design

The design and development of synthetic biology applications in a workflow often involve connecting modular components. Whereas computer-aided design tools are picking up in synthetic biology as in other areas of engineering, the methods for verifying the correct functioning of living technologies are still in their infancy. Especially, fine-tuning for the right promoter strength to match the design specifications is often a lengthy and expensive experimental process. In particular, the relationship between signal fidelity and noise in synthetic promoter design can be a key parameter that can affect the healthy functioning of the engineered organism. To this end, based on our previous work on synthetic promoters for the E. coli PhoBR two-component system, we make a case for using chemical reaction network models for computational verification of various promoter designs before a lab implementation. We provide an analysis of this system with extensive stochastic simulations at a single-cell level to assess the signal fidelity and noise relationship. We then show how quasi-steady-state analysis via ordinary differential equations can be used to navigate between models with different levels of detail. We compare stochastic simulations with our full and reduced models by using various metrics for assessing noise. Our analysis suggests that strong promoters with low unbinding rates can act as control tools for filtering out intrinsic noise in the PhoBR context. Our results confirm that even simpler models can be used to determine promoters with specific signal to noise characteristics.publishedVersio

How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks

International audienceWith the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic considerations and provide a theoretical result on the probability of the extinction of the disease. Based on this calibration, we explore the variability in disease spread by stochastic simulations. In particular, we demonstrate how important epidemic indices change as a function of the contagiousness of the disease and the connectivity of the network. Our results quantify the role of starting node degree in determining these indices, commonly used to describe epidemic spread

Stochastic simulations as a tool for assessing signal fidelity in gene expression in synthetic promoter design

The design and development of synthetic biology applications in a workflow often involve connecting modular components. Whereas computer-aided design tools are picking up in synthetic biology as in other areas of engineering, the methods for verifying the correct functioning of living technologies are still in their infancy. Especially, fine-tuning for the right promoter strength to match the design specifications is often a lengthy and expensive experimental process. In particular, the relationship between signal fidelity and noise in synthetic promoter design can be a key parameter that can affect the healthy functioning of the engineered organism. To this end, based on our previous work on synthetic promoters for the E. coli PhoBR two-component system, we make a case for using chemical reaction network models for computational verification of various promoter designs before a lab implementation. We provide an analysis of this system with extensive stochastic simulations at a single-cell level to assess the signal fidelity and noise relationship. We then show how quasi-steady-state analysis via ordinary differential equations can be used to navigate between models with different levels of detail. We compare stochastic simulations with our full and reduced models by using various metrics for assessing noise. Our analysis suggests that strong promoters with low unbinding rates can act as control tools for filtering out intrinsic noise in the PhoBR context. Our results confirm that even simpler models can be used to determine promoters with specific signal to noise characteristics