Markov chain aggregation and its application to rule-based modelling

Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov chain enumerates all possible reaction mixtures, rendering the analysis of the chain computationally demanding and often prohibitive in practice. We here describe how it is possible to efficiently find a smaller, aggregate chain, which preserves certain properties of the original one. Formal methods and lumpability notions are used to define algorithms for automated and efficient construction of such smaller chains (without ever constructing the original ones). We here illustrate the method on an example and we discuss the applicability of the method in the context of modelling large signalling pathways

Identification de seuils écologiques à partir des variations des communautés de phytoplancton entre les lacs : contribution à la définition de normes environnementales

International audienceIn aquatic ecosystems, the identification of ecological thresholds may be useful for managers as it can help to diagnose ecosystem health and to identify key levers to enable the success of preservation and restoration measures. A recent statistical method, gradient forest, based on random forests, was used to detect thresholds of phytoplankton community change in lakes along different environmental gradients. It performs exploratory analyses of multivariate biological and environmental data to estimate the location and importance of community thresholds along gradients. The method was applied to a data set of 224 French lakes which were characterized by 29 environmental variables and the mean abundances of 196 phytoplankton species. Results showed the high importance of geographic variables for the prediction of species abundances at the scale of the study. A second analysis was performed on a subset of lakes defined by geographic thresholds and presenting a higher biological homogeneity. Community thresholds were identified for the most important physico-chemical variables including water transparency, total phosphorus, ammonia, nitrates, and dissolved organic carbon. Gradient forest appeared as a powerful method at a first exploratory step, to detect ecological thresholds at large spatial scale. The thresholds that were identified here must be reinforced by the separate analysis of other aquatic communities and may be used then to set protective environmental standards after consideration of natural variability among lakes

KaDE: A Tool to Compile Kappa Rules into (Reduced) ODE Models

Tools paper trackInternational audienceKappa is a formal language that can be used to model sys- tems of biochemical interactions among proteins. It offers several se- mantics to describe the behaviour of Kappa models at different levels of abstraction. Each Kappa model is a set of context-free rewrite rules. One way to understand the semantics of a Kappa model is to read its rules as an implicit description of a (potentially infinite) reaction net- work. KaDE is interpreting this definition to compile Kappa models into reaction networks (or equivalently into sets of ordinary differential equations). KaDE uses a static analysis that identifies pairs of sites that are indistinguishable from the rules point of view, to infer backward and forward bisimulations, hence reducing the size of the underlying reaction networks without having to generate them explicitly. In this paper, we describe the main current functionalities of KaDE and we give some benchmarks on case studies

Coarse-grained brownian dynamics simulation of rule-based models

International audienceStudying spatial effects in signal transduction, such as co-localization along scaffold molecules, comes at a cost of complexity. In this paper, we propose a coarse-grained, particle-based spatial simulator, suited for large signal transduction models. Our approach is to combine the particle-based reaction and diffusion method, and (non-spatial) rule-based modeling: the location of each molecular complex is abstracted by a spheric particle, while its internal structure in terms of a site-graph is maintained explicit. The particles diffuse inside the cellular compartment and the colliding complexes stochastically interact according to a rule-based scheme. Since rules operate over molecular motifs (instead of full complexes), the rule set compactly describes a combinatorial or even infinite number of reactions. The method is tested on a model of Mitogen Activated Protein Kinase (MAPK) cascade of yeast pheromone response signaling. Results demonstrate that the molecules of the MAPK cascade co-localize along scaffold molecules, while the scaffold binds to a plasma membrane bound upstream component, localizing the whole signaling complex to the plasma membrane. Especially we show, how rings stabilize the resulting molecular complexes and derive the effective dissociation rate constant for it

Powering the ABC multidrug exporter LmrA: How nucleotides embrace the ion-motive force.

LmrA is a bacterial ATP-binding cassette (ABC) multidrug exporter that uses metabolic energy to transport ions, cytotoxic drugs, and lipids. Voltage clamping in a Port-a-Patch was used to monitor electrical currents associated with the transport of monovalent cationic HEPES+ by single-LmrA transporters and ensembles of transporters. In these experiments, one proton and one chloride ion are effluxed together with each HEPES+ ion out of the inner compartment, whereas two sodium ions are transported into this compartment. Consequently, the sodium-motive force (interior negative and low) can drive this electrogenic ion exchange mechanism in cells under physiological conditions. The same mechanism is also relevant for the efflux of monovalent cationic ethidium, a typical multidrug transporter substrate. Studies in the presence of Mg-ATP (adenosine 5'-triphosphate) show that ion-coupled HEPES+ transport is associated with ATP-bound LmrA, whereas ion-coupled ethidium transport requires ATP binding and hydrolysis. HEPES+ is highly soluble in a water-based environment, whereas ethidium has a strong preference for residence in the water-repelling plasma membrane. We conclude that the mechanism of the ABC transporter LmrA is fundamentally related to that of an ion antiporter that uses extra steps (ATP binding and hydrolysis) to retrieve and transport membrane-soluble substrates from the phospholipid bilayer.This research was supported by the Biotechnology and Biological Sciences Research Council grants BB/R00224X/1, BB/I002383/1 and BB/K017713/1, and Medical Research Council grant G0401165 (to H.W.V.V.). We are also grateful for funding by the Human Frontier Science Program (grant RGP0034/2013), Strategic International Cooperative Program (Japan Science and Technology Agency, Japan) and Royal Society (UK) for collaborative research between H.W.V.V. and S.M. C.H.F.L. received a research studentship of Peterhouse, Cambridge. Y.S.K.K. received a Federal Training Award from the Ministry of Health in Malaysia. H.S. and S.R. were supported by the Cambridge Commonwealth, European and International Trust

Syntactic Markovian Bisimulation for Chemical Reaction Networks

In chemical reaction networks (CRNs) with stochastic semantics based on continuous-time Markov chains (CTMCs), the typically large populations of species cause combinatorially large state spaces. This makes the analysis very difficult in practice and represents the major bottleneck for the applicability of minimization techniques based, for instance, on lumpability. In this paper we present syntactic Markovian bisimulation (SMB), a notion of bisimulation developed in the Larsen-Skou style of probabilistic bisimulation, defined over the structure of a CRN rather than over its underlying CTMC. SMB identifies a lumpable partition of the CTMC state space a priori, in the sense that it is an equivalence relation over species implying that two CTMC states are lumpable when they are invariant with respect to the total population of species within the same equivalence class. We develop an efficient partition-refinement algorithm which computes the largest SMB of a CRN in polynomial time in the number of species and reactions. We also provide an algorithm for obtaining a quotient network from an SMB that induces the lumped CTMC directly, thus avoiding the generation of the state space of the original CRN altogether. In practice, we show that SMB allows significant reductions in a number of models from the literature. Finally, we study SMB with respect to the deterministic semantics of CRNs based on ordinary differential equations (ODEs), where each equation gives the time-course evolution of the concentration of a species. SMB implies forward CRN bisimulation, a recently developed behavioral notion of equivalence for the ODE semantics, in an analogous sense: it yields a smaller ODE system that keeps track of the sums of the solutions for equivalent species.Comment: Extended version (with proofs), of the corresponding paper published at KimFest 2017 (http://kimfest.cs.aau.dk/

Genetic counselling for psychiatric disorders: accounts of psychiatric health professionals in the United Kingdom

Genetic counselling is not routinely offered for psychiatric disorders in the United Kingdom through NHS regional clinical genetics departments. However, recent genomic advances, confirming a genetic contribution to mental illness, are anticipated to increase demand for psychiatric genetic counselling. This is the first study of its kind to employ qualitative methods of research to explore accounts of psychiatric health professionals regarding the prospects for genetic counselling services within clinical psychiatry in the UK. Data were collected from 32 questionnaire participants, and 9 subsequent interviewees. Data analysis revealed that although participants had not encountered patients explicitly demanding psychiatric genetic counselling, psychiatric health professionals believe that such a service would be useful and desirable. Genomic advances may have significant implications for genetic counselling in clinical psychiatry even if these discoveries do not lead to genetic testing. Psychiatric health professionals describe clinical genetics as a skilled profession capable of combining complex risk communication with much needed psychosocial support. However, participants noted barriers to the implementation of psychiatric genetic counselling services including, but not limited to, the complexities of uncertainty in psychiatric diagnoses, patient engagement and ethical concerns regarding limited capacity

Process Simulation and Control Optimization of a Blast Furnace Using Classical Thermodynamics Combined to a Direct Search Algorithm

Several numerical approaches have been proposed in the literature to simulate the behavior of modern blast furnaces: finite volume methods, data-mining models, heat and mass balance models, and classical thermodynamic simulations. Despite this, there is actually no efficient method for evaluating quickly optimal operating parameters of a blast furnace as a function of the iron ore composition, which takes into account all potential chemical reactions that could occur in the system. In the current study, we propose a global simulation strategy of a blast furnace, the 5-unit process simulation. It is based on classical thermodynamic calculations coupled to a direct search algorithm to optimize process parameters. These parameters include the minimum required metallurgical coke consumption as well as the optimal blast chemical composition and the total charge that simultaneously satisfy the overall heat and mass balances of the system. Moreover, a Gibbs free energy function for metallurgical coke is parameterized in the current study and used to fine-tune the simulation of the blast furnace. Optimal operating conditions and predicted output stream properties calculated by the proposed thermodynamic simulation strategy are compared with reference data found in the literature and have proven the validity and high precision of this simulation

Exact Hybrid Particle/Population Simulation of Rule-Based Models of Biochemical Systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility. © 2014 Hogg et al