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

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

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/

Finite-size and correlation-induced effects in Mean-field Dynamics

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

Scalable context-dependent analysis of emergency egress models

Pervasive environments offer an increasing number of services to a large number of people moving within these environments, including timely information about where to go and when, and contextual information about the surrounding environment. This information may be conveyed to people through public displays or direct to a person's mobile phone. People using these services interact with the system but they are also meeting other people and performing other activities as relevant opportunities arise. The design of such systems and the analysis of collective dynamic behaviour of people within them is a challenging problem. We present results on a novel usage of a scalable analysis technique in this context. We show the validity of an approach based on stochastic process-algebraic models by focussing on a representative example, i.e. emergency egress. The chosen case study has the advantage that detailed data is available from studies employing alternative analysis methods, making cross-methodology comparison possible. We also illustrate how realistic, context-dependent human behaviour, often observed in emergency egress, can naturally be embedded in the models, and how the effect of such behaviour on evacuation can be analysed in an efficient and scalable way. The proposed approach encompasses both the agent modelling viewpoint, as system behaviour emerges from specific (discrete) agent interaction, and the population viewpoint, when classes of homogeneous individuals are considered for a (continuous)approximation of overall system behaviour

Re-Assembly of the Genome of Francisella tularensis Subsp. holarctica OSU18

Francisella tularensis is a highly infectious human intracellular pathogen that is the causative agent of tularemia. It occurs in several major subtypes, including the live vaccine strain holarctica (type B). F. tularensis is classified as category A biodefense agent in part because a relatively small number of organisms can cause severe illness. Three complete genomes of subspecies holarctica have been sequenced and deposited in public archives, of which OSU18 was the first and the only strain for which a scientific publication has appeared [1]. We re-assembled the OSU18 strain using both de novo and comparative assembly techniques, and found that the published sequence has two large inversion mis-assemblies. We generated a corrected assembly of the entire genome along with detailed information on the placement of individual reads within the assembly. This assembly will provide a more accurate basis for future comparative studies of this pathogen

Intrinsic noise alters the frequency spectrum of mesoscopic oscillatory chemical reaction systems

Mesoscopic oscillatory reaction systems, for example in cell biology, can exhibit stochastic oscillations in the form of cyclic random walks even if the corresponding macroscopic system does not oscillate. We study how the intrinsic noise from molecular discreteness influences the frequency spectrum of mesoscopic oscillators using as a model system a cascade of coupled Brusselators away from the Hopf bifurcation. The results show that the spectrum of an oscillator depends on the level of noise. In particular, the peak frequency of the oscillator is reduced by increasing noise, and the bandwidth increased. Along a cascade of coupled oscillators, the peak frequency is further reduced with every stage and also the bandwidth is reduced. These effects can help understand the role of noise in chemical oscillators and provide fingerprints for more reliable parameter identification and volume measurement from experimental spectra

Curriculum factors influencing knowledge of communication skills among medical students

Background Communication training builds on the assumption that understanding of the concepts related to professional communication facilitates the training. We know little about whether students' knowledge of clinical communication skills is affected by their attendance of communication training courses, or to what degree other elements of the clinical training or curriculum design also play a role. The aim of this study was to determine which elements of the curriculum influence acquisition of knowledge regarding clinical communication skills by medical students. Methods The study design was a cross-sectional survey performed in the four Norwegian medical schools with different curricula, spring 2003. A self-administered questionnaire regarding knowledge of communication skills (an abridged version of van Dalen's paper-and-pencil test) was sent to all students attending the four medical schools. A total of 1801 (59%) students responded with complete questionnaires. Results At the end of the 1st year of study, the score on the knowledge test was higher in students at the two schools running communication courses and providing early patient contact (mean 81%) than in the other two medical schools (mean 69–75%, P ≤ 0.001), with students studying a traditional curriculum scoring the lowest. Their scores increased sharply towards the end of the 3rd year, during which they had been subjected to extensive patient contact and had participated in an intensive communication course (77% vs. 72% the previous year, P ≤ 0.01). All students scored generally lower in academic years in which there was no communication training. However, at the end of the final year the difference between the schools was only 5% (81% vs. 86%, P ≤ 0.001). Conclusion The acquisition of knowledge regarding communication skills by medical students may be optimised when the training is given together with extensive supervised patient contact, especially if this teaching takes place in the initial years of the curriculum