Combining formal methods and Bayesian approach for inferring discrete-state stochastic models from steady-state data.

Stochastic population models are widely used to model phenomena in different areas such as cyber-physical systems, chemical kinetics, collective animal behaviour, and beyond. Quantitative analysis of stochastic population models easily becomes challenging due to the combinatorial number of possible states of the population. Moreover, while the modeller easily hypothesises the mechanistic aspects of the model, the quantitative parameters associated to these mechanistic transitions are difficult or impossible to measure directly. In this paper, we investigate how formal verification methods can aid parameter inference for population discrete-time Markov chains in a scenario where only a limited sample of population-level data measurements-sample distributions among terminal states-are available. We first discuss the parameter identifiability and uncertainty quantification in this setup, as well as how the existing techniques of formal parameter synthesis and Bayesian inference apply. Then, we propose and implement four different methods, three of which incorporate formal parameter synthesis as a pre-computation step. We empirically evaluate the performance of the proposed methods over four representative case studies. We find that our proposed methods incorporating formal parameter synthesis as a pre-computation step allow us to significantly enhance the accuracy, precision, and scalability of inference. Specifically, in the case of unidentifiable parameters, we accurately capture the subspace of parameters which is data-compliant at a desired confidence level.

Extracting individual characteristics from population data reveals a negative social effect during honeybee defence.

Honeybees protect their colony against vertebrates by mass stinging and they coordinate their actions during this crucial event thanks to an alarm pheromone carried directly on the stinger, which is therefore released upon stinging. The pheromone then recruits nearby bees so that more and more bees participate in the defence. However, a quantitative understanding of how an individual bee adapts its stinging response during the course of an attack is still a challenge: Typically, only the group behaviour is effectively measurable in experiment; Further, linking the observed group behaviour with individual responses requires a probabilistic model enumerating a combinatorial number of possible group contexts during the defence; Finally, extracting the individual characteristics from group observations requires novel methods for parameter inference. We first experimentally observed the behaviour of groups of bees confronted with a fake predator inside an arena and quantified their defensive reaction by counting the number of stingers embedded in the dummy at the end of a trial. We propose a biologically plausible model of this phenomenon, which transparently links the choice of each individual bee to sting or not, to its group context at the time of the decision. Then, we propose an efficient method for inferring the parameters of the model from the experimental data. Finally, we use this methodology to investigate the effect of group size on stinging initiation and alarm pheromone recruitment. Our findings shed light on how the social context influences stinging behaviour, by quantifying how the alarm pheromone concentration level affects the decision of each bee to sting or not in a given group size. We show that recruitment is curbed as group size grows, thus suggesting that the presence of nestmates is integrated as a negative cue by individual bees. Moreover, the unique integration of exact and statistical methods provides a quantitative characterisation of uncertainty associated to each of the inferred parameters.

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 signaling pathways.

Patterns of hippocampal tau pathology differentiate neurodegenerative dementias.

BACKGROUND/AIMS: Deposits of phosphorylated tau protein and convergence of pathology in the hippocampus are the hallmarks of neurodegenerative tauopathies. Thus we aimed to evaluate whether regional and cellular vulnerability patterns in the hippocampus distinguish tauopathies or are influenced by their concomitant presence. METHODS: We created a heat map of phospho-tau (AT8) immunoreactivity patterns in 24 hippocampal subregions/layers in individuals with Alzheimer's disease (AD)-related neurofibrillary degeneration (n = 40), Pick's disease (n = 8), progressive supranuclear palsy (n = 7), corticobasal degeneration (n = 6), argyrophilic grain disease (AGD, n = 18), globular glial tauopathy (n = 5), and tau-astrogliopathy of the elderly (n = 10). AT8 immunoreactivity patterns were compared by mathematical analysis. RESULTS: Our study reveals disease-specific hot spots and regional selective vulnerability for these disorders. The pattern of hippocampal AD-related tau pathology is strongly influenced by concomitant AGD. Mathematical analysis reveals that hippocampal involvement in primary tauopathies is distinguishable from early-stage AD-related neurofibrillary degeneration. CONCLUSION: Our data demonstrate disease-specific AT8 immunoreactivity patterns and hot spots in the hippocampus even in tauopathies, which primarily do not affect the hippocampus. These hot spots can be shifted to other regions by the co-occurrence of tauopathies like AGD. Our observations support the notion that globular glial tauopathies and tau-astrogliopathy of the elderly are distinct entities.

Markov chain aggregation and its applications to combinatorial reaction networks.

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.