No abstract

In this paper, we present a parametric sensitivity analysis (SA) methodology for continuous time and continuous space Markov processes represented by stochastic differential equations. Particularly, we focus on stochastic molecular dynamics as described by the Langevin equation. The utilized SA method is based on the computation of the information-theoretic (and thermodynamic) quantity of relative entropy rate (RER) and the associated Fisher information matrix (FIM) between path distributions, and it is an extension of the work proposed by Y. Pantazis and M. A. Katsoulakis [J. Chem. Phys. 138, 054115 (2013)]. A major advantage of the pathwise SA method is that both RER and pathwise FIM depend only on averages of the force field; therefore, they are tractable and computable as ergodic averages from a single run of the molecular dynamics simulation both in equilibrium and in non-equilibrium steady state regimes. We validate the performance of the extended SA method to two different molecular stochastic systems, a standard Lennard-Jones fluid and an all-atom methane liquid, and compare the obtained parameter sensitivities with parameter sensitivities on three popular and well-studied observable functions, namely, the radial distribution function, the mean squared displacement, and the pressure. Results show that the RER-based sensitivities are highly correlated with the observable-based sensitivities.

Abstract:We present a systematic coarse-graining (CG) strategy for many particle molecular systems based on cluster expansion techniques. We construct a hierarchy of coarse-grained Hamiltonians with interaction potentials consisting of two, three and higher body interactions. In this way, the suggested model becomes computationally tractable, since no information from long n-body (bulk) simulations is required in order to develop it, while retaining the fluctuations at the coarse-grained level. The accuracy of the derived cluster expansion based on interatomic potentials is examined over a range of various temperatures and densities and compared to direct computation of the pair potential of mean force. The comparison of the coarse-grained simulations is done on the basis of the structural properties, against detailed all-atom data. On the other hand, by construction, the approximate coarse-grained models retain, in principle, the thermodynamic properties of the atomistic model without the need for any further parameter fitting. We give specific examples for methane and ethane molecules in which the coarse-grained variable is the centre of mass of the molecule. We investigate different temperature (T) and density (ρ) regimes, and we examine differences between the methane and ethane systems. Results show that the cluster expansion formalism can be used in order to provide accurate effective pair and three-body CG potentials at high T and low ρ regimes. In the liquid regime, the three-body effective CG potentials give a small improvement over the typical pair CG ones; however, in order to get significantly better results, one needs to consider even higher order terms.

Inferring the driving equations of a dynamical system from population or time-course data is important in several scientific fields such as biochemistry, epidemiology, financial mathematics and many others. Despite the existence of algorithms that learn the dynamics from trajectorial measurements there are few attempts to infer the dynamical system straight from population data. In this work, we deduce and then computationally estimate the Fokker-Planck equation which describes the evolution of the population's probability density, based on stochastic differential equations. Then, following the USDL approach [22], we project the Fokker-Planck equation to a proper set of test functions, transforming it into a linear system of equations. Finally, we apply sparse inference methods to solve the latter system and thus induce the driving forces of the dynamical system. Our approach is illustrated in both synthetic and real data including non-linear, multimodal stochastic differential equations, biochemical reaction networks as well as mass cytometry biological measurements.

Single-cell measurements incorporate invaluable information regarding the state of each cell and its underlying regulatory mechanisms. The popularity and use of single-cell measurements are constantly growing. Despite the typically large number of collected data, the under-representation of important cell (sub-)populations negatively affects down-stream analysis and its robustness. Therefore, the enrichment of biological datasets with samples that belong to a rare state or manifold is overall advantageous. In this work, we train families of generative models via the minimization of Rényi divergence resulting in an adversarial training framework. Apart from the standard neural network-based models, we propose families of semi-interpretable generative models. The proposed models are further tailored to generate realistic gene expression measurements, whose characteristics include zero-inflation and sparsity, without the need of any data pre-processing. Explicit factors of the data such as measurement time, state or cluster are taken into account by our generative models as conditional variables. We train the proposed conditional models and compare them against the state-of-the-art on a range of synthetic and real datasets and demonstrate their ability to accurately perform data interpolation and augmentation.