Ordinary differential equations (ODEs) provide a powerful formalism to model molecular networks mechanistically. However, inferring the model structure, given a set of time course measurements and a large number of alternative molecular mechanisms, is a challenging and open research question. Existing search heuristics are designed only for finding a single best model configuration and cannot account for the uncertainty in selecting the network components. In this study, we present a novel Markov chain Monte Carlo approach for performing Bayesian model structure inference over ODE models. We formulate a Metropolis algorithm that explores the model space efficiently and is suitable for obtaining probabilistic inferences about the network structure. The method and its special parallelization possibilities are demonstrated using simulated data. Furthermore, we apply the method to a time course RNA sequencing data set to infer the structure of the transiently evolving core regulatory network that steers the T helper 17 (Th17) cell differentiation. Our results are in agreement with the earlier finding that the Th17 lineage-specific differentiation program evolves in three sequential phases. Further, the analysis provides us with probabilistic predictions on the molecular interactions that are active in different phases of Th17 cell differentiation.

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model’s capabilities to infer dynamics from sparse data and to simulate the system forward into future.

MOTIVATION: Cell differentiation is steered by extracellular signals that activate a cell type specific transcriptional program. Molecular mechanisms that drive the differentiation can be analyzed by combining mathematical modeling with population average data. For standard mathematical models, the population average data is informative only if the measurements come from a homogeneous cell culture. In practice, however, the differentiation efficiencies are always imperfect. Consequently, cell cultures are inherently mixtures of several cell types, which have different molecular mechanisms and exhibit quantitatively different dynamics. There is an urgent need for data-driven mathematical modeling approaches that can detect possible heterogeneity and, further, recover the molecular mechanisms from heterogeneous data. RESULTS: We develop a novel method that models a heterogeneous population using homogeneous subpopulations that evolve in parallel. Different subpopulations can represent different cell types and each subpopulation can have cell type specific molecular mechanisms. We present statistical methodology that can be used to quantify the effect of heterogeneity and to infer the subpopulation specific molecular interactions. After a proof of principle study with simulated data, we apply our methodology to analyze the differentiation of human Th17 cells using time-course RNA sequencing data. We construct putative molecular networks driving the T cell activation and Th17 differentiation and allow the cell populations to be split into two subpopulations in the case of heterogeneous samples. Our analysis shows that the heterogeneity indeed has a statistically significant effect on observed dynamics and, furthermore, our statistical methodology can infer both the subpopulation specific molecular mechanisms and the effect of heterogeneity. AVAILABILITY AND IMPLEMENTATION: An implementation of the method is available at http://research.ics.aalto.fi/csb/software/subpop/ CONTACT: [email protected] or [email protected] information: Supplementary data are available at Bioinformatics online.

MOTIVATION: Mechanistic models based on ordinary differential equations provide powerful and accurate means to describe the dynamics of molecular machinery which orchestrates gene regulation. When combined with appropriate statistical techniques, mechanistic models can be calibrated using experimental data and, in many cases, also the model structure can be inferred from time-course measurements. However, existing mechanistic models are limited in the sense that they rely on the assumption of static network structure and cannot be applied when transient phenomena affect, or rewire, the network structure. In the context of gene regulatory network inference, network rewiring results from the net impact of possible unobserved transient phenomena such as changes in signaling pathway activities or epigenome, which are generally difficult, but important, to account for. RESULTS: We introduce a novel method that can be used to infer dynamically evolving regulatory networks from time-course data. Our method is based on the notion that all mechanistic ordinary differential equation models can be coupled with a latent process that approximates the network structure rewiring process. We illustrate the performance of the method using simulated data and, further, we apply the method to study the regulatory interactions during T helper 17 (Th17) cell differentiation using time-course RNA sequencing data. The computational experiments with the real data show that our method is capable of capturing the experimentally verified rewiring effects of the core Th17 regulatory network. We predict Th17 lineage specific subnetworks that are activated sequentially and control the differentiation process in an overlapping manner. AVAILABILITY AND IMPLEMENTATION: An implementation of the method is available at http://research.ics.aalto.fi/csb/software/lem/ CONTACTS: [email protected] or [email protected].

BACKGROUND: Biochemical systems are inherently noisy due to the discrete reaction events that occur in a random manner. Although noise is often perceived as a disturbing factor, the system might actually benefit from it. In order to understand the role of noise better, its quality must be studied in a quantitative manner. Computational analysis and modeling play an essential role in this demanding endeavor. RESULTS: We implemented a large nonlinear signal transduction network combining protein kinase C, mitogen-activated protein kinase, phospholipase A2, and β isoform of phospholipase C networks. We simulated the network in 300 different cellular volumes using the exact Gillespie stochastic simulation algorithm and analyzed the results in both the time and frequency domain. In order to perform simulations in a reasonable time, we used modern parallel computing techniques. The analysis revealed that time and frequency domain characteristics depend on the system volume. The simulation results also indicated that there are several kinds of noise processes in the network, all of them representing different kinds of low-frequency fluctuations. In the simulations, the power of noise decreased on all frequencies when the system volume was increased. CONCLUSIONS: We concluded that basic frequency domain techniques can be applied to the analysis of simulation results produced by the Gillespie stochastic simulation algorithm. This approach is suited not only to the study of fluctuations but also to the study of pure noise processes. Noise seems to have an important role in biochemical systems and its properties can be numerically studied by simulating the reacting system in different cellular volumes. Parallel computing techniques make it possible to run massive simulations in hundreds of volumes and, as a result, accurate statistics can be obtained from computational studies.