MICRAT: a novel algorithm for inferring gene regulatory networks using time series gene expression data.

BACKGROUND: Reconstruction of gene regulatory networks (GRNs), also known as reverse engineering of GRNs, aims to infer the potential regulation relationships between genes. With the development of biotechnology, such as gene chip microarray and RNA-sequencing, the high-throughput data generated provide us with more opportunities to infer the gene-gene interaction relationships using gene expression data and hence understand the underlying mechanism of biological processes. Gene regulatory networks are known to exhibit a multiplicity of interaction mechanisms which include functional and non-functional, and linear and non-linear relationships. Meanwhile, the regulatory interactions between genes and gene products are not spontaneous since various processes involved in producing fully functional and measurable concentrations of transcriptional factors/proteins lead to a delay in gene regulation. Many different approaches for reconstructing GRNs have been proposed, but the existing GRN inference approaches such as probabilistic Boolean networks and dynamic Bayesian networks have various limitations and relatively low accuracy. Inferring GRNs from time series microarray data or RNA-sequencing data remains a very challenging inverse problem due to its nonlinearity, high dimensionality, sparse and noisy data, and significant computational cost, which motivates us to develop more effective inference methods. RESULTS: We developed a novel algorithm, MICRAT (Maximal Information coefficient with Conditional Relative Average entropy and Time-series mutual information), for inferring GRNs from time series gene expression data. Maximal information coefficient (MIC) is an effective measure of dependence for two-variable relationships. It captures a wide range of associations, both functional and non-functional, and thus has good performance on measuring the dependence between two genes. Our approach mainly includes two procedures. Firstly, it employs maximal information coefficient for constructing an undirected graph to represent the underlying relationships between genes. Secondly, it directs the edges in the undirected graph for inferring regulators and their targets. In this procedure, the conditional relative average entropies of each pair of nodes (or genes) are employed to indicate the directions of edges. Since the time delay might exist in the expression of regulators and target genes, time series mutual information is combined to cooperatively direct the edges for inferring the potential regulators and their targets. We evaluated the performance of MICRAT by applying it to synthetic datasets as well as real gene expression data and compare with other GRN inference methods. We inferred five 10-gene and five 100-gene networks from the DREAM4 challenge that were generated using the gene expression simulator GeneNetWeaver (GNW). MICRAT was also used to reconstruct GRNs on real gene expression data including part of the DNA-damaged response pathway (SOS DNA repair network) and experimental dataset in E. Coli. The results showed that MICRAT significantly improved the inference accuracy, compared to other inference methods, such as TDBN, etc. CONCLUSION: In this work, a novel algorithm, MICRAT, for inferring GRNs from time series gene expression data was proposed by taking into account dependence and time delay of expressions of a regulator and its target genes. This approach employed maximal information coefficients for reconstructing an undirected graph to represent the underlying relationships between genes. The edges were directed by combining conditional relative average entropy with time course mutual information of pairs of genes. The proposed algorithm was evaluated on the benchmark GRNs provided by the DREAM4 challenge and part of the real SOS DNA repair network in E. Coli. The experimental study showed that our approach was comparable to other methods on 10-gene datasets and outperformed other methods on 100-gene datasets in GRN inference from time series datasets.

Modeling spatial aspects of intracellular dopamine signaling.

Dopamine binding to various dopamine receptors activates multiple intracellular signaling molecules, some of which interact with calcium activated signaling pathways. Many experiments measure agonist-stimulated elevations in signaling molecules using prolonged, diffuse application, whereas the response of neurons to transient and spatially localized stimuli is more important. Computational modeling is an approach for investigating the spatial extent, time course, and interaction of postsynaptic signaling molecules activated by dopamine and other transmembrane receptors. NeuroRD is a simulation algorithm which can simulate large numbers of pathways and molecules in multiple spines attached to a dendrite. We explain how to gather the information needed to develop computational models, to implement such models in NeuroRD, to perform simulations, and to analyze the simulated data from these models.

Improved spatial direct method with gradient-based diffusion to retain full diffusive fluctuations.

The spatial direct method with gradient-based diffusion is an accelerated stochastic reaction-diffusion simulation algorithm that treats diffusive transfers between neighboring subvolumes based on concentration gradients. This recent method achieved a marked improvement in simulation speed and reduction in the number of time-steps required to complete a simulation run, compared with the exact algorithm, by sampling only the net diffusion events, instead of sampling all diffusion events. Although the spatial direct method with gradient-based diffusion gives accurate means of simulation ensembles, its gradient-based diffusion strategy results in reduced fluctuations in populations of diffusive species. In this paper, we present a new improved algorithm that is able to anticipate all possible microscopic fluctuations due to diffusive transfers in the system and incorporate this information to retain the same degree of fluctuations in populations of diffusing species as the exact algorithm. The new algorithm also provides a capability to set the desired level of fluctuation per diffusing species, which facilitates adjusting the balance between the degree of exactness in simulation results and the simulation speed. We present numerical results that illustrate the recovery of fluctuations together with the accuracy and efficiency of the new algorithm.

An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping.

Stochastic simulation of reaction-diffusion systems enables the investigation of stochastic events arising from the small numbers and heterogeneous distribution of molecular species in biological cells. Stochastic variations in intracellular microdomains and in diffusional gradients play a significant part in the spatiotemporal activity and behavior of cells. Although an exact stochastic simulation that simulates every individual reaction and diffusion event gives a most accurate trajectory of the system's state over time, it can be too slow for many practical applications. We present an accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems designed to improve the speed of simulation by reducing the number of time-steps required to complete a simulation run. This method is unique in that it employs two strategies that have not been incorporated in existing spatial stochastic simulation algorithms. First, diffusive transfers between neighboring subvolumes are based on concentration gradients. This treatment necessitates sampling of only the net or observed diffusion events from higher to lower concentration gradients rather than sampling all diffusion events regardless of local concentration gradients. Second, we extend the non-negative Poisson tau-leaping method that was originally developed for speeding up nonspatial or homogeneous stochastic simulation algorithms. This method calculates each leap time in a unified step for both reaction and diffusion processes while satisfying the leap condition that the propensities do not change appreciably during the leap and ensuring that leaping does not cause molecular populations to become negative. Numerical results are presented that illustrate the improvement in simulation speed achieved by incorporating these two new strategies.

The role of type 4 phosphodiesterases in generating microdomains of cAMP: large scale stochastic simulations.

Cyclic AMP (cAMP) and its main effector Protein Kinase A (PKA) are critical for several aspects of neuronal function including synaptic plasticity. Specificity of synaptic plasticity requires that cAMP activates PKA in a highly localized manner despite the speed with which cAMP diffuses. Two mechanisms have been proposed to produce localized elevations in cAMP, known as microdomains: impeded diffusion, and high phosphodiesterase (PDE) activity. This paper investigates the mechanism of localized cAMP signaling using a computational model of the biochemical network in the HEK293 cell, which is a subset of pathways involved in PKA-dependent synaptic plasticity. This biochemical network includes cAMP production, PKA activation, and cAMP degradation by PDE activity. The model is implemented in NeuroRD: novel, computationally efficient, stochastic reaction-diffusion software, and is constrained by intracellular cAMP dynamics that were determined experimentally by real-time imaging using an Epac-based FRET sensor (H30). The model reproduces the high concentration cAMP microdomain in the submembrane region, distinct from the lower concentration of cAMP in the cytosol. Simulations further demonstrate that generation of the cAMP microdomain requires a pool of PDE4D anchored in the cytosol and also requires PKA-mediated phosphorylation of PDE4D which increases its activity. The microdomain does not require impeded diffusion of cAMP, confirming that barriers are not required for microdomains. The simulations reported here further demonstrate the utility of the new stochastic reaction-diffusion algorithm for exploring signaling pathways in spatially complex structures such as neurons.

Topology-graph directed separating boundary surfaces approximation of nonmanifold neuroanatomical structures: application to mouse brain olfactory bulb.

Boundary surface approximation of 3-D neuroanatomical regions from sparse 2-D images (e.g., mouse brain olfactory bulb structures from a 2-D brain atlas) has proven to be difficult due to the presence of abutting, shared boundary surfaces that are not handled by traditional boundary-representation data structures and surfaces-from-contours algorithms. We describe a data structure and an algorithm to reconstruct separating surfaces among multiple regions from sparse cross-sectional contours. We define a topology graph for each region, that describes the topological skeleton of the region's boundary surface and that shows between which contours the surface patches should be generated. We provide a graph-directed triangulation algorithm to reconstruct surface patches between contours. We combine our graph-directed triangulation algorithm together with a piecewise parametric curve fitting technique to ensure that abutting or shared surface patches are precisely coincident. We show that our method overcomes limitations in 1) traditional contours-from-surfaces algorithms that assume binary, not multiple, regionalization of space, and in 2) few existing separating surfaces algorithms that assume conversion of input into a regular volumetric grid, which is not possible with sparse interplanar resolution.