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.

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.

BackgroundReconstruction 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.ResultsWe 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 showe...