Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations.

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

Stochastic simulation of the spatio-temporal dynamics of reaction-diffusion systems: the case for the bicoid gradient.

Reaction-diffusion systems are mathematical models that describe how the concentrations of substances distributed in space change under the influence of local chemical reactions, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose solution predicts how diffusion causes the concentration field to change with time. This change is proportional to the diffusion coefficient. If the solute moves in a homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and solute. However, in nonhomogeneous and structured media the assumption of constant intracellular diffusion coefficient is not necessarily valid, and, consequently, the diffusion coefficient is a function of the local concentration of solvent and solutes. In this paper we propose a stochastic model of reaction-diffusion systems, in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces. We then describe the software tool Redi (REaction-DIffusion simulator) which we have developed in order to implement this model into a Gillespie-like stochastic simulation algorithm. Finally, we show the ability of our model implemented in the Redi tool to reproduce the observed gradient of the bicoid protein in the Drosophila Melanogaster embryo. With Redi, we were able to simulate with an accuracy of 1% the experimental spatio-temporal dynamics of the bicoid protein, as recorded in time-lapse experiments obtained by direct measurements of transgenic bicoidenhanced green fluorescent protein.

GPU computing for systems biology.

The development of detailed, coherent, models of complex biological systems is recognized as a key requirement for integrating the increasing amount of experimental data. In addition, in-silico simulation of bio-chemical models provides an easy way to test different experimental conditions, helping in the discovery of the dynamics that regulate biological systems. However, the computational power required by these simulations often exceeds that available on common desktop computers and thus expensive high performance computing solutions are required. An emerging alternative is represented by general-purpose scientific computing on graphics processing units (GPGPU), which offers the power of a small computer cluster at a cost of approximately $400. Computing with a GPU requires the development of specific algorithms, since the programming paradigm substantially differs from traditional CPU-based computing. In this paper, we review some recent efforts in exploiting the processing power of GPUs for the simulation of biological systems.

The Beta Workbench: a computational tool to study the dynamics of biological systems.

We introduce the Beta Workbench (BWB), a scalable tool built on top of the newly defined BlenX language to model, simulate and analyse biological systems. We show the features and the incremental modelling process supported by the BWB on a running example based on the mitogen-activated kinase pathway. Finally, we provide a comparison with related approaches and some hints for future extensions.

A high quality draft consensus sequence of the genome of a heterozygous grapevine variety.

BACKGROUND: Worldwide, grapes and their derived products have a large market. The cultivated grape species Vitis vinifera has potential to become a model for fruit trees genetics. Like many plant species, it is highly heterozygous, which is an additional challenge to modern whole genome shotgun sequencing. In this paper a high quality draft genome sequence of a cultivated clone of V. vinifera Pinot Noir is presented. PRINCIPAL FINDINGS: We estimate the genome size of V. vinifera to be 504.6 Mb. Genomic sequences corresponding to 477.1 Mb were assembled in 2,093 metacontigs and 435.1 Mb were anchored to the 19 linkage groups (LGs). The number of predicted genes is 29,585, of which 96.1% were assigned to LGs. This assembly of the grape genome provides candidate genes implicated in traits relevant to grapevine cultivation, such as those influencing wine quality, via secondary metabolites, and those connected with the extreme susceptibility of grape to pathogens. Single nucleotide polymorphism (SNP) distribution was consistent with a diffuse haplotype structure across the genome. Of around 2,000,000 SNPs, 1,751,176 were mapped to chromosomes and one or more of them were identified in 86.7% of anchored genes. The relative age of grape duplicated genes was estimated and this made possible to reveal a relatively recent Vitis-specific large scale duplication event concerning at least 10 chromosomes (duplication not reported before). CONCLUSIONS: Sanger shotgun sequencing and highly efficient sequencing by synthesis (SBS), together with dedicated assembly programs, resolved a complex heterozygous genome. A consensus sequence of the genome and a set of mapped marker loci were generated. Homologous chromosomes of Pinot Noir differ by 11.2% of their DNA (hemizygous DNA plus chromosomal gaps). SNP markers are offered as a tool with the potential of introducing a new era in the molecular breeding of grape.

Genome-wide transcriptional analysis of grapevine berry ripening reveals a set of genes similarly modulated during three seasons and the occurrence of an oxidative burst at vèraison.

BACKGROUND: Grapevine (Vitis species) is among the most important fruit crops in terms of cultivated area and economic impact. Despite this relevance, little is known about the transcriptional changes and the regulatory circuits underlying the biochemical and physical changes occurring during berry development. RESULTS: Fruit ripening in the non-climacteric crop species Vitis vinifera L. has been investigated at the transcriptional level by the use of the Affymetrix Vitis GeneChip which contains approximately 14,500 unigenes. Gene expression data obtained from berries sampled before and after véraison in three growing years, were analyzed to identify genes specifically involved in fruit ripening and to investigate seasonal influences on the process. From these analyses a core set of 1477 genes was found which was similarly modulated in all seasons. We were able to separate ripening specific isoforms within gene families and to identify ripening related genes which appeared strongly regulated also by the seasonal weather conditions. Transcripts annotation by Gene Ontology vocabulary revealed five overrepresented functional categories of which cell wall organization and biogenesis, carbohydrate and secondary metabolisms and stress response were specifically induced during the ripening phase, while photosynthesis was strongly repressed. About 19% of the core gene set was characterized by genes involved in regulatory processes, such as transcription factors and transcripts related to hormonal metabolism and signal transduction. Auxin, ethylene and light emerged as the main stimuli influencing berry development. In addition, an oxidative burst, previously not detected in grapevine, characterized by rapid accumulation of H2O2 starting from véraison and by the modulation of many ROS scavenging enzymes, was observed. CONCLUSION: The time-course gene expression analysis of grapevine berry development has identified the occurrence of two well distinct phases along the process. The pre-véraison phase represents a reprogramming stage of the cellular metabolism, characterized by the expression of numerous genes involved in hormonal signalling and transcriptional regulation. The post-véraison phase is characterized by the onset of a ripening-specialized metabolism responsible for the phenotypic traits of the ripe berry. Between the two phases, at véraison, an oxidative burst and the concurrent modulation of the anti-oxidative enzymatic network was observed. The large number of regulatory genes we have identified represents a powerful new resource for dissecting the mechanisms of fruit ripening control in non-climacteric plants.