Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

Large-scale protein structure modeling of the Saccharomyces cerevisiae genome

The function of a protein generally is determined by its three-dimensional (3D) structure. Thus, it would be useful to know the 3D structure of the thousands of protein sequences that are emerging from the many genome projects. To this end, fold assignment, comparative protein structure modeling, and model evaluation were automated completely. As an illustration, the method was applied to the proteins in the Saccharomyces cerevisiae (baker’s yeast) genome. It resulted in all-atom 3D models for substantial segments of 1,071 (17%) of the yeast proteins, only 40 of which have had their 3D structure determined experimentally. Of the 1,071 modeled yeast proteins, 236 were related clearly to a protein of known structure for the first time; 41 of these previously have not been characterized at all.

The Development of Cell Processes Induced by tau Protein Requires Phosphorylation of Serine 262 and 356 in the Repeat Domain and Is Inhibited by Phosphorylation in the Proline-rich Domains

The differentiation of neurons and the outgrowth of neurites depends on microtubule-associated proteins such as tau protein. To study this process, we have used the model of Sf9 cells, which allows efficient transfection with microtubule-associated proteins (via baculovirus vectors) and observation of the resulting neurite-like extensions. We compared the phosphorylation of tau23 (the embryonic form of human tau) with mutants in which critical phosphorylation sites were deleted by mutating Ser or Thr residues into Ala. One can broadly distinguish two types of sites, the KXGS motifs in the repeats (which regulate the affinity of tau to microtubules) and the SP or TP motifs in the domains flanking the repeats (which contain epitopes for antibodies diagnostic of Alzheimer’s disease). Here we report that both types of sites can be phosphorylated by endogenous kinases of Sf9 cells, and that the phosphorylation pattern of the transfected tau is very similar to that of neurons, showing that Sf9 cells can be regarded as an approximate model for the neuronal balance between kinases and phosphatases. We show that mutations in the repeat domain and in the flanking domains have opposite effects. Mutations of KXGS motifs in the repeats (Ser262, 324, and 356) strongly inhibit the outgrowth of cell extensions induced by tau, even though this type of phosphorylation accounts for only a minor fraction of the total phosphate. This argues that the temporary detachment of tau from microtubules (by phosphorylation at KXGS motifs) is a necessary condition for establishing cell polarity at a critical point in space or time. Conversely, the phosphorylation at SP or TP motifs represents the majority of phosphate (>80%); mutations in these motifs cause an increase in cell extensions, indicating that this type of phosphorylation retards the differentiation of the cells.

Three-dimensional modeling of and ligand docking to vitamin D receptor ligand binding domain

The ligand binding domain of the human vitamin D receptor (VDR) was modeled based on the crystal structure of the retinoic acid receptor. The ligand binding pocket of our VDR model is spacious at the helix 11 site and confined at the β-turn site. The ligand 1α,25-dihydroxyvitamin D3 was assumed to be anchored in the ligand binding pocket with its side chain heading to helix 11 (site 2) and the A-ring toward the β-turn (site 1). Three residues forming hydrogen bonds with the functionally important 1α- and 25-hydroxyl groups of 1α,25-dihydroxyvitamin D3 were identified and confirmed by mutational analysis: the 1α-hydroxyl group is forming pincer-type hydrogen bonds with S237 and R274 and the 25-hydroxyl group is interacting with H397. Docking potential for various ligands to the VDR model was examined, and the results are in good agreement with our previous three-dimensional structure-function theory.

A numerical strategy for efficient modeling of the equatorial wave guide

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss–Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

Ras Family GTPases Control Growth of Astrocyte Processes

Astrocytes in neuron-free cultures typically lack processes, although they are highly process-bearing in vivo. We show that basic fibroblast growth factor (bFGF) induces cultured astrocytes to grow processes and that Ras family GTPases mediate these morphological changes. Activated alleles of rac1 and rhoA blocked and reversed bFGF effects when introduced into astrocytes in dissociated culture and in brain slices using recombinant adenoviruses. By contrast, dominant negative (DN) alleles of both GTPases mimicked bFGF effects. A DN allele of Ha-ras blocked bFGF effects but not those of Rac1-DN or RhoA-DN. Our results show that bFGF acting through c-Ha-Ras inhibits endogenous Rac1 and RhoA GTPases thereby triggering astrocyte process growth, and they provide evidence for the regulation of this cascade in vivo by a yet undetermined neuron-derived factor.

Statistical modeling of large microarray data sets to identify stimulus-response profiles

A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.

Mutational analysis and molecular modeling of the nonapeptide hormone binding domains of the [Arg8]vasotocin receptor.

To identify determinants that form nonapeptide hormone binding domains of the white sucker Catostomus commersoni [Arg8]vasotocin receptor, chimeric constructs encoding parts of the vasotocin receptor and parts of the isotocin receptor have been analyzed by [(3,5-3H)Tyr2, Arg8]vasotocin binding to membranes of human embryonic kidney cells previously transfected with the different cDNA constructs and by functional expression studies in Xenopus laevis oocytes injected with mutant cRNAs. The results indicate that the N terminus and a region spanning the second extracellular loop and its flanking transmembrane segments, which contains a number of amino acid residues that are conserved throughout the nonapeptide receptor family, contribute to the affinity of the receptor for its ligand. Nonapeptide selectivity, however, is mainly defined by transmembrane region VI and the third extracellular loop. These results are complemented by a molecular model of the vasotocin receptor obtained by aligning its sequence with those of other G-protein coupled receptors as well as that of bacteriorhodopsin. The model indicates that amino acid residues of transmembrane regions II-VII that are located close to the extracellular surface also contribute to the binding of vasotocin.