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.

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.

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.

The design, computer modeling, solution structure, and biological evaluation of synthetic analogs of bryostatin 1

The bryostatins are a unique family of emerging cancer chemotherapeutic candidates isolated from marine bryozoa. Although the biochemical basis for their therapeutic activity is not known, these macrolactones exhibit high affinities for protein kinase C (PKC) isozymes, compete for the phorbol ester binding site on PKC, and stimulate kinase activity in vitro and in vivo. Unlike the phorbol esters, they are not first-stage tumor promoters. The design, computer modeling, NMR solution structure, PKC binding, and functional assays of a unique class of synthetic bryostatin analogs are described. These analogs (7b, 7c, and 8) retain the putative recognition domain of the bryostatins but are simplified through deletions and modifications in the C4-C14 spacer domain. Computer modeling of an analog prototype (7a) indicates that it exists preferentially in two distinct conformational classes, one in close agreement with the crystal structure of bryostatin 1. The solution structure of synthetic analog 7c was determined by NMR spectroscopy and found to be very similar to the previously reported structures of bryostatins 1 and 10. Analogs 7b, 7c, and 8 bound strongly to PKC isozymes with Ki = 297, 3.4, and 8.3 nM, respectively. Control 7d, like the corresponding bryostatin derivative, exhibited weak PKC affinity, as did the derivative, 9, lacking the spacer domain. Like bryostatin, acetal 7c exhibited significant levels of in vitro growth inhibitory activity (1.8–170 ng/ml) against several human cancer cell lines, providing an important step toward the development of simplified, synthetically accessible analogs of the bryostatins.

Flows of knowledge from universities and federal laboratories: Modeling the flow of patent citations over time and across institutional and geographic boundaries

The extent to which new technological knowledge flows across institutional and national boundaries is a question of great importance for public policy and the modeling of economic growth. In this paper we develop a model of the process generating subsequent citations to patents as a lens for viewing knowledge diffusion. We find that the probability of patent citation over time after a patent is granted fits well to a double-exponential function that can be interpreted as the mixture of diffusion and obsolescense functions. The results indicate that diffusion is geographically localized. Controlling for other factors, within-country citations are more numerous and come more quickly than those that cross country boundaries.

A combined kinetic and modeling study of the catalytic center subsites of human angiogenin.

Kinetic analysis and molecular modeling have been used to map the ribonucleolytic center of angiogenin (Ang). Pyrimidine nucleotides were found to interact very weakly with Ang, consistent with the inaccessible B1 pyrimidine binding site revealed by x-ray crystallography. Ang also lacks an effective phosphate binding site on the 5' side of B1. Although the B2 site that preferentially binds purines on the 3' side of B1 is also weak, its associated phosphate subsites make substantial contributions: both 3',5'-ADP and 5'-ADP have Ki values 6-fold lower than for 5'-AMP, and adding a 3'-phosphate to the substrate CpA increases Kcat/Km by 9-fold. Thus Ang has a functional P2 site on the 3' side of B2 and a site for a second phosphate on the 5' side of B2. Modeling of an Ang-d(ApTpApA) complex suggested that Arg-5 forms part of the P2 site and that a 2'-phosphate might bind more tightly than a 3'-phosphate. Both predictions were confirmed kinetically. The subsite map obtained by this combined approach indicated that 5'-diphosphoadenosine 2'-phosphate might be a more potent inhibitor than any of the nucleotides tested thus far. Indeed, its Ki value of 150 microM is 50-fold lower than that for the best nucleotide previously reported and 400-fold lower than the Km for the best dinucleotide substrate. This compound may serve as a suitable starting point for the eventual design of tight-binding inhibitors of Ang as antiangiogenic agents for human therapy.