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.

Characterization of the Saccharomyces cerevisiae ERG27 gene encoding the 3-keto reductase involved in C-4 sterol demethylation

The last unidentified gene encoding an enzyme involved in ergosterol biosynthesis in Saccharomyces cerevisiae has been cloned. This gene, designated ERG27, encodes the 3-keto sterol reductase, which, in concert with the C-4 sterol methyloxidase (ERG25) and the C-3 sterol dehydrogenase (ERG26), catalyzes the sequential removal of the two methyl groups at the sterol C-4 position. We developed a strategy to isolate a mutant deficient in converting 3-keto to 3-hydroxy-sterols. An ergosterol auxotroph unable to synthesize sterol or grow without sterol supplementation was mutagenized. Colonies were then selected that were nystatin-resistant in the presence of 3-ketoergostadiene and cholesterol. A new ergosterol auxotroph unable to grow on 3-ketosterols without the addition of cholesterol was isolated. The gene (YLR100w) was identified by complementation. Segregants containing the YLR100w disruption failed to grow on various types of 3-keto sterol substrates. Surprisingly, when erg27 was grown on cholesterol- or ergosterol-supplemented media, the endogenous compounds that accumulated were noncyclic sterol intermediates (squalene, squalene epoxide, and squalene dioxide), and there was little or no accumulation of lanosterol or 3-ketosterols. Feeding experiments in which erg27 strains were supplemented with lanosterol (an upstream intermediate of the C-4 demethylation process) and cholesterol (an end-product sterol) demonstrated accumulation of four types of 3-keto sterols identified by GC/MS and chromatographic properties: 4-methyl-zymosterone, zymosterone, 4-methyl-fecosterone, and ergosta-7,24 (28)-dien-3-one. In addition, a fifth intermediate was isolated and identified by 1H NMR as a 4-methyl-24,25-epoxy-cholesta-7-en-3-one. Implications of these results are discussed.

Covalent intermediate trapped in 2-keto-3-deoxy-6- phosphogluconate (KDPG) aldolase structure at 1.95-Å resolution

2-Keto-3-deoxy-6-phosphogluconate (KDPG) aldolase catalyzes the reversible cleavage of KDPG to pyruvate and glyceraldehyde-3-phosphate. The enzyme is a class I aldolase whose reaction mechanism involves formation of Schiff base intermediates between Lys-133 and a keto substrate. A covalent adduct was trapped by flash freezing KDPG aldolase crystals soaked with 10 mM pyruvate in acidic conditions at pH 4.6. Structure determination to 1.95-Å resolution showed that pyruvate had undergone nucleophilic attack with Lys-133, forming a protonated carbinolamine intermediate, a functional Schiff base precursor, which was stabilized by hydrogen bonding with active site residues. Carbinolamine interaction with Glu-45 indicates general base catalysis of several rate steps. Stereospecific addition is ensured by aromatic interaction of Phe-135 with the pyruvate methyl group. In the native structure, Lys-133 donates all of its hydrogen bonds, indicating the presence of an ɛ-ammonium salt group. Nucleophilic activation is postulated to occur by proton transfer in the monoprotonated zwitterionic pair (Glu-45/Lys-133). Formation of the zwitterionic pair requires prior side chain rearrangement by protonated Lys-133 to displace a water molecule, hydrogen bonded to the zwitterionic residues.

Recovery of respiration following the SOS response of Escherichia coli requires RecA-mediated induction of 2-keto-4-hydroxyglutarate aldolase.

Agents that damage DNA in Escherichia coli or interfere with its replication induce DNA repair and mutagenesis via the SOS response. This well-known activity is regulated by the RecA protein and the LexA repressor. Following repair or bypass of the DNA lesion, the cell returns to its resting state by a largely unknown process. We found that 2-keto-4-hydroxyglutarate aldolase (4-hydroxy-2-oxoglutarate aldolase; EC 4.1.3.16) is necessary for the recovery of respiration and that it is regulated by the SOS response. This protein was induced by DNA-damaging agents. Induction required RecA activation. When the LexA regulon was repressed, activation of RecA was not sufficient for induction, indicating the requirement for an additional protein under LexA control. Finally, a mutant in the corresponding hga gene was UV sensitive. 2-Keto-4-hydroxyglutarate aldolase also plays a role in respiratory metabolic pathways, which suggests a mechanism for respiration resumption during the termination of the SOS response.

Lipid A biosynthesis in Rhizobium leguminosarum: role of a 2-keto-3-deoxyoctulosonate-activated 4' phosphatase.

Lipid A from several strains of the N2-fixing bacterium Rhizobium leguminosarum displays significant structural differences from Escherichia coli lipid A, one of which is the complete absence of phosphate groups. However, the first seven enzymes of E. coli lipid A biosynthesis, leading from UDP-GlcNAc to the phosphorylated intermediate, 2-keto-3-deoxyoctulosonate (Kdo2)-lipid IVA, are present in R. leguminosarum. We now describe a membrane-bound phosphatase in R. leguminosarum extracts that removes the 4' phosphate of Kdo2-lipid IVA. The 4' phosphatase is selective for substrates containing the Kdo domain. It is present in extracts of R. leguminosarum biovars phaseoli, viciae, and trifolii but is not detectable in E. coli and Rhizobium meliloti. A nodulation-defective strain (24AR) of R. leguminosarum biovar trifolii, known to contain a 4' phosphatase residue on its lipid A, also lacks measurable 4' phosphatase activity. The Kdo-dependent 4' phosphatase appears to be a key reaction in a pathway for generating phosphate-deficient lipid A.

A potassium channel beta subunit related to the aldo-keto reductase superfamily is encoded by the Drosophila hyperkinetic locus.

Genetic and physiological studies of the Drosophila Hyperkinetic (Hk) mutant revealed defects in the function or regulation of K+ channels encoded by the Shaker (Sh) locus. The Hk polypeptide, determined from analysis of cDNA clones, is a homologue of mammalian K+ channel beta subunits (Kv beta). Coexpression of Hk with Sh in Xenopus oocytes increases current amplitudes and changes the voltage dependence and kinetics of activation and inactivation, consistent with predicted functions of Hk in vivo. Sequence alignments show that Hk, together with mammalian Kv beta, represents an additional branch of the aldo-keto reductase superfamily. These results are relevant to understanding the function and evolutionary origin of Kv beta.