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.

Molecular analysis of CaMnt1p, a mannosyl transferase important for adhesion and virulence of Candida albicans

There is an immediate need for identification of new antifungal targets in opportunistic pathogenic fungi like Candida albicans. In the past, efforts have focused on synthesis of chitin and glucan, which confer mechanical strength and rigidity upon the cell wall. This paper describes the molecular analysis of CaMNT1, a gene involved in synthesis of mannoproteins, the third major class of macromolecule found in the cell wall. CaMNT1 encodes an α-1,2-mannosyl transferase, which adds the second mannose residue in a tri-mannose oligosaccharide structure which represents O-linked mannan in C. albicans. The deduced amino acid sequence suggests that CaMnt1p is a type II membrane protein residing in a medial Golgi compartment. The absence of CaMnt1p reduced the ability of C. albicans cells to adhere to each other, to human buccal epithelial cells, and to rat vaginal epithelial cells. Both heterozygous and homozygous Camnt1 null mutants of C. albicans showed strong attenuation of virulence in guinea pig and mouse models of systemic candidosis, which, in guinea pigs, could be attributed to a decreased ability to reach and/or adhere internal organs. Therefore, correct CaMnt1p-mediated O-linked mannosylation of proteins is critical for adhesion and virulence of C. albicans.

Molecular evolution of integrins: Genes encoding integrin β subunits from a coral and a sponge

The integrin family of cell surface receptors is strongly conserved in higher animals, but the evolutionary history of integrins is obscure. We have identified and sequenced cDNAs encoding integrin β subunits from a coral (phylum Cnidaria) and a sponge (Porifera), indicating that these proteins existed in the earliest stages of metazoan evolution. The coral βCn1 and, especially, the sponge βPo1 sequences are the most divergent of the “β1-class” integrins and share a number of features not found in any other vertebrate or invertebrate integrins. Perhaps the greatest difference from other β subunits is found in the third and fourth repeats of the cysteine-rich stalk, where the generally conserved spacings between cysteines are highly variable, but not similar, in βCn1 and βPo1. Alternatively spliced cDNAs, containing a stop codon about midway through the full-length translated sequence, were isolated from the sponge library. These cDNAs appear to define a boundary between functional domains, as they would encode a protein that includes the globular ligand-binding head but would be missing the stalk, transmembrane, and cytoplasmic domains. These and other sequence comparisons with vertebrate integrins are discussed with respect to models of integrin structure and function.

Direct molecular level measurements of the electrostatic properties of a protein surface

In this work, we used direct measurements with the surface force apparatus to determine the pH-dependent electrostatic charge density of a single binding face of streptavidin. Mean field calculations have been used with considerable success to model electrostatic potential fields near protein surfaces, but these models and their inherent assumptions have not been tested directly at the molecular level. Using the force apparatus and immobilized, oriented monolayers of streptavidin, we measured a pI of 5–5.5 for the biotin-binding face of the protein. This differs from the pI of 6.3 for the soluble protein and confirms that we probed the local electrostatic features of the macromolecule. With finite difference solutions of the linearized Poisson–Boltzmann equation, we then calculated the pH-dependent charge densities adjacent to the same face of the protein. These calculated values agreed quantitatively with those obtained by direct force measurements. Although our study focuses on the pH-dependence of surface electrostatics, this direct approach to probing the electrostatic features of proteins is applicable to investigations of any perturbations that alter the charge distribution of the surfaces of immobilized molecules.

Biosynthetic control of molecular weight in the polymerization of the octasaccharide subunits of succinoglycan, a symbiotically important exopolysaccharide of Rhizobium meliloti

Succinoglycan, a symbiotically important exopolysaccharide of Rhizobium meliloti, is composed of polymerized octasaccharide subunits, each of which consists of one galactose and seven glucoses with succinyl, acetyl, and pyruvyl modifications. Production of specific low molecular weight forms of R. meliloti exported and surface polysaccharides, including succinoglycan, appears to be important for nodule invasion. In a previous study of the roles of the various exo gene products in succinoglycan biosynthesis, exoP, exoQ, and exoT mutants were found to synthesize undecaprenol-linked fully modified succinoglycan octasaccharide subunits, suggesting possible roles for their gene products in polymerization or transport. Using improved techniques for analyzing succinoglycan biosynthesis by these mutants, we have obtained evidence indicating that R. meliloti has genetically separable systems for the synthesis of high molecular weight succinoglycan and the synthesis of a specific class of low molecular weight oligosaccharides consisting of dimers and trimers of the octasaccharide subunit. Models to account for our unexpected findings are discussed. Possible roles for the ExoP, ExoQ, and ExoT proteins are compared and contrasted with roles that have been suggested on the basis of homologies to key proteins involved in the biosynthesis of O-antigens and of certain exported or capsular cell surface polysaccharides.

Molecular Cloning and Characterization of a Radial Spoke Head Protein of Sea Urchin Sperm Axonemes: Involvement of the Protein in the Regulation of Sperm Motility

Monoclonal antibodies raised against axonemal proteins of sea urchin spermatozoa have been used to study regulatory mechanisms involved in flagellar motility. Here, we report that one of these antibodies, monoclonal antibody D-316, has an unusual perturbating effect on the motility of sea urchin sperm models; it does not affect the beat frequency, the amplitude of beating or the percentage of motile sperm models, but instead promotes a marked transformation of the flagellar beating pattern which changes from a two-dimensional to a three-dimensional type of movement. On immunoblots of axonemal proteins separated by SDS-PAGE, D-316 recognized a single polypeptide of 90 kDa. This protein was purified following its extraction by exposure of axonemes to a brief heat treatment at 40°C. The protein copurified and coimmunoprecipitated with proteins of 43 and 34 kDa, suggesting that it exists as a complex in its native form. Using D-316 as a probe, a full-length cDNA clone encoding the 90-kDa protein was obtained from a sea urchin cDNA library. The sequence predicts a highly acidic (pI = 4.0) protein of 552 amino acids with a mass of 62,720 Da (p63). Comparison with protein sequences in databases indicated that the protein is related to radial spoke proteins 4 and 6 (RSP4 and RSP6) of Chlamydomonas reinhardtii, which share 37% and 25% similarity, respectively, with p63. However, the sea urchin protein possesses structural features distinct from RSP4 and RSP6, such as the presence of three major acidic stretches which contains 25, 17, and 12 aspartate and glutamate residues of 34-, 22-, and 14-amino acid long stretches, respectively, that are predicted to form α-helical coiled-coil secondary structures. These results suggest a major role for p63 in the maintenance of a planar form of sperm flagellar beating and provide new tools to study the function of radial spoke heads in more evolved species.

Rapid evolution in plant chitinases: Molecular targets of selection in plant-pathogen coevolution

Many pathogen recognition genes, such as plant R-genes, undergo rapid adaptive evolution, providing evidence that these genes play a critical role in plant-pathogen coevolution. Surprisingly, whether rapid adaptive evolution also occurs in genes encoding other kinds of plant defense proteins is unknown. Unlike recognition proteins, plant chitinases attack pathogens directly, conferring disease resistance by degrading chitin, a component of fungal cell walls. Here, we show that nonsynonymous substitution rates in plant class I chitinase often exceed synonymous rates in the plant genus Arabis (Cruciferae) and in other dicots, indicating a succession of adaptively driven amino acid replacements. We identify individual residues that are likely subject to positive selection by using codon substitution models and determine the location of these residues on the three-dimensional structure of class I chitinase. In contrast to primate lysozymes and plant class III chitinases, structural and functional relatives of class I chitinase, the adaptive replacements of class I chitinase occur disproportionately in the active site cleft. This highly unusual pattern of replacements suggests that fungi directly defend against chitinolytic activity through enzymatic inhibition or other forms of chemical resistance and identifies target residues for manipulating chitinolytic activity. These data also provide empirical evidence that plant defense proteins not involved in pathogen recognition also evolve in a manner consistent with rapid coevolutionary interactions.

Large vortex-like structure of dipole field in computer models of liquid water and dipole-bridge between biomolecules

We propose a framework to describe the cooperative orientational motions of water molecules in liquid water and around solute molecules in water solutions. From molecular dynamics (MD) simulation a new quantity “site-dipole field” is defined as the averaged orientation of water molecules that pass through each spatial position. In the site-dipole field of bulk water we found large vortex-like structures of more than 10 Å in size. Such coherent patterns persist more than 300 ps although the orientational memory of individual molecules is quickly lost. A 1-ns MD simulation of systems consisting of two amino acids shows that the fluctuations of site-dipole field of solvent are pinned around the amino acids, resulting in a stable dipole-bridge between side-chains of amino acids. The dipole-bridge is significantly formed even for the side-chain separation of 14 Å, which corresponds to five layers of water. The way that dipole-bridge forms sensitively depends on the side-chain orientations and thereby explains the specificity in the solvent-mediated interactions between biomolecules.

A comparison of the potential role of the tetrodotoxin-insensitive sodium channels, PN3/SNS and NaN/SNS2, in rat models of chronic pain

Alterations in sodium channel expression and function have been suggested as a key molecular event underlying the abnormal processing of pain after peripheral nerve or tissue injury. Although the relative contribution of individual sodium channel subtypes to this process is unclear, the biophysical properties of the tetrodotoxin-resistant current, mediated, at least in part, by the sodium channel PN3 (SNS), suggests that it may play a specialized, pathophysiological role in the sustained, repetitive firing of the peripheral neuron after injury. Moreover, this hypothesis is supported by evidence demonstrating that selective “knock-down” of PN3 protein in the dorsal root ganglion with specific antisense oligodeoxynucleotides prevents hyperalgesia and allodynia caused by either chronic nerve or tissue injury. In contrast, knock-down of NaN/SNS2 protein, a sodium channel that may be a second possible candidate for the tetrodotoxin-resistant current, appears to have no effect on nerve injury-induced behavioral responses. These data suggest that relief from chronic inflammatory or neuropathic pain might be achieved by selective blockade or inhibition of PN3 expression. In light of the restricted distribution of PN3 to sensory neurons, such an approach might offer effective pain relief without a significant side-effect liability.

Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

Unifying theory of hypoxia tolerance: molecular/metabolic defense and rescue mechanisms for surviving oxygen lack.

We develop a unifying theory of hypoxia tolerance based on information from two cell level models (brain cortical cells and isolated hepatocytes) from the highly anoxia tolerant aquatic turtle and from other more hypoxia sensitive systems. We propose that the response of hypoxia tolerant systems to oxygen lack occurs in two phases (defense and rescue). The first lines of defense against hypoxia include a balanced suppression of ATP-demand and ATP-supply pathways; this regulation stabilizes (adenylates) at new steady-state levels even while ATP turnover rates greatly decline. The ATP demands of ion pumping are down-regulated by generalized "channel" arrest in hepatocytes and by "spike" arrest in neurons. Hypoxic ATP demands of protein synthesis are down-regulated probably by translational arrest. In hypoxia sensitive cells this translational arrest seems irreversible, but hypoxia-tolerant systems activate "rescue" mechanisms if the period of oxygen lack is extended by preferentially regulating the expression of several proteins. In these cells, a cascade of processes underpinning hypoxia rescue and defense begins with an oxygen sensor (a heme protein) and a signal-transduction pathway, which leads to significant gene-based metabolic reprogramming-the rescue process-with maintained down-regulation of energy-demand and energy-supply pathways in metabolism throughout the hypoxic period. This recent work begins to clarify how normoxic maintenance ATP turnover rates can be drastically (10-fold) down-regulated to a new hypometabolic steady state, which is prerequisite for surviving prolonged hypoxia or anoxia. The implications of these developments are extensive in biology and medicine.

Checkpoints in the progression of autoimmune disease: lessons from diabetes models.

In the last few years, data from experiments employing transgenic models of autoimmune disease have strengthened a particular concept of autoimmunity: disease results not so much from cracks in tolerance induction systems, leading to the generation of anti-self repertoire, as from the breakdown of secondary systems that keep these cells in check. T cells with anti-self specificities are readily found in disease-free individuals but ignore target tissues. This is also the case in some transgenic models, in spite of overwhelming numbers of autoreactive cells. In other instances, local infiltration and inflammation result, but they are well tolerated for long periods of time and do not terminally destroy target tissue. We review the possible molecular and cellular mechanisms that underlie these situations, with a particular emphasis on the destruction of pancreatic beta cells in transgenic models of insulin-dependent disease.

Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.

Molecular design of the N-methyl-D-aspartate receptor binding site for phencyclidine and dizolcipine.

The N-methyl-D-aspartate receptor (NMDAR), a pivotal entity for synaptic plasticity and excitotoxicity in the brain, is a target of psychotomimetic drugs such as phencyclidine (PCP) and dizolcipine (MK-801). In contrast, a related glutamate receptor, the alpha-amino-3-hydroxy-5-methyl-4-isoxazole propionate/kainate receptor GluR1, is weakly sensitive to these drugs. Three point mutations on GluR1, mimicking homologous residues on the NMDAR, confer the PCP and MK-801 blockade properties that are characteristic of the NMDAR--namely, high potency, voltage dependence, and use dependence. The molecular determinants that specify the PCP block appear confined to the putative M2 transmembrane segment, whereas the sensitivity to MK-801 requires an interplay between residues from M2 and M3. Given the plausible involvement of the NMDAR in the etiology of several neurodegenerative diseases and in excitotoxic neuronal cell death, tailored glutamate receptors with specific properties may be models for designing and screening new drugs targeted to prevent glutamate-mediated neural damage.

The CuA center of cytochrome-c oxidase: electronic structure and spectra of models compared to the properties of CuA domains.

The electronic structure and spectrum of several models of the binuclear metal site in soluble CuA domains of cytochrome-c oxidase have been calculated by the use of an extended version of the complete neglect of differential overlap/spectroscopic method. The experimental spectra have two strong transitions of nearly equal intensity around 500 nm and a near-IR transition close to 800 nm. The model that best reproduces these features consists of a dimer of two blue (type 1) copper centers, in which each Cu atom replaces the missing imidazole on the other Cu atom. Thus, both Cu atoms have one cysteine sulfur atom and one imidazole nitrogen atom as ligands, and there are no bridging ligands but a direct Cu-Cu bond. According to the calculations, the two strong bands in the visible region originate from exciton coupling of the dipoles of the two copper monomers, and the near-IR band is a charge-transfer transition between the two Cu atoms. The known amino acid sequence has been used to construct a molecular model of the CuA site by the use of a template and energy minimization. In this model, the two ligand cysteine residues are in one turn of an alpha-helix, whereas one ligand histidine is in a loop following this helix and the other one is in a beta-strand.