Multistationary and Oscillatory Modes of Free Radicals Generation by the Mitochondrial Respiratory Chain Revealed by a Bifurcation Analysis

The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS) that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial respiration with cellular metabolism. Here, a bifurcation analysis of a sequence of the electron transport chain models of increasing complexity was used to analyze the contribution of individual components to the modes of respiratory chain behavior. Our algorithm constructed models as large systems of ordinary differential equations describing the time evolution of the distribution of redox states of the respiratory complexes. The most complete model of the respiratory chain and linked metabolic reactions predicted that condensed mitochondria produce more ROS at low succinate concentration and less ROS at high succinate levels than swelled mitochondria. This prediction was validated by measuring ROS production under various swelling conditions. A numerical bifurcation analysis revealed qualitatively different types of multistationary behavior and sustained oscillations in the parameter space near a region that was previously found to describe the behavior of isolated mitochondria. The oscillations in transmembrane potential and ROS generation, observed in living cells were reproduced in the model that includes interaction of respiratory complexes with the reactions of TCA cycle. Whereas multistationarity is an internal characteristic of the respiratory chain, the functional link of respiration with central metabolism creates oscillations, which can be understood as a means of auto-regulation of cell metabolism.     

A Coupled Oscillatory Model Mimicking Avian Circadian Regulatory Systems

Much evidence indicates that the pineal gland and thesuprachiasmatic nucleus (SCN) are the primary pacemakers in the housesparrow, Passer domesticus. The interactions between the pineal andSCN predicted by the neuroendocrine loop model indicates that uncouplingwould cause the two oscillators to damp out in constant darkness. Basedupon the original neuroendocrine loop model, a mathematical frameworkof the house sparrow circadian regulatory organization that incorporatesdamping and co-inhibitory coupling has been formulated. The proposedmodel clearly indicates that two coupled oscillators must be 180^°out of the phase for sustaining oscillations. From damping coefficients,which can be determined from experimental data, other parameters suchas external stimuli (interaction coefficient) and characteristicfrequencies can then be computed. Based upon earlier studies and simulations,we conclude that the sparrow pineal gland dampens more rapidly than does theSCN, suggesting that the SCN are probably more important in sparrowsthan previously thought. The model also provides the explanations ofendogenous circadian period (tau) alteration. Finally, we extend this modelto other avian and to mammalian circadian systems. We suggest that avianand mammalian circadian systems may differ in damping coefficients ofpineal glands and the degree of SCN dominance.     

A Structural and Biochemical Model of Processive Chitin Synthesis

Chitin synthases (CHS) produce chitin, an essential component of the fungal cell wall. The molecular mechanism of processive chitin synthesis is not understood, limiting the discovery of new inhibitors of this enzyme class. We identified the bacterial glycosyltransferase NodC as an appropriate model system to study the general structure and reaction mechanism of CHS. A high throughput screening-compatible novel assay demonstrates that a known inhibitor of fungal CHS also inhibit NodC. A structural model of NodC, on the basis of the recently published BcsA cellulose synthase structure, enabled probing of the catalytic mechanism by mutagenesis, demonstrating the essential roles of the DD and QXXRW catalytic motifs. The NodC membrane topology was mapped, validating the structural model. Together, these approaches give insight into the CHS structure and mechanism and provide a platform for the discovery of inhibitors for this antifungal target.     

Robustness Analysis of Stochastic Biochemical Systems

We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.     

Structural Alphabets for Protein Structure Classification: A Comparison Study

Finding structural similarities between proteins often helps reveal shared functionality, which otherwise might not be detected by native sequence information alone. Such similarity is usually detected and quantified by protein structure alignment. Determining the optimal alignment between two protein structures, however, remains a hard problem. An alternative approach is to approximate each three-dimensional protein structure using a sequence of motifs derived from a structural alphabet. Using this approach, structure comparison is performed by comparing the corresponding motif sequences or structural sequences. In this article, we measure the performance of such alphabets in the context of the protein structure classification problem. We consider both local and global structural sequences. Each letter of a local structural sequence corresponds to the best matching fragment to the corresponding local segment of the protein structure. The global structural sequence is designed to generate the best possible complete chain that matches the full protein structure. We use an alphabet of 20 letters, corresponding to a library of 20 motifs or protein fragments having four residues. We show that the global structural sequences approximate well the native structures of proteins, with an average coordinate root mean square of 0.69 Å over 2225 test proteins. The approximation is best for all α-proteins, while relatively poorer for all β-proteins. We then test the performance of four different sequence representations of proteins (their native sequence, the sequence of their secondary-structure elements, and the local and global structural sequences based on our fragment library) with different classifiers in their ability to classify proteins that belong to five distinct folds of CATH. Without surprise, the primary sequence alone performs poorly as a structure classifier. We show that addition of either secondary-structure information or local information from the structural sequence considerably improves the classification accuracy. The two fragment-based sequences perform better than the secondary-structure sequence but not well enough at this stage to be a viable alternative to more computationally intensive methods based on protein structure alignment.     

Biochemical and Structural Properties of Mouse Kynurenine Aminotransferase III

Kynurenine aminotransferase III (KAT III) has been considered to be involved in the production of mammalian brain kynurenic acid (KYNA), which plays an important role in protecting neurons from overstimulation by excitatory neurotransmitters. The enzyme was identified based on its high sequence identity with mammalian KAT I, but its activity toward kynurenine and its structural characteristics have not been established. In this study, the biochemical and structural properties of mouse KAT III (mKAT III) were determined. Specifically, mKAT III cDNA was amplified from a mouse brain cDNA library, and its recombinant protein was expressed in an insect cell protein expression system. We established that mKAT III is able to efficiently catalyze the transamination of kynurenine to KYNA and has optimum activity at relatively basic conditions of around pH 9.0 and at relatively high temperatures of 50 to 60°C. In addition, mKAT III is active toward a number of other amino acids. Its activity toward kynurenine is significantly decreased in the presence of methionine, histidine, glutamine, leucine, cysteine, and 3-hydroxykynurenine. Through macromolecular crystallography, we determined the mKAT III crystal structure and its structures in complex with kynurenine and glutamine. Structural analysis revealed the overall architecture of mKAT III and its cofactor binding site and active center residues. This is the first report concerning the biochemical characteristics and crystal structures of KAT III enzymes and provides a basis toward understanding the overall physiological role of mammalian KAT III in vivo and insight into regulating the levels of endogenous KYNA through modulation of the enzyme in the mouse brain.     

Structural and Biochemical Analysis of the Sheath of Phormidium uncinatum

The sheath of the filamentous, gliding cyanobacterium Phormidium uncinatum was studied by using light and electron microscopy. In thin sections and freeze fractures the sheath was found to be composed of helically arranged carbohydrate fibrils, 4 to 7 nm in diameter, which showed a substantial degree of crystallinity. As in all other examined motile cyanobacteria, the arrangement of the sheath fibrils correlates with the motion of the filaments during gliding motility; i.e., the fibrils formed a right-handed helix in clockwise-rotating species and a left-handed helix in counterclockwise-rotating species and were radially arranged in nonrotating cyanobacteria. Since sheaths could only be found in old immotile cultures, the arrangement seems to depend on the process of formation and attachment of sheath fibrils to the cell surface rather than on shear forces created by the locomotion of the filaments. As the sheath in P. uncinatum directly contacts the cell surface via the previously identified surface fibril forming glycoprotein oscillin (E. Hoiczyk and W. Baumeister, Mol. Microbiol. 26:699–708, 1997), it seems reasonable that similar surface glycoproteins act as platforms for the assembly and attachment of the sheaths in cyanobacteria. In P. uncinatum the sheath makes up approximately 21% of the total dry weight of old cultures and consists only of neutral sugars. Staining reactions and X-ray diffraction analysis suggested that the fibrillar component is a homoglucan that is very similar but not identical to cellulose which is cross-linked by the other detected monosaccharides. Both the chemical composition and the rigid highly ordered structure clearly distinguish the sheaths from the slime secreted by the filaments during gliding motility.     

Enzyme Isomerization and Concentration Oscillations in Five-Component Biochemical Systems

The kinetic behavior of mnemonic enzymes is analyzed. Based on sufficient conditions for initiation of oscillations, the possibility of concentration oscillations in an open five-component enzymatic system is shown.     

Structural and Biochemical Characterization of Yeast Monothiol Glutaredoxin Grx6

Glutaredoxins (Grxs) are a ubiquitous family of proteins that reduce disulfide bonds in substrate proteins using electrons from reduced glutathione (GSH). The yeast Saccharomyces cerevisiae Grx6 is a monothiol Grx that is localized in the endoplasmic reticulum and Golgi compartments. Grx6 consists of three segments, a putative signal peptide (M1-I36), an N-terminal domain (K37-T110), and a C-terminal Grx domain (K111-N231, designated Grx6C). Compared to the classic dithiol glutaredoxin Grx1, Grx6 has a lower glutathione disulfide reductase activity but a higher glutathione S-transferase activity. In addition, similar to human Grx2, Grx6 binds GSH via an iron-sulfur cluster in vitro. The N-terminal domain is essential for noncovalent dimerization, but not required for either of the above activities. The crystal structure of Grx6C at 1.5 Å resolution revealed a novel two-strand antiparallel β-sheet opposite the GSH binding groove. This extra β-sheet might also exist in yeast Grx7 and in a group of putative Grxs in lower organisms, suggesting that Grx6 might represent the first member of a novel Grx subfamily.     

A Combination of Structural and Cis-Regulatory Factors Drives Biochemical Differences in Drosophila melanogaster Malic Enzyme

The evolutionary significance of molecular variation is still contentious, with much current interest focusing on the relative contribution of structural changes in proteins versus regulatory variation in gene expression. We present a population genetic and biochemical study of molecular variation at the malic enzyme locus (Men) in Drosophila melanogaster. Two amino acid polymorphisms appear to affect substrate-binding kinetics, while only one appears to affect thermal stability. Interestingly, we find that enzyme activity differences previously assigned to one of the polymorphisms may, instead, be a function of linked regulatory differences. These results suggest that both regulatory and structural changes contribute to differences in protein function. Our examination of the Men coding sequences reveals no evidence for selection acting on the polymorphisms, but earlier work on this enzyme indicates that the biochemical variation observed has physiological repercussions and therefore could potentially be under natural selection.     

Biochemical Systems as Generators of Local and Global Limit Cycles

It has recently been noted (8) that the global limit cycle (hard self-excitation) is apparently not uncommon in nature, especially in biochemical systems. This idea is confirmed by a more detailed study of many biochemical systems with quite different topological structures.

The present paper describes some of the cases considered; they were deliberately chosen to be simple, but they almost all have the following properties: for one set of parameters, the linearization method shows that there is a local limit cycle (soft self-excitation); for other parameters, the systems may have global limit cycles.     

Biochemical Systems as Generators of Local and Global Limit Cycles

It has recently been noted (8) that the global limit cycle (hard self-excitation) is apparently not uncommon in nature, especially in biochemical systems. This idea is confirmed by a more detailed study of many biochemical systems with quite different topological structures.

The present paper describes some of the cases considered; they were deliberately chosen to be simple, but they almost all have the following properties: for one set of parameters, the linearization method shows that there is a local limit cycle (soft self-excitation); for other parameters, the systems may have global limit cycles.     

Systematic Structural Characterization of Metabolites in Arabidopsis via Candidate Substrate-Product Pair Networks

Plant metabolomics is increasingly used for pathway discovery and to elucidate gene function. However, the main bottleneck is the identification of the detected compounds. This is more pronounced for secondary metabolites as many of their pathways are still underexplored. Here, an algorithm is presented in which liquid chromatography–mass spectrometry profiles are searched for pairs of peaks that have mass and retention time differences corresponding with those of substrates and products from well-known enzymatic reactions. Concatenating the latter peak pairs, called candidate substrate-product pairs (CSPP), into a network displays tentative (bio)synthetic routes. Starting from known peaks, propagating the network along these routes allows the characterization of adjacent peaks leading to their structure prediction. As a proof-of-principle, this high-throughput cheminformatics procedure was applied to the Arabidopsis thaliana leaf metabolome where it allowed the characterization of the structures of 60% of the profiled compounds. Moreover, based on searches in the Chemical Abstract Service database, the algorithm led to the characterization of 61 compounds that had never been described in plants before. The CSPP-based annotation was confirmed by independent MSⁿ experiments. In addition to being high throughput, this method allows the annotation of low-abundance compounds that are otherwise not amenable to isolation and purification. This method will greatly advance the value of metabolomics in systems biology.     

Parametric Sensitivity Analysis of Oscillatory Delay Systems with an Application to Gene Regulation

A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change. An oscillatory protein synthesis model whose properties are modulated by RNA interference is used as an example. This model consists of a set of coupled delay-differential equations involving three delays. Sensitivity analyses are carried out at several operating points. Comments on the evolutionary implications of the results are offered.     

Classification and Structural Comparison of Full-Length cDNAs for Pathogenesis-Related Proteins

Fourteen cDNA clones of pathogenesis-related (PR) proteins, PR1a and PR1b of tobacco were obtained and classified into six groups based on restriction enzyme maps. To assign the groups to different classes of PR1 proteins, all the clones were partially sequenced and compared with amino acid sequences of PR1a and PR1b. Two groups of these corresponded to PR1a and four to PR1b. The results indicate that there are at least two kinds of PR1a mRNAs and four kinds of PR1b mRNAs. In fact, one cDNA insert hybridized to at least six to seven DNA fragments in restriction enzyme fragments of Samsun NN genomic DNA, indicating that the PR1 protein genes exist as a multigene family in the tobacco genome. Two sequences of essentially full-length cDNAs for PR1a and PR1b were determined and compared. The coding sequences of two cDNAs share 93% homology and the deduced amino acid sequences of PR1a and PR1b precursors, which are synthesized as larger precursors containing signal peptides, are 91% homologous. The homology of mature PR1a and PR1b regions is higher than that of larger precursors, 94% in the nucleotide sequence and 93% in the amino acid sequence, whereas that of the signal peptide regions is 80 and 90%, respectively. The hydropathy patterns and the secondary structures predicted by Chou-Fasman rules are similar to tomato PR protein in the half-side of the C terminus, which suggests that the half-C terminus side is important for the function of PR1 proteins.