Catastrophe theory of dopaminergic transmission: a revised dopamine hypothesis of schizophrenia

Mathematical modeling of experimentally observed parameters of dopaminergic neuronal activity suggests the occurrence of multiple equilibrium states in neurons characterized by certain precisely defined properties of the tyrosine hydroxylating system. These equilibria may become unstable under certain conditions and transitions between multiple states are predicted. In addition, modeling of the spatial interactions of dopamine neurons within a neural net leads to domain wall soliton-like solutions of neuronal firing. In the discrete spatial case, these equations are isomorphic to those of the Ising model of phase transitions in lattice spins.The hypothesis is proposed that the occurrence of multiple stable equilibrium states rather than excessive dopaminergic transmission forms the pathophysiological basis of the schizophrenic thought disorder.The model is internally consistent with known clinical effects of drugs such as neuroleptics, reserpine and amphetamine. In agreement with postmortem and other studies, the theory predicts the lack of increased concentrations of dopamine or its major metabolite, homovanillic acid, in brain and cerebrospinal fluid of schizophrenics.The mathematical model is compatible with the theory that postulates an attention deficit as an underlying mechanism of schizophrenic psychosis and allows for a possible genetic heterogeneity of the disease.     

Solvation of the folding-transition state in Pseudomonas aeruginosa azurin is modulated by metal: Solvation of azurin's folding nucleus

The role of water in protein folding, specifically its presence or not in the transition-state structure, is an unsolved question. There are two common classes of folding-transition states: diffuse transition states, in which almost all side chains have similar, rather low phi (phi) values, and polarized transition states, which instead display distinct substructures with very high phi-values. Apo-and zinc-forms of Pseudomonas aeruginosa azurin both fold in two-state equilibrium and kinetic reactions; while the apo-form exhibits a polarized transition state, the zinc form entails a diffuse, moving transition state. To examine the presence of water in these two types of folding-transition states, we probed the equilibrium and kinetic consequences of replacing core valines with isosteric threonines at six positions in azurin. In contrast to regular hydrophobic-to-alanine phi-value analysis, valine-to-threonine mutations do not disrupt the core packing but stabilize the unfolded state and can be used to assess the degree of solvation in the folding-transition state upon combination with regular phi-values. We find that the transition state for folding of apo-azurin appears completely dry, while that for zinc-azurin involves partially formed interactions that engage water molecules. This distinct difference between the apo-and holo-folding nuclei can be rationalized in terms of the shape of the free-energy barrier.     

The role of intersubunit interactions for the stabilization of the T state of Escherichia coli aspartate transcarbamoylase

Homotropic cooperativity in Escherichia coli aspartate transcarbamoylase results from the substrate-induced transition from the T to the R state. These two alternate states are stabilized by a series of interdomain and intersubunit interactions. The salt link between Lys-143 of the regulatory chain and Asp-236 of the catalytic chain is only observed in the T state. When Asp-236 is replaced by alanine the resulting enzyme exhibits full activity, enhanced affinity for aspartate, no cooperativity, and no heterotropic interactions. These characteristics are consistent with an enzyme locked in the functional R state. Using small angle x-ray scattering, the structural consequences of the D236A mutant were characterized. The unliganded D236A holoenzyme appears to be in a new structural state that is neither T, R, nor a mixture of T and R states. The structure of the native D236A holoenzyme is similar to that previously reported for another mutant holoenzyme (E239Q) that also lacks intersubunit interactions. A hybrid version of aspartate transcarbamoylase in which one catalytic subunit was wild-type and the other had the D236A mutation was also investigated. The hybrid holoenzyme, with three of the six possible interactions involving Asp-236, exhibited homotropic cooperativity, and heterotropic interactions consistent with an enzyme with both T and R functional states. Small angle x-ray scattering analysis of the unligated hybrid indicated that the enzyme was in a new structural state more similar to the T than to the R state of the wild-type enzyme. These data suggest that three of the six intersubunit interactions involving D236A are sufficient to stabilize a T-like state of the enzyme and allow for an allosteric transition.     

Molecular dynamics simulations of active site mutants of triosephosphate isomerase

Molecular dynamics simulations of triosephosphate isomerase (TIM) and of some active site TIM mutants were performed in an attempt to elucidate possible interactions important for catalytic activity and binding. A variety of active site residues in TIM have been altered, resulting in all cases in decreases in catalytic activity. Second-site suppressor mutants were characterized for two of these active site mutants. The pseudorevertants have increased activity compared to the single mutant from which they were derived and, surprisingly, in both cases the increase in activity is a result of the replacement of an active site serine for proline. We performed simulations of wild-type TIM and the active site mutants with the substrate dihydroxyacetone phosphate bound both noncovalently and covalently. The noncovalent complexes were used to examine interactions important to binding while the covalent complexes are models of the transition state structure for enolization, which is the rate-determining step for the mutants. The difference between these two states, then, is related to the catalytic activity. We found various protein-substrate interactions that improved in the noncovalent mutant complexes, which correlates with the experimentally observed increase in binding affinity upon mutation. In the covalent complexes we observed improved electrostatic stabilization of the transition state upon introduction of Pro, which is also consistent with the experimental data. Our simulations reproduce the highly co-operative nature of the interactions in the active site and suggest that this approach may be useful for identifying particularly promising sites for mutation.     

Idiotypic regulation of B cell differentiation

We study the equilibrium properties of idiotypically interacting B cell clones in the case where only the differentiation of B cells is affected by idiotypic interactions. Furthermore, we assume that clones may recognize and be stimulated by self antigen in the same fashion as by antiantibodies. For idiotypically interacting pairs of non-autoreactive clones we observe three qualitatively different dynamical regimes. In the first regime, at small antibody production an antibody-free fixed point, the virgin state, is the only attractor of the system. For intermediate antibody production, a symmetric activated state replaces the virgin state as the only attractor of the system. For large antibody production, finally, the symmetric activated state gives way to two asymmetric activated states where one clone suppresses the other clone. If one or both clones in the pair are autoreactive there is no virgin state. However, we still observe the switch from an almost symmetric activated state to two asymmetric activated states. The two asymmetric activated states at high antibody production have profoundly different implications for a self antigen which is recognized by one of the clones of the pair. In the attractor characterized by high autoantibody concentration the self antigen is attacked vigorously by the immune system while in the opposite steady state the tiny amount of autoantibody hardly affects the self antigen. Accordingly, we call the first state the autoimmune state and the second the tolerant state. In the tolerant state the autoreactive clone is down-regulated by its anti-idiotype providing an efficient mechanism to prevent an autoimmune reaction. However, the antibody production required to achieve this anti-idiotypic control of autoantibodies is rather large.     

Ligand-protein interaction in biomembrane carriers. The induced transition fit of transport catalysis

Carrier-linked transport through biomembranes is treated under the view of catalysis. As in enzymes, substrate-protein interaction yields catalytic energy in overcoming the activation barrier. At variance with enzymes, catalytic energy is concentrated on structural changes of the carrier rather than on the substrate destabilization for facilitating the global protein rearrangements during transport. A transition state is invoked in which the binding site assumes the best fit to the substrate, whereas in the two ground (internal and external) states, the fit is poor. The maximum binding energy released in the transition state provides catalytic energy to enable the large carrier protein transformations associated with transport. This "induced transition fit" (ITF) of carrier catalysis provides a framework of rules, concerning specificity, unidirectional versus exchange type transport, directing inhibitors to the ground state instead of the transition state, and excluding simultaneous chemical and transport catalysis (vectorial group translocation). The possible role of external energy sources (ATP and Deltapsi) in supplementing the catalytic energy is elucidated. The analysis of the structure-function relationship based on new carrier structures may be challenged to account for the workings of the ITF.     

Role of the electrostatic interactions in pre-orientation of subunits in the formation of protein-protein complexes

Theoretical estimation of contribution of the electrostatic interactions to pre-orientation of ribonuclease subunits in process of complex formation was carried out. The subunit was considered as a multipole consisting of partial charges of all atoms of the molecule. The object of investigation was a system of two subunits with their centers of gravity fixed at some distance in vacuum. It was proposed that each subunit independently could rotate freely around its fixed center of gravity. The relative orientation states of the subunits in such system were searched at which the system has electrostatic energy minima (equilibrium states). In first approximation the equilibrium states were found using especially designed approximate method for electrostatic interaction energy calculation, which permitted to calculate and compare the energies of the system in 24(5) (approximately 8 10(6)) states with different mutual orientation of subunits. The angular coordinates of the found equilibrium states were further specified by calculation with gradient sliding method. Angular coordinates of the equilibrium states and the shapes of energy surface cuts along each coordinate angle were calculated also for the intersubunits distances diminished down to 50 angstroms. The dispersions of the angular coordinates of equilibrium states caused by heat movement (at T=300 degrees) and their changes with shortening the distance between centers of gravity of subunits were estimated. Mutual orientation of subunits in the equilibrium states of the system under consideration was found to be similar to their mutual orientations in complex. Also it was found that relaxation time of the system, caused by electrostatic interaction of subunits, after removing the system from an equilibrium state, is much less in vacuum than the mean time between their Brownian collisions at room temperature. It follows from these results that in the case of ribonuclease in vacuum the electrostatic interactions of its subunits must be strong enough to realize the effective pre-orientation of subunits during their Brownian approach from distances of the order 100 angstroms. Preliminary consideration taking into account the effect of surrounding water molecules on the electrostatic interactions of ribonuclease subunits showed that weakening of the interaction must be much less than in the case when one uses in its calculation the macroscopic dielectric permeability value equal to 80. So the results obtained for vacuum seem to be true for water solution also. More strict theoretical analysis of this problem will be carried out in the following publication.     

The excluding effects of sucrose on a protein chemical degradation pathway: methionine oxidation in subtilisin

The conformational stabilization of proteins by sucrose has been previously attributed to a preferential exclusion mechanism. The present study links this mechanism to stability against a chemical degradation pathway for subtilisin. Oxidation of a methionine residue adjacent to the active site to the sulfoxide form compromises subtilisin's enzymatic activity. In the presence of hydrogen peroxide and borate buffer, a borate-hydrogen peroxide complex binds to subtilisin's active site prior to the formation of methionine sulfoxide. Sucrose decreases the oxidation rate by limiting the accessibility of the complex to the methionine at the partially buried active site. The stabilization mechanism of sucrose is based on shifting the equilibrium of transiently expanding native conformations of subtilisin to favor the most compact states. Enzymatic parameter determination (kcat, KM) and hydrogen-deuterium exchange measurements confirm the limited conformational mobility of the enzyme in the presence of sucrose. Further support for limited mobility as the cause of oxidation inhibition by sucrose comes from the findings that neither viscosity nor possible interactions of sucrose with hydrogen peroxide, hydroxyl radicals, or borate can adequately explain the inhibition. The volume exclusion of sucrose from subtilisin is used to estimate the extent by which the native state of subtilisin must expand in solution to allow oxidation. The surface area of the oxidation-competent state is ca. 3.9% greater than that of the native state.     

On the degradation of forest ecosystems by extreme events: Statistical Model Checking of a hybrid model

In this paper, we study the vulnerability of forest ecosystems perturbed by extreme events, such as those arising from climate change. To investigate the complex interactions between the biological dynamics of the forest and the climatic activity, we construct an original hybrid model, obtained by coupling a continuous reaction–diffusion system, which describes the spatio-temporal dynamics of the forest ecosystem, with a discrete probabilistic process, which models the possible occurrences of extreme events. Properties of ecological interest are considered: invariance of the persistence equilibrium, attraction to the extinction equilibrium and emergence of degraded states. Those properties of the hybrid model are verified through an extension of the Statistical Model Checking framework. We establish the existence of a threshold above which the persistence equilibrium of the forest ecosystem is compromised and give a numerical assessment of this threshold in terms of the probability and intensity of extreme events. We also present non-trivial parameter conditions for which the forest ecosystem converges to a degraded savanna-like state.     

Tuning of Catalytic Activity by Thermoelectric Materials for Carbon Dioxide Hydrogenation

An innovative use of a thermoelectric material (BiCuSeO) as a support and promoter of catalysis for CO₂ hydrogenation is reported here. It is proposed that the capability of thermoelectric materials to shift the Fermi level and work function of a catalyst lead to an exponential increase of catalytic activity for catalyst particles deposited on its surface. Experimental results show that the CO₂ conversion and CO selectivity are increased significantly by a thermoelectric Seebeck voltage. This suggests that the thermoelectric effect can not only increase the reaction rate but also change chemical equilibrium, which leads to the change of thermodynamic equilibrium for the conversion of CO₂ in its hydrogenation reactions. It is also shown that this thermoelectric promotion of catalysis enables BiCuSeO oxide itself to have a high catalytic activity for CO₂ hydrogenation. The generic nature of the mechanism suggests the possibility that many catalytic chemical reactions can be tuned in situ to achieve much higher reaction rates, or at lower temperatures, or have better desired selectivity through changing the backside temperature of the thermoelectric support.     

The contribution of individual interchain interactions to the stabilization of the T and R states of Escherichia coli aspartate transcarbamoylase

Stabilization of the T and R allosteric states of Escherichia coli aspartate transcarbamoylase is governed by specific intra- and interchain interactions. The six interchain interactions between Glu-239 in one catalytic chain of one catalytic trimer with both Lys-164 and Tyr-165 of a different catalytic chain in the other catalytic trimer have been shown to be involved in the stabilization of the T state. In this study a series of hybrid versions of aspartate transcarbamoylase was studied to determine the minimum number of these Glu-239 interactions necessary to maintain homotropic cooperativity and the T allosteric state. Hybrids with zero, one, and two Glu-239 stabilizing interactions do not exhibit cooperativity, whereas the hybrids with three or more Glu-239 stabilizing interactions exhibit cooperativity. The hybrid enzymes with one or more of the Glu-239 stabilizing interactions also exhibit heterotropic interactions. Two hybrids with three Glu-239 stabilizing interactions, in different geometric relationships, had identical properties. From this and previous studies, it is concluded that the 239 stabilizing interactions play a critical role in the manifestation of homotropic cooperativity in aspartate transcarbamoylase by the stabilization of the T state of the enzyme. As substrate binding energy is utilized, more and more of the T state stabilizing interactions are relaxed, and finally the enzyme shifts to the R state. In the case of the Glu-239 stabilizing interactions more than three of the interactions must be broken before the enzyme shifts to the R state. The interactions between the catalytic and regulatory chains and between the two catalytic trimers of aspartate transcarbamoylase provide a global set of interlocking interactions that stabilize the T and R states of the enzyme. The substrate-induced local conformational changes observed in the structure of the isolated catalytic subunit drive the quaternary T to R transition of aspartate transcarbamoylase and functionally induced homotropic cooperativity.     

Hydrolases on silica surfaces: Coverage-activity–molecular property relationships revealed

A set of recommendations to maintain high activity of immobilized enzymes is developed based on direct observation via AFM. This helps to close knowledge gaps that often lead to poor performance of nanobiocatalysts for chemical synthesis. Molecule-level height and volume distribution analyses from high-resolution AFM images were applied to Candida antarctica Lipase B (CALB), subtilisin Carlsberg, and the Lipase from Thermomyces lanuginosus (TLL) deposited on model silica surfaces. Ensembles of flexible or “soft” enzymes appear separated when interactions with the surface are considerable at low surface coverage but form highly entangled structures of increased conformational stability at high surface coverage. By contrast, ensembles of rigid or “hard” enzymes appear to maintain stable aggregates even under strong interaction with the surface. The more rigid the enzyme the higher its tendency to remain in a densely packed state that is able to withstand surface-induced conformational transitions detrimental to catalysis. Weakening of surface-protein interactions for “soft” enzymes will prevent single-molecule immobilization, which reduces catalytic competency through structural changes. Multi-layer coverage in enzyme immobilization should generally be avoided due to mass transfer limitations.     

Analysis of gene network robustness based on saturated fixed point attractors

The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is used as an illustration of the practical application of this analytical treatment.     

Three critical hydrogen bonds determine the catalytic activity of the Diels-Alderase ribozyme

Compared to protein enzymes, our knowledge about how RNA accelerates chemical reactions is rather limited. The crystal structures of a ribozyme that catalyzes Diels–Alder reactions suggest a rich tertiary architecture responsible for catalysis. In this study, we systematically probe the relevance of crystallographically observed ground-state interactions for catalytic function using atomic mutagenesis in combination with various analytical techniques. The largest energetic contribution apparently arises from the precise shape complementarity between transition state and catalytic pocket: A single point mutant that folds correctly into the tertiary structure but lacks one H-bond that normally stabilizes the pocket is completely inactive. In the rate-limiting chemical step, the dienophile is furthermore activated by two weak H-bonds that contribute ∼7–8 kJ/mol to transition state stabilization, as indicated by the 25-fold slower reaction rates of deletion mutants. These H-bonds are also responsible for the tight binding of the Diels–Alder product by the ribozyme that causes product inhibition. For high catalytic activity, the ribozyme requires a fine-tuned balance between rigidity and flexibility that is determined by the combined action of one inter-strand H-bond and one magnesium ion. A sharp 360° turn reminiscent of the T-loop motif observed in tRNA is found to be important for catalytic function.     

Relationship between thermodynamic driving force and one-way fluxes in reversible processes

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a theorem that relates forward and reverse fluxes and free energy for any chemical process operating in a steady state. This relationship, which is a generalization of equilibrium conditions to the case of a chemical process occurring in a nonequilibrium steady state in dilute solution, provides a novel equivalent definition for chemical reaction free energy. In addition, it is shown that previously unrelated theories introduced by Ussing and Hodgkin and Huxley for transport of ions across membranes, Hill for catalytic cycle fluxes, and Crooks for entropy production in microscopically reversible systems, are united in a common framework based on this relationship.     

Kinetic and spectroscopic evidence for three actomyosin:ADP states in smooth muscle

Smooth muscle myosin II undergoes an additional movement of the regulatory domain with ADP release that is not seen with fast skeletal muscle myosin II. In this study, we have examined the interactions of smooth muscle myosin subfragment 1 with ADP to see if this additional movement corresponds to an identifiable state change. These studies indicate that for this myosin:ADP, both the catalytic site and the actin-binding site can each assume one of two conformations. Relatively loose coupling between these two binding sites leads to three discrete actin-associated ADP states. Following an initial, weakly bound state, binding of myosin:ADP to actin shifts the equilibrium toward a mixture of two states that each bind actin strongly but differ in the conformation of their catalytic sites. By contrast, fast myosins, including Dictyostelium myosin II, have reciprocal coupling between the actin- and ADP-binding sites, so that either actin or nucleotide, but not both, can be tightly bound. This uncoupling, which generates a second strongly bound actomyosin ADP state in smooth muscle, would prolong the fraction of the ATPase cycle time that this actomyosin spends in a force-generating conformation and may be central to explaining the physiologic differences between this and other myosins.     

F+ tunable laser activity and interaction of atomic halogens (F,Cl and Br) at the low coordinated surface sites of SrOAb initio and DFT calculations

The twofold potential of F+ color centers at the low coordinated surfaces of SrO for providing tunable laser activity and adsorption properties for atomic halogens (F, Cl and Br) has been investigated using ab initio electronic structure calculations. SrO clusters of variable sizes were embedded in simulated Coulomb fields that closely approximate the Madelung fields of the host surfaces and the nearest neighbor ions to F+ were allowed to relax to equilibrium. Based on Stokes shifted optical transition bands and horizontal shifts along the configuration coordinate diagrams, the F+ laser activity was found to decrease as the coordination number of the surface ions decreases from 5 (flat) to 4 (edge) to 3 (corner). An attempt has been made to explain this result in terms of Madelung potentials and optical-optical conversion efficiencies. All relaxed excited states are deep below the conduction bands of the perfect ground states, implying that F+ is a laser-suitable defect. The most laser active flat surface is the least probable for relaxed excited state orientational destruction of F+. The excited state at the edge has the highest energy, implying exciton (energy) transfer to the flat and edge sites. F+ relaxation and defect-formation energies increase with increasing surface coordination number. The Glasner-Tompkins relation between the fundamental optical absorption of F+ in solids and the fundamental absorption of the host crystals can be generalized to include the low coordinated surfaces of SrO. The F+ color center changes the nature of halogen-surface interaction (adsorption energies) from physical adsorption to chemical adsorption. The halogen-surface interactions increase with increasing electronegativity of the halogen. The calculated adsorption energies can be explained in terms of surface electrostatic potentials, and the covalent spin pairing mechanism plays a dominant role in determining adsorbate-substrate interactions.     

A novel mechanism of V-type zinc inhibition of glutamate dehydrogenase results from disruption of subunit interactions necessary for efficient catalysis

Bovine glutamate dehydrogenase is potently inhibited by zinc and the major impact is on V(max) suggesting a V-type effect on catalysis or product release. Zinc inhibition decreases as glutamate concentrations decrease suggesting a role for subunit interactions. With the monocarboxylic amino acid norvaline, which gives no evidence of subunit interactions, zinc does not inhibit. Zinc significantly decreases the size of the pre-steady state burst in the reaction but does not affect NADPH binding in the enzyme-NADPH-glutamate complex that governs the steady state turnover, again suggesting that zinc disrupts subunit interactions required for catalytic competence. While differential scanning calorimetry suggests zinc binds and induces a slightly conformationally more rigid state of the protein, limited proteolysis indicates that regions in the vicinity of the antennae regions and the trimer-trimer interface become more flexible. The structures of glutamate dehydrogenase bound with zinc and europium show that zinc binds between the three dimers of subunits in the hexamer, a region shown to bind novel inhibitors that block catalytic turnover, which is consistent with the above findings. In contrast, europium binds to the base of the antenna region and appears to abrogate the inhibitory effect of zinc. Structures of various states of the enzyme have shown that both regions are heavily involved in the conformational changes associated with catalytic turnover. These results suggest that the V-type inhibition produced with glutamate as the substrate results from disruption of subunit interactions necessary for efficient catalysis rather than by a direct effect on the active site conformation.     

Detection of site-specific binding and co-binding of ligands to macromolecules using 19F NMR

Study of ligand-macromolecular interactions by 19F nuclear magnetic resonance (NMR) spectroscopy affords many opportunities for obtaining molecular biochemical and pharmaceutical information. This is due to the absence of a background fluorine signal, as well as the relatively high sensitivity of 19F NMR. Use of fluorine-labeled ligands enables one to probe not only binding and co-binding phenomena to macromolecules, but also can provide data on binding constants, stoichiometries, kinetics, and conformational properties of these complexes. Under conditions of slow exchange and macromolecule-induced chemical shifts, multiple 19F NMR resonances can be observed for free and bound ligands. These shifted resonances are a direct correlate of the concentration of ligand bound in a specific state rather than the global concentrations of bound or free ligand which are usually determined using other techniques such as absorption spectroscopy or equilibrium dialysis. Examples of these interactions are demonstrated both from the literature and from interactions of 5-fluorotryptophan, 5-fluorosalicylic acid, flurbiprofen, and sulindac sulfide with human serum albumin. Other applications of 19F NMR to study of these interactions in vivo, as well for receptor binding and metabolic tracing of fluorinated drugs and proteins are discussed.