Expansion of the "Sodium World" through Evolutionary Time and Taxonomic Space.

In 1986, Vladimir Skulachev and his colleagues coined the term "Sodium World" for the group of diverse organisms with sodium (Na)-based bioenergetics. Albeit only few such organisms had been discovered by that time, the authors insightfully noted that "the great taxonomic variety of organisms employing the Na-cycle points to the ubiquitous distribution of this novel type of membrane-linked energy transductions". Here we used tools of bioinformatics to follow expansion of the Sodium World through the evolutionary time and taxonomic space. We searched for those membrane protein families in prokaryotic genomes that correlate with the use of the Na-potential for ATP synthesis by different organisms. In addition to the known Na-translocators, we found a plethora of uncharacterized protein families; most of them show no homology with studied proteins. In addition, we traced the presence of Na-based energetics in many novel archaeal and bacterial clades, which were recently identified by metagenomic techniques. The data obtained support the view that the Na-based energetics preceded the proton-dependent energetics in evolution and prevailed during the first two billion years of the Earth history before the oxygenation of atmosphere. Hence, the full capacity of Na-based energetics in prokaryotes remains largely unexplored. The Sodium World expanded owing to the acquisition of new functions by Na-translocating systems. Specifically, most classes of G-protein-coupled receptors (GPCRs), which are targeted by almost half of the known drugs, appear to evolve from the Na-translocating microbial rhodopsins. Thereby the GPCRs of class A, with 700 representatives in human genome, retained the Na-binding site in the center of the transmembrane heptahelical bundle together with the capacity of Na-translocation. Mathematical modeling showed that the class A GPCRs could use the energy of transmembrane Na-potential for increasing both their sensitivity and selectivity. Thus, GPCRs, the largest protein family coded by human genome, stem from the Sodium World, which encourages exploration of other Na-dependent enzymes of eukaryotes.

Electron Transfer through the Acceptor Side of Photosystem I: Interaction with Exogenous Acceptors and Molecular Oxygen.

This review considers the state-of-the-art on mechanisms and alternative pathways of electron transfer in photosynthetic electron transport chains of chloroplasts and cyanobacteria. The mechanisms of electron transport control between photosystems (PS) I and II and the Calvin-Benson cycle are considered. The redistribution of electron fluxes between the noncyclic, cyclic, and pseudocyclic pathways plays an important role in the regulation of photosynthesis. Mathematical modeling of light-induced electron transport processes is considered. Particular attention is given to the electron transfer reactions on the acceptor side of PS I and to interactions of PS I with exogenous acceptors, including molecular oxygen. A kinetic model of PS I and its interaction with exogenous electron acceptors has been developed. This model is based on experimental kinetics of charge recombination in isolated PS I. Kinetic and thermodynamic parameters of the electron transfer reactions in PS I are scrutinized. The free energies of electron transfer between quinone acceptors A1A/A1B in the symmetric redox cofactor branches of PS I and iron-sulfur clusters FX, FA, and FB have been estimated. The second-order rate constants of electron transfer from PS I to external acceptors have been determined. The data suggest that byproduct formation of superoxide radical in PS I due to the reduction of molecular oxygen in the A1 site (Mehler reaction) can exceed 0.3% of the total electron flux in PS I.

Mechanism of primary and secondary ion-radical pair formation in photosystem I complexes.

The mechanisms of the ultrafast charge separation in reaction centers of photosystem I (PS I) complexes are discussed. A kinetic model of the primary reactions in PS I complexes is presented. The model takes into account previously calculated values of redox potentials of cofactors, reorganization energies of the primary P700(+)A0(-) and secondary P700(+)A1(-) ion-radical pairs formation, and the possibility of electron transfer via both symmetric branches A and B of redox-cofactors. The model assumes that the primary electron acceptor A0 in PS I is represented by a dimer of chlorophyll molecules Chl2A/Chl3A and Chl2B/Chl3B in branches A and B of the cofactors. The characteristic times of formation of P700(+)A0(-) and P700(+)A1(-) calculated on the basis of the model are close to the experimental values obtained by pump-probe femtosecond absorption spectroscopy. It is demonstrated that a small difference in the values of redox potentials between the primary electron acceptors A0A and A0B in branches A and B leads to asymmetry of the electron transfer in a ratio of 70 : 30 in favor of branch A. The secondary charge separation is thermodynamically irreversible in the submicrosecond range and is accompanied by additional increase in asymmetry between the branches of cofactors of PS I.

Prevention of peroxidation of cardiolipin liposomes by quinol-based antioxidants.

In mammalian mitochondria, cardiolipin molecules are the primary targets of oxidation by reactive oxygen species. The interaction of oxidized cardiolipin molecules with the constituents of the apoptotic cascade may lead to cell death. In the present study, we compared the effects of quinol-containing synthetic and natural amphiphilic antioxidants on cardiolipin peroxidation in a model system (liposomes of bovine cardiolipin). We found that both natural ubiquinol and synthetic antioxidants, even being introduced in micro- and submicromolar concentrations, fully protected the liposomal cardiolipin from peroxidation. The duration of their action, however, varied; it increased with the presence of either methoxy groups of ubiquinol or additional reduced redox groups (in the cases of rhodamine and berberine derivates). The concentration of ubiquinol in the mitochondrial membrane substantially exceeds the concentrations of antioxidants we used and would seem to fully prevent peroxidation of membrane cardiolipin. In fact, this does not happen: cardiolipin in mitochondria is oxidized, and this process can be blocked by amphiphilic cationic antioxidants (Y. N. Antonenko et al. (2008) Biochemistry (Moscow), 73, 1273-1287). We suppose that a fraction of mitochondrial cardiolipin could not be protected by natural ubiquinol; in vivo, peroxidation most likely threatens those cardiolipin molecules that, being bound within complexes of membrane proteins, are inaccessible to the bulky hydrophobic ubiquinol molecules diffusing in the lipid bilayer of the inner mitochondrial membrane. The ability to protect these occluded cardiolipin molecules from peroxidation may explain the beneficial therapeutic action of cationic antioxidants, which accumulate electrophoretically within mitochondria under the action of membrane potential.

Exciton interactions of chlorophyll tetramer in water-soluble chlorophyll-binding protein BoWSCP.

The exciton interaction of four chlorophyll a (Chl a) molecules in a symmetrical tetrameric complex of the water-soluble chlorophyll-binding protein BoWSCP was analyzed in the pH range of 3-11. Exciton splitting ΔE = 232 ± 2 cm-1 of the Qy band of Chl a into two subcomponents with relative intensities of 78.1 ± 0.7 % and 21.9 ± 0.7 % was determined by a joint decomposition of the absorption and circular dichroism spectra into Gaussian functions. The exciton coupling parameters were calculated based on the BoWSCP atomic structure in three approximations: the point dipole model, the distributed atomic monopoles, and direct ab initio calculations in the TDDFT/PCM approximation. The Coulomb interactions of monomers were calculated within the continuum model using three values of optical permittivity. The models based on the properties of free Chl a in solution suffer from significant errors both in estimating the absolute value of the exciton interaction and in the relative intensity of exciton transitions. Calculations within the TDDFT/PCM approximation reproduce the experimentally determined parameters of the exciton splitting and the relative intensities of the exciton bands. The following factors of pigment-protein and pigment-pigment interactions were examined: deviation of the macrocycle geometry from the planar conformation of free Chl; the formation of hydrogen bonds between the macrocycle and water molecules; the overlap of wave functions of monomers at close distances. The most significant factor is the geometrical deformation of the porphyrin macrocycle, which leads to an increase in the dipole moment of Chl monomer from 5.5 to 6.9 D and to a rotation of the dipole moment by 15° towards the cyclopentane ring. The contributions of resonant charge-transfer states to the wave functions of the Chl dimer were determined and the transition dipole moments of the symmetric and antisymmetric charge-transfer states were estimated.

Interaction of tetraphenylphosphonium and dodecyltriphenylphosphonium with lipid membranes and mitochondria.

The permeability of a planar lipid membrane (composed of diphytanoylphosphatidylcholine) for tetraphenylphosphonium (TPP) was investigated. The observed level of the diffusion potential generated as a function of the TPP concentration gradient differed from the theoretically expected value, possibly due to proton leakage of the membrane mediated by the traces of fatty acids in the phospholipid forming the membrane. Using the molecular dynamics approach to study movement of TPP and dodecyltriphenylphosphonium (C(12)TPP) with different affinity to the lipid bilayer through a bilayer lipid membrane, it was found that C(12)TPP has a greater affinity to the membrane surface than TPP. However, the two cations have the same activation energy for transmembrane transfer. Interaction of TPP and C(12)TPP with tightly-coupled mitochondria from the yeast Yarrowia lipolytica was also investigated. At low, micromolar concentrations, both cations are "relatively weak, mild uncouplers", do not shunt electron transfer along the respiratory chain, do not disturb (damage) the inner mitochondrial membrane, and profoundly promote the uncoupling effect of fatty acids. At higher concentrations they inhibit respiration in state 3, and at much higher concentrations they induce swelling of mitochondria, possibly due to their detergent action.

Proton transfer in Azotobacter vinelandii ferredoxin I: entatic Lys84 operates as elastic counterbalance for the proton-carrying Asp15.

In ferredoxin I from Azotobacter vinelandii, the reduction of a [3Fe-4S] iron-sulphur cluster is coupled with the protonation of the mu2S sulphur atom that is approx. 6 A away from the protein boundary. The recent study of the site-specific mutants of ferredoxin I led to the conclusion that a particular surface aspartic residue (Asp15) is solely responsible for the proton transfer to the mu2S atom by 'rapid penetrative excursions' (K. Chen, J. Hirst, R. Camba, C.A. Bonagura, C.D. Stout, B.K. Burgess, F.A. Armstrong, Nature 405 (2000) 814-817). In the same paper it has been reported that the replacement of Asp15 by glutamate led to the blockage of the enzyme, although glutamate, with its longer and more flexible side chain, should apparently do even better as a mobile proton carrier than aspartate. We tackled this puzzling incompetence of Glu15 by molecular dynamics simulations. It was revealed that the conformational alterations of Asp15 are energetically balanced by the straining of the nearby Lys84 side chain in wild-type ferredoxin I but not in the Asp15-->Glu mutant. Lys84 in ferredoxin I of A. vinelandii seems to represent the first case where the strained (entatic) conformation of a particular amino acid side chain could be directly identified in the ground state of an enzyme and assigned to a distinct mechanism of energy balance during the catalytic transition.

Contraction transitions of F1-F0 ATPase during catalytic turnover.

Strong acoustic pressure was applied to submitochondrial particles (SMP) from bovine heart in order to drive ATP synthesis by F1-F0 complex for the account of sound waves. We observed a net ATP production at two narrow frequency ranges, about 170 Hz and about 340 Hz, that corresponds to the resonance oscillations of experimental cuvette when the acoustic pressure had a magnitude of 100 kPa. The results can be explained quantitatively by contractive conformational changes of F1-F0 complex during catalytic turnover. Negative staining electron microscopy of SMP preparations was used to visualize the ADP(Mg2+)-induced conformational changes of F1-F0 complex. In the particles with high ATPase activity in the presence of phosphate the factors F1 and F0 formed a congregated domain plunged into the membrane without any observable stalk in between. The presence of ADP(Mg2+) caused a structural rearrangement of F1-F0 to the essentially different conformation: the domains F1 and F0 were dislodged distinctly from each other and connected by a long thin stalk. The latter conformation resembled well the usual bipartite profile of ATPase. The data indicate that besides rotation, the catalytic turnover of ATP synthase is also accompanied by stretch transitions of F1-F0 complex.

Coupling of proton flow to ATP synthesis in Rhodobacter capsulatus: F(0)F(1)-ATP synthase is absent from about half of chromatophores.

F(0)F(1)-ATP synthase (H(+)-ATP synthase, F(0)F(1)) utilizes the transmembrane protonmotive force to catalyze the formation of ATP from ADP and inorganic phosphate (P(i)). Structurally the enzyme consists of a membrane-embedded proton-translocating F(0) portion and a protruding hydrophilic F(1) part that catalyzes the synthesis of ATP. In photosynthetic purple bacteria a single turnover of the photosynthetic reaction centers (driven by a short saturating flash of light) generates protonmotive force that is sufficiently large to drive ATP synthesis. Using isolated chromatophore vesicles of Rhodobacter capsulatus, we monitored the flash induced ATP synthesis (by chemoluminescence of luciferin/luciferase) in parallel to the transmembrane charge transfer through F(0)F(1) (by following the decay of electrochromic bandshifts of intrinsic carotenoids). With the help of specific inhibitors of F(1) (efrapeptin) and of F(0) (venturicidin), we decomposed the kinetics of the total proton flow through F(0)F(1) into (i) those coupled to the ATP synthesis and (ii) the de-coupled proton escape through F(0). Taking the coupled proton flow, we calculated the H(+)/ATP ratio; it was found to be 3.3+/-0.6 at a large driving force (after one saturating flash of light) but to increase up to 5.1+/-0.9 at a smaller driving force (after a half-saturating flash). From the results obtained, we conclude that our routine chromatophore preparations contained three subsets of chromatophore vesicles. Chromatophores with coupled F(0)F(1) dominated in fresh material. Freezing/thawing or pre-illumination in the absence of ADP and P(i) led to an increase in the fraction of chromatophores with at least one de-coupled F(0)(F(1)). The disclosed fraction of chromatophores that lacked proton-conducting F(0)(F(1)) (approx. 40% of the total amount) remained constant upon these treatments.

Reduction and protonation of the secondary quinone acceptor of Rhodobacter sphaeroides photosynthetic reaction center: kinetic model based on a comparison of wild-type chromatophores with mutants carrying Arg-->Ile substitution at sites 207 and 217 in the L-subunit.

After the light-induced charge separation in the photosynthetic reaction center (RC) of Rhodobacter sphaeroides, the electron reaches, via the tightly bound ubiquinone QA, the loosely bound ubiquinone Q(B) After two subsequent flashes of light, Q(B) is reduced to ubiquinol Q(B)H2, with a semiquinone anion Q-(B) formed as an intermediate after the first flash. We studied Q(B)H2 formation in chromatophores from Rb. sphaeroides mutants that carried Arg-->Ile substitution at sites 207 and 217 in the L-subunit. While Arg-L207 is 17 A away from Q(B), Arg-L217 is closer (9 A) and contacts the Q(B)-binding pocket. From the pH dependence of the charge recombination in the RC after the first flash, we estimated deltaG(AB), the free energy difference between the Q-(A)Q(B) and Q(A)Q-(B) states, and pK212, the apparent pK of Glu-L212, a residue that is only 4 A away from Q(B). As expected, the replacement of positively charged arginines by neutral isoleucines destabilized the Q-(B) state in the L217RI mutant to a larger extent than in the L207RI one. Also as expected, pK212 increased by approximately 0.4 pH units in the L207RI mutant. The value of pK212 in the L217RI mutant decreased by 0.3 pH units, contrary to expectations. The rate of the Q-(A)Q-(B)-->Q(A)Q(B)H2 transition upon the second flash, as monitored by electrometry via the accompanying changes in the membrane potential, was two times faster in the L207RI mutant than in the wild-type, but remained essentially unchanged in the L217RI mutant. To rationalize these findings, we developed and analyzed a kinetic model of the Q-(A)Q-(B)-->Q(A)Q(B)H2 transition. The model properly described the available experimental data and provided a set of quantitative kinetic and thermodynamic parameters of the Q(B) turnover. The non-electrostatic, 'chemical' affinity of the QB site to protons proved to be as important for the attracting protons from the bulk, as the appropriate electrostatic potential. The mutation-caused changes in the chemical proton affinity could be estimated from the difference between the experimentally established pK2J2 shifts and the expected changes in the electrostatic potential at Glu-L212, calculable from the X-ray structure of the RC. Based on functional studies, structural data and kinetic modeling, we suggest a mechanistic scheme of the QB turnover. The detachment of the formed ubiquinol from its proximal position next to Glu-L212 is considered as the rate-limiting step of the reaction cycle.

Transient accumulation of elastic energy in proton translocating ATP synthase.

ATP synthase is conceived as a rotatory engine with two reversible drives, the proton-transporting membrane portion, F0, and the catalytic peripheral portion, F1. They are mounted on a central shaft (subunit gamma) and held together by an eccentric bearing. It is established that the hydrolysis of three molecules of ATP in F1 drives the shaft over a full circle in three steps of 120 degrees each. Proton flow through F0 probably generates a 12-stepped rotation of the shaft so that four proton-translocating steps of 30 degrees each drive the synthesis of one molecule of ATP. We addressed the elasticity of the transmission between F0 and F1 in a model where the four smaller steps in F0 load a torsional spring which is only released under liberation of ATP from F1. The kinetic model of an elastic ATP synthase described a wealth of published data on the synthesis/hydrolysis of ATP by F0F1 and on proton conduction by F0 as function of the pH and the protonmotive force. The pK values of the proton-carrying group interacting with the acidic and basic sides of the membrane were estimated as 5.3-6.4 and 8.0-8.3, respectively.

Flash-induced electrogenic reactions in the SA(L223) reaction center mutant in Rhodobacter sphaeroides chromatophores.

The charge transfer events in the SA(L223) reaction center mutant Rhodobacter sphaeroides chromatophores were investigated by direct electrometry. Besides the primary charge separation, the small stigmatellin-sensitive electrogenic reaction due to the electron transfer from the primary to the secondary quinone acceptor in the reaction center complex was observed after the first flash. The second flash-induced electrogenic phase of the secondary quinone protonation and subsequent electrogenic reactions of the cytochrome bc1 complex were much slower than those in chromatophores of the wild type. It is suggested that replacement of Ser-L223 by Ala impairs both specific proton-conducting pathways leading to the secondary quinone QB.

ATP-synthase of Rhodobacter capsulatus: coupling of proton flow through F0 to reactions in F1 under the ATP synthesis and slip conditions.

A stepwise increasing membrane potential was generated in chromatophores of the phototrophic bacterium Rhodobacter capsulatus by illumination with short flashes of light. Proton transfer through ATP-synthase (measured by electrochromic carotenoid bandshift and by pH-indicators) and ATP release (measured by luminescence of luciferin-luciferase) were monitored. The ratio between the amount of protons translocated by F0F1 and the ATP yield decreased with the flash number from an apparent value of 13 after the first flash to about 5 when averaged over three flashes. In the absence of ADP, protons slipped through F0F1. The proton transfer through F0F1 after the first flash contained two kinetic components, of about 6 ms and 20 ms both under the ATP synthesis conditions and under slip. The slower component of proton transfer was substantially suppressed in the absence of ADP. We attribute our observations to the mechanism of energy storage in the ATP-synthase needed to couple the transfer of four protons with the synthesis of one molecule of ATP. Most probably, the transfer of initial protons of each tetrad creates a strain in the enzyme that slows the translocation of the following protons.

Temperature dependence of the electrogenic reaction in the QB site of the Rhodobacter sphaeroides photosynthetic reaction center: the QA-QB --> QAQB- transition.

The temperature dependencies for the kinetics and relative amplitudes of electrogenic reaction(s) coupled with the first reduction of the secondary quinone acceptor QB were measured with dark-adapted chromatophores of Rhodobacter sphaeroides. The kinetics, while acceptably fitted by a single exponent at room temperature, clearly split into two components below 15 degrees C (rise times, 25 micros and 300 micros at pH 7.0 and 10 degrees C) with the slow phase ousting the fast one at pH > 9.0. The activation energies of the fast and slow phases were estimated at pH 7.0 as < 10 kJ/mol and 60-70 kJ/mol, respectively. To explain the kinetic heterogeneity of the QB --> QB- transition, we suggest two possible conformations for the neutral oxidized ubiquinone at the QB site: one with a hydrogen bond between the side chain carboxyl of Glu-L212 and the methoxy oxygen at C3 of the QB ring (QB-H-Glu centers) and the other one, without this bond (QB:Glu- centers). The fast phase is attributed to QA- QB-H-Glu --> QA QB-H-Glu transition, whereas the slow one to the QA- QB:Glu- --> QA- QB-H-Glu --> QA QB(-)-H-Glu transition.

Inter-subunit rotation and elastic power transmission in F0F1-ATPase.

ATP synthase (F-ATPase) produces ATP at the expense of ion-motive force or vice versa. It is composed from two motor/generators, the ATPase (F1) and the ion translocator (F0), which both are rotary steppers. They are mechanically coupled by 360 degrees rotary motion of subunits against each other. The rotor, subunits gamma(epsilon)C10-14, moves against the stator, (alphabeta)3delta(ab2). The enzyme copes with symmetry mismatch (C3 versus C10-14) between its two motors, and it operates robustly in chimeric constructs or with drastically modified subunits. We scrutinized whether an elastic power transmission accounts for these properties. We used the curvature of fluorescent actin filaments, attached to the rotating c ring, as a spring balance (flexural rigidity of 8.10(-26) N x m2) to gauge the angular profile of the output torque at F0 during ATP hydrolysis by F1. The large average output torque (56 pN nm) proved the absence of any slip. Angular variations of the torque were small, so that the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the three-fold stepping and high activation barrier (>40 kJ/mol) of the driving motor (F1) itself, the rather constant output torque seen by F0 implied a soft elastic power transmission between F1 and F0. It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate under load of the two counteracting and stepping motors/generators.

[Kinetic model of the action of oligomeric enzymes using phosphofructokinase as an example. II. General formulation of the hierarchical model]. / Modelirovanie kinetiki deistviia oligomernykh fermentov na primere fosfofruktokinazy. II. Obshchaia formulirovka ierarkhicheskoi modeli.

A general approach is suggested to describe the steady-state kinetics of the oligomeric enzymes on the base of the generalized statistical Ising model. Detailed analysis is given for the case of a oligomeric enzyme with a hierarchical supramolecular organization. A protomer of this enzyme composed of several equivalent subunits represents the quarternary level of structure. In their turn the finite or infinite number of protomers is associated into a oligomer thus creating a new "quinternary" level of the enzyme organization. The model accounts for the ligand-induced homotrophic cooperative interactions: firstly, between the neighbouring protomers and secondly, between the subunits of the same protomer. The influence of protomer conformation on the subunit state and the cooperativity induction caused by two-ligand binding are also taken into consideration. Monod-Wyman-Changeux's and Koshland's models are shown to be special limit cases of the suggested general theory.

[Simulation of the kinetics of oligomeric enzymes as illustrated by phosphofructokinase. I. General analysis of experimental data and the choice of an adequate model]. / Modelirovanie kinetiki deistviia oligomernykh fermentov na primere fosfofruktokinazy. I. Obshchii analiz éksperimental'nykh dannykh i vybor adekvatnoi modeli.

On the example of complex allosteric kinetics of phosphofructokinase from human erythrocytes we analysed the applicability of the Monod-Wyman-Changeux and association--dissociation models to the unified description of the kinetics of the oligomeric enzymes. It was shown that these models were not sufficient to construct an adequate phosphofructokinase model. We propose to use the unidimensional Izing model for this purpose. It was analysed in the monosubstrate case for the high enzyme concentration range. The ways to generalize the Izing model as the basis of the universal model for the oligomeric enzyme's kinetics were analysed.

[Modeling of the activity kinetics of oligomer enzymes using phosphofructokinase as an example. III. A polyligand model]. / Modelirovanie kinetiki deistviia oligomernykh fermentov na primere fosfofruktokinazy. III. Rassmotrenie mnogoligandnykh modelei.

A general statistical-thermodynamical theory of the oligomeric enzymes was applied for description of the complex regulatory properties of human erythrocyte phosphofructokinase (PFC, EC 2.7.1.11), experimental data were obtained by Wenzel et al. (Eur. J. Biochem. 1976. V. 61. P. 181). Simple two-ligand and hierarchical three-ligand models for polymeric enzymes were analysed. In hierarchical model structural PFK unit (protomer) was treated as tetramer so both interactions between subunits inside the protomer and between protomers themselves were considered. It was shown that except active center of fructoso-6-phosphate (F6P) binding and two or more inhibiting centers of ATP binding. F6P binding by active centers of different subunits inside the protomer caused negative cooperative interactions but F6P binding by activating centers of the same subunits causes positive interactions. The F6P dissociation constant for activating centers is essentially higher than for active centers. ATP binding by inhibiting centers of the protomer causes very high positive cooperative interactions between neighbouring protomers leading to distinguish additional "quaternary" level of the enzyme structure. Numerical non-linear identification for the parameters of these two models was given and five experimental curves were quantitatively described in the wide range of ligand concentrations (0.01-15 mM F6P and 1-5 mM ATP) for high enzyme concentration (greater than 0.5 mkg/ml).

[The Ising model for the description of allosteric kinetics of polymeric enzymes]. / Ispol'zovanie modeli Izinga dlia opisaniia allostericheskoi kinetiki polimernykh fermentov.

A new class of models for the description of the complex allosteric kinetics of oligomeric enzymes has been offered. Its regulation can be realized at the expense of two types of the cooperative interactions. First, the cooperative interaction of the neighboring enzyme protomers is examined on the basis of one-dimensional Ising model; second, subunits that compose the protomer are described by analogy with the model of indirect cooperation of Monod--Wyman--Changeux. The methods of statistical physics open approach to the unification of the models of allosteric regulation in the modern biochemistry. A detailed analysis of the one-ligand model of the polymeric enzymes was performed and possible ways of its generalization were shown.

[Description of the kinetics of allosteric polymeric enzymes with 2 ligands based on the generalized Ising model]. / Opisanie kinetiki allostericheskikh polimernykh fermentov s uchastiem dvukh ligandov na osnove obobshchennoi modeli Izinga.

The two-ligand model for allosteric regulation of complex polymeric enzymes is offered. Two types of cooperative interactions are observed--the cooperative transformations inside the promoter and interactions of promoters themselves--along with the direct interaction of two ligands inside each subunit. The solution of the model is given and its kinetic properties are discussed.