Effects of deuterium oxide on elementary steps in the ATPase reaction. Evidence for the similarity of key intermediates in contractile and transport ATPase.

The effects of D2O on the elementary steps in the contractile and transport ATPase [EC 3.6.1.3] reactions were studied, and the following results were obtained: 1. The rate of H-meromyosin ATPase in the steady state decreased in D2O to 60% of that in H2O. Deuterium oxide did not affect the size or rate of the initial burst of Pi liberation, i.e. the amount or rate of formation of the reactive myosin-phosphate-ADP complex, MADPP. Moreover, neither the rate of change in the fluorescence spectrum of H-meromyosin induced by ATP (the rate of formation of the second enzyme-ATP complex, M2ATP) nor the rate constant of decomposition of MADPP into M degrees + ADP + Pi was affected by D2O. However, the equilibrium constant of the step M2ATP in equilibrium MADPP decreased in D2O to about 1/2 the value in H2O. 2. In the case of the Na+-K+-dependent ATPase reactin, neither the rate constant of formation of the second enzyme-ATP complex, E2ATP, nor that of decomposition of a phosphorylated intermediate, EADP approximately P, was affected by D2O. However, the equilibrium constant of the step E2ATP in equilibrium EADP approximately P decreased in D2O to about 1/2.5-1/4 of the value in H2O. These results suggest a similarity between the modes of binding of phosphate in MADPP in the myosin ATPase reaction and in EADP approximatley P in the Na+-K+-dependent ATPase reaction.     

Reaction intermediates of H-meromyosin-ATPase and ultraviolet difference spectrum of H-meromyosin induced by ATP.

UV Difference spectra of H-meromyosin (HMM) during the steady state of the myosin-ATPase reaction [EC 3.6.1.3] were measured in 1.5 and 0.05M KC1 in the presence of 5mM MgC1(2) and 20mM Tris-HC1 at pH 8.0 and 24 degrees, using pyruvate kinase [EC 2.7.1.40] and phosphoenolpyruvate to regenerate ATP. It was found that the difference spectrum and its dependence on ATP concentration were the same in 1.5M KC1 as in 0.05M KC1. On the bases of these and other results, the nature of the intermediates of HMM ATPase in the steady-state reaction of HMM ATPase was discussed.     

Reaction intermediates formed by myofibrils during the ATPase reaction under relaxed conditions

The species and amounts of intermediates formed by myosin in myofibrils during the ATPase reaction under relaxed conditions were examined. The amount of total nucleotides (ADP + ATP) bound to myofibrils, determined by a centrifugation method or a rapid filtration method, was 0.86 mol/mol myosin head. The amount of bound ADP, determined as the ADP remaining in the mixture after free ADP had been rapidly converted into ATP by an ATP-regenerating system, was found to be 0.67 mol/mol myosin head. We examined the time courses of free-Pi and total-Pi (TCA-Pi) formation after adding ATP to the myofibrils. The amount of Pi bound to myofibrils, calculated by subtracting the burst size of free Pi (0.23 mol/mol myosin head) from that of TCA-Pi (0.60 mol/mol myosin head), was found to be 0.37 mol/mol myosin head. The amount of tightly bound ATP determined by an ATP-quenching method was very low (0.03 mol/mol myosin head). If there is no myosin-phosphate complex, then the amounts of the myosin-phosphate-ADP complex, MADPP, and the tightly bound myosin-ATP complex, M*ATP, are 0.37 and 0.03 mol/mol myosin head, respectively, whereas the amounts of myosin-ADP and loosely bound myosin-ATP complexes are 0.30 and 0.16 mol/mol myosin head, respectively. Thus, half of the myosin heads forms MADPP or M*ATP, and the equilibrium between MADPP and M*ATP shifts to the MADPP side. These results agree with those obtained for myosin in solution (Inoue, A., Takenaka, H., Arata, T., & Tonomura, Y. (1979) Adv. Biophys. 13, 1-194). Therefore, in relaxed myofibrils the active site of myosin does not interact with actin.     

Rotational dynamics of actin-bound intermediates in the myosin ATPase cycle.

We have used saturation-transfer electron paramagnetic resonance (ST-EPR) to detect the microsecond rotational motions of spin-labeled myosin subfragment one (MSL-S1) bound to actin in the presence of the ATP analogues AMPPNP (5'-adenylylimido diphosphate) and ATP gamma S [adenosine 5'-O-(3-thiotriphosphate)], which are believed to trap myosin in strongly and weakly bound intermediate states of the actomyosin ATPase cycle, respectively. Sedimentation binding measurements were used to determine the fraction of myosin heads bound to actin under ST-EPR conditions and the fraction of heads containing bound nucleotide. ST-EPR spectra were then corrected to obtain the spectrum corresponding to the ternary complex (actin.MSL-S1.nucleotide). The ST-EPR spectrum of MSL-S1.AMPPNP bound to actin is identical to that obtained in the absence of nucleotide (rigor complex), indicating no rotational motion of MSL-S1 relative to actin on the microsecond time scale. However, MSL-S1-ATP gamma S bound to actin is rotationally mobile, with an effective rotational correlation time (tau r) of 17 +/- 2 microseconds. This motion is similar to that observed previously for actin-bound MSL-S1 during the steady-state hydrolysis of ATP [Berger et al. (1989) Proc. Natl. Acad. Sci. U.S.A. 86, 8753-8757]. We conclude that, in solution, the weakly bound actin-attached states of the myosin ATPase cycle undergo microsecond rotational motions, while the strongly bound intermediates do not, and that these motions are likely to be involved in the molecular mechanism of muscle contraction.     

Structural changes during the formation of early intermediates in the bacteriorhodopsin photocycle

Early intermediates of bacteriorhodopsin's photocycle were modeled by means of ab initio quantum mechanical/molecular mechanical and molecular dynamics simulations. The photoisomerization of the retinal chromophore and the formation of photoproducts corresponding to the early intermediates were simulated by molecular dynamics simulations. By means of the quantum mechanical/molecular mechanical method, the resulting structures were refined and the respective excitation energies were calculated. Two sequential intermediates were found with absorption maxima that exhibit red shifts from the resting state. The intermediates were therefore assigned to the K and KL states. In K, the conformation of the retinal chromophore is strongly deformed, and the N--H bond of the Schiff base points almost perpendicular to the membrane normal toward Asp-212. The strongly deformed conformation of the chromophore and weakened interaction of the Schiff base with the surrounding polar groups are the means by which the absorbed energy is stored. During the K-to-KL transition, the chromophore undergoes further conformational changes that result in the formation of a hydrogen bond between the N--H group of the Schiff base and Thr-89 as well as other rearrangements of the hydrogen-bond network in the vicinity of the Schiff base, which are suggested to play a key role in the proton transfer process in the later phase of the photocycle.     

Exploiting reaction intermediates of the ATPase reaction to elucidate the mechanism of transport by P-glycoprotein (ABCB1)

The transport cycle of ABC transporters in general and P-glycoprotein in particular has been extensively studied, but the molecular mechanism remains controversial. We identify stable reaction intermediates in the progression of the P-glycoprotein-mediated ATPase reaction equivalent to the enzyme-substrate (E.S, P-glycoprotein.ATP) and enzyme-product (E.P, P-glycoprotein.ADP.P(i)) reaction intermediates. These have been characterized using the photoaffinity analog 8-azido-[alpha-32P]ATP as well as under equilibrium conditions using [alpha-32P]ATP, in which a cross-linking step is not involved. Similar results were obtained when 8-azido-[alpha-32P]ATP or [alpha-32P]ATP was used. The reaction intermediates were characterized based on their kinetic properties and the nature (triphosphate/diphosphate) of the trapped nucleotide. Using this defined framework and the Walker B E556Q/E1201Q mutant that traps nucleotide in the absence of vanadate or beryllium fluoride, the high to low affinity switch in the transport substrate binding site can be attributed to the formation of the E.S reaction intermediate of the ATPase reaction. Importantly, the posthydrolysis E.P state continues to have low affinity for substrate, suggesting that conformational changes that form the E.S complex are coupled to the conformational change at the transport substrate site to do mechanical work. Thus, the formation of E.S reaction intermediate during a single turnover of the catalytic cycle appears to provide the initial power stroke for movement of drug substrate from inner leaflet to outer leaflet of lipid bilayer. This novel approach applies transition state theory to elucidate the mechanism of P-glycoprotein and other ABC transporters and has wider applications in testing cause-effect hypotheses in coupled systems.     

Calculations of free energy profiles for the staphylococcal nuclease catalyzed reaction

Calculations of the free energy profile for the first two (rate-limiting) steps of the staphylococcal nuclease catalyzed reaction are reported. The calculations are based on the empirical valence bond method in combination with free energy perturbation molecular dynamics simulations. The calculated activation free energy is in good agreement with experimental kinetic data, and the catalytic effect of the enzyme is reproduced without any arbitrary adjustment of parameters. The enormous reduction of the activation barrier (relative to the reference reaction in water) appears to be largely associated with the strong electrostatic effect of the Ca2+ ion and the two arginine residues in the active site. This favorable electrostatic environment reduces the cost of the general-base catalysis step by almost 15 kcal/mol (by stabilizing the OH- nucleophile) and then stabilizes the developing negative charge on the 5'-phosphate group in the second step of the reaction by about 19 kcal/mol. The basic features of the originally postulated enzyme mechanism (Cotton et al., 1979) are found to be compatible with the observed activation free energy. However, the proposed modification of the mechanism (Sepersu et al., 1987), in which Arg 87 interacts only with the pentacoordinated transition state, is supported by the simulations. Further calculations on the D21E mutant also give results in good agreement with kinetic data.     

Standard Gibbs energy of metabolic reactions: V. Enolase reaction

The glycolytic pathway is one of the most important pathways for living organisms, due to its role in energy production and as supplier of precursors for biosynthesis in living cells. This work focuses on determination of the standard Gibbs energy of reaction Δ^Rg′⁰ of the enolase reaction, the ninth reaction in the glycolysis pathway. Exact Δ^Rg′⁰ values are required to predict the thermodynamic feasibility of single metabolic reactions or even of metabolic reaction sequences under cytosolic conditions. So-called “apparent” standard data from literature are only valid at specific conditions. Nevertheless, such data are often used in pathway analyses, which might lead to misinterpretation of the results. In this work, equilibrium measurements were combined with activity coefficients in order to obtain new standard values Δ^Rg′⁰ for the enolase reaction that are independent of the cytosolic conditions. Reaction equilibria were measured at different initial substrate concentrations and temperatures of 298.15 K, 305.15 K and 310.15 K at pH 7. The activity coefficients were predicted using the equation of state electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT). The ePC-SAFT parameters were taken from literature or fitted to new experimentally determined osmotic coefficients and densities. At 298.15 K and pH 7, a Δ^Rg′⁰(298.15 K, pH 7) value of −2.8 ± 0.2 kJ mol⁻¹ was obtained. This value differs by up to 5 kJ mol⁻¹ from literature data. Reasons are the poorly defined “standard” conditions and partly undefined reaction conditions of literature works. Finally, using temperature-dependent equilibrium constants and the van ‘t Hoff equation, the standard enthalpy of reaction of Δ^Rh′⁰(298.15 K, pH 7) = 27 ± 10 kJ mol⁻¹ was determined, and a similar value was found by quantum-chemistry calculations.     

Role of a reaction coordinate in free energy calculations

Abstract

The free energy calculation method emerges as a viable technique for ‘in-silico’ calorimetry. Efficient sampling techniques and the good choice of a reaction path connecting the reactant and the product state enable accurate computations of the free energy differences. We argue that in many cases the thermodynamic integration technique has the lowest variance when the transformation between the reactant and the product state proceeds along the natural path of the studied chemical reaction. We provide examples of free energy calculations for the fragmentation of the charged clusters and the swapping reaction of oligomer formation in proteins that follow a tentative reaction mechanism.     

The chemical potential in solutions and the free energy of reaction

The expression for the chemical potential of a species in a multi-component solution is usually derived by a thermodynamic argument based on ideal gas theory. A direct statistical mechanical derivation is given below, using the methods of the preceding paper. The analysis is formulated in such a way that there is no need to introduce the notion of standard states. It is made clear why certain species (water, H⁺ in buffered systems) may be ignored in calculating the affinity (negative free energy change) of a chemical reaction. The equilibrium constant is expressed in terms of generalized phase integrals or partition functions.     

Binding of ouabain to Na+, K+-dependent ATPase during the ATPase reaction. Evidence for a dimer structure of the ATPase.

Na+, K+-dependent ATPase [EC 3.6.1.3] was purified from porcine kidney by the method of Lane et al. [(1973) J. Biol. Chem. 248, 7197-7200] with slight modifications [Yamaguchi, M. & Tonomura, Y., (1979) J. Biochem. 86, 509-523]. The amounts of a phosphorylated intermediate (EP) and ouabain bound to the enzyme during the ATPase reaction were measured in 2.1 mM MgCl2 and various concentrations of NaCl and KCl at pH 7.5 and 20 degrees C. In presence of NaCl and the absence of KCl, the molar ratio of the amounts of EP and bound ouabain was 1 : 2. In the presence of both NaCl and KCl, it was 1 : 1. In both cases, the amount of bound ouabain was equal to that of EP in the absence of ouabain. These findings suggest that the functional unit of the transport ATPase is a dimer.     

Calculation of mutational free energy changes in transition states for protein folding

Recent advances in experimental and computational methods have made it possible to determine with considerable accuracy the structures whose formation is rate limiting for the folding of some small proteins-the transition state ensemble, or TSE. We present a method to analyze and validate all-atom models of such structures. The method is based on the comparison of experimental data with the computation of the change in free energy of the TSE resulting from specific mutations. Each mutation is modeled individually in all members of an ensemble of transition state structures using a method originally developed to predict mutational changes in the stability of native proteins. We first apply this method to six proteins for which we have determined the TSEs with a technique that uses experimental mutational data (Phi-values) as restraints in the structure determination and find a highly significant correlation between the calculated free energy changes and those derived from experimental kinetic data. We then use the procedure to analyze transition state structures determined by molecular dynamics simulations of unfolding, again finding a high correlation. Finally, we use the method to estimate changes in folding rates of several hydrophobic core mutants of Fyn SH3. Taken together, these results show that the procedure developed here is a tool of general validity for analyzing, assessing, and improving the quality of the structures of transition states for protein folding.     

A free energy principle for the brain.

By formulating Helmholtz's ideas about perception, in terms of modern-day theories, one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts: using constructs from statistical physics, the problems of inferring the causes of sensory input and learning the causal structure of their generation can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on Empirical Bayes and hierarchical models of how sensory input is caused. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of cortical organisation and responses. In this paper, we show these perceptual processes are just one aspect of emergent behaviours of systems that conform to a free energy principle. The free energy considered here measures the difference between the probability distribution of environmental quantities that act on the system and an arbitrary distribution encoded by its configuration. The system can minimise free energy by changing its configuration to affect the way it samples the environment or change the distribution it encodes. These changes correspond to action and perception respectively and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment assumes that the system's state and structure encode an implicit and probabilistic model of the environment. We will look at the models entailed by the brain and how minimisation of its free energy can explain its dynamics and structure.     

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.