Fluorescence monitoring of the conformational change in alpha 2-macroglobulin induced by trypsin under second-order conditions: the macroglobulin acts both as a substrate and a competitive inhibitor of the protease

The reaction of bovine pancreatic trypsin with human plasma alpha(2)-macroglobulin (alpha(2)M) was studied at 25 degrees C, using equimolar mixtures of E and I in 50 mM potassium phosphate buffer, pH 7. The conformational change in alpha(2)M was monitored through the increase in protein fluorescence at 320 nm (exc lambda, 280 nm). At [alpha(2)M](0) =[E](0) =11.5-200 nM, the fluorescence change data fit the integrated second-order rate equation, (F(infinity) -F(0) )/(F(infinity) -F(t) )=1+k(i,obsd) [alpha(2)M](0) t, indicating that cleavage of the bait region in alpha(2)M was the rate-determining step. The apparent rate constant (k(i,obsd)) was found to be inversely related to reactant concentration. The kinetic behavior of the system was compatible with a model involving reversible, nonbait region binding of E to alpha(2)M, competitively limiting the concentration of E available for bait region cleavage. The intrinsic value of k(i) was (1.7+/-0.24) x 10(7) M(-1) s(-1).K(p), the inhibitory constant associated with peripheral binding, was estimated to be in the submicromolar range. The results of the present study point to a potential problem in interpreting kinetic data relating to protease-induced structural changes in macromolecular substrates. If there is nonproductive binding, as in the case of trypsin and alpha(2)M, and the reactions are monitored under pseudo first-order conditions ([S](0) >[E](0) ), an intrinsically second-order process (such as the rate-limiting bait region cleavage in alpha(2)M) may become kinetically indistinguishable from an intrinsically first-order process (e.g. rate-limiting conformational change). Hence an excess of one component over the other should be avoided in kinetic studies addressing such systems.     

Intrachain reactions of supercoiled DNA simulated by Brownian dynamics

We considered an irreversible biochemical intrachain reaction of supercoiled DNA as a random event that occurs, with certain probability, at the instant of collision between two reactive groups bound to distant DNA sites. Using the Brownian dynamics technique, we modeled this process for a supercoiled DNA molecule of 2.5 kb length in dilute aqueous solution at an NaCl concentration of 0.1 M. We calculated the mean reaction time tau(Sigma) as a function of the intrinsic second-order rate constant k(I), the reaction radius R, and the contour separation S of the reactive groups. At the diffusion-controlled limit (k(I) --> infinity), the kinetics of reaction are determined by the mean time tau(F) of the first collision. The dependence of tau(F) on R is close to inversely proportional, implying that the main contribution to the productive collisions is made by bending of the superhelix axis. At sufficiently small k(I), the mean reaction time can be satisfactory approximated by tau(Sigma) = tau(F)(app) + 1/(k(I)c(L)), where c(L) is the local concentration of one reactive group around the other, and tau is an adjustable parameter, which we called the apparent time of the first collision. The value of tau depends on R very weakly and is approximately equal to the mean time of the first collision caused by mutual reptation of two DNA strands forming the superhelix. The quasi-one-dimensional reptation process provides the majority of productive collisions at small k(I) values.     

Steady-state fluorescence polarization data in membranes. Resolution into physical parameters by an extended Perrin equation for restricted rotation of fluorophores

An extended Perrin equation is derived applicable to the restricted rotation of fluorophores. The equation results in a relation between time-resolved (r infinity) and steady-state fluorescence anisotropy (rs) data. This relation contains a parameter m, which expresses the difference between rotational diffusion in a lipid membrane and that in an isotropic reference oil having the same rs value. The relation is in agreement with rs, r infinity literature data for a variety of artificial and biological membranes labeled with various probes. Cholesterol and fatty acyl unsaturation affect the value of m, but temperature does not. The results indicate that, as far as fluorescence depolarization is concerned, either liposomes of saturated phospholipids without cholesterol or liposomes of unsaturated phospholipids containing cholesterol are good model systems for biological membranes. The accuracy of estimating order parameters or rotational diffusion constants from rs data is discussed. The formalism described here introduces a novel way of applying Arrhenius plots and allows for an unambiguous interpretation of rs data.     

Conformational selection or induced fit? A critical appraisal of the kinetic mechanism

For almost five decades, two competing mechanisms of ligand recognition, conformational selection and induced fit, have dominated our interpretation of ligand binding in biological macromolecules. When binding-dissociation events are fast compared to conformational transitions, the rate of approach to equilibrium, k(obs), becomes diagnostic of conformational selection or induced fit based on whether it decreases or increases, respectively, with the ligand concentration, [L]. However, this simple conclusion based on the rapid equilibrium approximation is not valid in general. Here we show that conformational selection is associated with a rich repertoire of kinetic properties, with k(obs) decreasing or increasing with [L] depending on the relative magnitude of the rate of ligand dissociation, k(off), and the rate of conformational isomerization, k(r). We prove that, even for the simplest two-step mechanism of ligand binding, a decrease in k(obs) with [L] is unequivocal evidence of conformational selection, but an increase in k(obs) with [L] is not unequivocal evidence of induced fit. Ligand binding to glucokinase, thrombin, and its precursor prethrombin-2 are used as relevant examples. We conclude that conformational selection as a mechanism for a ligand binding to its target may be far more common than currently believed.     

Catalysis by enzyme conformational change as illustrated by orotidine 5'-monophosphate decarboxylase

An energy decomposition scheme has been used to elucidate the importance of the changes of enzyme conformational substates to the reduction of the activation barrier in enzyme-catalyzed reactions. This analysis may be illustrated by the reaction of orotidine 5'-monophosphate decarboxylase, which exhibits a remarkable rate enhancement of over 17 orders of magnitude compared to the uncatalyzed process. The mechanism shows that the enzyme conformation is more distorted in the reactant state than in the transition state. The energy released from protein conformation relaxation provides the predominant contribution to the rate enhancement of orotidine 5'-monophosphate decarboxylase. The proposed mechanism is consistent with results from site-directed mutagenesis experiments, in which mutations distant from the reactive center can have significant effects on the catalytic rate enhancement (k(cat)), but rather a small influence on the binding affinity for the substrate (K(M)).     

Single channel gating events in tracer flux experiments I. Theory

Tracer ion flux measurements are a commonly used method for studying ion transport through membranes of cellular systems, where the rate of ion flow is determined by gating processes which control the opening and closing of transmembrane channels. Due to recent advances in the theoretical analysis of tracer flux from or into closed membrane structures (CMS), the mechanism of gating reactions can, in principle, be derived from flux data. A physically well founded analysis is presented for the dependence of the total tracer ion content of a collection of CMS on the gating processes. For functionally uncoupled gating units a mean single channel flux contribution [equation, see text] can be defined, where k is the intrinsic single channel flux coefficient, t the time over which flux is measured, and p(tau,t) is the probability that a given channel was open for a total period tau during t. This quantity reflects the mean time course of the tracer content due to flux through a single channel. Expressions for are derived that explicitly take into account a distribution in the lifetime of open channels. On the basis of the results, kinetic and thermodynamic parameters of multiphasic gating reactions can be determined from the time course of the overall tracer content in a colleciion of CMS.     

Effects of external protons on single cardiac sodium channels from guinea pig ventricular myocytes.

The effects of external protons on single sodium channel currents recorded from cell-attached patches on guinea pig ventricular myocytes were investigated. Extracellular protons reduce single channel current amplitude in a dose-dependent manner, consistent with a simple rapid channel block model where protons bind to a site within the channel with an apparent pKH of 5.10. The reduction in single channel current amplitude by protons is voltage independent between -70 and -20 mV. Increasing external proton concentration also shifts channel gating parameters to more positive voltages, consistent with previous macroscopic results. Similar voltage shifts are seen in the steady-state inactivation (h infinity) curve, the time constant for macroscopic current inactivation (tau h), and the first latency function describing channel activation. As pHo decreases from 7.4 to 5.5 the midpoint of the h infinity curve shifts from -107.6 +/- 2.6 mV (mean +/- SD, n = 16) to -94.3 +/- 1.9 mV (n = 3, P less than 0.001). These effects on channel gating are consistent with a reduction in negative surface potential due to titration of negative external surface charge. The Gouy-Chapman-Stern surface charge model incorporating specific proton binding provides an excellent fit to the dose-response curve for the shift in the midpoint of the h infinity curve with protons, yielding an estimate for total negative surface charge density of -1e/490 A2 and a pKH for proton binding of 5.16. By reducing external surface Na+ concentration, titration of negative surface charge can also quantitatively account for the reduction in single Na+ channel current amplitude, although we cannot rule out a potential role for channel block. Thus, titration by protons of a single class of negatively charged sites may account for effects on both single channel current amplitude and gating.     

Correlation of acid-induced conformational transition of ferricytochrome <Emphasis Type="Italic">c</Emphasis> with cyanide binding kinetics

A relation between pH-induced conformational transitions of horse heart ferricytochrome c and the kinetics of external ligand coordination to heme iron was investigated by optical spectroscopy, circular dichroism and viscometry. The dependencies of both the association, k (a), and dissociation rate constants of cyanide binding on pH were determined from kinetic measurements. The association rate constant exhibits a bell-shaped form of dependence on pH in the region where this protein unfolds. The maximum of the dependence of k (a) on pH is found to be coincident with the pK values of conformational transitions of ferricytochrome c in solutions with both low and high ionic strengths. This observation is explained in terms of ferricytochrome c unfolding, which is characterized by two processes: the gradual opening of the heme crevice accompanied by the detachment of the axial Met80 and its replacement with a water molecule. The former process enhances the rate, whereas the latter results in the inhibition of the rate of cyanide binding.     

Conformational dynamics of the alphaM3 transmembrane helix during acetylcholine receptor channel gating

Muscle acetylcholine receptors are synaptic ion channels that "gate" between closed- and open-channel conformations. We used Phi-value analysis to probe the transition state of the diliganded gating reaction with regard to residues in the M3, membrane-spanning helix of the muscle acetylcholine receptor alpha-subunit. Phi (a fraction between 1 and 0) parameterizes the extent to which a mutation changes the opening versus the closing rate constant and, for a linear reaction mechanism, the higher the Phi-value, the "earlier" the gating motion. In the upper half of alphaM3 the gating motions of all five tested residues were temporally correlated (Phi approximately 0.30) and serve to link structural changes occurring at the middle of the M2, pore-lining helix with those occurring at the interface of the extracellular and transmembrane domains. alphaM3 belongs to a complex and diverse set of synchronously moving parts that change structure relatively late in the channel-opening process. The propagation of the gating Brownian conformational cascade has a complex spatial distribution in the transmembrane domain.     

Parallel double helices of DNA. Conformational analysis of regular helices with the second order symmetry axis

We have performed a conformational analysis of DNA double helices with parallel directed backbone strands connected with the second order symmetry axis being at the same time the helix axis. The calculations were made for homopolymers poly(dA).poly(dA), poly(dC).poly(dC), poly(dG) poly(dG), and poly(dT).poly(dT). All possible variants of hydrogen bonding of base pairs of the same name were studied for each polymer. The maps of backbone chain geometrical existence were constructed. Conformational and helical parameters corresponding to local minima of conformational energy of "parallel" DNA helices, calculated at atom-atom approximation, were determined. The dependence of conformational energy on the base pair and on the hydrogen bond type was analysed. Two major conformational advantageous for "parallel" DNA's do not depend much on the hydrogen-bonded base pair type were indicated. One of them coincided with the conformational region typical for "antiparallel" DNA, in particular for the B-form DNA. Conformational energy of "parallel" DNA depends on the base pair type and for the most part is similar to the conformational energy of "antiparallel" B-DNA.     

Parallel Double Helices of DNA. Conformational Analysis of Regular Helices with the Second Order Symmetry Axis

Abstract

We have performed a conformational analysis of DNA double helices with parallel directed backbone strands connected with the second order symmetry axis being at the same time the helix axis. The calculations were made for homopolymers poly(dA) · poly(dA), poly(dC) · poly(dC), poly(dG) poly(dG), and poly(dT) · poly(dT). All possible variants of hydrogen bonding of base pairs of the same name were studied for each polymer. The maps of backbone chain geometrical existence were constructed. Conformational and helical parameters corresponding to local minima of conformational energy of “parallel” DNA helices, calculated at atom-atom approximation, were determined. The dependence of conformational energy on the base pair and on the hydrogen bond type was analysed. Two major conformational advantageous for “parallel” DNA's do not depend much on the hydrogen-bonded base pair type were indicated. One of them coincided with the conformational region typical for “antiparallel” DNA in particular for the B-form DNA Conformational energy of “parallel” DNA depends on the base pair type and for the most part is similar to the conformational energy of “antiparallel” B-DNA.     

Brownian and essential dynamics studies of the HIV-1 integrase catalytic domain

The three-dimensional structure of the active site region of the enzyme HIV-1 integrase is not unambiguously known. This region includes a flexible peptide loop that cannot be well resolved in crystallographic determinations. Here we present two different computational approaches with different levels of resolution and on different time-scales to understand this flexibility and to analyze the dynamics of this part of the protein. We have used molecular dynamics simulations with an atomic model to simulate the region in a realistic and reliable way for 1 ns. It is found that parts of the loop wind up after 300 ps to extend an existing helix. This indicates that the helix is longer than in the earlier crystal structures that were used as basis for this study. Very recent crystal data confirms this finding, underlining the predictive value of accurate MD simulations. Essential dynamics analysis of the MD trajectory yields an anharmonic motion of this loop. We have supplemented the MD data with a much lower resolution Brownian dynamics simulation of 600 ns length. It provides ideas about the slow-motion dynamics of the loop. It is found that the loop explores a conformational space much larger than in the MD trajectory, leading to a "gating"-like motion with respect to the active site.     

The determination of the conformational properties of nucleic acids in solution from NMR data

A program, NUCFIT, has been written for simulating the effects of conformational averaging on nuclear Overhauser enhancement (NOE) intensities for the spin systems found in nucleic acids. Arbitrary structures can be generated, and the NOE time courses can be calculated for truncated one-dimensional NOEs, two-dimensional NOE and rotating frame NOE spectroscopy (NOESY and ROESY) experiments. Both isotropic and anisotropic molecular rotation can be treated, using Woessner's formalism (J. Chem. Phys. (1962) 37, 647-654). The effects of slow conformational averaging are simulated by taking population-weighted means of the conformations present. Rapid motions are allowed for by using order parameters which can be supplied by the user, or calculated for specific motional models using the formalism of Tropp (J. Chem. Phys. (1980) 72, 6035-6043). NOE time courses have been simulated for a wide variety of conformations and used to determine the quality of structure determinations using NMR data for nucleic acids. The program also allows grid-searching with least-squares fitting of structures to experimental data, including the effects of spin-diffusion, conformational averaging and rapid internal motions. The effects of variation of intra and internucleotide conformational parameters on NOE intensities has been systematically explored. It is found that (i) the conformation of nucleotides is well determined by realistic NOE data sets, (ii) some of the helical parameters, particularly the base pair roll, are poorly determined even for extensive, noise-free data sets, (iii) conformational averaging of the sugars by pseudorotation has at most second-order influence on the determination of other parameters and (iv) averaging about the glycosidic torsion bond also has, in most cases, an insignificant effect on the determination of the conformation of nucleotides.     

Do enzymes bind their substrates in the ground state because of a physico-chemical requirement?

Transition state theory has provided no convincing explanation for the nearly universal observation of complexes of enzymes with substrates. Bimolecular catalytic reactions are assumed here to take place through reactive encounter complexes defined as the subset of reactant state species able to proceed directly to low lying energy levels at the transition state. By assessing the probability of these complexes from the maximum efficiency of intramolecular reactions, an upper limit for the rate constants promoted by hypothetical catalysts unable to bind substrates is deduced. This limit, which is below the ordinary range of bimolecular rate constants (k(cat)/K(M)) for enzyme reactions, results from a kinetic limitation in the formation of reactive encounter complexes. Exceeding this limit requires a stabilization of these complexes. Using the terminology of transition state theory, the need for enzymes to form complexes with substrates is then expressed as a necessity to restore Boltzmann distribution at the transition state.     

Catalysis-Enhancement via Rotary Fluctuation of F1-ATPase

Protein conformational fluctuations modulate the catalytic powers of enzymes. The frequency of conformational fluctuations may modulate the catalytic rate at individual reaction steps. In this study, we modulated the rotary fluctuation frequency of F₁-ATPase (F₁) by attaching probes with different viscous drag coefficients at the rotary shaft of F₁. Individual rotation pauses of F₁ between rotary steps correspond to the waiting state of a certain elementary reaction step of ATP hydrolysis. This allows us to investigate the impact of the frequency modulation of the rotary fluctuation on the rate of the individual reaction steps by measuring the duration of rotation pauses. Although phosphate release was significantly decelerated, the ATP-binding and hydrolysis steps were less sensitive or insensitive to the viscous drag coefficient of the probe. Brownian dynamics simulation based on a model similar to the Sumi-Marcus theory reproduced the experimental results, providing a theoretical framework for the role of rotational fluctuation in F₁ rate enhancement.     

Catalysis-Enhancement via Rotary Fluctuation of F1-ATPase

Protein conformational fluctuations modulate the catalytic powers of enzymes. The frequency of conformational fluctuations may modulate the catalytic rate at individual reaction steps. In this study, we modulated the rotary fluctuation frequency of F₁-ATPase (F₁) by attaching probes with different viscous drag coefficients at the rotary shaft of F₁. Individual rotation pauses of F₁ between rotary steps correspond to the waiting state of a certain elementary reaction step of ATP hydrolysis. This allows us to investigate the impact of the frequency modulation of the rotary fluctuation on the rate of the individual reaction steps by measuring the duration of rotation pauses. Although phosphate release was significantly decelerated, the ATP-binding and hydrolysis steps were less sensitive or insensitive to the viscous drag coefficient of the probe. Brownian dynamics simulation based on a model similar to the Sumi-Marcus theory reproduced the experimental results, providing a theoretical framework for the role of rotational fluctuation in F₁ rate enhancement.     

Gating current noise produced by Brownian models of a voltage sensor

The activation of voltage-dependent ion channels is associated with the movement of gating charges, which give rise to gating currents. Although gating currents from a single channel are too small to be detected, analysis of the fluctuations of macroscopic gating currents from a population of channels allows a good guess of their magnitude. The analysis of experimental gating current fluctuations, when interpreted in terms of a rate model of channel activation and assuming sufficiently high bandwidth, is in accordance with the presence of a main step along the activation pathway carrying a charge of 2.3–2.4 e₀. To give a physical interpretation to these results and to relate them to the known atomic structure of the voltage sensor domain, we used a Brownian model of voltage-dependent gating based on atomic detail structure, that follows the laws of electrodynamics. The model predicts gating currents and gating current fluctuations essentially similar to those experimentally observed. The detailed study of the model output, also performed by making several simplifications aimed at understanding the basic dependencies of the gating current fluctuations, suggests that in real channels the voltage sensor moves along a sequence of intermediate states separated by relatively low (<5 kT) energy barriers. As a consequence, crossings of successive gating charges through the gating pore become very frequent, and the corresponding current shots are often seen to overlap because of the relatively high filtering. Notably, this limited bandwidth effect is at the origin of the relatively high single-step charge experimentally detected.     

Effects of calcium binding on the side-chain methyl dynamics of calbindin D9k: a 2H NMR relaxation study

The effects of Ca(2+) binding on the side-chain methyl dynamics of calbindin D(9k) have been characterized by (2)H NMR relaxation rate measurements. Longitudinal, transverse in-phase, quadrupolar order, transverse anti-phase and double quantum relaxation rates are reported for both the apo and Ca(2+)-loaded states of the protein at two magnetic field strengths. The relatively large size of the data set allows for a detailed analysis of the underlying conformational dynamics by spectral density mapping and model-free fitting procedures. The results reveal a correlation between a methyl group's distance from the Ca(2+) binding sites and its conformational dynamics. Several methyl groups segregate into two limiting classes, one proximal and the other distal to the binding sites. Methyl groups in these two classes respond differently to Ca(2+) binding, both in terms of the timescale and amplitude of their fluctuations. Ca(2+) binding elicits a partial immobilization among methyl groups in the proximal class, which is consistent with previous studies of calbindin's backbone dynamics. The distal class, however, exhibits a trend that could not be inferred from the backbone data in that its mobility actually increases with Ca(2+) binding. We have introduced the term polar dynamics to describe this type of organization across the molecule. The trend may represent an important mechanism by which calbindin D(9k) achieves high affinity binding while minimizing the corresponding loss of conformational entropy.     

Interfacial Friction and Collective Diffusion in Nanopores

A simple Brownian model for the collective dynamics of a fluid confined by rigid walls is described for which the collective velocity autocorrelation function (CVACF) decays exponentially. Using this approach, a new method of calculating the Maxwell velocity slip coefficients from the collective diffusion coefficient, obtained from equilibrium molecular dynamics, is proposed. A comparison of the slip coefficients for a range of fluid densities with the results obtained from the tangential velocity loss of the colliding particles in non-equilibrium simulations show excellent agreement.