Photoinduced electron transfer in the cytochrome c/cytochrome c oxidase complex using thiouredopyrenetrisulfonate-labeled cytochrome c. Optical multichannel detection

Intramolecular electron transfer in the electrostatic cytochrome c oxidase/cytochrome c complex was investigated using a novel photoactivatable dye. Laser photolysis of thiouredopyrenetrisulfonate (TUPS), covalently linked to cysteine 102 on yeast iso-1-cytochrome c, generates a triplet state of the dye, which donates an electron to cytochrome c, followed by electron transfer to cytochrome c oxidase. Time-resolved optical absorption difference spectra were collected at delay times from 100 ns to 200 ms between 325 and 650 nm. On the basis of singular value decomposition (SVD) and multiexponential fitting, three apparent lifetimes were resolved. A sequential kinetic mechanism is proposed from which the microscopic rate constants and spectra of the intermediates were determined. The triplet state of TUPS donates an electron to cytochrome c with a forward rate constant of approximately 2.0 x 10(4) s(-1). A significant fraction of the triplet returns back to the ground state on a similar time scale. The reduction of cytochrome c is followed by faster electron transfer from cytochrome c to Cu(A), with the equilibrium favoring the reduced cytochrome c. Subsequently, Cu(A) equilibrates with heme a with an apparent rate constant of approximately 1 x 10(4) s(-1). On a millisecond time scale, the oxidized TUPS returns to the ground state and heme a becomes reoxidized. The extracted intermediate spectra are in excellent agreement with model spectra of the postulated intermediates, supporting the proposed mechanism.     

Extracting kinetic rate constants from surface plasmon resonance array systems

Surface plasmon resonance imaging systems, such as Flexchip from Biacore, are capable of monitoring hundreds of reaction spots simultaneously within a single flow cell. Interpreting the binding kinetics in a large-format flow cell presents a number of potential challenges, including accounting for mass transport effects and spot-to-spot sample depletion. We employed a combination of computer simulations and experimentation to characterize these effects across the spotted array and established that a simple two-compartment model may be used to accurately extract intrinsic rate constants from the array under mass transport-limited conditions. Using antibody systems, we demonstrate that the spot-to-spot variability in the binding kinetics was <9%. We also illustrate the advantage of globally fitting binding data from multiple spots within an array for a system that is mass transport limited.     

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.     

Occupancy of two primary chloride-binding sites in Natronobacterium pharaonis halorhodopsin is a necessary condition for active anion transport

The existence of two primary chloride-binding sites was found on the basis of the study of halorhodopsin spectra at different chloride concentrations. SVD analysis of the spectra revealed two chloride-dependent components at low chloride concentration (0.1-10 mM). Global fitting of SVD components found K _D values of 0.47 mM and 5.2 mM with unitity Hill coefficients. The second K _D coincides with the apparent K _D of the photovoltage response of halorhodopsin.     

Kinetic coupling between protein folding and prolyl isomerization. I. Theoretical models.

Kinetic models were developed to describe the influence of prolyl peptide bond isomerization on the kinetics of reversible protein folding for cases in which structural intermediates do not occur. In the simulations, the number of prolyl residues and the relative rates of folding and isomerization were varied. The experimentally observed rate constants were found to be identical with the intrinsic rate constants of folding and isomerization only when folding remains much faster than prolyl isomerization throughout the transition region. When the rate of folding becomes similar to or lower than the rate of isomerization, the observed kinetic parameters are complex functions of all microscopic rate constants. In particular, the observed folding rates in the transition region decrease with the number of prolyl residues. Pseudo two-state kinetics with single folding and unfolding reactions are observed in several cases, although the apparent folding rates depend strongly on prolyl isomerization reactions in the unfolded chain. This virtual simplicity can easily lead to misinterpretation of kinetic data. Additional phases can be resolved when refolding is started from the fast-folding species (UF). The coupling between folding and prolyl peptide bond isomerization also modifies the dependence on denaturant concentration of the apparent rate constants of folding. We suggest several tests to detect and characterize the contributions of folding and isomerization steps to the observed folding kinetics.     

Analyzing complicated protein folding kinetics rapidly by analytical Laplace inversion using a Tikhonov regularization variant

Kinetic experiments provide much information about protein folding mechanisms. Time-resolved signals are often best described by expressions with many exponential terms, but this hinders the extraction of rate constants by nonlinear least squares (NLS) fitting. Numerical inverse Laplace transformation, which converts a time-resolved dataset into a spectrum of amplitudes as a function of rate constant, allows easy estimation of the rate constants, amplitudes, and number of processes underlying the data. Here, we present a Tikhonov regularization-based method that converts a dataset into a rate spectrum, subject to regularization constraints, without requiring an iterative search of parameter space. This allows more rapid generation of rate spectra as well as analysis of datasets too noisy to process by existing iterative search algorithms. This method's simplicity also permits highly objective, largely automatic analysis with minimal human guidance. We show that this regularization method reproduces results previously obtained by NLS fitting and that it is effective for analyzing datasets too complex for traditional fitting methods. This method's reliability and speed, as well as its potential for objective, model-free analysis, make it extremely useful as a first step in analysis of complicated noisy datasets and an excellent guide for subsequent NLS analysis.     

The kinetic pathway of folding of barnase

To search for folding intermediates, we have examined the folding and unfolding kinetics of wild-type barnase and four representative mutants under a wide range of conditions that span two-state and multi-state kinetics. The choice of mutants and conditions provided in-built controls for artifacts that might distort the interpretation of kinetics, such as the non-linearity of kinetic and equilibrium data with concentration of denaturant. We measured unfolding rate constants over a complete range of denaturant concentration by using by 1H/2H-exchange kinetics under conditions that favour folding, conventional stopped-flow methods at higher denaturant concentrations and continuous flow. Under conditions that favour multi-state kinetics, plots of the rate constants for unfolding against denaturant concentration fitted quantitatively to the equation for three-state kinetics, with a sigmoid component for a change of rate determining step, as did the refolding kinetics. The position of the transition state on the reaction pathway, as measured by solvent exposure (the Tanford beta value) also moved with denaturant concentration, fitting quantitatively to the same equations with a change of rate determining step. The sigmoid behaviour disappeared under conditions that favoured two-state kinetics. Those data combined with direct structural observations and simulation support a minimal reaction pathway for the folding of barnase that involves two detectable folding intermediates. The first intermediate, I(1), is the denatured state under physiological conditions, D(Phys), which has native-like topology, is lower in energy than the random-flight denatured state U and is suggested by molecular dynamics simulation of unfolding to be on-pathway. The second intermediate, I(2), is high energy, and is proven by the change in rate determining step in the unfolding kinetics to be on-pathway. The change in rate determining step in unfolding with structure or environment reflects the change in partitioning of this intermediate to products or starting materials.     

On true and apparent Michaelis constants in enzymology. I. Differences

Differences between both true and apparent rate constants and Michaelis constants have been examined. Rate constants of elementary stages of real mechanisms are true ones. True Michaelis constant Km is expressed by equation Km = (k(-1) + k2)/k. True constants may be determined for reliable mechanism only for which the equation of initial rate was obtained which displays physical sense of these constants and permits to find the method of their calculation. The true constant values are independent of concentration of reactants, activators, inhibitors, extraneous agents and pH. The apparent rate constants are such constants of the composite reaction which are observed when this reaction is described by the equation of simple reaction. Michaelis constant calculated by a half of the ultimate constant is an apparent constant. The apparent constants may be functions of several true rate constants and/or concentrations of reacting substances. The evident physical sense of apparent constants being absent, only formal relation between the reaction rate and reactant concentration independent of the investigated mechanism is provided.     

Robust reconstruction of the rate constant distribution using the phase function method

Many biological processes exhibit complex kinetic behavior that involves a nontrivial distribution of rate constants. Characterization of the rate constant distribution is often critical for mechanistic understandings of these processes. However, it is difficult to extract a rate constant distribution from data measured in the time domain. This is due to the numerical instability of the inverse Laplace transform, a long-standing mathematical challenge that has hampered data analysis in many disciplines. Here, we present a method that allows us to reconstruct the probability distribution of rate constants from decay data in the time domain, without fitting to specific trial functions or requiring any prior knowledge of the rate distribution. The robustness (numerical stability) of this reconstruction method is numerically illustrated by analyzing data with realistic noise and theoretically proved by the continuity of the transformations connecting the relevant function spaces. This development enhances our ability to characterize kinetics and dynamics of biological processes. We expect this method to be useful in a broad range of disciplines considering the prevalence of complex exponential decays in many experimental systems.     

Kinetics of ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor. I. A computer simulation of the influence of mass transport.

The influence of mass transport on ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor, was investigated. A one-dimensional computer model for the mass transport of ligand between the bulk solution and the polymer gel and within the gel was employed, and the influence of the diffusion coefficient, the partition coefficient, the thickness of the matrix, and the distribution of immobilized receptor were studied for a variety of conditions. Under conditions that may apply to many published experimental studies, diffusion within the matrix was found to decrease the overall ligand transport significantly. For relatively slow reactions, small spatial gradients of free and bound ligand in the gel are found, whereas for relatively rapid reactions strong inhomogeneities of ligand within the gel occur before establishment of equilibrium. Several types of deviations from ideal pseudo-first-order binding progress curves are described that resemble those of published experimental data. Extremely transport limited reactions can in some cases be fitted with apparently ideal binding progress curves, although with apparent reaction rates that are much lower than the true reaction rates. Nevertheless, the ratio of the apparent rate constants can be semiquantitatively consistent with the true equilibrium constant. Apparently "cooperative" binding can result from high chemical on rates at high receptor saturation. Dissociation in the presence of transport limitation was found to be well described empirically by a single or a double exponential, with both apparent rate constants considerably lower than the intrinsic chemical rate constant. Transport limitations in the gel can introduce many generally unknown factors into the binding progress curve. The simulations suggest that unexpected deviations from ideal binding progress curves may be due to highly transport influenced binding kinetics. The use of a thinner polymer matrix could significantly increase the range of detectable rate constants.     

Conformational diversity of acid-denatured cytochrome c studied by a matrix analysis of far-UV CD spectra.

The singular value decomposition (SVD) analysis was applied to a large set of far-ultraviolet circular dichroism (far-UV CD) spectra (100-400 spectra) of horse heart cytochrome c (cyt c). The spectra were collected at pH 1.7-5.0 in (NH4)2SO4, sorbitol and 2,2,2-trifluoroethanol (TFE) solutions. The present purpose is to develop a rigorous matrix method applied to far-UV CD spectra to resolve in details conformational properties of proteins in the non-native (or denatured) regions. The analysis established that three basis spectral components are contained in a data set of difference spectra (referred to the spectrum of the native state) used here. By a further matrix transformation, any observed spectrum could be decomposed into fractions of the native (N), the molten-globule (MG), the highly denatured (D), and the alcohol-induced helical (H) spectral forms. This method could determine fractional transition curves of each conformer as a function of solution conditions, which gave the results consistent with denaturation curves of cyt c monitored by other spectroscopic methods. The results in sorbitol solutions, for example, suggested that the preferential hydration effect of the co-solvent stabilizes the MG conformer of cyt c. This report has found that the systematic SVD analysis of the far-UV CD spectra is a powerful tool for the conformational analysis of the non-native species of a protein when it is suitably supplemented with other experimental methods.     

Kinetic Modeling of Receptor-Ligand Binding Applied to Positron Emission Tomographic Studies with Neuroleptic Tracers

Positron emission tomography (PET) with labeled neuroleptics has made possible the study of neurotransmitter-receptor systems in vivo. In this study we investigate the kinetics of the 3,4-dihydroxyphenylethylamine (dopamine) receptor-ligand binding using PET data from a series of experiments in the baboon with the 18F-labeled drugs spiperone, haloperidol, and benperidol. Models used to describe these systems are based on first-order kinetics which applies at high specific activity (low receptor occupancy). The parameters governing the uptake and loss of drug from the brain were found by fitting PET data from regions with little or no receptor concentration (cerebellum) and from experiments in which specific binding was blocked by pretreatment with the drug (+)-butaclamol. Receptor constants were determined by fitting data from receptor-containing structures. Correcting the arterial plasma activities (the model driving function) for the presence of drug metabolites was found to be important in the modeling of these systems.     

Antibody-antigen interactions measured by surface plasmon resonance: global fitting of numerical integration algorithms

The interactions between adenylate kinase (AK) and a monoclonal antibody against AK (McAb3D3) were examined by means of optical biosensor technology, and the sensograms were fitted to four models using numerical integration algorithms. The interaction of a solution of McAb3D3 with immobilized AK follows a double exponential function and the data fitted well to an inhomogeneous ligand model. The interaction of a solution AK with immobilized McAb3D3 follows a single exponential function and the data fitted well to a pseudo-first order reaction model. The true association constants of AK binding to McAb3D3 in solution were obtained from competition BIAcore measurements. The difference in results obtained with solid-phase BIAcore and competition BIAcore may be due to rebinding of the dissociated analyte to the immobilized surface. The results obtained with BIAcore are compared to those obtained by ELISA methods. We suggest that the best method for analysis of BIAcore data is direct, global fitting of sensorgrams to numerical integration algorithms corresponding to the different possible models for binding.     

Temperature and pH dependence of the metarhodopsin I-metarhodopsin II kinetics and equilibria in bovine rod disk membrane suspensions

The kinetics of the relaxation of bleached bovine rod disk membrane suspensions from metarhodopsin I into the equilibrium between metarhodopsins I and II were determined at pHs between 5.9 and 8.1 and at temperatures between -1 and 15 degrees C. From these data, thermodynamic equations were generated by two-way linear regression that simultaneously describe the functional dependence on pH and temperature of the pseudo-first-order and true forward rate constants, the reverse and observed rate constants, and the equilibrium constant. Using these equations, we obtained the thermodynamic parameters and the apparent net proton uptake for the transitions from metarhodopsin I to metarhodopsin II and from metarhodopsin I to the activated intermediate. The reversibility of this equilibrium and the effect of aging of the preparation on the measured rate constants were investigated.     

Kinetic characterization of TAR RNA-Tat peptide and neomycin interactions by acoustic wave biosensor

The kinetics of binding of short Tat peptides and an aminoglycoside molecule to the human immunodeficiency virus-type 1(HIV-1) TAR RNA and to a bulge mutant analogue (MTAR) is studied in a biosensor format by monitoring the time course of the response in a series resonance frequency, using an acoustic wave biosensor. Association and dissociation rate constants are evaluated by fitting the experimental data to a simple 1:1 (Langmuir) model. Kinetic rate and equilibrium dissociation constants show that MTAR-peptide complexes are subject to a higher dissociation rate and are less stable compared to the corresponding TAR-peptide complexes. In addition, longer peptides display enhanced discrimination ability than a shorter peptide according to the equilibrium dissociation constants evaluated using this technique. K(D) values for TAR-Tat vs. MTAR-Tat complexes are 2.6 vs. 3.8 microM for Tat-12, 0.87 vs. 4.3 microM for Tat-18 and 0.93 vs. 1.6 microM for Tat-20. The equilibrium dissociation constant for TAR-neomycin complex is 12.4 microM and it is comparable to the values obtained from non-biosensor type assays. These findings are in parallel with those cited in the literature and the results from this study underline the potential of the acoustic wave sensor for detailed biophysical analysis of nucleic acid-ligand binding.     

Characterization of macromolecular heterogeneity by equilibrium sedimentation techniques

New graphical procedures have been developed to investigate the heterogeneity of protein preparations using sedimentation equilibrium. The heterogeneous systems that can be studied include self-associating systems contaminated by incompetent monomer, self-associating systems contaminated by non-dissociating oligomer and simple non-interacting monomer-oligmer disperse systems. The new procedures are based on the concentration dependence of the apparent association constants estimated by a non-linear least square fitting program (NONLIN), on the assumption of conservation of mass during sedimentation and on the applications of several standard techniques for statistical inferences of NONLIN estimations. The procedures outlined here can detect various types of heterogeneity, discriminate amongst different types of heterogeneity, estimate the amount of contaminant causing heterogeneity and determine the true equilibrium constant of the self-associating components. The procedures appear to be sensitive, accurate and easily applicable when tested using both protein samples and computer simulated data.     

Nanosecond photolysis of rhodopsin: evidence for a new, blue-shifted intermediate

Early photolysis intermediates of native bovine rhodopsin (RHO) are investigated by nanosecond laser photolysis near physiological temperature. Absorption difference spectra are collected after excitation with 477-, 532-, and 560-nm laser pulses of various energies and with 477-nm laser excitation at 5, 12, 17, 21, and 32 degrees C. The data are analyzed by using singular-value decomposition (SVD) and a global exponential fitting routine. Two rate constants associated with distinct spectral changes are observed during the time normally associated with the decay of bathorhodopsin to lumirhodopsin. Various models consistent with this observation are considered. A sequential model in which there is a reversible step between a bathorhodopsin intermediate and a new intermediate (BSI), which is blue-shifted relative to lumirhodopsin, is shown to best fit the data. The temperature dependence of the observed and calculated rate constants leads to linear Arrhenius plots. Extrapolation of the temperature dependence suggests that BSI should not be observable after rhodopsin photolysis at temperatures below -100 degrees C. The results are discussed with regard to the artificial visual pigments cis-5,6-dihydroisorhodopsin and 13-demethylrhodopsin. It is proposed that the rate of the BATHO to BSI transition is limited by the relaxation of the strained all-trans-retinal chromophore within a tight protein environment. The transition to LUMI involves chromophore relaxation concurrent with protein relaxation. While the first process is strongly affected by changes in the chromophore, the second transition seems to be determined more by protein relaxation.     

Determination of relative rate constants for in vitro RNA processing reactions by internal competition

Studies of RNA recognition and catalysis typically involve measurement of rate constants for reactions of individual RNA sequence variants by fitting changes in substrate or product concentration to exponential or linear functions. A complementary approach is determination of relative rate constants by internal competition, which involves quantifying the time-dependent changes in substrate or product ratios in reactions containing multiple substrates. Here, we review approaches for determining relative rate constants by analysis of both substrate and product ratios and illustrate their application using the in vitro processing of precursor transfer RNA (tRNA) by ribonuclease P as a model system. The presence of inactive substrate populations is a common complicating factor in analysis of reactions involving RNA substrates, and approaches for quantitative correction of observed rate constants for these effects are illustrated. These results, together with recent applications in the literature, indicate that internal competition offers an alternate method for analyzing RNA processing kinetics using standard molecular biology methods that directly quantifies substrate specificity and may be extended to a range of applications.