Multiwavelength analysis of the kinetics of reduction of cytochrome aa3 by cytochrome c

Tracking Equilibrium and Nonequilibrium Shifts in Data with TREND

Principal component analysis (PCA) discovers patterns in multivariate data that include spectra, microscopy, and other biophysical measurements. Direct application of PCA to crowded spectra, images, and movies (without selecting peaks or features) was shown recently to identify their equilibrium or temporal changes. To enable the community to utilize these capabilities with a wide range of measurements, we have developed multiplatform software named TREND to Track Equilibrium and Nonequilibrium population shifts among two-dimensional Data frames. TREND can also carry this out by independent component analysis. We highlight a few examples of finding concurrent processes. TREND extracts dual phases of binding to two sites directly from the NMR spectra of the titrations. In a cardiac movie from magnetic resonance imaging, TREND resolves principal components (PCs) representing breathing and the cardiac cycle. TREND can also reconstruct the series of measurements from selected PCs, as illustrated for a biphasic, NMR-detected titration and the cardiac MRI movie. Fidelity of reconstruction of series of NMR spectra or images requires more PCs than needed to plot the largest population shifts. TREND reads spectra from many spectroscopies in the most common formats (JCAMP-DX and NMR) and multiple movie formats. The TREND package thus provides convenient tools to resolve the processes recorded by diverse biophysical methods.

Simultaneous measurements of fast optical and proton current kinetics in the bacteriorhodopsin photocycle using an enhanced spectrophotometer

A one-of-a-kind high speed optical multichannel spectrometer was designed and built at NIH and described in this journal in 1997 [J.W. Cole, R.W. Hendler, P.D. Smith, H.A. Fredrickson, T.J. Pohida, W.S. Friauf. A high speed optical multichannel analyzer. J Biochem Biophys Methods 1997;35:16-174.]. The most unique aspect of this instrument was the ability to follow an entire time course from a single activation using a single sample. The instrument has been used to study rapid kinetic processes in the photon-driven bacteriorhodopsin photocycle and electron transport from cytochrome c to cytochrome aa3 and from cytochrome aa3 to oxygen. The present paper describes a second generation instrument with a number of important enhancements which significantly improve its capabilities for multichannel kinetic studies. An example application is presented in which the kinetics of photon-induced proton flow across the biological membrane is measured simultaneously with the individual steps of the photocycle determined optically. Matching the time constants for the two processes indicates which molecular transformations are associated with major proton movements.

Fluorescence absorbance inner-filter decomposition: the role of emission shape on estimates of free Ca(2+) using Rhod-2

A method for decomposing complex emission spectra by correcting for known inner-filter effects is described. This approach builds on previous work using a linear combination of model emission spectra and combines the known absorption characteristics of the system to fit the composite emission spectrum. Rhod-2, which has a small Stokes shift and significant self-absorption, was used as the model system. By adding the absorption characteristics of Rhod-2 to the model, the degree of fit was significantly improved, thus minimizing residuals, and accurately predicted the spectral shape changes with increasing concentration, [Rhod-2]. More complex studies were conducted with Rhod-2 in isolated cardiac mitochondria with multiple emission and absorption elements. By including known absorbances to the spectral decomposition, the overall precision increased almost four fold. Moreover, this approach eliminated the significant [Rhod-2] dependence on the apparent K(50) and therefore improved the accuracy of free [Ca(2+)] calculations. These data demonstrate that secondary inner-filter correction can significantly improve spectral decomposition of complex emission spectra, which are used in a variety of biological applications.

Approximating the product spectrum and product concentrations in continuous photochemical reactions

Several approximations to a common photochemical rate law, in which the rate is proportional to the fraction of light absorbed by the reactant chromophore, have been developed to permit the product spectrum to be determined from a sequence of spectra during irradiation that exhibit isosbestic points. The methods were tested on the photolysis of [Cr(NH(3))(6)](3+) and [Cr(en)(3)](3+) (en = ethylenediamine) in water, and [Fe(Et(2)dtc)(3)], tris(diethyldithiocarbamato)iron(III), in CHCl(3).

A method for dynamic spectrophotometric measurements in vivo using principal component analysis-based spectral deconvolution

A method was developed for dynamic spectrophotometric measurements in vivo in the presence of non-specific spectral changes due to external disturbances. This method was used to measure changes in mitochondrial respiratory pigment redox states in photoreceptor cells of live, white-eyed mutants of the blowfly Calliphora vicina. The changes were brought about by exchanging the atmosphere around an immobilised animal from air to N2 and back again by a rapid gas exchange system. During an experiment reflectance spectra were measured by a linear CCD array spectrophotometer. This method involves the pre-processing steps of difference spectra calculation and digital filtering in one and two dimensions. These were followed by time-domain principal component analysis (PCA). PCA yielded seven significant time domain principal component vectors and seven corresponding spectral score vectors. In addition, through PCA we also obtained a time course of changes common to all wavelengths-the residual vector, corresponding to non-specific spectral changes due to preparation movement or mitochondrial swelling. In the final step the redox state time courses were obtained by fitting linear combinations of respiratory pigment difference spectra to each of the seven score vectors. The resulting matrix of factors was then multiplied by the matrix of seven principal component vectors to yield the time courses of respiratory pigment redox states. The method can be used, with minor modifications, in many cases of time-resolved optical measurements of multiple overlapping spectral components, especially in situations where non-specific external influences cannot be disregarded.

Regulation of the bacteriorhodopsin photocycle and proton pumping in whole cells of Halobacterium salinarium

Single-turnover kinetics of the bacteriorhodopsin photocycle and proton-pumping capabilities of whole cells were studied. It was found that the Delta mu (tilde)H+ of the cell had a profound influence on the kinetics and components of the cycle. For example, comparing the photocycle in whole cells to that seen in PM preparations, we found that (1) the single-turnover time of the cycle was increased approximately 10-fold, (2) the mole fraction of M-fast (at high actinic light) decreased from 50 to 20%, and (3) the time constant for M-slow increased significantly. The level of Delta mu(tilde)H+ was dependent on respiration, ATP formation and breakdown, and the magnitude of a pre-existing K+ diffusion gradient. The size of the Delta mu(tilde)H+ could be manipulated by additions of HCN, nigericin, and DCCD (N,N'-dicyclohexylcarbodamide). At higher levels of Delta mu(tilde)H+, further changes in the photocycle were seen. (4) Two slower components of M-decay appeared as major components. (5) The apparent conversion of the M-fast to the O intermediate disappeared. (6) A partial reversal of an early photocycle step occurred. The photocycle of intact cells could be changed to that seen in purple membrane suspensions by the energy-uncoupler CCCP or by lysis of the cells. In fresh whole cells, light-induced proton pumping was not seen until the K+ diffusion potential was dissipated and proton accumulation facilitated by use of a K+-H+ exchanger (nigericin), respiration was inhibited by HCN, and ATP synthesis and breakdown were inhibited by DCCD. In stored cells, the pre-existing K+ diffusion gradient was diminished through slow diffusion, and only DCCD and HCN were required to elicit proton extrusion.

Applicability of the Kubelka-Munk theory for the evaluation of reflectance spectra demonstrated for haemoglobin-free perfused heart tissue

Reflectance spectrometry is a useful tool for studying in vivo kinetic changes in the oxygen saturation of haemoglobin and myoglobin as well as the redox state of cytochromes. A method is given which allows the quantification of tissue reflectance spectra using multicomponent analysis. This method utilizes the Kubelka-Munk theory for modelling the measured tissue spectra. To test this approach, reflectance spectra of a haemoglobin-free perfused guinea pig heart were measured by a fast scanning spectrophotometer (100 spectra/s, spectral resolution 1.0 nm) and evaluated using the component absorbance spectra measured separately. A relative mean spectral residual error of 0.15% was achieved by least-squares fitting. Using statistical error propagation, oxygenation of myoglobin is obtained within a relative precision of 1%, and the redox state of cytochromes aa3 and c are determined simultaneously within a margin of 3%; the results for the redox-state of cytochrome b, however, are less precise. Special component error functions are presented to provide a reliability measure for the concentration prediction using this multicomponent assay. The consistency of the theory and the component absorptivity data is tested by regressing the actual concentrations obtained for each of the redox pair components during the various states of tissue oxygenation. A method is described for the recognition and reduction of systematic errors.

A high speed optical multichannel analyzer

An optical multichannel analyzer capable of recording spectra at sampling rates up to 100 kHz is described. The instrument, designed to gather data on the kinetic reaction mechanisms of biological preparations such as cytochrome oxidase and bacteriorhodopsin, features a massively parallel approach in which each photosensing element of the detector array has a dedicated amplifier, integrator, analog to digital converter, and sample buffer. The design has 92 such elements divided in two separate arrays, each of which sits at the focal plane of a 1/4 m Ebert spectrometer. The spectrometers may be tuned to cover independent, 130 nm wide, regions of the spectrum from 350 nm to 900 nm with a dispersion of 2.8 nm per element. Each detection channel has 12-bit resolution with an electronic dark count of 1 count and may be sampled 1024 times during a single experiment with dynamically variable sampling intervals from 10 microseconds to several seconds. Time averaging of up to thousands of consecutive laser-initiated kinetic cycles allows analyses of spectral changes < 0.001 optical density units. A personal computer with custom software provides a number of features: entry of experiment parameters; transfer of data from temporary buffers to permanent files; real time display; multiple spectrum averaging; and control and synchronization of associated system hardware. Optical fibers or lenses provide coupling from a parabolic reflector Xenon arc monitoring light source, through the sample chamber, to the entry slit of the monochromator. The instrument has been used for extensive studies on the rapid kinetics and definition of reaction sequences of the energy-transducing enzymes cytochrome oxidase and bacteriorhodopsin. Some results from these studies are discussed.

Multichannel analysis of single-turnover kinetics of cytochrome aa3 reduction of O2

The single-turnover kinetics of the oxidation of cytochrome aa3 by O2 have been studied using a new approach. Up to 1000 whole spectra covering both the Soret and alpha regions were sequentially collected at room temperature from single samples with a time resolution of 10 microns. All of the spectral and time information were used in analyses based on singular value decomposition. Four spectral transitions (i.e., intermediates) were distinguished with time constants near 0.01, 0.1, 1.1, and 30 ms. Two different kinds of sequential models were evaluated, one linear and the other branched. Although past kinetic analyses have emphasized the linear sequential model, the complexity of the intramolecular electron transfer in this enzyme suggests that a branched model be considered. This is especially true in a single-turnover experiment where earlier optical and EPR studies have pointed unequivocally to a branched model [Clore et al. (1980) Biochem. J. 185, 139-154; Blair et al. (1985) J. Am. Chem. Soc. 107, 7389-7399]. In the present study, analysis of spectral data in terms of the linear model did not reveal the formation and decay of the expected oxyferryl intermediate, whereas analysis of the branched model did. The results obtained using the branched model are consistent with all of the available evidence from a broad range of physical techniques that have been applied to examine the single-turnover kinetics of the oxidation of reduced cytochrome aa3 by O2.

Intramolecular electron transfer in yeast flavocytochrome b2 upon one-electron photooxidation of the fully reduced enzyme: evidence for redox state control of heme-flavin communication

Flavocytochrome b2, which has been fully reduced using L-lactate, can be rapidly oxidized by 1 equiv using the laser-generated triplet state of 5-deazariboflavin. Parallel photoinduced oxidation occurs at the reduced heme and at the fully reduced FMN (FMNH2) prosthetic groups of different enzyme monomers, producing the anion semiquinone of FMN and a ferric heme. Following the initial oxidation reaction, rapid intramolecular reduction of the ferric heme occurs with concomitant oxidation of FMNH2, generating the neutral FMN semiquinone. The observed rate constant for this intramolecular electron transfer is 2200 s-1, which is 1 order of magnitude larger than the turnover number under these conditions. A slower reduction of the heme prosthetic group also occurs with an observed rate constant of approximately 10 s-1, perhaps due to intersubunit electron transfer from reduced FMN to heme. The rapid intramolecular electron transfer between the FMNH2 and ferric heme is eliminated upon addition of excess pyruvate (Ki = 3.8 mM). This latter result indicates that pyruvate inhibition of catalytic turnover apparently can occur at the FMNH2-->heme electron transfer step. These results markedly differ from those previously obtained (Walker, M. C., & Tollin, G. (1991) Biochemistry 30, 5546-5555) and confirmed here for electron transfer within the one-electron reduced enzyme and for the effect of pyruvate binding, suggesting that intramolecular communication between the heme and flavin prosthetic groups can be controlled by the redox state of the enzyme and by ligand binding to the active site.

Membrane-mediated control of the bacteriorhodopsin photocycle

The ability of actinic light to modify the proportion of fast and slow forms of the M intermediate (i.e., Mf and M(s)) in the bacteriorhodopsin (BR) photocycle is lost by exposure of the purple membrane (PM) to 0.05% Triton for 1-2 min. The decay path of Mf through the O intermediate is also lost, and new, much slower kinetic forms of M appear. In this brief exposure, the trimer structure for BR, as measured by circular dichroism (CD) exciton coupling and sedimentability, is unaffected. The optical properties of the treated PM are affected within seconds of exposure to the detergent as indicated by an increase in transmittance and a blue shift in the wavelength of maximum absorbance for the ground state. Different concentrations of Triton cause reproducibly different changes in the kinetics of the system. These observations support the view that the BR trimer-membrane interaction is important in controlling the BR photocycle.

Influence of excitation energy on the bacteriorhodopsin photocycle

Kinetic curves for the bacteriorhodopsin (BR) photocycle were obtained both at 570 and at 412 nm at a series of increasing levels of intensity of the exciting laser. Singular value decomposition (SVD) of these curves showed two transitions in the kinetic profiles that occurred at specific levels of actinic light. This means that the photocycle was influenced by photon density in two ways. In a separate application of SVD, time-resolved optical spectra were analyzed at each of many levels of exciting laser intensities. The studies showed that the transition at the low level of laser intensity was due principally to an increase in the amount of BR that was turning over. The transition at the higher level of laser intensity showed a fundamental change in kinetics of the photocycle. At low intensity levels, the fast form of M (Mf) predominated, whereas at high levels the slow form of M (Ms) predominated. A distinction was found between Mf and Ms, in that the former decayed directly to the O intermediate whereas the latter decayed directly to BR.

Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners

Singular value decomposition (SVD) is deeply rooted in the theory of linear algebra, and because of this is not readily understood by a large group of researchers who could profit from its application. In this paper, we discuss the subject on a level that should be understandable to scientists who are not well versed in linear algebra. However, because it is necessary that certain key concepts in linear algebra be appreciated in order to comprehend what is accomplished by SVD, we present the section, 'Bare basics of linear algebra'. This is followed by a discussion of the theory of SVD. Next we present step-by-step examples to illustrate how SVD is applied to deconvolute a titration involving a mixture of three pH indicators. One noiseless case is presented as well as two cases where either a fixed or varying noise level is present. Finally, we discuss additional deconvolutions of mixed spectra based on the use of the pseudoinverse.