Practical model fitting approaches to the direct extraction of NMR parameters simultaneously from all dimensions of multidimensional NMR spectra.

A maximum likelihood (ML)-based approach has been established for the direct extraction of NMR parameters (e.g., frequency, amplitude, phase, and decay rate) simultaneously from all dimensions of a D-dimensional NMR spectrum. The approach, referred to here as HTFD-ML (hybrid time frequency domain maximum likelihood), constructs a time-domain model composed of a sum of exponentially-decaying sinusoidal signals. The apodized Fourier transform of this time-domain signal is a model spectrum that represents the 'best-fit' to the equivalent frequency-domain data spectrum. The desired amplitude and frequency parameters can be extracted directly from the signal model constructed by the HTFD-ML algorithm. The HTFD-ML approach presented here, as embodied in the software package CHIFIT, is designed to meet the challenges posed by model fitting of D-dimensional NMR data sets, where each consists of many data points (10(8) is not uncommon) encoding information about numerous signals (up to 10(5) for a protein of moderate size) that exhibit spectral overlap. The suitability of the approach is demonstrated by its application to the concerted analysis of a series of ten 2D 1H-15N HSQC experiments measuring 15N T1 relaxation. In addition to demonstrating the practicality of performing maximum likelihood analysis on large, multidimensional NMR spectra, the results demonstrate that this parametric model-fitting approach provides more accurate amplitude and frequency estimates than those obtained from conventional peak-based analysis of the FT spectrum. The improved performance of the model fitting approach derives from its ability to take into account the simultaneous contributions of all signals in a crowded spectral region (deconvolution) as well as to incorporate prior knowledge in constructing models to fit the data.

Light-dependent modification of Photosystem II in spinach leaves.

In dark-adapted spinach leaves approximately one third of the Photosystem II (PS II) reaction centers are impaired in their ability to transfer electrons to Photosystem I. Although these 'inactive' PS II centers are capable of reducing the primary quinone acceptor, QA, oxidation of QA (-) occurs approximately 1000 times more slowly than at 'active' centers. Previous studies based on dark-adapted leaves show that minimal energy transfer occurs from inactive centers to active centers, indicating that the quantum yield of photosynthesis could be significantly impaired by the presence of inactive centers. The objective of the work described here was to determine the performance of inactive PS II centers in light-adapted leaves. Measurements of PS II activity within leaves did not indicate any increase in the concentration of active PS II centers during light treatments between 10 s and 5 min, showing that inactive centers are not converted to active centers during light treatment. Light-induced modification of inactive PS II centers did occur, however, such that 75% of these centers were unable to sustain stable charge separation. In addition, the maximum yield of chlorophyll fluorescence associated with inactive PS II centers decreased substantially, despite the lack of any overall quenching of the maximum fluorescence yield. The effect of light treatment on inactive centers was reversed in the dark within 10-20 mins. These results indicate that illumination changes inactive PS II centers into a form that quenches fluorescence, but does not allow stable charge separation across the photosynthetic membrane. One possibility is that inactive centers are converted into centers that quench fluorescence by formation of a radical, such as reduced pheophytin or oxidized P680. Alternatively, it is possible that inactive PS II centers are modified such that absorbed excitation energy is dissipated thermally, through electron cycling at the reaction center.

Theory and application of the maximum likelihood principle to NMR parameter estimation of multidimensional NMR data.

A general theory has been developed for the application of the maximum likelihood (ML) principle to the estimation of NMR parameters (frequency and amplitudes) from multidimensional time-domain NMR data. A computer program (ChiFit) has been written that carries out ML parameter estimation in the D-1 indirectly detected dimensions of a D-dimensional NMR data set. The performance of this algorithm has been tested with experimental three-dimensional (HNCO) and four-dimensional (HN(CO)-CAHA) data from a small protein labeled with 13C and 15N. These data sets, with different levels of digital resolution, were processed using ChiFit for ML analysis and employing conventional Fourier transform methods with prior extrapolation of the time-domain dimensions by linear prediction. Comparison of the results indicates that the ML approach provides superior frequency resolution compared to conventional methods, particularly under conditions of limited digital resolution in the time-domain input data, as is characteristic of D-dimensional NMR data of biomolecules. Close correspondence is demonstrated between the results of analyzing multidimensional time-domain NMR data by Fourier transformation, Bayesian probability theory [Chylla, R.A. and Markley, J.L. (1993) J. Biomol. NMR, 3, 515-533], and the ML principle.

Improved frequency resolution in multidimensional constant-time experiments by multidimensional Bayesian analysis.

The resolution of spectral frequencies in NMR data obtained from discrete Fourier transformation (DFT) along D constant-time dimensions can be improved significantly through extrapolation of the D-dimensional free induction decay (FID) by multidimensional Bayesian analysis. Starting from Bayesian probability theory for parameter estimation and model detection of one-dimensional time-domain data [Bretthorst, (1990) J. Magn. Reson., 88, 533-551; 552-570; 571-595], a theory for the D-dimensional case has been developed and implemented in an algorithm called BAMBAM (BAyesian Model Building Algorithm in Multidimensions). BAMBAM finds the most probable sinusoidal model to account for the systematic portion of any D-dimensional stationary FID. According to the parameters estimated by the algorithm, the FID is extrapolated in D dimensions prior to apodization and Fourier transformation. Multidimensional Bayesian analysis allows for the detection of signals not resolved by the DFT alone or even by sequential one-dimensional extrapolation from mirror-image linear prediction prior to the DFT. The procedure has been tested with a theoretical two-dimensional dataset and with four-dimensional HN(CO)CAHA (Kay et al. (1992) J. Magn. Reson., 98, 443-450) data from a small protein (8 kDa) where BAMBAM was applied to the 13C alpha and H alpha constant-time dimensions.

Light saturation response of inactive photosystem II reaction centers in spinach.

The effective absorption cross section of inactive photosystem II (PS II) centers, which is the product of the effective antenna size and the quantum yield for photochemistry, was investigated by comparing the light saturation curves of inactive PS II and active reaction centers in intact chloroplasts and thylakoid membranes of spinach (Spinacia oleracea). Inactive PS II centers are defined as the impaired PS II reaction centers that require greater than 50 ms for the reoxidation of QA (-) subsequent to a single turnover flash. Active reaction centers are defined as the rapidly turning over PS II centers (recovery time less than 50 ms) and all of the PS I centers. The electrochromic shift, measured by the flash-induced absorbance increase at 518 nm, was used to probe the activity of the reaction centers. Light saturation curves were generated for inactive PS II centers and active reaction centers by measuring the extent of the absorbance increase at 518 nm induced by red actinic flashes of variable energy. The light saturation curves show that inactive PS II centers required over twice as many photons as active reaction centers to achieve the same yield. The ratio of the flash energy required for 50% saturation for active reaction centers (PS II active + PS I) compared to inactive PS II centers was 0.45±0.04 in intact chloroplasts, and 0.54±0.11 in thylakoid membranes. Analysis of the light saturation curves using a Poisson statistical model in which the ratio of the antenna size of active PS II centers to that of PS I is considered to range from 1 to 1.5, indicates that the effective absorption cross section of inactive PS II centers was 0.54-0.37 times that of active PS II centers. If the quantum yield for photochemistry is assumed to be one, we estimate that the antenna system serving the inactive PS II centers contains approx. 110 chlorophyll molecules.

Inactive Photosystem II Complexes in Leaves : Turnover Rate and Quantitation.

The flash-induced electrochromic shift, measured by the amplitude of the rapid absorbance increase at 518 nanometers (DeltaA518), was used to determine the amount of charge separation within photosystems II and I in spinach (Spinacia oleracea L.) leaves. The recovery time of the reaction centers was determined by comparing the amplitudes of DeltaA518 induced by two flashes separated by a variable time interval. The recovery of the DeltaA518 on the second flash revealed that 20% of the reaction centers exhibited a recovery half-time of 1.7 +/- 0.3 seconds, which is 1000 times slower than normally active reaction centers. Measurements using isolated thylakoid membranes showed that photosystem I constituted 38% of the total number of reaction centers, and that the photosystem I reaction centers were nearly fully active, indicating that the slowly turning over reaction centers were due solely to photosystem II. The results demonstrate that in spinach leaves approximately 32% of the photosystem II complexes are effectively inactive, in that their contribution to energy conversion is negligible. Additional evidence for inactive photosystem II complexes in spinach leaves was provided by fluorescence induction measurements, used to monitor the oxidation kinetics of the primary quinone acceptor of photosystem II, Q(A), after a short flash. The measurements showed that in a fraction of the photosystem II complexes the oxidation of Q(A) (-) was slow, displaying a half-time of 1.5 +/- 0.3 seconds. The kinetics of Q(A) (-) oxidation were virtually identical to the kinetics of the recovery of photosystem II determined from the electrochromic shift. The key difference between active and inactive photosystem II centers is that in the inactive centers the oxidation rate of Q(A) (-) is slow compared to active centers. Measurements of the electrochromic shift in detached leaves from several different species of plants revealed a significant fraction of slowly turning over reaction centers, raising the possibility that reaction centers that are inefficient in energy conversion may be a common feature in plants.