Optimization of resolution and sensitivity of 4D NOESY using Multi-dimensional Decomposition

Highly resolved multi-dimensional NOE data are essential for rapid and accurate determination of spatial protein structures such as in structural genomics projects. Four-dimensional spectra contain almost no spectral overlap inherently present in lower dimensionality spectra and are highly amenable to application of automated routines for spectral resonance location and assignment. However, a high resolution 4D data set using conventional uniform sampling usually requires unacceptably long measurement time. Recently we have reported that the use of non-uniform sampling and multi-dimensional decomposition (MDD) can remedy this problem. Here we validate accuracy and robustness of the method, and demonstrate its usefulness for fully protonated protein samples. The method was applied to 11 kDa protein PA1123 from structural genomics pipeline. A systematic evaluation of spectral reconstructions obtained using 15–100% subsets of the complete reference 4D ¹H–¹³C–¹³C–¹H NOESY spectrum has been performed. With the experimental time saving of up to six times, the resolution and the sensitivity per unit time is shown to be similar to that of the fully recorded spectrum. For the 30% data subset we demonstrate that the intensities in the reconstructed and reference 4D spectra correspond with a correlation coefficient of 0.997 in the full range of spectral amplitudes. Intensities of the strong, middle and weak cross-peaks correlate with coefficients 0.9997, 0.9965, and 0.83. The method does not produce false peaks. 2% of weak peaks lost in the 30% reconstruction is in line with theoretically expected noise increase for the shorter measurement time. Together with good accuracy in the relative line-widths these translate to reliable distance constrains derived from sparsely sampled, high resolution 4D NOESY data.     

Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins

Central to structural studies of biomolecules are multidimensional experiments. These are lengthy to record due to the requirement to sample the full Nyquist grid. Time savings can be achieved through undersampling the indirectly-detected dimensions combined with non-Fourier Transform (FT) processing, provided the experimental signal-to-noise ratio is sufficient. Alternatively, resolution and signal-to-noise can be improved within a given experiment time. However, non-FT based reconstruction of undersampled spectra that encompass a wide signal dynamic range is strongly impeded by the non-linear behaviour of many methods, which further compromises the detection of weak peaks. Here we show, through an application to a larger α-helical membrane protein under crowded spectral conditions, the potential use of compressed sensing (CS) l (1)-norm minimization to reconstruct undersampled 3D NOESY spectra. Substantial signal overlap and low sensitivity make this a demanding application, which strongly benefits from the improvements in signal-to-noise and resolution per unit time achieved through the undersampling approach. The quality of the reconstructions is assessed under varying conditions. We show that the CS approach is robust to noise and, despite significant spectral overlap, is able to reconstruct high quality spectra from data sets recorded in far less than half the amount of time required for regular sampling.     

Differences in lysine pKa values may be used to improve NMR signal dispersion in reductively methylated proteins

Reductive methylation of lysine residues in proteins offers a way to introduce ¹³C methyl groups into otherwise unlabeled molecules. The ¹³C methyl groups on lysines possess favorable relaxation properties that allow highly sensitive NMR signal detection. One of the major limitations in the use of reductive methylation in NMR is the signal overlap of ¹³C methyl groups in NMR spectra. Here we show that the uniform influence of the solvent on chemical shifts of exposed lysine methyl groups could be overcome by adjusting the pH of the buffering solution closer to the pKa of lysine side chains. Under these conditions, due to variable pKa values of individual lysine side chains in the protein of interest different levels of lysine protonation are observed. These differences are reflected in the chemical shift differences of methyl groups in reductively methylated lysines. We show that this approach is successful in four different proteins including Ca²⁺-bound Calmodulin, Lysozyme, Ca²⁺-bound Troponin C, and Glutathione S-Transferase. In all cases significant improvement in NMR spectral resolution of methyl signals in reductively methylated proteins was obtained. The increased spectral resolution helps with more precise characterization of protein structural rearrangements caused by ligand binding as shown by studying binding of Calmodulin antagonist trifluoperazine to Calmodulin. Thus, this approach may be used to increase resolution in NMR spectra of ¹³C methyl groups on lysine residues in reductively methylated proteins that enhances the accuracy of protein structural assessment. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Two-dimensional 1H NMR studies of histidine-containing protein from Escherichia coli. 1. Sequential resonance assignments

Two-dimensional NMR studies at 500 MHz have been performed on the histidine-containing protein (HPr) from Escherichia coli. HPr is one of the phosphocarrier proteins involved in the bacterial phosphoenolpyruvate:sugar phosphotransferase system that is responsible for the concomitant phosphorylation and translocation of a number of sugars. Sequential resonance assignments of HPr are complete. The conventional method of sequential assignments involving J-correlated spectroscopy (COSY) and nuclear Overhauser spectroscopy (NOESY) has been supplemented by optimized relayed coherence transfer spectroscopy (RELAY) to help overcome the spectral overlap that is inevitable in the spectra of proteins the size of HPr. RELAY experiments were performed in H2O to obtain NH-C beta H connectivities and in D2O to obtain C alpha H-C gamma H connectivities. The abundance of relayed coherence transfer peaks in the two experiments greatly aided in the assignment process of the complicated protein spectrum. The assignments lay the groundwork for the determination of the solution structure of HPr, as described in the accompanying paper [Klevit, R. E., & Waygood, E. B. (1986) Biochemistry (third paper of three in this issue)].     

Protein localization in living cells and tissues using FRET and FLIM

Interacting proteins assemble into molecular machines that control cellular homeostasis in living cells. While the in vitro screening methods have the advantage of providing direct access to the genetic information encoding unknown protein partners, they do not allow direct access to interactions of these protein partners in their natural environment inside the living cell. Using wide-field, confocal, or two-photon (2p) fluorescence resonance energy transfer (FRET) microscopy, this information can be obtained from living cells and tissues with nanometer resolution. One of the important conditions for FRET to occur is the overlap of the emission spectrum of the donor with the absorption spectrum of the acceptor. As a result of spectral overlap, the FRET signal is always contaminated by donor emission into the acceptor channel and by the excitation of acceptor molecules by the donor excitation wavelength. Mathematical algorithms are required to correct the spectral bleed-through signal in wide-field, confocal, and two-photon FRET microscopy. In contrast, spectral bleed-through is not an issue in FRET/FLIM imaging because only the donor fluorophore lifetime is measured; also, fluorescence lifetime imaging microscopy (FLIM) measurements are independent of excitation intensity or fluorophore concentration. The combination of FRET and FLIM provides high spatial (nanometer) and temporal (nanosecond) resolution when compared to intensity-based FRET imaging. In this paper, we describe various FRET microscopy techniques and its application to protein-protein interactions.     

Protein NMR structure determination with automated NOE-identification in the NOESY spectra using the new software ATNOS

Novel algorithms are presented for automated NOESY peak picking and NOE signal identification in homonuclear 2D and heteronuclear-resolved 3D [¹H,¹H]-NOESY spectra during de novoprotein structure determination by NMR, which have been implemented in the new software ATNOS (automated NOESY peak picking). The input for ATNOS consists of the amino acid sequence of the protein, chemical shift lists from the sequence-specific resonance assignment, and one or several 2D or 3D NOESY spectra. In the present implementation, ATNOS performs multiple cycles of NOE peak identification in concert with automated NOE assignment with the software CANDID and protein structure calculation with the program DYANA. In the second and subsequent cycles, the intermediate protein structures are used as an additional guide for the interpretation of the NOESY spectra. By incorporating the analysis of the raw NMR data into the process of automated de novoprotein NMR structure determination, ATNOS enables direct feedback between the protein structure, the NOE assignments and the experimental NOESY spectra. The main elements of the algorithms for NOESY spectral analysis are techniques for local baseline correction and evaluation of local noise level amplitudes, automated determination of spectrum-specific threshold parameters, the use of symmetry relations, and the inclusion of the chemical shift information and the intermediate protein structures in the process of distinguishing between NOE peaks and artifacts. The ATNOS procedure has been validated with experimental NMR data sets of three proteins, for which high-quality NMR structures had previously been obtained by interactive interpretation of the NOESY spectra. The ATNOS-based structures coincide closely with those obtained with interactive peak picking. Overall, we present the algorithms used in this paper as a further important step towards objective and efficient de novoprotein structure determination by NMR.     

Covariance NMR in higher dimensions: application to 4D NOESY spectroscopy of proteins

Elucidation of high-resolution protein structures by NMR spectroscopy requires a large number of distance constraints that are derived from nuclear Overhauser effects between protons (NOEs). Due to the high level of spectral overlap encountered in 2D NMR spectra of proteins, the measurement of high quality distance constraints requires higher dimensional NMR experiments. Although four-dimensional Fourier transform (FT) NMR experiments can provide the necessary kind of spectral information, the associated measurement times are often prohibitively long. Covariance NMR spectroscopy yields 2D spectra that exhibit along the indirect frequency dimension the same high resolution as along the direct dimension using minimal measurement time. The generalization of covariance NMR to 4D NMR spectroscopy presented here exploits the inherent symmetry of certain 4D NMR experiments and utilizes the trace metric between donor planes for the construction of a high-resolution spectral covariance matrix. The approach is demonstrated for a 4D (13)C-edited NOESY experiment of ubiquitin. The 4D covariance spectrum narrows the line-widths of peaks strongly broadened in the FT spectrum due to the necessarily short number of increments collected, and it resolves otherwise overlapped cross peaks allowing for an increase in the number of NOE assignments to be made from a given dataset. At the same time there is no significant decrease in the positive predictive value of observing a peak as compared to the corresponding 4D Fourier transform spectrum. These properties make the 4D covariance method a potentially valuable tool for the structure determination of larger proteins and for high-throughput applications in structural biology.     

Structural determination of biomolecular interfaces by nuclear magnetic resonance of proteins with reduced proton density

Protein interactions are important for understanding many molecular mechanisms underlying cellular processes. So far, interfaces between interacting proteins have been characterized by NMR spectroscopy mostly by using chemical shift perturbations and cross-saturation via intermolecular cross-relaxation. Although powerful, these techniques cannot provide unambiguous estimates of intermolecular distances between interacting proteins. Here, we present an alternative approach, called REDSPRINT (REDduced/Standard PRoton density INTerface identification), to map protein interfaces with greater accuracy by using multiple NMR probes. Our approach is based on monitoring the cross-relaxation from a source protein (or from an arbitrary ligand that need not be a protein) with high proton density to a target protein (or other biomolecule) with low proton density by using isotope-filtered nuclear Overhauser spectroscopy (NOESY). This methodology uses different isotropic labeling for the source and target proteins to identify the source-target interface and also determine the proton density of the source protein at the interface for protein-protein or protein-ligand docking. Simulation indicates significant gains in sensitivity because of the resultant relaxation properties, and the utility of this technique, including a method for direct determination of the protein interface, is demonstrated for two different protein–protein complexes.     

In-cell NMR for protein-protein interactions (STINT-NMR)

We describe an in-cell NMR-based method for mapping the structural interactions (STINT-NMR) that underlie protein-protein complex formation. This method entails sequentially expressing two (or more) proteins within a single bacterial cell in a time-controlled manner and monitoring their interactions using in-cell NMR spectroscopy. The resulting NMR data provide a complete titration of the interaction and define structural details of the interacting surfaces at atomic resolution. Unlike the case where interacting proteins are simultaneously overexpressed in the labeled medium, in STINT-NMR the spectral complexity is minimized because only the target protein is labeled with NMR-active nuclei, which leaves the interactor protein(s) cryptic. This method can be combined with genetic and molecular screens to provide a structural foundation for proteomic studies. The protocol takes 4 d from the initial transformation of the bacterial cells to the acquisition of the NMR spectra.     

Automated assignment and 3D structure calculations using combinations of 2D homonuclear and 3D heteronuclear NOESY spectra

The NOAH/DIAMOD suite uses feedback filtering and self-correcting distance geometry to generate 3D structures from unassigned NOESY spectra. In this study we determined the minimum set of experiments needed to generate a high quality structure bundle. Different combinations of 3D ¹⁵N-edited, ¹³C-edited HSQC-NOESY and 2D homonuclear ¹H-¹H NOESY spectra of the 77 amino acid protein, myeloid progenitor inhibitory factor-1 (MPIF-1) were used as input for NOAH/DIAMOD calculations. The quality of the assignments of NOESY cross peaks and the accuracy of the automatically generated 3D structures were compared to those obtained with a conventional manual procedure. Combining data from two types of experiments synergistically increased the number of peaks assigned unambiguously in both individual spectra. As a general trend for the accuracy of the structures we observed structural variations in the backbone fold of the final structures of about 2 Å for single spectral data, of 1 Å to 1.5 Å for double spectral data, and of 0.6 Å for triple spectral data sets. The quality of the assignments and 3D structures from the optimal data using all three spectra were similar to those obtained from traditional assignment methods with structural variations within the bundle of 0.6 Å and 1.3 Å for backbone and heavy atoms, respectively. Almost all constraints (97%) of the automatic NOESY cross peak assignments were cross compatible with the structures from the conventional manual assignment procedure, and an even larger proportion (99%) of the manually derived constraints were compatible with the automatically determined 3D structures. The two mean structures determined by both methods differed only by 1.3 Å rmsd for the backbone atoms in the well-defined regions of the protein. Thus NOAD/DIAMOD analysis of spectra from labeled proteins provides a reliable method for high throughput analysis of genomic targets.     

Resolution and sensitivity of high field nuclear magnetic resonance spectroscopy

NMR frequency assignments are usually considered a prerequisite for the analysis of NOESY spectra, in turn required for the calculation of biomolecular structures. In contrast, as we propose here, relatively high numbers of unambiguous NOE identities can be consistently achieved in an automated manner by relying only on grouping resonances into connected spin systems. To achieve this goal, we have developed for proteins two protocols, SPI and BACUS, based on Bayesian inference. SPI (Grishaev and Llinás, 2002c) produces a list of the (1)H resonance frequencies from homo- and hetero-nuclear multidimensional spectra, grouped into effective spin systems. BACUS automatically establishes probabilistic identities of NOESY cross-peaks in terms of the chemical shifts provided by SPI. BACUS requires neither assignment of resonances nor an initial structural model. It successfully copes with chemical shift overlap and does so without cycling through 3D structure calculations. The method exploits the self-consistency of the NOESY graph by taking advantage of a network of J- as well as NOE-connected "reporter" protons sorted via SPI. BACUS was validated by tests on experimental NOESY data recorded for the col 2 and kringle 2 domains.     

Susceptibility of Different Proteins to Flow-Induced Conformational Changes Monitored with Raman Spectroscopy

By directly monitoring stirred protein solutions with Raman spectroscopy, the reversible unfolding of proteins caused by fluid shear is examined for several natural proteins with varying structural properties and molecular weight. While complete denaturation is not observed, a wide range of spectral variances occur for the different proteins, indicating subtle conformational changes that appear to be protein-specific. A number of significant overall trends are apparent from the study. For globular proteins, the overall extent of spectral variance increases with protein size and the proportion of β-structure. For two less structured proteins, fetuin and α-casein, the observed changes are of relatively low magnitude, despite the greater molecular structural mobility of these proteins. This implies that other protein-specific factors, such as posttranslational modifications, may also be significant. Individual band changes occurring in the spectral profiles of each individual protein are also discussed in detail.     

Four-dimensional heteronuclear correlation experiments for chemical shift assignment of solid proteins

Chemical shift assignment is the first step in all established protocols for structure determination of uniformly labeled proteins by NMR. The explosive growth in recent years of magic-angle spinning (MAS) solid-state NMR (SSNMR) applications is largely attributable to improved methods for backbone and side-chain chemical shift correlation spectroscopy. However, the techniques developed so far have been applied primarily to proteins in the size range of 5–10 kDa, despite the fact that SSNMR has no inherent molecular weight limits. Rather, the degeneracy inherent to many 2D and 3D SSNMR spectra of larger proteins has prevented complete unambiguous chemical shift assignment. Here we demonstrate the implementation of 4D backbone chemical shift correlation experiments for assignment of solid proteins. The experiments greatly reduce spectral degeneracy at a modest cost in sensitivity, which is accurately described by theory. We consider several possible implementations and investigate the CANCOCX pulse sequence in detail. This experiment involves three cross polarization steps, from H to CA[i], CA[i] to N[i], and N[i] to C′[i−1], followed by a final homonuclear mixing period. With short homonuclear mixing times (<20 ms), backbone correlations are observed with high sensitivity; with longer mixing times (>200 ms), long-range correlations are revealed. For example, a single 4D experiment with 225 ms homonuclear mixing time reveals ∼200 uniquely resolved medium and long-range correlations in the 56-residue protein GB1. In addition to experimental demonstrations in the 56-residue protein GB1, we present a theoretical analysis of anticipated improvements in resolution for much larger proteins and compare these results in detail with the experiments, finding good agreement between experiment and theory under conditions of stable instrumental performance.     

Prediction of peak overlap in NMR spectra

Peak overlap is one of the major factors complicating the analysis of biomolecular NMR spectra. We present a general method for predicting the extent of peak overlap in multidimensional NMR spectra and its validation using both, experimental data sets and Monte Carlo simulation. The method is based on knowledge of the magnetization transfer pathways of the NMR experiments and chemical shift statistics from the Biological Magnetic Resonance Data Bank. Assuming a normal distribution with characteristic mean value and standard deviation for the chemical shift of each observable atom, an analytic expression was derived for the expected overlap probability of the cross peaks. The analytical approach was verified to agree with the average peak overlap in a large number of individual peak lists simulated using the same chemical shift statistics. The method was applied to eight proteins, including an intrinsically disordered one, for which the prediction results could be compared with the actual overlap based on the experimentally measured chemical shifts. The extent of overlap predicted using only statistical chemical shift information was in good agreement with the overlap that was observed when the measured shifts were used in the virtual spectrum, except for the intrinsically disordered protein. Since the spectral complexity of a protein NMR spectrum is a crucial factor for protein structure determination, analytical overlap prediction can be used to identify potentially difficult proteins before conducting NMR experiments. Overlap predictions can be tailored to particular classes of proteins by preparing statistics from corresponding protein databases. The method is also suitable for optimizing recording parameters and labeling schemes for NMR experiments and improving the reliability of automated spectra analysis and protein structure determination.     

Prospects for resonance assignments in multidimensional solid-state NMR spectra of uniformly labeled proteins

Summary The feasibility of assigning the backbone ¹⁵N and ¹³C NMR chemical shifts in multidimensional magic angle spinning NMR spectra of uniformly isotopically labeled proteins and peptides in unoriented solid samples is assessed by means of numerical simulations. The goal of these simulations is to examine how the upper limit on the size of a peptide for which unique assignments can be made depends on the spectral resolution, i.e., the NMR line widths. Sets of simulated three-dimensional chemical shift correlation spectra for artificial peptides of varying length are constructed from published liquid-state NMR chemical shift data for ubiquitin, a well-characterized soluble protein. Resonance assignments consistent with these spectra to within the assumed spectral resolution are found by a numerical search algorithm. The dependence of the number of consistent assignments on the assumed spectral resolution and on the length of the peptide is reported. If only three-dimensional chemical shift correlation data for backbone ¹⁵N and ¹³C nuclei are used, and no residue-specific chemical shift information, information from amino acid side-chain signals, and proton chemical shift information are available, a spectral resolution of 1 ppm or less is generally required for a unique assignment of backbone chemical shifts for a peptide of 30 amino acid residues.     

MQ-HNCO-TROSY for the measurement of scalar and residual dipolar couplings in larger proteins: application to a 557-residue IgFLNa16-21

We describe a novel pulse sequence, MQ-HNCO-TROSY, for the measurement of scalar and residual dipolar couplings between amide proton and nitrogen in larger proteins. The experiment utilizes the whole 2T_N polarization transfer delay for labeling of ¹⁵N chemical shift in a constant time manner, which efficiently doubles the attainable resolution in ¹⁵N dimension with respect to the conventional HNCO-TROSY experiment. In addition, the accordion principle is employed for measuring (J + D)_NHs, and the multiplet components are selected with the generalized version of the TROSY scheme introduced by Nietlispach (J Biomol NMR 31:161–166, 2005). Therefore, cross peak overlap is diminished while the time period during which the ¹⁵N spin is susceptible to fast transverse relaxation associated with the anti-TROSY transition is minimized per attainable resolution unit. The proposed MQ-HNCO-TROSY scheme was employed for measuring RDCs in high molecular weight protein IgFLNa16-21 of 557 residues, resulting in 431 experimental RDCs. Correlations between experimental and back-calculated RDCs in individual domains gave relatively low Q-factors (0.19–0.39), indicative of sufficient accuracy that can be obtained with the proposed MQ-HNCO-TROSY experiment in high molecular weight proteins.     

Four-dimensional 13C/13C-edited nuclear Overhauser enhancement spectroscopy of a protein in solution: application to interleukin 1 beta

A four-dimensional 13C/13C-edited NOESY experiment is described which dramatically improves the resolution of protein NMR spectra and enables the straightforward assignment of nuclear Overhauser effects involving aliphatic and/or aromatic protons in larger proteins. The experiment is demonstrated for uniformly (greater than 95%) 13C-labeled interleukin 1 beta, a protein of 153 residues and 17.4 kDa, which plays a key role in the immune response. NOEs between aliphatic and/or aromatic protons are first spread out into a third dimension by the 13C chemical shift of the carbon atom attached to the originating proton and subsequently into a fourth dimension by the 13C chemical shift of the carbon atom attached to the destination proton. Thus, each NOE cross peak is labeled by four chemical shifts. By this means, ambiguities in the assignment of NOEs that arise from chemical shift overlap and degeneracy are completely removed. Further, NOEs between protons with the same chemical shifts can readily be detected providing their attached carbon atoms have different 13C chemical shifts. The design of the pulse sequence requires special care to minimize the level of artifacts arising from undesired coherence transfer pathways, and in particular those associated with "diagonal" peaks which correspond to magnetization that has not been transferred from one proton to another.(ABSTRACT TRUNCATED AT 250 WORDS)     

Resolution enhanced homonuclear carbon decoupled triple resonance experiments for unambiguous RNA structural characterization

Large RNAs (>30 nucleotides) suffer from extensive resonance overlap that can seriously hamper unambiguous structural characterization. Here we present a set of 3D multinuclear NMR experiments with improved and optimized resolution and sensitivity for aiding with the assignment of RNA molecules. In all these experiments strong base and ribose carbon–carbon couplings are eliminated by homonuclear band-selective decoupling, leading to improved signal to noise and resolution of the C5, C6, and C1′ carbon resonances. This decoupling scheme is applied to base-type selective ¹³C-edited NOESY, ¹³C-edited TOCSY (HCCH, CCH), HCCNH, and ribose H1C1C2 experiments. The 3D implementation of the HCCNH experiment with both carbon and nitrogen evolution enables direct correlation of ¹³C and ¹⁵N resonances at different proton resonant frequencies. The advantages of the new experiments are demonstrated on a 36 nucleotides hairpin RNA from domain 5 (D5) of the group II intron Pylaiella littoralis using an abbreviated assignment strategy. These four experiments provided additional separation for regions of the RNA that have overlapped chemical shift resonances, and enabled the assignment of critical D5 bulge nucleotides that could not be assigned using current experimental schemes.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s10858-005-5093-6     

An efficient strategy for assignment of cross-peaks in 3D heteronuclear NOESY experiments

The question is addressed of how maximal structural NOE data on double labelled proteins can be acquired with a minimal set of NOESY experiments. Two 3D-NOESY spectra are reported which, in concert with other commonly used spectra, provide a convenient strategy for NOE assignment. The 3D CNH-NOESY and 3D NCH-NOESY provide NOE connectivities between amide protons and carbon-bound protons and constitute orthogonal heteronuclear filters which eliminate diagonal signals, considerably improving spectral quality. Two different heteronuclear chemical shift dimensions are recorded in the spectra, thus exploiting the extra dispersion of the heteronucleus and considerably simplifying assignment.     

1H NMR investigation of manganese peroxidase from Phanerochaete chrysosporium. A comparison with other peroxidases.

1H NMR spectra at 200- and 600-MHz of manganese peroxidase from Phanerochaete chrysosporium and of its cyanide derivative are reported. The spectrum of the native protein is very similar to that of other peroxidases. The assignment of the spectrum of the cyanide derivative has been performed through 1D NOE, 2D NOESY, and COSY experiments. This protein is very similar to lignin peroxidase, the only meaningful difference being the shift of H delta 2 of the proximal histidine. The spectra of the cyanide derivative of these two proteins are compared with those of horseradish peroxidase and cytochrome c peroxidase. The shift pattern of the protons of the proximal histidine is discussed relative to the structural properties which affect the Fe3+/Fe2+ redox potential.