Development of a method for reconstruction of crowded NMR spectra from undersampled time-domain data

NMR is a unique methodology for obtaining information about the conformational dynamics of proteins in heterogeneous biomolecular systems. In various NMR methods, such as transferred cross-saturation, relaxation dispersion, and paramagnetic relaxation enhancement experiments, fast determination of the signal intensity ratios in the NMR spectra with high accuracy is required for analyses of targets with low yields and stabilities. However, conventional methods for the reconstruction of spectra from undersampled time-domain data, such as linear prediction, spectroscopy with integration of frequency and time domain, and analysis of Fourier, and compressed sensing were not effective for the accurate determination of the signal intensity ratios of the crowded two-dimensional spectra of proteins. Here, we developed an NMR spectra reconstruction method, “conservation of experimental data in analysis of Fourier” (Co-ANAFOR), to reconstruct the crowded spectra from the undersampled time-domain data. The number of sampling points required for the transferred cross-saturation experiments between membrane proteins, photosystem I and cytochrome b ₆ f, and their ligand, plastocyanin, with Co-ANAFOR was half of that needed for linear prediction, and the peak height reduction ratios of the spectra reconstructed from truncated time-domain data by Co-ANAFOR were more accurate than those reconstructed from non-uniformly sampled data by compressed sensing.     

Temporal Data Set Reduction Based on D-Optimality for Quantitative FLIM-FRET Imaging

Fluorescence lifetime imaging (FLIM) when paired with Förster resonance energy transfer (FLIM-FRET) enables the monitoring of nanoscale interactions in living biological samples. FLIM-FRET model-based estimation methods allow the quantitative retrieval of parameters such as the quenched (interacting) and unquenched (non-interacting) fractional populations of the donor fluorophore and/or the distance of the interactions. The quantitative accuracy of such model-based approaches is dependent on multiple factors such as signal-to-noise ratio and number of temporal points acquired when sampling the fluorescence decays. For high-throughput or in vivo applications of FLIM-FRET, it is desirable to acquire a limited number of temporal points for fast acquisition times. Yet, it is critical to acquire temporal data sets with sufficient information content to allow for accurate FLIM-FRET parameter estimation. Herein, an optimal experimental design approach based upon sensitivity analysis is presented in order to identify the time points that provide the best quantitative estimates of the parameters for a determined number of temporal sampling points. More specifically, the D-optimality criterion is employed to identify, within a sparse temporal data set, the set of time points leading to optimal estimations of the quenched fractional population of the donor fluorophore. Overall, a reduced set of 10 time points (compared to a typical complete set of 90 time points) was identified to have minimal impact on parameter estimation accuracy (≈5%), with in silico and in vivo experiment validations. This reduction of the number of needed time points by almost an order of magnitude allows the use of FLIM-FRET for certain high-throughput applications which would be infeasible if the entire number of time sampling points were used.     

Fast evaluation of protein dynamics from deficient <Superscript>15</Superscript>N relaxation data

Simple and convenient method of protein dynamics evaluation from the insufficient experimental ¹⁵N relaxation data is presented basing on the ratios, products, and differences of longitudinal and transverse ¹⁵N relaxation rates obtained at a single magnetic field. Firstly, the proposed approach allows evaluating overall tumbling correlation time (nanosecond time scale). Next, local parameters of the model-free approach characterizing local mobility of backbone amide N–H vectors on two different time scales, S² and R _ex , can be elucidated. The generalized order parameter, S², describes motions on the time scale faster than the overall tumbling correlation time (pico- to nanoseconds), while the chemical exchange term, R _ex , identifies processes slower than the overall tumbling correlation time (micro- to milliseconds). Advantages and disadvantages of different methods of data handling are thoroughly discussed.     

Secondary structures of peptides: 5 · 15N n.m.r. CP/MAS spectroscopy of solid polypeptides and gramicidin-S

30.5 MHz ¹⁵N m.m.r. (CP/MAS) spectra of various solid polypeptides were measured using the cross-polarization/magic angle spinning technique. In order to obtain optimum signal-to-noise ratios, relatively short contact times (1 ± 0.5 ms) are required, because the cross-polarization times (T_NH) are short and because the proton rotating-frame relaxation times (T_1p) are in the order of 20 ms. The ¹⁵N n.m.r. signals of copolypeptides may be sensitive to sequence effects; yet they are in most cases more sensitive to the nature of the secondary structure. The signals of α-helices absorb ca. 8–10 ppm upfield of β-sheet structures, whereas the polyglycine II helix absorbs downfield. The natural abundance spectrum of crystalline gramicidin-S exhibits a signal at ?247 ppm, a characteristic chemical shift of the antiparallel pleated sheet structure.     

Practical considerations for investigation of protein conformational dynamics by <Superscript>15</Superscript>N <Emphasis Type="Italic">R</Emphasis><Subscript>1ρ</Subscript> relaxation dispersion

It is becoming increasingly apparent that proteins are not static entities and that their function often critically depends on accurate sampling of multiple conformational states in aqueous solution. Accordingly, the development of methods to study conformational states in proteins beyond their ground-state structure (“excited states”) has crucial biophysical importance. Here we investigate experimental schemes for optimally probing chemical exchange processes in proteins on the micro- to millisecond timescale by ¹⁵N R _1ρ relaxation dispersion. The schemes use selective Hartmann–Hahn cross-polarization (CP) transfer for excitation, and derive peak integrals from 1D NMR spectra (Korzhnev et al. in J Am Chem Soc 127:713–721, 2005; Hansen et al. in J Am Chem Soc 131:3818–3819, 2009). Simulation and experiment collectively show that in such CP-based schemes care has to be taken to achieve accurate suppression of undesired off-resonance coherences, when using weak spin-lock fields. This then (i) ensures that relaxation dispersion profiles in the absence of chemical exchange are flat, and (ii) facilitates extraction of relaxation dispersion profiles in crowded regions of the spectrum. Further improvement in the quality of the experimental data is achieved by recording the free-induction decays in an interleaved manner and including a heating-compensation element. The reported considerations will particularly benefit the use of CP-based R _1ρ relaxation dispersion to analyze conformational exchange processes in larger proteins, where resonance line overlap becomes the main limiting factor.     

Effect of Confinement on Melting in Slit-Shaped Pores: Experimental and Simulation Study of Aniline in Activated Carbon Fibers

Abstract

We report both experimental and molecular simulation studies of the melting behavior of aniline confined within an activated carbon fiber having slit-shaped pores. Dielectric relaxation spectroscopy is used to determine the transition temperatures and also the dielectric relaxation times over the temperature range 240 to 340 K. For the confined system two transitions were observed, one at 298 K and a second transition at 324 K. The measured relaxation times indicate that the low temperature phase (below 298 K) is a crystalline or partially crystalline solid phase, while that above 324 K is a liquid-like phase; for the intermediate phase, in the range 298–324 K, the relaxation times are of the order 10^?5s, which is typical of a hexatic phase. The melting temperature of the confined system is well above that of bulk aniline, which is 267 K. The simulations are carried out using the Grand Canonical Monte Carlo method together with Landau free energy calculations, and phase transitions are located as state points where the grand free energies of two confined phases are equal. The nature of these phases is determined by analysis of in-plane pair positional and orientational correlation functions. The simulations also show two transitions. The first is a transition from a two-dimensional hexagonal crystal phase to a hexatic phase at 296 K; the second transition is from the hexatic to a liquid-like phase at 336 K. Confinement within the slit-shaped pores appears to stabilize the hexatic phase, which is the stable phase over a wider temperature range than for quasi-two-dimensional thin films.     

Analysis of problems encountered in the determination of amino acid enantiomeric ratios by gas chromatography

A previously described procedure for determining the enantiomeric ratios of amino acids has produced inconsistent results when determining relatively low (≤0.110) d/l ratios. The method involves synthesis of diastereomeric N-trifluoroacetyl-l-prolyl-d/l-amino acid ester dipeptides which are resolved by gas chromatography (GC). We have found that triethylamine, which is added to maintain a basic pH during the coupling reaction, racemizes the chiral reagent N-trifluoroacetyl-l-prolyl chloride (TPC). Coupling of partially racemized TPC to d/l-amino acid esters results in the formation of four dipeptides (two pairs of enantiomers) instead of the expected two diastereomeric dipeptides. The enantiomeric dipeptides coelute on an achiral GC column, resulting in erroneous d/l ratios. More accurate d/l ratios are obtained by preparing the volatile N-trifluoroacetyl-d/l-amino acid isopropyl ester derivative which can be separated into its enantiomers on a chiral GC column such as the Chirasil-Val III (registered trademark of Applied Science Laboratories).     

Factors affecting the quantification of biomolecular interactions by fluorescence cross-correlation spectroscopy

Fluorescence cross-correlation spectroscopy (FCCS) is used to determine interactions and dissociation constants (K_ds) of biomolecules. The determination of a K_d depends on the accurate measurement of the auto- and cross-correlation function (ACF and CCF) amplitudes. In the case of complete binding, the ratio of the CCF/ACF amplitudes is expected to be 1. However, measurements performed on tandem fluorescent proteins (FPs), in which two different FPs are linked, yield CCF/ACF amplitude ratios of ～0.5 or less for different FCCS schemes. We use single wavelength FCCS and pulsed interleaved excitation FCCS to measure various tandem FPs constituted of different red and green FPs and determine the causes for this suboptimal ratio. The main causes for the reduced CCF/ACF amplitude ratio are differences in observation volumes for the different labels, the existence of dark FPs due to maturation problems, photobleaching, and to a lesser extent Förster (or fluorescence) resonance energy transfer between the labels. We deduce the fraction of nonfluorescent proteins for EGFP, mRFP, and mCherry as well as the differences in observation volumes. We use this information to correct FCCS measurements of the interaction of Cdc42, a small Rho-GTPase, with its effector IQGAP1 in live cell measurements to obtain a label-independent value for the K_d.     

Relaxation dynamics of the gel to liquid-crystalline transition of phosphatidylcholine bilayers. Effects of chainlength and vesicle size.

The relaxation kinetics of the gel to liquid-crystalline transition of five phosphatidylcholine (DC14PC to DC18PC) bilayer dispersions have been investigated using volume perturbation calorimetry, a steady-state technique which subjects a sample to sinusoidal changes in volume. Temperature and pressure responses to the volume perturbation are measured to monitor the relaxation to a new equilibrium position. The amplitude demodulation and phase shift of these observables are analyzed with respect to the perturbation frequency to yield relaxation times and amplitudes. In the limit of low perturbation frequency, the temperature and pressure responses are proportional to the equilibrium excess heat capacity and bulk modulus, respectively. At all temperatures, the thermal response data are consistent with a single primary relaxation process of the lipid. The less accurate bulk modulus data exhibit two relaxation times, but it is not clear whether they reflect lipid processes or are characteristic of the instrument. The observed thermal relaxation behavior of all multilamellar vesicles are quantitatively similar. The relaxation times vary from approximately 50 ms to 4 s, with a pronounced maximum at a temperature just greater than Tm, the temperature of the excess heat capacity maximum. Large unilamellar vesicles also exhibit a single relaxation process, but without a pronounced maximum in the relaxation time. Their relaxation time is approximately 80 ms over most of the transition range.     

Quantitative analysis of backbone motion in proteins using MAS solid-state NMR spectroscopy

We present a comprehensive analysis of protein dynamics for a micro-crystallin protein in the solid-state. Experimental data include ¹⁵N T ₁ relaxation times measured at two different magnetic fields as well as ¹H–¹⁵N dipole, ¹⁵N CSA cross correlated relaxation rates which are sensitive to the spectral density function J(0) and are thus a measure of T ₂ in the solid-state. In addition, global order parameters are included from a ¹H,¹⁵N dipolar recoupling experiment. The data are analyzed within the framework of the extended model-free Clore–Lipari–Szabo theory. We find slow motional correlation times in the range of 5 and 150 ns. Assuming a wobbling in a cone motion, the amplitude of motion of the respective amide moiety is on the order of 10° for the half-opening angle of the cone in most of the cases. The experiments are demonstrated using a perdeuterated sample of the chicken α-spectrin SH3 domain.     

Determination of the Backbone Mobility of Ribonuclease T1 and its 2′GMP Complex Using Molecular Dynamics Simulations and NMR Relaxation Data

Abstract

The results of 1-nanosecond molecular dynamics simulations of the enzyme ribonuclease T1 and its 2′GMP complex in water are presented. A classification of the angular reorientations of the backbone amide groups is achieved via a transformation of NH-vector trajectories into several coordinate frames, thus unravelling contributions of NH-bond librations and backbone dihedral angle fluctuations.

The former turned out to be similar for all amides, as characterized by correlation times of librational motions in a subpicosecond scale, angular amplitudes of about 10–12° for out-of-peptide-plane displacements of the NH-bond and 3–5° for the in-plane displacements, whereas the contributions of much slower backbone dihedral angle fluctuations strongly depend on the secondary structure. Correlation functions relevant for NMR were obtained and analyzed utilizing the ‘model-free’ approach (Lipari, G. and Szabo, A. (1982) J. Am. Chem. Soc. 104, 4546–4559,4559-4570; Clore et al., (1990) J. Am. Chem. Soc. 112, 4989–4991). The dependence of the amplitude of local motion on the residue location in the backbone is in good agreement with the results of NMR relaxation measurements and X-ray data. The protein dynamics is characterized by a highly restricted local motion of those parts of the backbone with defined secondary structure as well as by a high flexibility in loop regions. The comparison of results derived from different periods of the trajectory (of 50 ps and 1 ns duration, 1000 points sampled) reveals a dependence of the observed dynamic picture on the characteristic time scale of the experimental method used. Comparison of the MD data for the free and liganded enzyme clearly indicates a restriction of the mobility within certain regions of the backbone upon inhibitor binding.     

Practical aspects of the 2D 15N-[1h]-NOE experiment

The heteronuclear ¹⁵N-NOE experiment was extensively tested with respect to statistical and systematic experimental error. The dependence of signal intensity in the NOE experiment and in the reference experiment on the saturation and relaxation time was experimentally investigated. The statistics of the experimental values were accessed by numerous repetitions of identical set-ups. As a model system a protein of typical size for NMR studies was chosen, i.e., a 120 amino acid residues containing fragment of the F-actin binding gelation factor (ABP-120). The fragment exhibits fast dynamics that are accessible with the ¹⁵N-NOE experiment with various amplitudes. The results of this study show that commonly used parameters are only adequate for accurate measurement of motions with moderate amplitude. Highly flexible parts require longer delay times and thus more experimental time than commonly used. On the other hand, a qualitative or semi-quantitative assessment of a protein's mobility on fast times scales can be obtained from rapidly recorded experiments with unusual short delay times. The findings of this study are of equal importance for highly accurate measurement of the ¹⁵N-NOE as well as for quick identification of mobile or even unstructured residues/parts of a protein.     

Kinetics of recombination of photoseparated charges in Rhodobacter sphaeroides reaction centers analyzed by relaxation rate constant distribution

We studied the kinetics of dark recombination of charges photoseparated between the bacteriochlorophyll dimer (P) and the quinone acceptors of the photosynthetic reaction centers (RCs) of Rhodobacter sphaeroides. The time of light activation was varied from 1 to 60 s. The relaxation rate constant distribution was computed from experimental kinetic curves of charge recombination, using our original method whereby relaxation curves are approximated by a set of Gaussian-like peaks in the time domain that correspond to different conformational sub-states of RCs. With increasing photoactivation exposure, some peaks shift toward longer relaxation times. A ‘bifurcation’ of the slower peak is observed at exposures of 20–30 s. The phenomenon is interpreted as evidence of a conformational transition induced by separated charges in the RC structure.     

Analysis of excited-state processes by phase-modulation fluorescence spectroscopy

Fluorescence phase shift and demodulation methods were used in the analysis of excited-state reactions and to investigate solvent relaxation around fluorophores in viscous solvents. The chosen samples illustrate the results expected for fluorophores bound to biological macromolecules. These moderately simple samples served to test the theoretical predictions described in the preceding paper (J.R. Lakowicz and A.B. Balter, Biophys. Chem. 16 (1982) 99.) and to illustrate the characteristic features of phase-modulation data expected from samples which display time-dependent spectral shifts. The excited-stale protonation of acridine and exciplex formation between anthracene and diethylaniline provided examples of one-step reactions in which the lifetimes of the initially excited and the reacted species were independent of emission wavelength. Using these samples we demonstrated the following: (I) Wavelength-dependent phase shift and demodulation values can be used to prove the occurrence of an excited-state process. Proof is obtained by observation of phase angles (φ) larger than 90° or by measurement of ratios of m/cos φ > 1, where m is the modulation of the emission relative to that of the excitation. (2) For a two-state process the individual emission spectra of each state can be calculated from the wavelength-dependent phase and modulation data. (3) The phase difference or demodulation factor between the initially excited and the reacted states reveals directly the fluorescence lifetime of the product of the reaction. (4) Phase-sensitive detection of fluorescence can be used to prove that the lifetimes of both the initially excited and the reacted states are independent of emission wavelength. (5) If steady-state spectra of the individual species are known, then phase-sensitive emission spectra can be used to measure the lifetimes of the individual components irrespective of the extent of spectral overtap. (6) Spectral regions of constant lifetime can be identified by the ratios of phase-sensitive emission spectra. In addition, we examined 6-propionyl-2-dimethylaminonaphthalene(PRODAN) and N-acetyl-l-tryptophanamide (NATA) in viscous solvents where the solvent relaxation times were comparable to the fluorescence lifetimes. Using PRODAN in n-butanol we used m/cos φ measurements, relative to the blue edge of the emission, to demonstrate that solvent relaxation requires more than a single step. For NATA in propylene glycol we used phase-sensitive detection of fluorescence to directly record the emission spectra of the initially excited and the solvent relaxed states. These measurements can be easily extended to fluorophores which are bound to proteins and membranes and are likely to be useful in studies of the dynamic properties of biopolymers.     

Cyanea capillata Bell Kinematics Analysis through Corrected In Situ Imaging and Modeling Using Strategic Discretization Techniques

Obtaining accurate kinematic data of animals is essential for many biological studies and bio-inspired engineering. Many animals, however, are either too large or too delicate to transport to controlled environments where accurate kinematic data can be easily obtained. Often, in situ recordings are the only means available but are often subject to multi-axis motion and relative magnification changes with time leading to large discrepancies in the animal kinematics. Techniques to compensate for these artifacts were applied to a large jellyfish, Cyanea capillata, freely swimming in ocean waters. The bell kinematics were captured by digitizing exumbrella profiles for two full swimming cycles. Magnification was accounted for by tracking a reference point on the ocean floor and by observing the C. capillata exumbrella arclength in order to have a constant scale through the swimming cycles. A linear fit of the top bell section was used to find the body angle with respect to the camera coordinate system. Bell margin trajectories over two swimming cycles confirmed the accuracy of the correction techniques. The corrected profiles were filtered and interpolated to provide a set of time-dependent points along the bell. Discrete models of the exumbrella were used to analyze the bell kinematics. Exumbrella discretization was conducted using three different methods. Fourier series were fitted to the discretized models and subsequently used to analyze the bell kinematics of the C. capillata. The analysis showed that the bell did not deform uniformly over time with different segments lagging behind each other. Looping of the bell trajectory between contraction and relaxation was also present through most of the exumbrella. The bell margin had the largest looping with an outer path during contraction and inner path during relaxation. The subumbrella volume was approximated based on the exumbrella kinematics and was found to increase during contraction.     

Implementation and evaluation of relative and absolute quantification in shotgun proteomics with label-free methods

Tandem mass spectrometry allows for fast protein identification in a complex sample. As mass spectrometers get faster, more sensitive and more accurate, methods were devised by many academic research groups and commercial suppliers that allow protein research also in quantitative respect. Since label-free methods are an attractive alternative to labeling approaches for proteomics researchers seeking for accurate quantitative results we evaluated several open-source analysis tools in terms of performance on two reference data sets, explicitly generated for this purpose.In this paper we present an implementation, T3PQ (Top 3 Protein Quantification), of the method suggested by Silva and colleagues for LC-MS^E applications and we demonstrate its applicability to data generated on FT-ICR instruments acquiring in data dependent acquisition (DDA) mode. In order to validate this method and to show its usefulness also for absolute protein quantification, we generated a reference data set of a sample containing four different proteins with known concentrations. Furthermore, we compare three other label-free quantification methods using a complex biological sample spiked with a standard protein in defined concentrations. We evaluate the applicability of these methods and the quality of the results in terms of robustness and dynamic range of the spiked-in protein as well as other proteins also detected in the mixture. We discuss drawbacks of each method individually and consider crucial points for experimental designs. The source code of our implementation is available under the terms of the GNU GPLv3 and can be downloaded from sourceforge (http://fqms.svn.sourceforge.net/svnroot/fqms). A tarball containing the data used for the evaluation is available on the FGCZ web server (http://fgcz-data.uzh.ch/public/T3PQ.tgz).     

A comparison of methods for determining compartmental analysis parameters

The traditional method for determining compartmental analysis parameters relies on a visual selection of data points to be used for regression of data from each cellular compartment. This method is appropriate when the compartments are kinetically discrete and are easily discernible. However, where treatment effects on compartment parameters are being evaluated, a more objective method for determining initial parameters is desirable.

Three methods were examined for determining initial isotopic contents and half-times of ⁸⁶Rb elution from cellular compartments using theoretical data with known parameters. Experimental data from roots of Douglas fir (Pseudotsuga menziesii [Mirb.] Franco) and barley (Hordeum vulgare L.) intact seedlings were also used. The three methods were a visually assisted, linear regression on data of semilog plot of isotope elution versus time, a microcomputer-assisted, linear regression on semilog plot where maximization of the square of the correlation coefficient (r²) was the criterion to determine data points needed for each regression and a mainframe computer-assisted, direct nonlinear regression on elution data using a model of the sum of three exponential decay functions. The visual method resulted in the least accurate estimates of compartmental analysis parameters. The microcomputer-assisted and nonlinear regression methods calculated the parameters equally well.

     

A general survey of the proton,spin-lattice relaxation-times of monosaccharide derivatives

A Fourier-transform method has been used to determine the spin-lattice relaxation-times (T₁, values) of some of the proton resonances of a selection of carbohydrate derivatives, including pyranoid and furanoid sugars, deoxy sugars, and acetamido sugars in aqueous solution, and some esterified sugars in benzene solution. A discussion is given of the methods used to process the experimental data, and of the chemical relevance of the dependences observed. The use of selective deuteration to identify contributions to intramolecular, dipole-dipole relaxation, and of partial relaxation to remove a water resonance, is each illustrated.