Fundamental equation of thermodynamics for protein-ligand binding

For the internal energy and every thermodynamic potential that can be defined by a Legendre transform, there is a fundamental equation that contains all the thermodynamic information about a system. For a system involving the binding of molecular oxygen and hydrogen ions by a protein, fundamental equations are given for the Gibbs energy G, the transformed Gibbs energy G' at specified pH, and the further transformed Gibbs energy G" at specified pH and specified concentration of molecular oxygen. The Maxwell equations for these various Gibbs energies are important because they provide the connection with experimentally determined properties and increase our understanding of these properties. Measurements of the average number of oxygen molecules bound as a function of T, pH and concentration of molecular oxygen make it possible to calculate Delta(f)G"(o) of the reactant. Maxwell equations make it possible to calculate the average number of hydrogen ions bound, Delta(f)S"(o), Delta(f)H"(o) and their partial derivatives. These relations are illustrated with numerical calculations on a simple reaction system.     

Protein dynamics studied by NMR

The results of NMR studies using several nuclei indicate that proteins have considerable internal mobility. The most obvious is the mobility of side-chains. This mobility is general on the exterior surfaces but extends internally in a differential way. The functional value of surface mobility concerns both on and off rates of ligand binding (e.g. metal ions and parts of substrates) and protein/protein interactions. The mobility, which indicates that recognition is more in the hand-in-glove class than in the lock-in-key class, makes for a modified view of the specificity of protein interactions. Thus, fast on/off systems cannot be as selective as slower systems. Segmental mobility of proteins is considered in the context of protein secondary structure. The least mobile segments are the -sheet and the tight -turn. Mobility is always possible for, but not within, rod-like helices and in loose turns. Many examples are given and the importance of mobility in molecular machines is described. Finally, examples are given of virtually random-coil proteins, segments, and linker regions between domains and the functional value of such extremely dynamic regions of proteins is discussed.This work is based on a lecture at the EBSA Symposium, organised by the Italian Biophysical Society (S.I.B.P.A.), Tabiano Terme, September 1992     

Backbone dynamics of the channel-forming antibiotic zervamicin IIB studied by 15N NMR relaxation

The backbone dynamics of the channel-forming peptide antibiotic zervamicin IIB (Zrv-IIB) in methanol were studied by 15N nuclear magnetic resonance relaxation measurements at 11.7, 14.1 and 18.8 T magnetic fields. The anisotropic overall rotation of the peptide was characterized based on 15N relaxation data and by hydrodynamic calculations. 'Model-free' analysis of the relaxation data showed that the peptide is fairly rigid on a sub-nanosecond time-scale. The residues from the polar side of Zrv-IIB helix are involved in micro-millisecond time-scale conformational exchange. The conformational exchange observed might indicate intramolecular processes or specific intermolecular interactions of potential relevance to Zrv-IIB ion channel formation.     

Active site dynamics in NADH oxidase from Thermus thermophilus studied by NMR spin relaxation

We have characterized the backbone dynamics of NADH oxidase from Thermus thermophilus (NOX) using a recently-developed suite of NMR experiments designed to isolate exchange broadening, together with (15)N R (1), R (1ρ ), and {(1)H}-(15)N steady-state NOE relaxation measurements performed at 11.7 and 18.8 T. NOX is a 54?kDa homodimeric enzyme that belongs to a family of structurally homologous flavin reductases and nitroreductases with many potential biotechnology applications. Prior studies have suggested that flexibility is involved in the catalytic mechanism of the enzyme. The active site residue W47 was previously identified as being particularly important, as its level of solvent exposure correlates with enzyme activity, and it was observed to undergo "gating" motions in computer simulations. The NMR data are consistent with these findings. Signals from W47 are dynamically broadened beyond detection and several other residues in the active site have significant R ( ex ) contributions to transverse relaxation rates. In addition, the backbone of S193, whose side chain hydroxyl proton hydrogen bonds directly with the FMN cofactor, exhibits extensive mobility on the ns-ps timescale. We hypothesize that these motions may facilitate structural rearrangements of the active site that allow NOX to accept both FMN and FAD as cofactors.     

Conformational equilibria of valine studied by dynamics simulation.

The conformational probability distribution of a valine residue in the valine dipeptide and of the valine side chain in an alpha-helix, as well as the change in helix stability for replacing alanine with valine, has been calculated by molecular dynamics simulations of explicitly hydrated systems: dipeptide, tetrapeptide and 10-, 14- and 18-residue oligoalanine helices. All computed free-energy differences are means from at least eight separate slow-growth simulations, four in each direction and are reported with their root-mean-square deviations. Different values for the change in free energy of folding (delta delta G degrees) have been calculated with the use of forcefields having an all-atom and a central-atom representation of methyl groups, etc. The value obtained with the all-atom forcefield agrees well with new experimental values (3 kJ/mol = 0.7 kcal/mol). Furthermore, the most stable valine side-chain rotamer in the helix is different for these two representations. The most stable rotamer for the all atom conformation is the same one that predominates for valines in alpha-helices in proteins of known conformation. The lower conformational freedom of the valine side chain in the helix contributes 1 kJ/mol to the difference in stability computed with the all-atom potential; unfavorable interactions of the side chain with helix, even in the most stable conformation, further increase delta delta G degrees.     

Actin dynamics studied by solid-state NMR spectroscopy

Solid-state nuclear magnetic resonance spectroscopy was used to study the motion of ²H and ¹⁹F probes attached to the skeletal muscle actin residues Cys-10, Lys-61 and Cys-374. The probe resonances were observed in dried and hydrated G-actin, F-actin and F-actin-myosin subfragment-1 complexes. Restricted motion was exhibited by ¹⁹F probes attached to Cys-10 and Cys-374 on actin. The dynamics of probes attached to dry cysteine powder or F-actin were very similar and the binding of myosin had little effect indicating that the local probe environment imposes the major influence on motion in the solid state. Correlation times determined for the solid state probes indicated that they were undergoing some rapid internal motion in both G-actin and F-actin such as domain twisting. The probe size influenced the motion in G-actin and appeared to sense monomer rotation but not in F-actin where segmental mobility and intramonomer co-ordination appeared to dominate.     

Conformational transition of an α-helix studied by molecular dynamics

Molecular dynamics simulations were performed on a 20-residue polyalanine helix and a spontaneous transition from a kinked to a straight conformation was observed. The kinetics of the transition was analyzed within the framework of the Kramers model for chemical reactions and within a random walk model. The Kramers model which is based on diffusion along a one-dimensional reaction pathway and the crossing of an energy barrier was found to be inadequate. Instead, a random walk model based on diffusion in the high-dimensional phase space of the system was found to be compatible with the data. The high dimensionality of the phase space permits the system to circumvent high energy barriers and diffuse rapidly at about constant energy, but decelerates the reaction since in the labyrinth of pathways the transition state is reached rarely.     

Refined solution structure and backbone dynamics of 15N-labeled C12A-p8MTCP studied by NMR relaxation

MTCP1 (for Mature-T-Cell Proliferation) was the first gene unequivocally identified in the group of uncommon leukemias with a mature phenotype. The three-dimensional solution structure of the human p8^MTCP protein encoded by the MTCP1 oncogene has been previously determined by homonuclear proton two-dimensional NMR methods at 600 MHz: it consists of an original scaffold comprising three -helices, associated with a new cysteine motif. Two of the helices are covalently paired by two disulfide bridges, forming an -hairpin which resembles an antiparallel coiled-coil. The third helix is orientated roughly parallel to the plane defined by the -antiparallel motif and appears less well defined. In order to gain more insight into the details of this new scaffold, we uniformly labeled with nitrogen-15 a mutant of this protein (C12A-p8^MTCP1) in which the unbound cysteine at position 12 has been replaced by an alanine residue, thus allowing reproducibly high yields of recombinant protein. The refined structure benefits from 211 additional NOEs, extracted from ¹⁵N-edited 3D experiments, and from a nearly complete set of angular restraints allowing the estimation of the helical content of the structured part of the protein. Moreover, measurements of ¹⁵ N spin relaxation times and heteronuclear ¹⁵ N¹HNOEs provided additional insights into the dynamics of the protein backbone. The analysis of the linear correlation between J(0) and J() was used to interpret relaxation parameters. It appears that the apparent relative disorder seen in helix III is not simply due to a lack of experimental constraints, but associated with substantial contributions of sub-nanosecond motions in this segment.     

Effects of amantadine on the dynamics of membrane-bound influenza A M2 transmembrane peptide studied by NMR relaxation

The molecular motions of membrane proteins in liquid-crystalline lipid bilayers lie at the interface between motions in isotropic liquids and in solids. Specifically, membrane proteins can undergo whole-body uniaxial diffusion on the microsecond time scale. In this work, we investigate the ¹H rotating-frame spin-lattice relaxation (T _1ρ) caused by the uniaxial diffusion of the influenza A M2 transmembrane peptide (M2TMP), which forms a tetrameric proton channel in lipid bilayers. This uniaxial diffusion was proved before by ²H, ¹⁵N and ¹³C NMR lineshapes of M2TMP in DLPC bilayers. When bound to an inhibitor, amantadine, the protein exhibits significantly narrower linewidths at physiological temperature. We now investigate the origin of this line narrowing through temperature-dependent ¹H T _1ρ relaxation times in the absence and presence of amantadine. Analysis of the temperature dependence indicates that amantadine decreases the correlation time of motion from 2.8 ± 0.9 μs for the apo peptide to 0.89 ± 0.41 μs for the bound peptide at 313 K. Thus the line narrowing of the bound peptide is due to better avoidance of the NMR time scale and suppression of intermediate time scale broadening. The faster diffusion of the bound peptide is due to the higher attempt rate of motion, suggesting that amantadine creates better-packed and more cohesive helical bundles. Analysis of the temperature dependence of $ { \ln }\left( {T_{1\rho }^{ - 1} } \right) $ indicates that the activation energy of motion increased from 14.0 ± 4.0 kJ/mol for the apo peptide to 23.3 ± 6.2 kJ/mol for the bound peptide. This higher activation energy indicates that excess amantadine outside the protein channel in the lipid bilayer increases the membrane viscosity. Thus, the protein-bound amantadine speeds up the diffusion of the helical bundles while the excess amantadine in the bilayer increases the membrane viscosity.     

Conformational dynamics of recoverin's Ca2+-myristoyl switch probed by 15N NMR relaxation dispersion and chemical shift analysis

Recoverin, a member of the neuronal calcium sensor (NCS) branch of the calmodulin superfamily, serves as a calcium sensor in retinal rod cells. Ca²⁺‐induced conformational changes in recoverin promote extrusion of its covalently attached myristate, known as the Ca²⁺‐myristoyl switch. Here, we present nuclear magnetic resonance (NMR) relaxation dispersion and chemical shift analysis on ¹⁵N‐labeled recoverin to probe main chain conformational dynamics. ¹⁵N NMR relaxation data suggest that Ca²⁺‐free recoverin undergoes millisecond conformational dynamics at particular amide sites throughout the protein. The addition of trace Ca²⁺ levels (0.05 equivalents) increases the number of residues that show detectable relaxation dispersion. The Ca²⁺‐dependent chemical shifts and relaxation dispersion suggest that recoverin has an intermediate conformational state (I) between the sequestered apo state (T) and Ca²⁺ saturated extruded state (R): T ? I ? R. The first step is a fast conformational equilibrium ([T]/[I] < 100) on the millisecond time scale (τ_exδω < 1). The final step (I ? R) is much slower (τ_exδω > 1). The main chain structure of I is similar in part to the structure of half‐saturated E85Q recoverin with a sequestered myristoyl group. We propose that millisecond dynamics during T ? I may transiently increase the exposure of Ca²⁺‐binding sites to initiate Ca²⁺ binding that drives extrusion of the myristoyl group during I ? R. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

Strong and weak binding of water to proteins studied by NMR triple-quantum filtered relaxation spectroscopy of (17)O-water

The triple-quantum filtered (TQF) spin-echo signal of (17)O-water, in the presence of proteins, was analysed to yield estimates of the number of weakly, and strongly bound water molecules. The analysis used a constrained direct iterative regression procedure with a three-state model of fast-exchange. Thus, the population size of free, weakly, and strongly bound water were determined simultaneously. The two fractions of the bound water were estimated by using correlation time(s) estimated in other studies. Bovine serum albumin (BSA), basic pancreatic trypsin inhibitor (BPTI), lysozyme and oxyhaemoglobin were studied. Of the four proteins, BSA contained the largest number of strongly and weakly bound water molecules, there being approximately 30 of the former and approximately 3000 of the latter under conditions of high protein concentration. The correlation time of the proteins increases with their concentration in solution, and when this was taken into account for BSA the estimated number of strongly bound water molecules did not change significantly. This NMR technique, and data analysis, will probably also be useful in studies of water binding and mobility in various systems including hydrogels, protein networks, membranes, cells and tissues.     

Structure and dynamics of two elastin-like polypentapeptides studied by NMR spectroscopy

The structure and dynamics of two synthetic elastin-like polypentapeptides, poly(G(1)V(1)G(2)V(2)P) and poly(AV(1)GV(2)P), were studied in D(2)O and H(2)O at various temperatures by using (1)H, (2)H,(13)C, and (15)N NMR spectra, relaxations, and PGSE self-diffusivity measurement. Signal assignments were made using COSY, NOESY, HXCORR, HSQC, HMBC, and SSLR INEPT techniques. Temperature-induced conformation changes were studied using (3)J(NHCH) couplings, NOESY connectivity, chemical shifts, and signal intensities. Hydrodynamic radii were derived from self-diffusion coefficients measured by the pulsed-gradient spin-echo (PGSE) method. Selective hydration (hydrophilic or hydrophobic) was explored using NOESY and ROESY spectral methods and longitudinal and transverse (1)H relaxation of HOD and quadrupolar (2)H relaxation of D(2)O. Four different physical states were discerned in different temperature regions for both polymers: state I of a rather extended, statistically shaped and fully hydrated polymer below the critical temperature (approximately 299-300 K); state II, a relatively coiled and globular but disordered preaggregation state, developing in a rather narrow region, 300-303 K, in the case of poly(AV(1)GV(2)P) and in a broader region, overlapping with the next one, in poly(G(1)V(1)G(2)V(2)P); state III, a tightly coiled, more compact state in the region 303-313 K; and, finally, state IV, an aggregated (and eventually flocculating and sedimenting) state beyond 313 K. States II-IV coexist in varying proportions in the whole temperature range above 299 K. A structure characterized by a beta-turn stabilized by H-bonding between the Ala carbonyl and Val(2) NH groups of poly(AV(1)GV(2)P) was detected by NOESY just above the transition temperature. States II and III are progressively more stripped of their hydration sheath but retain some molecules of water confined and relatively immobilized in their coils.     

Microsecond timescale backbone conformational dynamics in ubiquitin studied with NMR R1rho relaxation experiments

NMR spin relaxation experiments are used to characterize the dynamics of the backbone of ubiquitin. Chemical exchange processes affecting residues Ile 23, Asn 25, Thr 55, and Val 70 are characterized using on- and off-resonance rotating-frame 15N R1rho relaxation experiments to have a kinetic exchange rate constant of 25,000 sec(-1) at 280 K. The exchange process affecting residues 23, 25, and 55 appears to result from disruption of N-cap hydrogen bonds of the alpha-helix and possibly from repacking of the side chain of Ile 23. Chemical exchange processes affecting other residues on the surface of ubiquitin are identified using 1H-15N multiple quantum relaxation experiments. These residues are located near or at the regions known to interact with various enzymes of the ubiquitin-dependent protein degradation pathway.     

Protein-protein and protein-ligand interactions studied by electrospray-ionization mass spectrometry

Preservation of non-covalent interactions in biopolymer mass spectrometry offers new approaches to binding analysis. Recent work from our laboratory is reviewed here and discussed with reference to recent literature in the field. Three issues are considered in particular: hydrophobically stabilized complexes, pH-dependent transitions, and linked protein-ligand and protein-protein binding equilibria.     

Physicochemical bases for protein folding,dynamics, and protein-ligand binding

Proteins are essential parts of living organisms and participate in virtually every process within cells.As the genomic sequences for increasing number of organisms are completed,research into how proteins can perform such a variety of functions has become much more intensive because the value of the genomic sequences relies on the accuracy of understanding the encoded gene products.Although the static three-dimensional structures of many proteins are known,the functions of proteins are ultimately governed by their dynamic characteristics,including the folding process,conformational fluctuations,molecular motions,and protein-ligand interactions.In this review,the physicochemical principles underlying these dynamic processes are discussed in depth based on the free energy landscape(FEL)theory.Questions of why and how proteins fold into their native conformational states,why proteins are inherently dynamic,and how their dynamic personalities govern protein functions are answered.This paper will contribute to the understanding of structure-function relationship of proteins in the post-genome era of life science research.     

Weak substrate binding to transport proteins studied by NMR.

The weak binding of sugar substrates fails to induce any quantifiable physical changes in the L-fucose-H+ symport protein, FucP, from Escherichia coli, and this protein lacks any strongly binding ligands for competitive binding assays. Access to substrate binding behavior is however possible using NMR methods which rely on substrate immobiliza-tion for detection. Cross-polarization from proton to carbon spins could detect the portion of 13C-labeled substrate associated with 0.2 micromol of the functional transport system overexpressed in the native membranes. The detected substrate was shown to be in the FucP binding site because its signal was diminished by the unlabeled substrates L-fucose and L-galactose but was unaffected by a three- to fivefold molar excess of the non-transportable stereoisomer D-fucose. FucP appeared to bind both anomers of its substrates equally well. An NMR method, designed to measure the rate of substrate exchange, could show that substrate exchanged slowly with the carrier center (>10(-1) s), although its dynamics are not necessarily coupled strongly to this site within the protein. Relaxation measurements support this view that fluctuations in the interaction with substrate would be confined to the binding site in this transport system.     

Protein dynamics studied by rotating frame 15N spin relaxation times

Summary Conformational rate processes in aqueous solutions of uniformly ¹⁵N-labeled pancreatic trypsin inhibitor (BPTI) at 36°C were investigated by measuring the rotating frame relaxation times of the backbone ¹⁵N spins as a function of the spin-lock power. Two different intramolecular exchange processes were identified. A first local rate process involved the residues Cys³⁸ and Arg³⁹, had a correlation time of about 1.3 ms, and was related to isomerization of the chirality of the disulfide bond Cys¹⁴-Cys³⁸. A second, faster motional mode was superimposed on the disulfide bond isomerization and was tentatively attributed to local segmental motions in the polypeptide sequence-Cys¹⁴-Ala¹⁵-Lys¹⁶-. The correlation time for the overall rotational tumbling of the protein was found to be 2 ns, using the assumption that relaxation is dominated by dipolar coupling and chemical shift anistropy modulated by isotropic molecular reorientation.Abbreviations BPTI basic pancreatic trypsin inhibitor - 2D two-dimensional - COSY 2D correlation spectroscopy - TOCSY 2D total correlation spectroscopy - RF radio frequency - CW continuous wave - TPPI time-proportional phase incrementation - CSA chemical shift anisotropy - T₁ longitudinal relaxation time - T₂ transverse relaxation time - T₁ relaxation time in the rotating frame , correlation time for overall rotational reorientation of the protein - _ex ^s , _ex ^f , correlation times for two conformational exchange processes (slow and fast).     

NMR studies of dynamics in RNA and DNA by 13C relaxation

RNA and DNA molecules experience motions on a wide range of time scales, ranging from rapid localized motions to much slower collective motions of entire helical domains. The many functions of RNA in biology very often require this molecule to change its conformation in response to biological signals in the form of small molecules, proteins or other nucleic acids, whereas local motions in DNA may facilitate protein recognition and allow enzymes acting on DNA to access functional groups on the bases that would otherwise be buried in Watson-Crick base pairs. Although these statements make a compelling case to study the sequence dependent dynamics in nucleic acids, there are few residue-specific studies of nucleic acid dynamics. Fortunately, NMR studies of dynamics of nucleic acids and nucleic acids-protein complexes are gaining increased attention. The aim of this review is to provide an update of the recent progress in studies of nucleic acid dynamics by NMR based on the application of solution relaxation techniques.