Chemical relaxation of co-operative conformational transitions of linear biopolymers

The kinetics and chemical relaxation of co-operative conformational changes of linear (bio)polymers (e.g. helix-coil transitions of polypeptides) are discussed on the basis of the linear ISING model. Chemical relaxation is in general shown to be described by 4N−5 relaxation times if the polymer chain consists of N elementary reaction sites. It is pointed out that nevertheless substantial simplifications of the theory can be achieved in many special cases of practical interest. Sufficiently short chains exhibit first-order kinetics resulting in a single relaxation time whereas for certain medium chain lengths zero-order kinetics plays a principal role in the relaxation process. For the particularly interesting case of very long chains a set of four relaxation equations is derived. The corresponding relaxation times are calculated assuming strong co-operativity and slow nucleation rates. However, it is almost exclusively the largest one of these relaxation times which actually controls the conformational change as turns out by means of a new approach to compute amplitude factors.     

Pulsed field electrophoresis

Pulsed field electrophoresis, or PFE, provides good separation between large molecules that under constant field electrophoresis are hard to isolate. This is due to the weak dependence of the constant field mobility on the molecular weight for these large molecules. If a spectrum of relaxation times exists that describes the recovery of the mobility to its constant field value after a reversal of the field, then we show that molecules with differing molecular weights are separated into two groups. Those with short relaxation times are unaffected by the cycling of the field and those with long relaxation times exhibit reduced mobilities. If the molecules adopt conformations that decrease their mobility initially, after a field reversal we demonstrate that a minimum develops in the mobility as a junction of the relaxation time. Using the model we demonstrate that effects of varying the switching times as a function of time. We predict that exponential rather than linear dependencies of the switching times on time increase the range of molecular weights over which enhanced separation can occur.     

Isotope effects on electron tunneling reactions in biological systems conformational mobility of proteins

Effects of D2O substitution on electron transport reactions in proteins were analysed on the basis of generally adopted ideas of electronic vibration interactions and conformational mobility of macromolecules. At the molecular level, a mechanism for cytochrome c oxidation was established. On the basis of general viscosity and elasticity properties of proteins, the effects of temperature and chemical composition of the medium on conformational relaxation were analysed. For chromatophores of photosynthetising bacteria, a mechanism is discussed by which abnormal effects of temperature and abnormal isotope effects may be exercised on charge recombination.     

Study of bovine carbonic anhydrase by 13C-NMR-spectroscopy

The study of internal mobility in enzymes is of considerable importance for the understanding of their catalytic function, which cannot be adequately described as a property of a rigid protein. [13C]NMR spectroscopy permits simultaneous and selective observation of spectral lines from carbon atoms in many different residues in the enzyme with the chemical shift and relaxation parameters sensitive to structure, conformation and local motion. The changes in internal mobility in bovine carbonic anhydrase B (carbonate hydrolase, EC 4.2.1.1) in the native form and at various stages of denaturation are studied. Measurements of the relaxation parameters (T1, T1 rho) and of the NOE of 13C nuclei in the native protein showed that the extensive beta-sheet together with groups in the active center has a considerable internal librational mobility with tau G about 10(-11) s. This librational mobility is fairly uniform for all the alpha-carbons in the native enzyme. The use of a semiempirical modification of the motional theory proposed by Woessner allows to use simultaneously all the relaxation parameters measured in order to determine reliable values of the various correlation times.     

X-ray analysis of the kinetics of Escherichia coli lipid and membrane structural transitions

Synchrotron radiation was used to follow the time course of the transitions, induced by temperature jump, in Escherichia coli membranes and their lipid extracts isolated from a fatty acid auxotroph grown with different fatty acids. We measured the relaxation times associated with the phase transitions as well as with the conformational transition of the hydrocarbon chains and observed different behavior as a function of chemical composition. Relaxation times of about 1-2 s were found at a hexagonal to lamellar phase transition and within a lamellar phase whose parameters display important variations with temperature when the conformational transition takes place. On the other hand, no delay was observed for a phase transition where large lipid or water diffusion was not needed. We have shown that phase transitions and conformational transitions are, to a large extent, uncoupled and that the relaxation times corresponding to the latter transition could be related to the size of the ordered domains. In all cases, the order to disorder conformational transition is more rapid than the disorder to order transition. Finally, the relaxation times of the disorder to order transition observed with the membranes and with their lipid extracts were found to be strongly correlated, indicating that the proteins do not play a role in this transition.     

Caldesmon inhibits both force development and transition of actin monomers from "OFF" to "ON" conformational state by changing its position in thin filaments

We have investigated the effect of caldesmon on the actin conformational state and its position at force generation in glycerinated fibers upon transformation from relaxation to rigor. F-actin and caldesmon were labeled with TRITC-phalloidin or acrylodan, respectively, and the orientation and mobility of the probes were calculated. Transition from relaxation to rigor was accompanied by force development and by the changes in orientation and mobility of TRITC-phalloidin that were typical for actin monomer transformation from the "OFF" to the "ON" conformational state. In the presence of caldesmon, both the force developed by the fibers and the changes in the orientation and mobility of TRITC-phalloidin were markedly decreased. In contrast, the orientation and mobility of acrylodan change essentially showed the displacement of the caldesmon molecules and the changes in its mobility. The results are evidence that structure and/or mode of the attachment of caldesmon to actin modulates both the force production and transition of actin monomers from "OFF" to "ON" conformations in the ATPase cycle.     

Ion-conformational interaction and charge transport through channels of biological membranes

This work proposes a theory of charge transport through channels in biological membranes, based on ion flow interaction with charged groups of protein macromolecules that form the channel. Displacements of the groups are due to conformational changes of the protein molecule, the relaxation times of which are much larger than the average time of ion ocurrence in the channel. Ion flow is assumed to depend on the conformational changes and vice-versa. The resulting self-organizing ion-conformational system is described by a set of nonlinear differential equations for conformational variables and average occupancy of the channel by ions. The system exhibits multistable behaviour in a certain range of control parameters (potential difference, input ion flow). The stationary states of the system may be identified with the states of discrete conductivity of the ionic channels.     

Microsecond-to-millisecond conformational dynamics demarcate the GluR2 glutamate receptor bound to agonists glutamate, quisqualate, and AMPA

Chemical shift changes and internal motions on microsecond-to-millisecond time scales of the S1S2 ligand-binding domain of the GluR2 ionotropic glutamate receptor have been studied by NMR spectroscopy in the presence of the agonists glutamic acid (glutamate), quisqualic acid (quisqualate), and alpha-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid (AMPA). Although the crystal structures of the three agonist-bound forms of GluR2 S1S2 ligand-binding domain are very similar, chemical shift changes imply that AMPA-bound GluR2 S1S2 is conformationally distinct from glutamate- and quisqualate-bound forms of GluR2 S1S2. NMR spin relaxation measurements for backbone amide (15)N nuclei reveal that GluR2 S1S2 exhibits reduced chemical exchange line broadening, resulting from microsecond-to-millisecond conformational dynamics, in AMPA-bound compared to glutamate- and quisqualate-bound states. The largest changes in line broadening are observed for two regions of GluR2 S1S2: Val683 and the segment around Lys716-Cys718. The differences in binding affinity of these agonists do not explain the differences in microsecond-to-millisecond conformational dynamics because quisqualate and AMPA bind with similar affinities that are 10-fold greater than the affinity of glutamate. Differences in conformational mobility may reflect differences in the binding mode of AMPA in the GluR2 S1S2 active site compared to the other two ligands. The sites of conformational mobility in GluR2 S1S2 imply that subtle differences exist between the agonists glutamate, quisqualate, and AMPA in modulating glutamate receptor function.     

15N spin-lattice relaxation study of linear peptides: Preliminary results on Leu-enkephalin and Tyr-Gly-Gly-Phe

The ability of ¹⁵N relaxation measurements in conformational analysis of linear peptides was studied using Leu-enkephalin: Tyr-Gly-Gly-Phe-Leu and and related tetrapeptide Tyr-Gly-Gly-Phe 95 % ¹⁵N enriched. ¹⁵N spin-lattice relaxation times measured at different temperatures in Me₂SO solution indicate the presence of highly preferential folded structures in both peptides. A marked dependence of T₁ upon the motional effects (segmental rather than anisotropic overall) was observed, while hydrogen bonding affects weakly the relaxation times. From a comparison of ¹⁵N relaxation parameters it appears that the tetrapeptide exhibits a more rigid structure than Leu-enkephalin, in accordance with previous ¹H NMR studies. This paper provides evidence for the usefulness of ¹⁵N T₁ as a mobility probe (independent from ¹³C) in the investigation of the conformational dynamics of peptides.     

Conformational plasticity of the lipid transfer protein SCP2

The nonspecific lipid transfer protein sterol carrier protein 2 (SCP2) is involved in organellar fatty acid metabolism. A hydrophobic cavity in the structure of SCP2 accommodates a wide variety of apolar ligands such as cholesterol derivatives or fatty acyl-coenzyme A (CoA) conjugates. The properties of this nonspecific lipid binding pocket are explored using NMR chemical shift perturbations, paramagnetic relaxation enhancement, amide hydrogen exchange, and 15N relaxation measurements. A common binding cavity shared by different physiological ligands is identified. NMR relaxation measurements reveal that residues in the three C-terminal alpha-helices within the lipid binding region exhibit mobility at fast (picosecond to nanosecond) and slow (microsecond to millisecond) time scales. Ligand binding is associated with a considerable loss of peptide backbone mobility. The observed conformational dynamics in SCP2 may play a role for the access of hydrophobic ligands to an occluded binding pocket. The C-terminal peroxisomal targeting signal of SCP2 is specifically recognized by the Pex5p receptor protein, which conducts cargo proteins toward the peroxisomal organelle. Neither the C-terminal targeting signal nor the N-terminal precursor sequence interferes with lipid binding by SCP2. The alpha-helices involved in lipid binding also mediate a secondary interaction interface with the Pex5p receptor. Silencing of conformational dynamics of the peptide backbone in these helices upon either lipid or Pex5p binding might communicate the loading state of the cargo protein to the targeting receptor.     

Kinetics of allosteric conformational transition of a macromolecule prior to ligand binding

Two fundamentally different mechanisms of ligand binding are commonly encountered in biological kinetics. One mechanism is a sequential multistep reaction in which the bimolecular binding step is followed by first-order steps. The other mechanism includes the conformational transition of the macromolecule, before the ligand binding, followed by the ligand binding process to one of the conformational states. In stopped-flow kinetic studies, the reaction mechanism is established by examining the behavior of relaxation times and amplitudes as a function of the reactant concentrations. A major diagnostic tool for detecting the presence of a conformational equilibrium of the macromolecule, before the ligand binding, is the decreasing value of one of the reciprocal relaxation times with the increasing [ligand]. The sequential mechanism cannot generate this behavior for any of the relaxation times. Such dependence is intuitively understood on the basis of approximate expressions for the relaxation times that can be comprehensively derived, using the characteristic equation of the coefficient matrix and polynomial theory. Generally, however, the used approximations may not be fulfilled. On the other hand, the two kinetic mechanisms can always be distinguished, using the approach based on the combined application of pseudo-first-order conditions, with respect to the ligand and the macromolecule. The two experimental conditions differ profoundly in the extent of the effect of the ligand on the protein conformational equilibrium. In a large excess of the ligand, the conformational equilibrium of the macromolecule, before the ligand binding, is strongly affected by the binding process. However, in a large excess of the macromolecule, ligand binding does not perturb the internal equilibrium of the macromolecule. As a result, the normal mode, affected by the conformational transition, is absent in the observed relaxation process. In the case of a sequential mechanism, the number of relaxation times is not altered by different pseudo-first-order conditions. Thus, the approach provides a strong diagnostic criterion for detecting the presence of the conformational transition of the macromolecule and establishing the correct mechanism. Application of this approach is illustrated for the binding of 3'-O-(N-methylantraniloyl)-5'-diphosphate to the E. coli DnaC protein.     

Effects of calcium binding on the side-chain methyl dynamics of calbindin D9k: a 2H NMR relaxation study

The effects of Ca(2+) binding on the side-chain methyl dynamics of calbindin D(9k) have been characterized by (2)H NMR relaxation rate measurements. Longitudinal, transverse in-phase, quadrupolar order, transverse anti-phase and double quantum relaxation rates are reported for both the apo and Ca(2+)-loaded states of the protein at two magnetic field strengths. The relatively large size of the data set allows for a detailed analysis of the underlying conformational dynamics by spectral density mapping and model-free fitting procedures. The results reveal a correlation between a methyl group's distance from the Ca(2+) binding sites and its conformational dynamics. Several methyl groups segregate into two limiting classes, one proximal and the other distal to the binding sites. Methyl groups in these two classes respond differently to Ca(2+) binding, both in terms of the timescale and amplitude of their fluctuations. Ca(2+) binding elicits a partial immobilization among methyl groups in the proximal class, which is consistent with previous studies of calbindin's backbone dynamics. The distal class, however, exhibits a trend that could not be inferred from the backbone data in that its mobility actually increases with Ca(2+) binding. We have introduced the term polar dynamics to describe this type of organization across the molecule. The trend may represent an important mechanism by which calbindin D(9k) achieves high affinity binding while minimizing the corresponding loss of conformational entropy.     

Solid-state NMR investigation of the dynamics of the soluble and membrane-bound colicin Ia channel-forming domain.

Solid-state NMR spectroscopy was employed to study the molecular dynamics of the colicin Ia channel domain in the soluble and membrane-bound states. In the soluble state, the protein executes small-amplitude librations (with root-mean-square angular fluctuations of 0-10 degrees ) in the backbone and larger-amplitude motions (16-17 degrees ) in the side chains. Upon membrane binding, the motional amplitudes increase significantly for both the backbone (12-16 degrees ) and side chains (23-29 degrees ), as manifested by the reduction in the C-H and H-H dipolar couplings and (15)N chemical shift anisotropy. These motions occur not only on the pico- to nanosecond time scales, but also on the microsecond time scale, as revealed by the (1)H rotating-frame spin-lattice relaxation times. Average motional correlation times of 0.8 and 1.2 micros were extracted for the soluble and membrane-bound states, respectively. In comparison, both forms of the colicin Ia channel domain are completely immobile on the millisecond scale. These results indicate that the colicin Ia channel domain has enhanced conformational mobility in the lipid bilayer compared to the soluble state. This membrane-induced mobility increase is consistent with the loss of tertiary structure of the protein in the membrane, which was previously suggested by the extended helical array model [Zakharov et al. (1998) Proc. Natl. Acad. Sci. U.S.A. 95, 4282-4287]. An extended structure would also facilitate protein interactions with the mobile lipids and thus increase the protein internal motions. We speculate that the large mobility of the membrane-bound colicin Ia channel domain is a prerequisite for channel opening in the presence of a voltage gradient.     

The Topology of the Energy Landscapes of Macromolecules in the Torsion Angle Space and the Principle of the Minimum Energy Dissipation Rate in Conformational Relaxation

This article discusses some basic problems of structural biology and molecular dynamics simulation methods that need to be taken into account when considering, the protein folding problem, and prediction of 3D-structures for biopolymers. A multidimensional Fourier series expansions were formulated for the energy landscapes of the systems with conformational mobility, These energy landscape representations are correct from the viewpoint of the topology of the macromolecule configuration spaces. The problem of the single global minimum on the energy landscape for proteins is discussed and is formulated in tems of phase rules for the component of Fourier expansions. This rule is formally similar to the problem of diffraction on a multidimensional cubic lattice. The calibration of biopolymer force fields and their correspondence to topologically correct energy landscapes are discussed. Equations of motion were obtained in a matrix form for the relaxation of a representative point position on a multidimensional potential energy surface. The solutions of the equations for conformational relaxation were shown to obey the principle of the minimum energy dissipation rate at a given relaxation rate of potential energy (or folding rate).     

Molecular motion and conformation of cholesteryl esters in reconstituted high density lipoprotein by deuterium magnetic resonance

Reconstituted high density lipoprotein has been prepared by sonication and preparative ultracentrifugation of mixtures containing the apoprotein of high density lipoprotein, egg phosphatidylcholine, cholesteryl oleate, and acyl chain deuterated cholesteryl palmitate in aqueous buffer. The resulting structures have a size and chemical composition very similar to native high density lipoprotein. Deuterium NMR spectra and longitudinal relaxation times were obtained at approximately 25 degrees C. The variation of the 2H NMR line width with chain position is consistent with an average conformation such that the ester acyl chain is extended. In addition, 2H NMR line widths and longitudinal relaxation times indicate that the ester acyl chains possess significant mobility.     

Study of rabbit IgG, modified with carboxycarbonic anhydride of diethylenetriaminopentacetic acid

The affinity-purified by chromatography on immobilized antigen rabbit IgG was modified with mixed carboxycarbonic anhydride of DTPA which markedly alters the interaction of charged residues in the protein molecule. To study the correlation between the antigen binding activity and the conformational mobility of IgG, the reactivity of modified IgG towards conformational probes targeted at variable and constant IgG domains, was investigated. The antibody against CH2 domains of IgG, staphylococcal protein A and protein antigen ferritin were used as conformational probes. It was found that modification of IgG amino groups entails the global increase in conformational mobility involving the Fab fragments, CH2 and, probably, the CH3 domains of the Fc portion of IgG. Taking advantage of Fab fragments modification it was shown that two processes contribute to the global increase in the conformational mobility of IgG. These processes are: i) stimulation of segmental flexibility and, ii) increase in the mobility within the Fv domains of the Fab fragments.     

Ligand-induced changes in dynamics in the RT loop of the C-terminal SH3 domain of Sem-5 indicate cooperative conformational coupling

We report the effects of peptide binding on the (15)N relaxation rates and chemical shifts of the C-SH3 of Sem-5. (15)N spin-lattice relaxation time (T(1)), spin-spin relaxation time (T(2)), and ((1)H)-(15)N NOE were obtained from heteronuclear 2D NMR experiments. These parameters were then analyzed using the Lipari-Szabo model free formalism to obtain parameters that describe the internal motions of the protein. High-order parameters (S(2) > 0.8) are found in elements of regular secondary structure, whereas some residues in the loop regions show relatively low-order parameters, notably the RT loop. Peptide binding is characterized by a significant decrease in the (15)N relaxation in the RT loop. Concomitant with the change in dynamics is a cooperative change in chemical shifts. The agreement between the binding constants calculated from chemical shift differences and that obtained from ITC indicates that the binding of Sem-5 C-SH3 to its putative peptide ligand is coupled to a cooperative conformational change in which a portion of the binding site undergoes a significant reduction in conformational heterogeneity.     

Deuterium nuclear magnetic resonance studies of bile salt/phosphatidylcholine mixed micelles

Mixed micelles of deoxycholate (DOC) and 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) have been prepared in which the POPC was specifically deuterated in the 2-, 6-, 10-, or 16-position of the palmitoyl chain or in the N-methyl position of the choline head group. The deuterium nuclear magnetic resonance (2H NMR) spectrum of each of these specifically deuterated mixed micelles consists of a singlet whose line width depends upon the position of deuteration. Spin-spin relaxation times indicate a gradient of mobility along the POPC palmitoyl chain in the mixed micelle, with a large increase in mobility on going from the 10- to the 16-position. Spin-lattice relaxation times (T1's) demonstrate a similar gradient of mobility. Both trends in NMR relaxation behavior are consistent with a bilayer arrangement for the solubilized POPC. 2H T1 times for DOC/POPC micelles are significantly shorter than those measured in other bilayer systems, indicating unusually tight phospholipid acyl chain packing in the mixed micelle.     

The influence of hydration on the conformation of lysozyme studied by solid-state 13C-nmr spectroscopy

¹³C proton decoupled cross-polarization magic-angle spinning nmr spectra of lysozyme are reported as a function of hydration. Increases in hydration level enhance the resolution of the spectra, particularly in the aliphatic region, but has no significant effect on either the rotating frame proton spin–lattice relaxation time or the cross-relaxation time. The enhancement in spectral resolution with hydration is attributed to a decrease in the distribution of isotropic chemical shifts, which reflects a decrease in the distribution of conformational states sampled by the protein. Changes in the distribution of isotropic chemical shifts occur after the addition of water to the charged groups as coverage of the polar side chains and peptide groups takes place. The onset of this behavior occurs at a hydration level of about, 0.1–0.2 g water/g protein and is largely complete at about 0.3 g water/g protein, the same hydration range where changes in the heat capacity are observed. That hydrogen exchange of buried protons can occur at hydration levels significantly lower than those at which changes in the distribution of conformational states are first observed suggests that some motions that mediate exchange are already present in the dry protein. The preservation of efficient dipolar coupling indicates that the conformational rearrangements that do-occur on hydration are small and do not involve any significant overall expansion of free volume or weakening of interactions that would increase the reorientational freedom of protein groups. © 1993 John Wiley & Sons, Inc.     

Conformational exchange of aromatic side chains characterized by L-optimized TROSY-selected 13C CPMG relaxation dispersion

Protein dynamics on the millisecond time scale commonly reflect conformational transitions between distinct functional states. NMR relaxation dispersion experiments have provided important insights into biologically relevant dynamics with site-specific resolution, primarily targeting the protein backbone and methyl-bearing side chains. Aromatic side chains represent attractive probes of protein dynamics because they are over-represented in protein binding interfaces, play critical roles in enzyme catalysis, and form an important part of the core. Here we introduce a method to characterize millisecond conformational exchange of aromatic side chains in selectively (13)C labeled proteins by means of longitudinal- and transverse-relaxation optimized CPMG relaxation dispersion. By monitoring (13)C relaxation in a spin-state selective manner, significant sensitivity enhancement can be achieved in terms of both signal intensity and the relative exchange contribution to transverse relaxation. Further signal enhancement results from optimizing the longitudinal relaxation recovery of the covalently attached (1)H spins. We validated the L-TROSY-CPMG experiment by measuring fast folding-unfolding kinetics of the small protein CspB under native conditions. The determined unfolding rate matches perfectly with previous results from stopped-flow kinetics. The CPMG-derived chemical shift differences between the folded and unfolded states are in excellent agreement with those obtained by urea-dependent chemical shift analysis. The present method enables characterization of conformational exchange involving aromatic side chains and should serve as a valuable complement to methods developed for other types of protein side chains.