Protein motions, correlated

The Perrin plot enables us to obtain information concerning fluorophore motion. When the fluorophore is tightly bound to the protein, its motion will correspond to that of the protein. In this case, r will be equal to the protein rotational correlation time p, and A0 obtained experimentally from the Perrin plot will be equal to that measured at —45°C (Figure 11.3). 

Figure 14.1. Dependence of the spin-spin relaxation time (T2) and spin-lattice relaxation time (7)) on the motional correlation time xc. Approximate values of the expected line widths for small organic molecules, proteins, and lipids in a bilayer are indicated.

Steinhoff et al. (1989) measured the temperature and hydration dependence of the ESR spectra of hemoglobin spin-labeled at cysteine )8-93. They observed the critical temperature near 200 K, as described above, and the sensitivity of the spectrum to hydration level. Spectrum simulations suggested that there were two types of motion in the dry protein, a fast vibration of the label within a limited motion cone upon the addition of water, a hydration-dependent motion assigned to the fluctuations of the protein, of correlation time 10 sec in samples of high hydration and at 300 K. The temperature dependence of the motional properties of a spin probe (TEMPONE), diffused into hydrated single crystals, closely paralleled the motional properties of the label. This was taken to be evidence for coupling between the dynamical properties of the protein and the adjacent solvent. 

Experimental observations, such as the coincidence of onset of function with onset of protein motion and long-range connectivity, lead one to infer that correlated fluctuations are among the fundamental principles of enzyme activity. The proof of this inference, through the detection of cross-correlations, remains an open and difficult problem. There is a substantial body of evidence, however, that bears on the correlation of solvent and protein motions, and understanding of the details of this coupling is likely to come soon. 

It is well known that 2D NOESY is an effective method to study the three-dimensional (3D) structure of large molecules, such as proteins which have long motional correlation times.70-71 Cross-dipolar interaction peaks in a NOESY spectrum rely on the cross-relaxation of the longitudinal magnetization during the mixing time. One can extract valuable information about intermolecular distances from the intensity of the NOESY cross-peaks. The appearance of... 

Prompers and Briischweiler showed by quasiharmonic analysis that the conformational partition function of a globular protein sampled on the ns time scale can be factorized in good approximation into purely reorientational part, which determines heteronuclear NMR spin relaxation, and a remaining part that includes other types of intramolecular motions. Thus a thermodynamic interpretation of NMR relaxation parameters in proteins in the presence of motional correlations can be given. 

Description in atomic detail of correlated protein motions 342... 

In this section we will examine other kinds of correlated protein motions (with ps- or ns-timescales) and methods that can identify them. The rate-promoting vibrations we examined in the previous section are just one example of correlated protein motions. Because promoting vibrations involve residues in the immediate vicinity of donor and acceptor, it was relatively easy to identify them. In the more general case of extended correlated motions, it would be a challenge to identify residues that take part in them. In this section we describe two methods that have been successfully used for identifying atomic motions of interest, the TPS and the ED method. We will apply them to two enzymes we already studied in the previous section, LDH and PNP. 

Figure 65. Schematic diagram of the general behavior of the decay of NMR correlation functions in proteins. The physical origins for the decay in correlation resulting from the different kinds of protein motions are indicated.

On the subnanosecond time scale our basic knowledge of protein motions is almost complete that is, the types of motion that occur have been determined, their characteristics evaluated and the factors responsible for their properties delineated. Simulation methods have shown that the structural fluctuations in proteins are sizable particularly large fluctuations are found where steric constraints due to molecular packing are small (e.g., in the exposed sidechains and external loops), but substantial mobility is also found in the protein interior. Local atomic displacements are correlated in a manner that tends to minimize disturbances of the global structure of the protein. This often leads to fluctuations larger than would be permitted in a rigid polypeptide matrix. 

Protein motions in single FlAsH-labeled CaM molecules tethered to glass slides have been measured by anisotropy using time-correlated single-photon counting in a confocal microscope [46]. Average anisotropy values were similar to bulk measurements but showed wide variability from molecule to molecule. Decay rates indicated that rapid-scale protein motions occur in the N-terminal domain on a nanosecond timescale but limited signal-to-noise levels precluded detailed analysis. Comparable experiments with CaM labeled with Texas Red failed to detect such motions because of faster dye rotation, independent of the protein motions. 

Protein motions can contribute to catalysis in even more subtle ways. Correlated motions within a protein can push two substrates together, or push a substrate and a catalytic group together, placing reacting atoms in a conformation that is poised to move toward the transition state due to the close distance between the reacting atoms, as well as optimal overlap of the HOMO and LUMO. Correlated motions can also open channels that allow substrates to bind to a buried active site. 

Evidence for the importance of correlated motions that promote catalysis has emerged from a combination of structural, kinetic, and computational approaches. Enzymes that catalyze hydride transfer or electron transfer reactions have been studied most intensely. These reactions often occur via tunneling when rearrangement of the environment results in equalization of the energies of the particle to be transferred in the reactant and product wells. Protein motions that accomplish such energetic adjustments promote the reaction by allowing the particle to tunnel through the barrier. 

The role of protein motions in dihydrofolate reductase (DHFR) has been examined using molecular dynamics simulations as well as experimental studies of mutant enzymes. DHFR catalyzes transfer of hydride from NADPH to dihydrofolate via a tunneling mechanism. Molecular dynamics simulations of complexes of the enzyme with both substrates show both correlated and anticorrelated motions (see Figure 23). " Mutations... 

Tobi, D. and Bahar, I. (2005) Structural changes involved in protein binding correlate with intrinsic motions of proteins in the unbound state. Proceedings of the National Academy of Sciences of the United States of America, 102, 18908-18913. 

The role of protein side-chain motion in the slow dynamics of water around the protein surface is investigated by calculating the HB lifetime correlation function, S t), for two different conditions (i) when the side-chain protein motion is not constrained and (ii) when it is constrained. S i) showed a long-time tail in its natural condition the function initially decays slowly in its constrained condition compared to its natural condition and then decays to zero over a long time. 

In addition, protein motion reduces the retardation of the water dynamics, because the dimension of the water translational space is increased and at the same time the decay of the orientational correlation is accelerated. In spite of this accelerated dynamics, hydration water diffusion remains anomalous for a thermalized protein. 

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