Kramers rate theory is a milestone in chemical reaction research, but concerns regarding the basic understanding of condensed phase reaction rates of large molecules in viscous milieu persist. Experimental studies of Kramers theory rely on scaling reaction rates with inverse solvent viscosity, which is often equated with the bulk friction coefficient based on simple hydrodynamic relations. Apart from the difficulty of abstraction of the prefactor details from experimental data, it is not clear why the linearity of rate versus inverse viscosity, k ∝ η(-1), deviates widely for many reactions studied. In most cases, the deviation simulates a power law k ∝ η(-n), where the exponent n assumes fractional values. In rate-viscosity studies presented here, results for two reactions, unfolding of cytochrome c and cysteine protease activity of human ribosomal protein S4, show an exceedingly overdamped rate over a wide viscosity range, registering n values up to 2.4. Although the origin of this extraordinary reaction friction is not known at present, the results indicate that the viscosity exponent need not be bound by the 0-1 limit as generally suggested. For the third reaction studied here, thermal dissociation of CO from nativelike cytochrome c, the rate-viscosity behavior can be explained using Grote-Hynes theory of time-dependent friction in conjunction with correlated motions intrinsic to the protein. Analysis of the glycerol viscosity-dependent rate for the CO dissociation reaction in the presence of urea as the second variable shows that the protein stabilizing effect of subdenaturing amounts of urea is not affected by the bulk viscosity. It appears that a myriad of factors as diverse as parameter uncertainty due to the difficulty of knowing the exact reaction friction and both mode and consequences of protein-solvent interaction work in a complex manner to convey as though Kramers rate equation is not absolute.

It is well-known that hydrophobic effect play a major role in alcohol-protein interactions leading to structure unfolding. Studies with extremely alkaline cytochrome c (U(B) state, pH 13) in the presence of the first four alkyl alcohols suggests that the hydrophobic effect persistently overrides even though the protein carries a net charge of -17 under these conditions. Equilibrium unfolding of the U(B) state is accompanied by an unusual expansion of the chain involving an intermediate, I(alc), from which water is preferentially excluded, the extent of water exclusion being greater with the hydrocarbon content of the alcohol. The mobility and environmental averaging of side chains in the I(alc) state are generally constrained relative to those in the U(B) state. A few nuclear magnetic resonance-detected tertiary interactions are also found in the I(alc) state. The fact that the I(alc) state populates at low concentrations of methanol and ethanol and the fact that the extent of chain expansion in this state approaches that of the U(B) state indicate a definite influence of electrostatic repulsion severed by the low dielectric of the water/alcohol mixture. Interestingly, the U(B) ⇌ I(alc) segment of the U(B) ⇌ I(alc) ⇌ U equilibrium, where U is the unfolded state, accounts for roughly 85% of the total number of water molecules preferentially excluded in unfolding. Stopped-flow refolding results report on a submillisecond hydrophobic collapse during which almost the entire buried surface area associated with the U(B) state is recovered, suggesting the overwhelming influence of hydrophobic interaction over electrostatic repulsions.

Similarities in global properties of homopolymers and unfolded proteins provide approaches to mechanistic description of protein folding. Here, hydrodynamic properties and relaxation rates of the unfolded state of carbonmonoxide-liganded cytochrome c (cyt-CO) have been measured using nuclear magnetic resonance and laser photolysis methods. Hydrodynamic radius of the unfolded chain gradually increases as the solvent turns increasingly better, consistent with theory. Curiously, however, the rate of intrachain contact formation also increases with an increasing denaturant concentration, which, by Szabo, Schulten, and Schulten theory for the rate of intramolecular contact formation in a Gaussian polymer, indicates growing intramolecular diffusion. It is argued that diminishing nonbonded atom interactions with increasing denaturant reduces internal friction and, thus, increases the rate of polypeptide relaxation. Qualitative scaling of the extent of unfolding with nonbonded repulsions allows for description of internal friction by a phenomenological model. The degree of nonbonded atom interactions largely determines the extent of internal friction.

Internal friction in macromolecules is one of the curious phenomena that control conformational changes and reaction rates. It is held here that dispersion interactions and London-van der Waals forces between nonbonded atoms are major contributors to internal friction. To demonstrate this, the flipping motion of aromatic rings of F10 and Y97 amino acid residues of cytochrome c has been studied in glycerol/water mixtures by cross relaxation-suppressed exchange nuclear magnetic resonance spectroscopy. The ring-flip rate is highly overdamped by glycerol, but this is not due to the effect of protein-solvent interactions on the Brownian dynamics of the protein, because glycerol cannot penetrate into the protein to slow the internal collective motions. Sound velocity in the protein under matching solvent conditions shows that glycerol exerts its effect by rather smothering the protein interior to produce reduced molecular compressibility and root-mean-square volume fluctuation (δVRMS), implying an increased number of dispersion interactions of nonbonded atoms. Hence, δVRMS can be used as a proxy for internal friction. By using the ansatz that internal friction is related to nonbonded interactions by the equation f(n) = f0 + f1n + f2n(2) + ..., where the variable n is the extent of nonbonded interactions with fi coefficients, the barrier to aromatic ring rotation is found to be flat. Also interesting is the appearance of a turnover region in the δVRMS dependence of the ring-flip rate, suggesting anomalous internal diffusion. We conclude that cohesive forces among nonbonded atoms are major contributors to the molecular origin of internal friction.

Although RNA-binding proteins in plant phloem are believed to perform long-distance systemic transport of RNA in the phloem conduit, the structure of none of them is known. Arabidopsis thaliana phloem protein 16-1 (AtPP16-1) is such a putative mRNA transporter whose structure and backbone dynamics have been studied at pH 4.1 and 25 °C by high-resolution nuclear magnetic resonance spectroscopy. Results obtained using basic optical spectroscopic tools show that the protein is unstable with little secondary structure near the physiological pH of the phloem sap. Fluorescence-monitored titrations reveal that AtPP16-1 binds not only A. thaliana RNA (K ∼ 67 nM) but also sheared DNA and model dodecamer DNA, though the affinity for DNA is ∼15-fold lower. In the solution structure of the protein, secondary structural elements are formed by residues 3-9 (β1), 56-62 (β2), 133-135 (β3), and 96-110 (α-helix). Most of the rest of the chain segments are disordered. The N-terminally disordered regions (residues 10-55) form a small lobe, which conjoins the rest of the molecule via a deep and large irregular cleft that could have functional implications. The average order parameter extracted by model-free analysis of N relaxation and {H}-N heteronuclear NOE data is 0.66, suggesting less restricted backbone motion. The average conformational entropy of the backbone NH vectors is -0.31 cal mol K. These results also suggest structural disorder in AtPP16-1.