Are the native states of proteins kinetic traps?

Biophysical Chemistry, 1987

were performed on the internal motion of Trp 59 of ribonuclease T, (EC 3.1.27.3) in the free enzyme, 2'.GMP-enzyme complex and 3'-GMP-enzyme complex. The Trp 59 motion was also studied in the free enzyme using molecular dynamics simulations. Energetic analysis of activation barriers to the Trp 59 motion was performed using both the transition state theory and Kramers' theory. The activation parameters showed a dependence on solvent viscosity mdlcating the transrtion state approach m aqueous solution to be inadequate.

Computer Physics Communications, 2002

Several small globular proteins exhibit a simple two-state folding process (sharp transition). The rather short folding times of proteins (fast folders) indicate that folding is guided through some sequence of contact bindings. We discuss the possibility for reconciling a two-state folding event with a sequential folding process, i.e. a folding pathway in a schematic model of protein folding. We show that both single and multiple folding pathways can lead to an apparent two-state folding from a thermodynamic point of view. We also discuss water interactions in protein folding, leading to cold and warm destabilization of the protein.  2002 Published by Elsevier Science B.V. .no (A. Hansen). 0010-4655/02/$ -see front matter  2002 Published by Elsevier Science B.V. PII: S 0 0 1 0 -4 6 5 5 ( 0 2 ) 0 0 2 9 3 -X

Chemical Physics, 2008

We have developed a new simulation method to estimate the distance between the native state and the first transition state, and the distance between the intermediate state and the second transition state of a protein which mechanically unfolds via intermediates. Assuming that the end-to-end extension $\Delta R$ is a good reaction coordinate to describe the free energy landscape of proteins subjected to an external force, we define the midpoint extension $\Delta R^*$ between two transition states from either constant-force or constant loading rate pulling simulations. In the former case, $\Delta R^*$ is defined as a middle point between two plateaus in the time-dependent curve of $\Delta R$, while, in the latter one, it is a middle point between two peaks in the force-extension curve. Having determined $\Delta R^*$, one can compute times needed to cross two transition state barriers starting from the native state. With the help of the Bell and microscopic kinetic theory, force dependencies of these unfolding times can be used to locate the intermediate state and to extract unfolding barriers. We have applied our method to the titin domain I27 and the fourth domain of {\em Dictyostelium discoideum} filamin (DDFLN4), and obtained reasonable agreement with experiments, using the C$_{\alpha}$-Go model.

Journal of Theoretical Biology, 2007

In this work, we present a generalization of Zwanzig's protein unfolding analysis [Zwanzig, R., 1997. Two-state models of protein folding kinetics. Proc. Natl Acad. Sci. USA 94, 148-150; Zwanzig, R., 1995. Simple model of protein folding kinetics. Proc. Natl Acad. Sci. USA 92, 9801], in order to calculate the free energy change D D N F between the protein's native state N and its unfolded state D in a chemically induced denaturation. This Extended Zwanzig Model (EZM) is both based on an equilibrium statistical mechanics approach and the inclusion of experimental denaturation curves. It enables us to construct a suitable partition function Z and to derive an analytical formula for D D N F in terms of the number K of residues of the macromolecule, the average number n of accessible states for each single aminoacid and the concentration C 1=2 where the midpoint of the N$D transition occurs. The results of the EZM for proteins where chemical denaturation follows a sigmoidal-type profile, as it occurs for the case of the T70N human variant of lysozyme (PDB code: T70N) [Esposito, G., et al., 2003. J. Biol. Chem. 278, 25910-25918], can be splitted into two lines. First, EZM shows that for sigmoidal denaturation profiles, the internal degrees of freedom of the chain play an outstanding role in the stability of the native state. On the other hand, that under certain conditions DF can be written as a quadratic polynomial on concentration C 1=2 , i.e., DF $aC 2 1=2 þ bC 1=2 þ c, where a; b; c are constant coefficients directly linked to protein's size K and the averaged number of non-native conformations n. Such functional form for DF has been widely known to fit experimental measures in chemically induced protein denaturation [

http://jcp.aip.org/resource/1/jcpsa6/v135/i11/p114101_s1?isAuthorized=no . We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both stabilization or destabilization of the denatured state of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.

Biochemistry, 2008

Biochemistry, 2006

For many decades, protein folding experimentalists have worked with no information about the timescales of relevant protein folding motions and without methods for estimating the height of folding barriers. Experiments in protein folding have been interpreted using chemical models in which the folding process is characterized as a series of equilibria between two or more distinct states that interconvert with activated kinetics. Accordingly, the information to be extracted from experiment was circumscribed to apparent equilibrium constants and relative folding rates. Recent developments are changing this situation dramatically. The combination of fast-folding experiments with the development of analytical methods more closely connected to physical theory reveals that folding barriers in native conditions range from minimally high (~14 RT for the very slow folder AcP) to nonexisting. While slow-folding (i.e. 1 millisecond or longer) single domain proteins are expected to fold in a two-state fashion, microsecond-folding proteins should exhibit complex behavior arising from crossing marginal or negligible folding barriers. This realization opens a realm of exciting opportunities for experimentalists. The free energy surface of a protein with marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic from structural factors in folding. Kinetic experiments on these proteins provide the unique opportunity to measure folding dynamics directly. Furthermore, the complex distributions of time-dependent folding behaviors expected for these proteins might be accessible to single molecule measurements. Here, we discuss some of these recent developments in protein folding, emphasizing aspects that can serve as a guide for experimentalists interested in exploiting this new avenue of research.

Advances in Protein Chemistry, 2000

Journal of Physics: Condensed Matter, 2003

We show here that the temperature dependence of the amide-I band of myoglobin shows evidence for a low lying selftrapped state at 1626 cm À1 : This low-lying state has a 30 ps lifetime at 50 K; much longer than the relaxation time of the main amide-I band at 50 K: r

Biochemistry, 1998

The N-terminal domain of phosphoglycerate kinase (N-PGK) and domain 1 of the T-cell adhesion protein CD2 (CD2.d1) fold through rapidly formed and transiently populated intermediate states in reactions which have no kinetic complications arising from proline isomerization or disulfide bonding. We have evaluated the thermodynamic parameters (∆C p , change in heat capacity; ∆S, entropy change; ∆H, enthalpy change) for each experimentally accessible step in these folding reactions. Despite their different topologies and amino acid compositions, the individual steps [U-I (unfolded to intermediate state), I-t (intermediate to major transition state), and t-F (transition state to the fully folded state)] have closely similar qualitative properties in the two proteins. For both, the heat capacity changes are proportional to m-value changes (∆m) for every step in the reaction, but the ratio ∆C p /∆m is lower for N-PGK, presumably owing to a much larger compliment of aromatic amino acids in the core. According to measurements of ∆C p and ∆m, the I-states are highly condensed (65-70% for N-PGK and 40-45% dehydrated for CD2.d1), yet the changes in entropy in the U-to-I transition are small, showing that the entropy gained from desolvation must be balanced by that lost in ordering the chain. The high degree of conformational order in the I-state, implied by these measurements, is mirrored by the extensive, native secondary structure revealed by amide exchange measurements [