Protein Folding Dynamics:  Application of the Diffusion-Collision Model to the Folding of a Four-Helix Bundle

Abstract

A de novo designed four-helix bundle polypeptide with a modeled three-dimensional structure has been studied by chemical kinetics and Brownian dynamics simulations as an application of the diffusion-collision model. The complementary studies give information on kinetic pathways in the folding of the peptide and on the statistical propensities and time histories of the positions and orientations of the four helices.

The early folding kinetics of apomyoglobin

“…This time scale is consistent with the results of Brownian dynamics simulations of the movements and collisions of helix-turn-helix (Lee et al, 1987) and four-helix bundle (Yapa & Weaver, 1996) motifs. It is smaller than the estimates of Hagen et al…”

“…The diffusion-collision model of protein folding (Karplus & Weaver, 1976;Karplus & Weaver, 1994;Yapa & Weaver, 1996) has been applied to simulate the early folding kinetics of apomyoglobin by solving a set of first-order rate equations for the probabilities of the 64 folding states. The number of states is determined by the number of helix-helix contacts considered important in the kinetic pathways.…”

“…We take as an estimate of the folding time as described previously (Bashford et al, 1988;Karplus & Weaver, 1994;Yapa & Weaver, 1996 In Equation 3, Kjj are the elements of the rate matrix to be determined from two-microdomain model calculations. They are determined by the individual two-microdomain rates described above in Equations 1 and 2 (see Karplus & Weaver, 1994;Yapa & Weaver. 1996 for details).…”

“…Further molecular dynamics simulations such as those of Hirst and Brooks ( 1 995) are needed to improve our knowledge of microdomain properties. A possible approach is to incorporate transiently folding microdomains into Brownian dynamics (Ermak & McCammon, 1978;McCammon et al, 1980;Yapa et al, 1992;Schneller & Weaver, 1993;Yapa & Weaver, 1996) or other reduced (Pappu & Weaver, 1997) or simplified representation simulations, since the former are already into the microsecond 1 0.9 """_""""~" time regime (McCammon, 1996;Yapa & Weaver, 1996) in which important folding kinetic events take place. The recent work of Hoffmann and Knapp (1 997) illustrates the utility of this approach.…”

“…There is an apparent search problem in folding because the correct fold requires long-range interactions among the amino acids and statistical arguments (the Levinthal paradox (Levinthal, 1966(Levinthal, , 1968) show that a random search through all the possible conformations of even a moderately sized protein takes far too long for living systems. A possible mechanism by which a protein may make use of more sophisticated search procedures is the diffusion-collision model (Karplus & Weaver, 1976;Yapa & Weaver, 1996) in which fluctuating quasiparticles, called microdomains, which may be incipient secondary structures (a-helices, &sheets) or hydrophobic clusters move via diffusion and collide with other microdomains. Coalescence may occur between transiently folded, correctly oriented microdomains, and folding would then proceed as a series of coalescence steps.…”