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. 2000 Aug 1;97(16):8868-73.
doi: 10.1073/pnas.160259697.

Speeding molecular recognition by using the folding funnel: the fly-casting mechanism

B A Shoemaker  1 , J J Portman, P G Wolynes
Affiliations

Speeding molecular recognition by using the folding funnel: the fly-casting mechanism

B A Shoemaker et al. Proc Natl Acad Sci U S A. .

Abstract

Protein folding and binding are kindred processes. Many proteins in the cell are unfolded, so folding and function are coupled. This paper investigates how binding kinetics is influenced by the folding of a protein. We find that a relatively unstructured protein molecule can have a greater capture radius for a specific binding site than the folded state with its restricted conformational freedom. In this scenario of binding, the unfolded state binds weakly at a relatively large distance followed by folding as the protein approaches the binding site: the "fly-casting mechanism." We illustrate this scenario with the hypothetical kinetics of binding a single repressor molecule to a DNA site and find that the binding rate can be significantly enhanced over the rate of binding of a fully folded protein.

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Figures

Figure 1
Figure 1
The position of a protein surface residue as the protein is displaced from its operator-binding site as used in the free energy functional model. The native crystal structure defines a constant fiducial position of a surface residue (r′i) from the protein center of mass (Rcm). The fluctuations of residue i are centered about the mean position ri = 〈xi〉 (relative to the binding location, riB). If the protein is translated only without rotation (Ω = 0), then riB equals r′i so that the probability density of residue i can be described by P(xi − ri).
Figure 2
Figure 2
Free energy of binding for specific ensembles of arc repressor. The F(ΔR) curves are shown for the folded (red) and unfolded (green) minima as well as the fully ordered [(Q = 1 (black)] and disordered [Q = 0 (blue)] states at Tf. ΔR = R − R0 is the separation distance relative to that of the bound complex (R0). The effective capture radius is expanded by 8 Å for the unfolded state over the folded (which is 16 Å) and by 14 Å over that for the completely folded Q = 1 state. The orange curve is the free energy of the steepest descent path on the F(ΔR, Qp) surface shown in Fig. 3. Note the broken scales of R used to delineate the folding events, which occur in a narrow range of approach distance. The radius of the square well potential is b = R0 + 6.5 Å. The Debye–Waller factor for the folded residues is Δf = 1 Å, and for the unfolded chain Δu = 17 Å, which is the end-to-end distance of a random coil with 20 bond segments (the number of residues in the binding site).
Figure 3
Figure 3
Contour plots of the two-dimensional free energy surface (in units of kBTf) as a function of approach distance and contact ordering fraction Qp. ΔR = R − R0 is the separation distance relative to that of the bound complex (R0). The steepest descent paths are shown for the unfolded (red) and folded (green) states. At Tf, far from the binding site, the folded and unfolded structures are equally favorable. At ΔR = 20 Å, the unfolded state already feels the interaction falling to a lower contour while the folded state remains unaffected by the binding interaction. Qp for the unfolded ensemble hardly increases until ΔR = 8 Å, whereupon the free energy falls dramatically, while Qp increases by about 0.2. Closer in, the unfolded trajectory completes folding rapidly with binding. Parameters and broken scale in R are same as in Fig. 2.
Figure 4
Figure 4
A cartoon of how fly casting increases folding speed. At an approach distance Rcm, the partially folded ensemble is already able to form a few initial contacts to the binding site, while the folded structure remains out of range because of the smaller fluctuations in the folded state. Although these initial contacts are weak, they allow the protein to “reel” itself into the operator, completing folding and binding simultaneously. The increased capture radius allows the unfolded protein to find its specific binding site faster.
Figure 5
Figure 5
The fly-casting speedup ratio, ktot/kQ=1, is plotted vs. the unfolded protein concentration assuming a binding stability corresponding to experiment. For Kbind = Kexp, fly casting speeds up binding 1.6 times the rate of the fully formed (Qp = 1) protein through a range of reasonable protein concentrations. Parameters for the free energy functional are as in Fig. 2, and the contact radius is taken to be R0 = 3 Å.
Figure 6
Figure 6
Arrhenius plots for the total binding flux ktot (solid) and completely folded binding flux (dashed). Notice energetic interaction terms are constant here. Parameters are same as in Fig. 5.
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