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.W e often glibly state that a protein must be folded to function. The reasoning underlying this statement is that organizing complex networks of chemical reactions in the cell requires these reactions to be highly specific. This specificity is achieved ultimately by having a high degree of geometrical precision in molecular binding-the famous ''lock and key.'' Geometric precision accompanies the increased rigidity of a biomolecule once it has folded; thus, apparently, folding is required for specific function. It does come as a surprise, then, that many proteins in the cell appear to be unfolded most of the time (see ref. 1 and refs. therein). Several ideas about potential biological advantages of being unfolded have been proposed. For example, the rapid turnover of unfolded proteins because of proteolytic degradation may be required for cell-cycle regulation (2). Thermodynamic arguments have also been made suggesting that coupling folding and binding may allow greater equilibrium distinctions for binding to different sites (3). In this note, we investigate whether too much rigidity may conflict with the need for biomolecules to move during their function and is therefore a kinetic disadvantage. There is much evidence for residual flexibility in the folded state, which must be thought of as having an ensemble of conformations (4). Still, the range of motions allowed in the folded state, as measured by Debye-Waller factors (5), is more restricted than those allowed in an unfolded molecule, thus slowing the exploration of configuration space. Here, we illustrate, by means of a specific example of operator binding to DNA, how the speed of molecular recognition can be enhanced by having folding (necessary for the required specificity) occur during binding rather than before.Folding and binding are kindred phenomena. The similarity of binding and folding is clear at the thermodynamic level, where both processes involve accurately locating molecular fragments with respect to each other, reducing the configurational entropy, and simultaneously lowering the free energy by the exclusion of solvent and formation of hydrogen bonds and salt bridges (6, 7). At the structural level, the similarity between packing patterns between ...

The motion involved in barrier crossing for protein folding are investigated in terms of the chain dynamics of the polymer backbone, completing the microscopic description of protein folding presented in the previous paper. Local reaction coordinates are identified as collective growth modes of the unstable fluctuations about the saddle-points in the free energy surface. The description of the chain dynamics incorporates internal friction (independent of the solvent viscosity) arising from the elementary isomerizations of the backbone dihedral angles. We find that the folding rate depends linearly on the solvent friction for high viscosity, but saturates at low viscosity because of internal friction. For λ-repressor, the calculated folding rate prefactor, along with the free energy barrier from the variational theory, gives a folding rate that agrees well with the experimentally determined rate under highly stabilizing conditions, but the theory predicts too large a folding rate at the transition midpoint. This discrepancy obtained using a fairly complete quantitative theory inspires a new set of questions about chain dynamics, specifically detailed motions in individual contact formation.

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A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G. Wolynes, Phys. Rev. Lett. 81, 5237 (1998)]. We choose the λrepressor protein as an illustrative example and focus on how the polymer chain statistics influence free energy profiles and partially ordered ensembles of structures. In particular, we investigate the role of chain stiffness on the free energy profile and folding routes. We evaluate the applicability of simpler approximations in which the conformations of the protein molecule along the folding route are restricted to have residues that are either entirely folded or unfolded in contiguous stretches. We find that the folding routes obtained from only one contiguous folded region corresponds to a chain with a much greater persistence length than appropriate for natural protein chains, while the folding route obtained from two contiguous folded regions is able to capture the relatively folded regions calculated within the variational approach. The free energy profiles obtained from the contiguous sequence approximations have larger barriers than the more microscopic variational theory which is understood as a consequence of partial ordering.

We present a microscopic variational theory for the free energy surface of a fast folding protein that allows folding kinetics to be resolved to the residue level using Debye-Waller factors as local order parameters. We apply the method to the l-repressor protein and compare with site directed mutagenesis experiments. The formation of native structure and the free energy profile along the folding route are shown to be well described by the capillarity approximation but with some fine structure due to local folding topology. [S0031-9007(98)07855-7] PACS numbers: 87.15. -v Proteins fold on a configurational energy landscape that has the shape of a funnel [1]. As the protein moves down the funnel towards the native state, incomplete cancellation of the entropy and energy losses may result in free energy barriers. So far, proteins that fold fast exhibit single exponential kinetics [2], consistent with a free energy profile that has a single highest barrier along the progress coordinate. Central issues are the origin of the free energy barrier for fast folding proteins and how the ensemble of structures which represent the bottleneck is to be characterized. We address these questions using a variational approximation that describes ensembles of partially folded proteins at the highest level of resolution, i.e., the specific role of individual residues in guiding the protein to the native state is quantified. In the laboratory, Fersht has developed a probe of the transition state or bottleneck ensemble through protein engineering kinetic studies in which the sequence of the protein is altered by replacing residues one at a time [3]. The experiment yields the fraction of the time that the mutated site is in the native conformation in the bottleneck ensemble by comparing folding rates of the mutant to the wild type. Since this can be done for any residue in the sequence, these studies are inherently "site resolved." Resolving the transition state ensemble to this level is one way to monitor the average of the many routes taken as proteins fold.Previous analytic mean field theories and simulations have produced energy landscapes in one or two global dimensions characterizing the folding ensemble [4]. We develop here a free energy profile for proteins with a funneled landscape that is completely site resolved, i.e., one dimension per residue, by extending the mean field variational calculations presented in [5]. The underlying Hamiltonian explicitly incorporates chain stiffness and connectivity while the approximation employs a variational density that monitors local order parameters for folding akin to the Debye-Waller factors (also called temperature factors) for individual residues seen in x-ray crystallography.The basic Hamiltonian for an interacting polymer chain is H H chain 1 H int , where H chain is backbone potential and H int are the interactions between distant monomers along the chain. H chain is an effective harmonic potential bH chain 1͞2 P r i ? G ij ? r j 1 B P r 2 i , where ͕r i ͖ are the positions of t...