Dynamics of protein folding and catalytic action

Synchrotron-based X-ray protein crystallography is the ideal technique for determining the static atomic-scale struture of protein molecules and their complexes, provided sufficient material can be purified and crystallized. But it is the dynamic structure of a protein molecule which determines its function. One can see from Figure IV.1 that major reconformations of proteins are slow processes on the scale of the 20 fs XFEL pulse duration, requiring μs to ms to complete. What are the impor tant questions regarding the folding process [19, 20] to which the SwissFEL can contribute? Since the work of Anfinsen et al, in the early 1960’s [21], it is known that the folding of a protein is a reversible process; the native structure is a thermodynamically stable configuration, corresponding to a global minimum of the accessible free energy. But according to the “Levinthal paradox” (see Infobox), it is vir tually impossible for a protein molecule to sample all of the available structures. Dill and Chan [19] ask the question: “Among a multitude of possibilities, how does a protein find its equilibrium structure?” In its search for the minimum energy state, the protein can be thought to move on an energy sur face in (higherdimensional) conformational space, the shape of which is determined by the amino-acid sequence of the protein and by external factors such as pH, temperature, degree of solvation, and the presence of neighboring “chaperone” proteins (see Infobox). What is the nature of this energy sur face? Several schematic possibilities are shown in Figure IV.10 [19]. The Levinthal paradox is portrayed in Figure IV.10a – the “Levinthal golf course”: the unrealistic absence of an energy gradient presents the protein with an insurmountable entropic barrier to finding the minimum-energy state. The alternative of a narrow “folding pathway“ (Fig. IV.10b) is also deemed unrealsitic, since it fails to describe proteins which happen to land off the beaten road. Current thinking prefers the picture that the protein performs a diffusional motion on the “trickle funnel” landscape shown in Figure IV.10c: all the protein molecules are guided to the native state, albeit with possible detours around local energy maxima and entropic delays in regions of low gradient. It has been proposed that par t of the folding trajectory consists of “hydrophobic zipping” [22, 23]. This is “an opportunistic process in which local contacts (nearby in the sequence) form first, drawing in new contacts, wich create still other and increasingly nonlocal contacts and opor tunities of other intrachain interactions. Helices, turns and other local structures would be the first to zip” [19]. Dill and Chan [19] stress that it would be par ticularly valuable to have an experimental method capable of quantifying the time-dependent structural correlations occuring in an ensemble of identical fluctuating proteins (see Fig. IV.11). This, they argue, would provide important information on the nature of the energy landscape and on the diffusional trajectories followed by the folding and unfolding proteins. The time-space correlation method proposed by Kam (see Chapter III) for studying the static structure of biomolecules in solution could conceivably be extended, using the SwissFEL, to the investigation of such dynamic structural correlations. Examining the protein-folding energy landscape in detail, Henzler-Wildman and Kern [20] classify the energy barriers according to their heights into “tiers” 0, 1 and 2 (see Fig. IV.12). Tier 0 refers to barriers of several kBT, corresponding to “larger-amplitude collective motions between relatively small numbers of states.” Transitions between these states occur on the μs time-scale or slower and form the basis of many impor tant biological processes, including “enzyme catalysis, signal transduction and protein-protein interactions”. On the finer scales of tiers 1 and 2, a “large ensemble of structurally similar states that are separated by energy barriers of less than one kBT result in more local, small-amplitude ps to ns fluctuations at physiological temperature”. It has been determined that these fluctuations, involving, e.g., loop motions (ns) and side-chain rotations (ps), in effect “pre-sample” the characteristic motions of catalytic action. Still finer than tier 2 are the fs-scale fluctuations related to bond vibrations and interactions with the solvent. Henzler-Wildman and Kern differentiate between the large tier 0 “enthalpic barriers”, relevant to conformational conformational change and the “entropic barriers” on the scale of tiers 1 and 2, which are related to minor rearrangements among neighboring peptides and in their interactions with the solvent. Thus, whereas the coherence and high peak flux of the SwissFEL make it a power ful tool for quantifying large conformational changes of proteins, its real power lies in the ability to follow the pre-sampling of biologically impor tant pathways occuring via delicate fs-ps-ns fluctuations. Fundamental questions regarding protein dynamics, which the SwissFEL may help resolve, include [19, 20, 24]:
  • What are the predominant structures and the distance distributions in the unfolded state?
  • What is the “speed limit” for elementar y dynamics along the energy sur face?
  • How rugged is the energy landscape? A rugged landscape implies fluctuations among very different conformations.
  • Is it possible to measure not only averages of structural observables, but also correlations among their fluctuations (Fig. IV.11)?
  • Can minor conformational substates be predicted from known structures?
  • How can this knowledge and a dynamic view of proteins be used to help discover and develop novel therapeutic agents?

Levinthal’s paradox

In the late 1960’s, Cyrus Levinthal formulated the “Levinthal paradox” [27], which can be formulated as a stastical problem [28]: Consider a protein molecule composed of 100 residues, each of which can assume 3 different conformations. For the number of possible structures, this yields 3100 = 5 × 1047. Now assume that it takes (only) 100 fs to convert from one structure to another. It would thus require 5 × 1034 s = 1.6 × 1027 years to (systematically) explore all possibilities. The disagreement between this long time and the actual folding time (μs – ms) represents Levinthal’s paradox.










HANS FRAUENFELDER

born 1922 in Schaffhausen, Switzerland,
PhD from ETHZ
Quote from Ref. [29]:
To carry out their functions, most proteins must perform motions. These motions can either be thermal equilibrium fluctuations or non-equilibrium relaxations, caused for instance by reactions. In terms of the energy landscape, motions can be described as jumps of the system from substates to substates. A task of biological physics is the experimental study of these motions, their connections to structure, and to the energy landscape. Since the rate coefficients of fluctuations range from fs-1 to s-1 or possibly even less, it is clear that many different tools are needed. It has been known for some time that proteins share proper ties with glasses. Recent studies show that this similarity has unexpected aspects, related to the interaction of the protein proper with the bulk solvent and with its hydration shell. Consider first the large-scale fluctuations. A comparison of the rate coefficients, kp(T), for large-scale motions in proteins, for instance entry and exit of ligands, with the rate coefficient kα(T) of the bulk solvent shows that they have the same temperature dependence over many orders of magnitude. In other words, large-scale fluctuations of the protein are slaved to the fluctuations in the bulk solvent. These protein processes are controlled by enthalpy barriers in the solvent, not by protein-internal enthalpy barriers. But a puzzle appears: while kp(T) and kα(T) have the same temperature dependence, for some processes kp(T) is 105 times slower than kα(T)! What causes this slowing? It obviously must be entropy or, in other words, the large number of states in the protein. Here is where the energy landscape comes in. A process like the exit of a ligand is not like opening a rigid door. Many side chains must be in the right position, helices may have to move. Opening thus corresponds to a random walk in conformation space. Indeed, theory suppor ts such a picture. Significant proper ties of proteins follow from these experimental results: proteins work in close interaction with their environment, the environment controls the enthalpy barriers for large-scale motions; the protein proper contributes to the entropy as characterized through the energy landscape. A complete understanding of the energy landscape and of the related fluctuation and relaxation processes is still a dream, but it is a grand challenge for biological physics.