Coarsely resolved topography along protein folding pathways

The Physics of the Interactions Governing Folding and Association of Proteins

The review discusses the molecular origins of the forces and free energies that determine several things about proteins, and how experiment and theory reveal this information. The first subject is the stability of the folded, native structures. The second is the range of molecular mechanisms by which proteins find their way to those folded structures in laboratory environments. The third is the much more complex problem of how folding occurs in the cellular environment. This topic includes a discussion of crowding and of the roles of chaperone molecules. The review concludes with a discussion of protein aggregation and fibril formation and of misfolding and therapies associated with it.

Pathway heterogeneity in protein folding

We generate ab initio folding pathways in two single-domain proteins, hyperthermophile variant of protein G domain (1gb4) and ubiquitin (1ubi), both presumed to be two-state folders. Both proteins are endowed with the same topology but, as shown in this work, rely to a different extent on large-scale context to find their native folds. First, we demonstrate a generic feature of two-state folders: A downsizing of structural fluctuations is achieved only when the protein reaches a stationary plateau maximizing the number of highly protected hydrogen bonds. This enables us to identify the folding nucleus and show that folding does not become expeditious until a topology is generated that is able to protect intramolecular hydrogen bonds from water attack. Pathway heterogeneity is shown to be dependent on the extent to which the protein relies on large-scale context to fold, rather than on contact order: Proteins that can only stabilize native secondary structure by packing it against scaffolding hydrophobic moieties are meant to have a heterogeneous transition-state ensemble if they are to become successful folders (otherwise, successful folding would be too fortuitous an event.) We estimate mutational Phi values as ensemble averages and deconvolute individual-route contributions to the averaged two-state kinetic picture. Our results find experimental corroboration in the well-studied chymotrypsin inhibitor (CI2), while leading to verifiable predictions for the other two study cases.

How do we probe ubiquitin's pathway heterogeneity?

We identify folding pathways for ubiquitin and assess its extent of transition state (TS) heterogeneity using a kinetically controlled ab initio algorithm that generates a coarse-grained description of torsional dynamics. The algorithm computes the time evolution of backbone-motion constraints, finds optimized conformations within such constraints, evaluates local solvent environments, and rescales accordingly the energetic contributions to determine the transition to the next set of torsional constraints. Native and nonnative structural features are found in the TS ensemble determined from a pool of 72 successful runs whose final folds are within 4-5 A RMSD from native. Certain nonnative features at the TS are shown to be necessary to create a large-scale context that overrides local propensities. Such misfolds undergo a subsequent rearrangement on the downhill side of the energy profile. The effects of tunable bi-histidine metal-binding sites, point mutations, negative Phi-value mutations, and denaturant on kinetics are predicted.

Pathway diversity and concertedness in protein folding: an ab-initio approach

Making use of an ab-initio folding simulator, we generate in vitro pathways leading to the native fold in moderate size single- domain proteins. The assessment of pathway diversity is not biased by any a priori information on the native fold. We focus on two study cases, hyperthermophile variant of protein G domain (1gb4) and ubiquitin (1ubi), with the same topology but different context dependence in their native folds. We demonstrate that a quenching of structural fluctuations is achieved once the proteins find a stationary plateau maximizing the number of highly protected hydrogen bonds. This enables us to identify the folding nucleus and show that folding does not become expeditious until a concerted event takes place generating a topology able to prevent water attack on a maximal number of hydrogen bonds. This result is consistent with the standard nucleation mechanism postulated for two-state folders. Pathway diversity is correlated with the extent of conflict between local structural propensity and large-scale context, rather than with contact order: In highly context-dependent proteins, the success of folding cannot rely on a single fortuitous event in which local propensity is overruled by large-scale effects. We predict mutational Pi values on individual pathways, compute ensemble averages and predict extent of surface burial and percentage of hydrogen bonding on each component of the transition state ensemble, thus deconvoluting individual folding-route contributions to the averaged two-state kinetic picture. Our predicted kinetic isotopic effects find experimental support and lead to further probes. Finally, the molecular redesign potentiality of the method, aimed at increasing folding expediency, is explored.

Semiempirical prediction of protein folds

We introduce a semiempirical approach to predict ab initio expeditious pathways and native backbone geometries of proteins that fold under in vitro renaturation conditions. The algorithm is engineered to incorporate a discrete codification of local steric hindrances that constrain the movements of the peptide backbone throughout the folding process. Thus, the torsional state of the chain is assumed to be conditioned by the fact that hopping from one basin of attraction to another in the Ramachandran map (local potential energy surface) of each residue is energetically more costly than the search for a specific (Phi, Psi) torsional state within a single basin. A combinatorial procedure is introduced to evaluate coarsely defined torsional states of the chain defined "modulo basins" and translate them into meaningful patterns of long range interactions. Thus, an algorithm for structure prediction is designed based on the fact that local contributions to the potential energy may be subsumed into time-evolving conformational constraints defining sets of restricted backbone geometries whereupon the patterns of nonbonded interactions are constructed. The predictive power of the algorithm is assessed by (a) computing ab initio folding pathways for mammalian ubiquitin that ultimately yield a stable structural pattern reproducing all of its native features, (b) determining the nucleating event that triggers the hydrophobic collapse of the chain, and (c) comparing coarse predictions of the stable folds of moderately large proteins (N approximately 100) with structural information extracted from the protein data bank.

Topology to geometry in protein folding: beta-lactoglobulin

Evolution of protein structure from random coil to native is first represented topologically by its time-dependent sequences of discretized Ramachandran basins occupied by successive backbone residues. Introducing energetic and entropic criteria at each instant of observation transforms the description from a structurally ambiguous topological representation to an unambiguous geometric picture of the folding process. The method is applied with success to folding of beta-lactoglobulin, traditionally perplexing because of its reputed nonhierarchical folding pattern. This molecule passes through a stage, ca. 0.1 microseconds duration, of transient, "flickering" alpha-helical structure, until a bit of tertiary structure forms that stabilizes the system long enough to allow it to pass to its native beta-sheet.