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pathways and the energy landscape of protein folding: a synthesis ..

and the energy landscape of protein folding: A synthesis

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Pathways, and the Energy Landscape of Protein Folding: a Synthesis ..

There exists a saddle point in the energy funnel landscape where the transition state for a particular protein is found. The transition state in the energy funnel diagram is the conformation that must be assumed by every molecule of that protein if the protein wishes to finally assume the native structure. No protein may assume the native structure without first passing through the transition state. The transition state can be referred to as a variant or premature form of the native state rather than just another intermediary step. The folding of the transition state is shown to be rate-determining, and even though it exists in a higher energy state than the native fold, it greatly resembles the native structure. Within the transition state, there exists a nucleus around which the protein is able to fold, formed by a process referred to as "nucleation condensation" where the structure begins to collapse onto the nucleus.

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In one exception Weinkam et al. () simulated the folding course of a Cyt c mimic without side chains using a modified Gō model. The computer was initially told what the target native structure looks like, the calculation was instructed to assign more favorable energy as the mock residues draw closer to their normal partners, a multiatom cooperativity term was added, and outsized influence was given to the heme. The presumed shape and properties of the folding landscape did not enter the calculation except for the energetically downhill tendency. These instructions caused foldon units to emerge and associate to produce a stepwise folding pathway, resembling the Cyt c experiments. This success was considered to show that the experimental Cyt c result depends especially on the influence of the heme group, but other proteins with no prosthetic group are now known to fold through distinct intermediates and pathways. The significance of the Cyt c calculation is that it tends to identify the factors that determine the foldon-based behavior. As for any mathematical derivation, the factors that determine the output result must be coded into the initial premises. In the mock Cyt c simulation, the important factor seems to be the added cooperativity term, as emphasized in the foldon hypothesis.

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R. L. Baldwin took up the challenge and led the field in a multiyear effort to experimentally define kinetic folding intermediates and pathways (–). In a thoughtful protein folding review 20 y ago, Baldwin considered the disparate insights available at the time from both theory and experiment (). He highlighted uncertainties in the experimental evidence for classical pathways. Kinetic folding intermediates seemed to form asynchronously over a range of time scales. Equilibrium analogs of folding intermediates called molten globules yielded mixed results, sometimes agreeing with kinetic folding information and sometimes not. Baldwin’s article served to alert the experimental protein folding community to the new view of heterogeneous folding and helped to establish the current paradigm of a multipath funneled energy landscape.

A realization of the inability to equilibrate to a common structure (, ) and the ensemble nature of partially folded forms led the theoretical community to a very different more statistical “new view” (–). It was inferred that proteins must fold to their unique native state through multiple unpredictable routes and intermediate conformations. Another prominent inference configured the Anfinsen thermodynamic hypothesis () in terms of a funnel-shaped energy landscape diagram (), which pictures that proteins must fold energetically downhill (the Z axis) and shrink in conformational extent (the generalized XY plane) as they go (, –). To fill out the landscape picture, classical rate-determining kinetic barriers are often replaced by qualitative concepts such as ruggedness, frustration, and traps, and major species by deep wells, all forming a kind of metalanguage known as “energy landscape theory” (, –). The graphic funnel picture is a generic representation, independent of structural and thermodynamic detail and equally applicable to any protein, RNA, or other compact polymer. Although it provides no constraints that would exclude any realistic folding scenario, even a defined pathway model, it has been widely interpreted to require that proteins fold through many independent pathways.

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The concept of the binding funnel suggests that a systematic energy bias forms pathways between unbound and bound structures all the way to the bottom of the funnel. These pathways go through a rugged energy surface of the funnel. The frustration of local interactions and its distribution in proteins and their complexes has been studied and reported to correlate with the protein topology and functionality (–). Highly frustrated interactions are observed on the protein surface near the binding site (). The possibilities for experimental estimates of the landscape ruggedness of proteins and RNA have been considered (). In this study we show that both the ruggedness and the bias (slope) of a basin can be powerful discriminating factors for detecting funnel-type basins.

Spectrum properties of binding landscapes can be characterized by the z-score or by the modified z-score (,). The modified z-score is defined as the ratio of the energy gap between the native state and the average of the energy spectrum and the width of the energy spectrum weighted by entropy per contact in the power −1/2. Recent studies of protein-protein association () and protein-ligand binding (,) showed that the modified z-score has large values for well-formed funneled landscapes and can be used as a descriptor of binding affinity in search of specific inhibitors or potential drugs. Studies of the kinetics of biomolecular binding and kinetic pathways (–) showed that the binding time monotonically decreases with the increase of the modified z-score. Cooperative binding/folding was studied by single-molecule dynamics (,).

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The energy landscapes at different resolutions were ..

The protein folding phenomenon was largely an experimental endeavor until the formulation of an theory of proteins by Joseph Bryngelson and in the late 1980s and early 1990s. This approach introduced the This principle says that nature has chosen amino acid sequences so that the folded state of the protein is very stable. In addition, the undesired interactions between amino acids along the folding pathway are reduced, making the acquisition of the folded state a very fast process. Even though nature has reduced the level of in proteins, some degree of it remains up to now as can be observed in the presence of local minima in the energy landscape of proteins. A consequence of these evolutionarily selected sequences is that proteins are generally thought to have globally "funneled energy landscapes" (coined by ) that are largely directed toward the native state. This "" landscape allows the protein to fold to the native state through any of a large number of pathways and intermediates, rather than being restricted to a single mechanism. The theory is supported by both and experimental studies, and it has been used to improve methods for and . The description of protein folding by the leveling free-energy landscape is also consistent with the 2nd law of thermodynamics. Physically, thinking of landscapes in terms of visualizable potential or total energy surfaces simply with maxima, saddle points, minima, and funnels, rather like geographic landscapes, is perhaps a little misleading. The relevant description is really a high-dimensional phase space in which manifolds might take a variety of more complicated topological forms.

Protein folding funnels: the nature of the transition state ensemble

The unfolded polypeptide chain begins at the top of the funnel where it may assume the largest number of unfolded variations and is in its highest energy state. Energy landscapes such as these indicate that there are a large number of initial possibilities, but only a single native state is possible; however, it does not reveal the numerous folding pathways that are possible. A different molecule of the same exact protein may be able to follow marginally different folding pathways, seeking different lower energy intermediates, as long as the same native structure is reached. Different pathways may have different frequencies of utilization depending on the thermodynamic favorability of each pathway. This means that if one pathway is found to be more thermodynamically favorable than another, it is likely to be used more frequently in the pursuit of the native structure. As the protein begins to fold and assume its various conformations, it always seeks a more thermodynamically favorable structure than before and thus continues through the energy funnel. Formation of secondary structures is a strong indication of increased stability within the protein, and only one combination of secondary structures assumed by the polypeptide backbone will have the lowest energy and therefore be present in the native state of the protein. Among the first structures to form once the polypeptide begins to fold are alpha helices and beta turns, where alpha helices can form in as little as 100 nanoseconds and beta turns in 1 microsecond.

From Levinthal to pathways to funnels Ken A

The adequate description of protein-protein interactions is essential for understanding cell machinery. The intermolecular energy landscape determines structure, kinetics, and thermodynamics of macromolecule complexes. The major characteristics of the landscapes—the folding/binding funnel, the ruggedness of the terrain, etc.—are important for interpreting protein folding and interactions and providing guidelines for modeling (–). It has been shown that simple energy functions, including coarse-grained (low-resolution) models, reveal major landscape characteristics. The large-scale, systematic studies of protein-protein complexes confirmed the existence of the intermolecular binding funnel (,) and further revealed that the number of distinct energy basins is small and that they are well formed (funnel like) and correlated with known binding modes ().

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