Abstract
Protein folding occurs in a very high dimensional phase space with an exponentially large number of states, and according to the energy landscape theory it exhibits a topology resembling a funnel. In this statistical approach, the folding mechanism is unveiled by describing the local minima in an effective one-dimensional representation. Other approaches based on potential energy landscapes address the hierarchical structure of local energy minima through disconnectivity graphs. In this paper, we introduce a metric to describe the distance between any two conformations, which also allows us to go beyond the one-dimensional representation and visualize the folding funnel in 2D and 3D. In this way it is possible to assess the folding process in detail, e.g., by identifying the connectivity between conformations and establishing the paths to reach the native state, in addition to regions where trapping may occur. Unlike the disconnectivity maps method, which is based on the kinetic connections between states, our methodology is based on structural similarities inferred from the new metric. The method was developed in a 27-mer protein lattice model, folded into a 3×3×3 cube. Five sequences were studied and distinct funnels were generated in an analysis restricted to conformations from the transition-state to the native configuration. Consistent with the expected results from the energy landscape theory, folding routes can be visualized to probe different regions of the phase space, as well as determine the difficulty in folding of the distinct sequences. Changes in the landscape due to mutations were visualized, with the comparison between wild and mutated local minima in a single map, which serves to identify different trapping regions. The extension of this approach to more realistic models and its use in combination with other approaches are discussed.
Highlights
Understanding the processes leading to a protein folding into its native state is one of the important problems in molecular biophysics
The simulation of the folding dynamics probes the conformations associated with local minima within given time intervals
The suitability of the approach could be confirmed by comparing the funnels and folding routes for 5 sequences, where much larger folding times were estimated for sequences known to be difficult to fold
Summary
Understanding the processes leading to a protein folding into its native (functional) state is one of the important problems in molecular biophysics. In the 1960s, Anfinsen hypothesized that a protein in its native state and under physiological conditions would adopt such a structure with the lowest possible energy [1] Though this hypothesis turned out to be correct, no explanation was offered to explain the large range of characteristic folding times, which may vary from milliseconds to seconds. In what became known as the Levinthal Paradox, in 1969 Levinthal argued that, due to an exponentially large number of states, a random search for the native structure would take cosmological times [2] The solution to this paradox came from the energy landscape theory [3,4,5,6,7], which embeds the statistical nature of the folding process. Many aspects of the folding funnel can be inferred from this approach, such as analysis of conformational maps [16,17], folding mechanisms involving mutants [18], and topological features in the transition state [19]
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