Abstract
Calculation of the free energy of protein folding and delineation of its pre-organization are of foremost importance for understanding, predicting and designing biological macromolecules. Here, we introduce an energy smoothing variant of parallel tempering replica exchange Monte Carlo (REMS) that allows for efficient configurational sampling of flexible solutes under the conditions of molecular hydration. Its usage to calculate the thermal stability of a model globular protein, Trp cage TC5b, achieves excellent agreement with experimental measurements. We find that the stability of TC5b is attained through the coupled formation of local and non-local interactions. Remarkably, many of these structures persist at high temperature, concomitant with the origin of native-like configurations and mesostates in an otherwise macroscopically disordered unfolded state. Graph manifold learning reveals that the conversion of these mesostates to the native state is structurally heterogeneous, and that the cooperativity of their formation is encoded largely by the unfolded state ensemble. In all, these studies establish the extent of thermodynamic and structural pre-organization of folding of this model globular protein, and achieve the calculation of macromolecular stability ab initio, as required for ab initio structure prediction, genome annotation, and drug design.
Highlights
The importance of accurately defining the molecular ensembles of proteins was recognized early by Levinthal, who concluded that folding of a random coil by way of a diffusive search of its combinatorially vast conformational space is incompatible with the biological energies and timescales of protein folding [1]
Insofar as the free energy of flexible polymers can be described by a configurational partition function, our study shows that molecularly adapted variants of replica exchange, including replica exchange MC with energy smoothing (REMS) introduced here, can be used for the calculation of the free energy and cooperativity of protein folding ab initio
Some of these configurations persist in the molecular ensemble at high temperature (Fig. 6), concomitant with the pre-organization of TC5b’s folding by such ordered unfolded state ensemble (Table 1)
Summary
The importance of accurately defining the molecular ensembles of proteins was recognized early by Levinthal, who concluded that folding of a random coil by way of a diffusive search of its combinatorially vast conformational space is incompatible with the biological energies and timescales of protein folding [1]. Structured unfolded states have been observed in a variety proteins [6,7,8,9,10,11] It is unknown whether these macroscopically observed structures correspond to the conformations of individual residues, or to an average of microscopic configurational states that are composed of groups of residues. The former is consistent with the random, albeit conformationally biased (statistical) coil model of the unfolded state, and means that efficient folding is achieved largely by way of kinetic pathways. Establishment of the extent of such pre-organization determines the relative contribution of the hierarchical (thermodynamic) and framework (kinetic) folding mechanisms, and is of major importance for understanding, predicting and designing biological macromolecules
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