One-Dimensional Barrier-Preserving Free-Energy Projections of a β-sheet Miniprotein: New Insights into the Folding Process

Abstract

The conformational space of a 20-residue three-stranded antiparallel β-sheet peptide (double hairpin) was sampled by equilibrium folding/unfolding molecular dynamics simulations for a total of 20 µs. The resulting one-dimensional free-energy profiles (FEPs) provide a detailed description of the free-energy basins and barriers for the folding reaction. The similarity of the FEPs obtained using the probability of folding before unfolding (p fold) or the mean first passage time supports the robustness of the procedure. The folded state and the most populated free-energy basins in the denatured state are described by the one-dimensional FEPs, which avoid the overlap of states present in the usual one- or two-dimensional projections. Within the denatured state, a basin with fluctuating helical conformations and a heterogeneous entropic state are populated near the melting temperature at about 11% and 33%, respectively. Folding pathways from the helical basin or enthalpic traps (with only one of the two hairpins formed) reach the native state through the entropic state, which is on-pathway and is separated by a low barrier from the folded state. A simplified equilibrium kinetic network based on the FEPs shows the complexity of the folding reaction and indicates, as augmented by additional analyses, that the basins in the denatured state are connected primarily by the native state. The overall folding kinetics shows single-exponential behavior because barriers between the non-native basins and the folded state have similar heights.

Sampling the equilibrium kinetic network of Trp-cage in explicit solvent

“…55,56 However, the methods are different in spirit and in approach. The cut-based method has the advantage that it needs no prior information of the stable states, whereas MSTIS requires knowledge of the stable states.…”

Identification of the protein folding transition state from molecular dynamics trajectories

“…Therefore, the statistics of p fold N are bounded by the number of visits along the original MD trajectory to the respective node. A more accurate way to determine the same quantity is by analytical calculation on the equilibrium transition network 12,13 ͑ETN͒ with a procedure termed pfoldt. 13 The ETN is the capacitated graph whose nodes and links represent coarse-grained mesostates and transitions, respectively, sampled by MD simulations.…”

“…A more accurate way to determine the same quantity is by analytical calculation on the equilibrium transition network 12,13 ͑ETN͒ with a procedure termed pfoldt. 13 The ETN is the capacitated graph whose nodes and links represent coarse-grained mesostates and transitions, respectively, sampled by MD simulations. The evaluation of pfoldt is based on the complete information about p fold for a given commitment time commit as contained in the ETN, i.e., p fold ͑ commit ͒ is the solution of an equation system operating on the ETN.…”

Efficient Construction of Mesostate Networks from Molecular Dynamics Trajectories

“…DS2: Data are derived from recently published simulations on the intrinsically disordered peptide Aβ [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . 39 The trajectory contained 7.5x10 5 snapshots saved at an interval of 20 ps, and the same 144, partially redundant internal distances that DS1 was originally derived from were extracted at each frame (D = 144).…”

“…39 The trajectory contained 7.5x10 5 snapshots saved at an interval of 20 ps, and the same 144, partially redundant internal distances that DS1 was originally derived from were extracted at each frame (D = 144). For the data in Table 1, backbone (φ/ψ/ω) dihedral angles of residues 14-24 of the peptide (D = 66), their sine/cosine terms (D = 66), the respective terms weighted by inertial masses (see equation 6), or the Cartesian coordinates of backbone nitrogen and oxygen atoms of residues [14][15][16][17][18][19][20][21][22][23][24] (D = 66) were also extracted.…”