Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds

Abstract

A principal component analysis has been applied on equilibrium simulations of a beta-heptapeptide that shows reversible folding in a methanol solution. The analysis shows that the configurational space contains only three dense sub-states. These states of relatively low free energy correspond to the "native" left-handed helix, a partly helical intermediate, and a hairpin-like structure. The collection of unfolded conformations form a relatively diffuse cloud with little substructure. Internal hydrogen-bonding energies were found to correlate well with the degree of folding. The native helical structure folds from the N terminus; the transition from the major folding intermediate to the native helical structure involves the formation of the two most C-terminal backbone hydrogen bonds. A four-state Markov model was found to describe transition frequencies between the conformational states within error limits, indicating that memory-effects are negligible beyond the nanosecond time-scale. The dominant native state fluctuations were found to be very similar to unfolding motions, suggesting that unfolding pathways can be inferred from fluctuations in the native state. The low-dimensional essential subspace, describing 69% of the collective atomic fluctuations, was found to converge at time-scales of the order of one nanosecond at all temperatures investigated, whereas folding/unfolding takes place at significantly longer time-scales, even above the melting temperature.

Algorithmic dimensionality reduction for molecular structure analysis

“…A similar finding was reported for equilibrium simulations of the reversible folding of a ␤-heptapeptide in a methanol solution. 8 In this case, the effective variables explaining 69% of the collective atomic fluctuations were found to converge within 1 ns, despite the significantly longer time scales required for folding.…”

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.…”

“…10,11 The use of geometric clustering to identify fine-grained mesostates a constituting a conformational space network at equilibrium is a very powerful technique as these networks in principle are able to represent both thermodynamics and kinetics of the system in detail. [12][13][14][15][16] Computing these networks requires that simulation data are sampled frequently enough to resolve transitions of interest between those mesostates that exchange most rapidly. This is linked to the chosen resolution of mesostates.…”

“…38,39 Alternatively, fixed partition algorithms such as the approximate K-centers (K-medoids) algorithms 40,41 are in use. 15,19,37,42 All aforementioned methods scale superlinearly with dataset size (because in fixed partitioning schemes, the number of mesostates, K, will have to be proportional to N unless sampling is exhaustive). Post-processing of initial results may involve application of similar or more rigorous algorithms such as strictly hierarchical schemes.…”