On the calculation of puckering free energy surfaces

Abstract

Cremer-Pople puckering coordinates appear to be the natural candidate variables to explore the conformational space of cyclic compounds, and in literature different parametrizations have been used to this end. However, while every parametrization is equivalent in identifying conformations, it is not obvious that they can also act as proper collective variables for the exploration of the puckered conformations free energy surface. It is shown that only the polar parametrization is fit to produce an unbiased estimate of the free energy landscape. As an example, the case of a six-membered ring, glucuronic acid, is presented, showing the artefacts that are generated when a wrong parametrization is used.

Puckering free energy of pyranoses: A NMR and metadynamics-umbrella sampling investigation

“…This is because along the radial direction no meta-stabilities occur, and the radial coordinate Q relaxes fast enough to be ergodic for every reasonable set of potential (that is, when the bond lengths are rigid or quasi-rigid). As we showed in a previous work 72 , not every representation of the Cremer-Pople coordinates is equivalent to the end of being used as collective variables for a conformational search. In particular, any two-dimensional subset of Cremer-Pople coordinates whose functional form involves also biasing forces along the direction of Q might suffer from lack of ergodicity and, therefore, lead to biased sampling 84 .…”

“…72. For each of the 16 d-aldopyranoses, a system composed of the respective sugar ring in a cubic simulation box filled with 504 water molecule was set up.…”

Modelling of β-d-glucopyranose ring distortion in different force fields: a metadynamics study

“…35 In this study, the conformational free energy surface of b-D-glucopyranose (b-D-Glcp) was calculated in the space of three ring-puckering coordinates using three carbohydrate-tuned force fields, namely GLYCAM06, 11 OPLS 14 and GROMOS 45a4. 13 The application of three puckering coordinates (q x , q y and q z ) allows for modelling of both chair conformations and helps avoid most of the artifacts discussed in the study of Sega et al 36 Free energy surfaces were calculated in vacuum and in explicitly modelled water. Parameters of metadynamics (height and widths of hills) were chosen to obtain maximum accuracy in terms of free energy convergence.…”

Pickett angles and Cremer–Pople coordinates as collective variables for the enhanced sampling of six-membered ring conformations

“…Even though CP and SP coordinates are equally fit to describe puckered conformers from a purely geometrical point of view, differences can arise due to the shape of the puckering free energy hypersurfaces. Usually, in six-membered rings the CP puckering amplitude Q is not a slow degree of freedom, as it does not present metastabilities, and its free energy profile is such that conformers are generally populating only a thin spherical shell of the CP conformational globe [9]. It is therefore sufficient to introduce a biasing potential along the angular CP variables only, in order to get a proper exploration of the conformational phase space.…”

“…Nevertheless, the CP approach has become the most widely employed way to describe puckered conformers. The calculation of puckering free energy landscapes, and the determination of conformer populations has been the subject of a series of recent computer simulation investigations [8][9][10][11][12], apparently stimulated by the possibilities offered by recent developments in accelerated dynamics methods. Among those works, Strauss-Pickett (SP) dihedrals [13][14][15] have been also employed, as an alternative to CP variables, to perform the exploration of the puckering free energy space.…”