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

Autieri, Emmanuel; Sega, Marcello; Pederiva, Francesco; Guella, Graziano

doi:10.1063/1.3476466

Cited by 52 publications

(99 citation statements)

References 100 publications

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“…12 shows, the string rapidly converges to a path that crosses the equatorial boat and skew-boat intermediates, ending up in the

{}^{1}C_{4}

conformation. This pathway is in qualitative agreement with that found by Autieri, 57 in spite of the differences in the force-field used. It also resembles that reported by Ardèvol et al 58 based on Car-Parrinello metadynamics simulations in vacuum, as well as that found by Spiwok et al 59 for β -D glucopyranose with the same force-field used here.…”

Section: Resultssupporting

confidence: 90%

“…13, image 51). This intermediate was detected by Autieri et al 57 but not by Spiwok et al, 59 due to the particular chirality of β -D glucopyranose. The last free-energy barrier, towards

{}^{1}C_{4}

, requires again uphill forces in several atoms (Fig.…”

Section: Resultsmentioning

confidence: 79%

“…Briefly, these coordinates represent the deviation of a six-membered ring with respect to an ideal plane, by using three values, namely Q , θ and φ , which define a set of polar coordinates. Following the implementation of Autieri et al, 57 these are defined by:

q_{x} = Q \sin θ \sin ϕ = - \sqrt{\frac{1}{3}} \sum_{j = 1}^{6} z_{j} \sin true[\frac{2 π}{3} (j - 1) true],

q_{y} = Q \sin θ \cos ϕ = \sqrt{\frac{1}{3}} \sum_{j = 1}^{6} z_{j} \cos true[\frac{2 π}{3} (j - 1) true],

q_{z} = Q \cos θ = \sqrt{\frac{1}{6}} \sum_{j = 1}^{6} {(- 1)}^{j - 1} z_{j}

where z j is the distance of each atom of the ring with respect to the mean plane passing through the ring itself. In this space the conformations of the molecule are depicted in a spherical projection with the two chair conformations

{}^{4}C_{1}

and

{}^{1}C_{4}

positioned at opposite poles.…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

String Method for Calculation of Minimum Free-Energy Paths in Cartesian Space in Freely Tumbling Systems

Branduardi

Faraldo‐Gómez

2013

J. Chem. Theory Comput.

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The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string.

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“…12 shows, the string rapidly converges to a path that crosses the equatorial boat and skew-boat intermediates, ending up in the

{}^{1}C_{4}

Section: Resultssupporting

confidence: 90%

“…13, image 51). This intermediate was detected by Autieri et al 57 but not by Spiwok et al, 59 due to the particular chirality of β -D glucopyranose. The last free-energy barrier, towards

{}^{1}C_{4}

, requires again uphill forces in several atoms (Fig.…”

Section: Resultsmentioning

confidence: 79%

q_{x} = Q \sin θ \sin ϕ = - \sqrt{\frac{1}{3}} \sum_{j = 1}^{6} z_{j} \sin true[\frac{2 π}{3} (j - 1) true],

q_{y} = Q \sin θ \cos ϕ = \sqrt{\frac{1}{3}} \sum_{j = 1}^{6} z_{j} \cos true[\frac{2 π}{3} (j - 1) true],

q_{z} = Q \cos θ = \sqrt{\frac{1}{6}} \sum_{j = 1}^{6} {(- 1)}^{j - 1} z_{j}

{}^{4}C_{1}

and

{}^{1}C_{4}

positioned at opposite poles.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

String Method for Calculation of Minimum Free-Energy Paths in Cartesian Space in Freely Tumbling Systems

Branduardi

Faraldo‐Gómez

2013

J. Chem. Theory Comput.

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“…for saturated and unsaturated lipid molecules with phosphocholine or phosphoglycerol head groups, 31 and for hexapyranose-based carbohydrate molecules. 32−34 …”

Section: Introductionmentioning

confidence: 99%

Testing of the GROMOS Force-Field Parameter Set 54A8: Structural Properties of Electrolyte Solutions, Lipid Bilayers, and Proteins

Reif

Winger

Oostenbrink

2013

J. Chem. Theory Comput.

101

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The GROMOS 54A8 force field [Reif et al. J. Chem. Theory Comput.2012, 8, 3705–3723] is the first of its kind to contain nonbonded parameters for charged amino acid side chains that are derived in a rigorously thermodynamic fashion, namely a calibration against single-ion hydration free energies. Considering charged moieties in solution, the most decisive signature of the GROMOS 54A8 force field in comparison to its predecessor 54A7 can probably be found in the thermodynamic equilibrium between salt-bridged ion pair formation and hydration. Possible shifts in this equilibrium might crucially affect the properties of electrolyte solutions or/and the stability of (bio)molecules. It is therefore important to investigate the consequences of the altered description of charged oligoatomic species in the GROMOS 54A8 force field. The present study focuses on examining the ability of the GROMOS 54A8 force field to accurately model the structural properties of electrolyte solutions, lipid bilayers, and proteins. It is found that (i) aqueous electrolytes involving oligoatomic species (sodium acetate, methylammonium chloride, guanidinium chloride) reproduce experimental salt activity derivatives for concentrations up to 1.0 m (1.0-molal) very well, and good agreement between simulated and experimental data is also reached for sodium acetate and methylammonium chloride at 2.0 m concentration, while not even qualitative agreement is found for sodium chloride throughout the whole range of examined concentrations, indicating a failure of the GROMOS 54A7 and 54A8 force-field parameter sets to correctly account for the balance between ion–ion and ion–water binding propensities of sodium and chloride ions; (ii) the GROMOS 54A8 force field reproduces the liquid crystalline-like phase of a hydrated DPPC bilayer at a pressure of 1 bar and a temperature of 323 K, the area per lipid being in agreement with experimental data, whereas other structural properties (volume per lipid, bilayer thickness) appear underestimated; (iii) the secondary structure of a range of different proteins simulated with the GROMOS 54A8 force field at pH 7 is maintained and compatible with experimental NMR data, while, as also observed for the GROMOS 54A7 force field, α-helices are slightly overstabilized with respect to 310-helices; (iv) with the GROMOS 54A8 force field, the side chains of arginine, lysine, aspartate, and glutamate residues appear slightly more hydrated and present a slight excess of oppositely-charged solution components in their vicinity, whereas salt-bridge formation properties between charged residues at the protein surface, as assessed by probability distributions of interionic distances, are largely equivalent in the GROMOS 54A7 and 54A8 force-field parameter sets.

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“…There were also attempts to do US corrections on the free energy surface obtained from MTD. [22][23][24][25] Here we combine US and MTD to sample orthogonal coordinates and reconstruct the free energy surface by a combination of Tiwary-Parrinello reweighting scheme and US reweighting within WHAM. First we carefully study the method on a model potential for which the exact free energy barriers are known.…”

Section: Introductionmentioning

confidence: 99%

Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics

2016

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Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, in order to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories.

show abstract

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

Cited by 52 publications

References 100 publications

String Method for Calculation of Minimum Free-Energy Paths in Cartesian Space in Freely Tumbling Systems

String Method for Calculation of Minimum Free-Energy Paths in Cartesian Space in Freely Tumbling Systems

Testing of the GROMOS Force-Field Parameter Set 54A8: Structural Properties of Electrolyte Solutions, Lipid Bilayers, and Proteins

Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics

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