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Tunable Coarse Graining for Monte Carlo Simulations of Proteins via Smoothed Energy Tables: Direct and Exchange Simulations.

Spiriti J, Zuckerman DM - J Chem Theory Comput (2014)

Bottom Line: For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations.Chem.Theory Comput.2006, 2, 656-666).

View Article: PubMed Central - PubMed

Affiliation: Department of Computational and Systems Biology, University of Pittsburgh , Pittsburgh, Pennsylvania 15213, United States.

ABSTRACT
Many commonly used coarse-grained models for proteins are based on simplified interaction sites and consequently may suffer from significant limitations, such as the inability to properly model protein secondary structure without the addition of restraints. Recent work on a benzene fluid (Lettieri S.; Zuckerman D. M.J. Comput. Chem.2012, 33, 268-275) suggested an alternative strategy of tabulating and smoothing fully atomistic orientation-dependent interactions among rigid molecules or fragments. Here we report our initial efforts to apply this approach to the polar and covalent interactions intrinsic to polypeptides. We divide proteins into nearly rigid fragments, construct distance and orientation-dependent tables of the atomistic interaction energies between those fragments, and apply potential energy smoothing techniques to those tables. The amount of smoothing can be adjusted to give coarse-grained models that range from the underlying atomistic force field all the way to a bead-like coarse-grained model. For a moderate amount of smoothing, the method is able to preserve about 70-90% of the α-helical structure while providing a factor of 3-10 improvement in sampling per unit computation time (depending on how sampling is measured). For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations. For a β hairpin, secondary structure is also preserved, albeit for a narrower range of the smoothing parameter and, consequently, for a more modest improvement in sampling. We have also applied the new method in a "resolution exchange" setting, in which each replica runs a Monte Carlo simulation with a different degree of smoothing. We obtain exchange rates that compare favorably to our previous efforts at resolution exchange (Lyman E.; Zuckerman D. M.J. Chem. Theory Comput.2006, 2, 656-666).

No MeSH data available.


Related in: MedlinePlus

Smoothing kernelsand effect of smoothing on interaction potentials.(a) Plots of the smoothing kernels wtrans(γij) and worient(χij) given in eqs 4 and 6 for smoothing scaleγ0 = χ0 = 60°. (b) Contourplots of interaction energy between peptide-bond fragments of identicalorientation as a function of angular scale of smoothing. Blue contourrepresents interaction energy of +1.0 kcal/mol; red contour representsinteraction energy of −1.0 kcal/mol.
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fig2: Smoothing kernelsand effect of smoothing on interaction potentials.(a) Plots of the smoothing kernels wtrans(γij) and worient(χij) given in eqs 4 and 6 for smoothing scaleγ0 = χ0 = 60°. (b) Contourplots of interaction energy between peptide-bond fragments of identicalorientation as a function of angular scale of smoothing. Blue contourrepresents interaction energy of +1.0 kcal/mol; red contour representsinteraction energy of −1.0 kcal/mol.

Mentions: Because thesmoothing kernels wtrans and worient are solutions to the diffusionequation in their respective spaces, this smoothing procedure canbe interpreted as allowing the Boltzmann probability, exp(−βU), to diffuse along the angular and orientationalcoordinates. The angular scales γ0 and χ0 control the extent of this diffusion and therefore the degreeof translational or orientational smoothing. For γ0 = χ0 = 0, no smoothing takes place and the interactionenergy is equivalent to that given by the atomistic force field, withrelatively small errors that come from the finite resolution of thetable. In the limit as γ0 → ∞ and χ0 → ∞, all variation in the interaction energywith the angular coordinates (θ, ϕ, ϕ′, θ′,ψ′) is eliminated, and the interaction potential becomesa spherically symmetric potential, dependent only on the interfragmentdistance r. Thus, by adjusting the values of γ0 and χ0, and constructing tables accordingly,we can obtain a continuous range of protein force fields, rangingfrom a united-atom force field all the way to a MARTINI-like coarse-grainedmodel with spherical “beads” centered on the centerof mass of each fragment. Figure 2b shows thistransformation, and a plot of the kernel functions wtrans(γ) and worient(χ) for γ0 = 60° and χ0 = 60° is shown in Figure 2a.


Tunable Coarse Graining for Monte Carlo Simulations of Proteins via Smoothed Energy Tables: Direct and Exchange Simulations.

Spiriti J, Zuckerman DM - J Chem Theory Comput (2014)

Smoothing kernelsand effect of smoothing on interaction potentials.(a) Plots of the smoothing kernels wtrans(γij) and worient(χij) given in eqs 4 and 6 for smoothing scaleγ0 = χ0 = 60°. (b) Contourplots of interaction energy between peptide-bond fragments of identicalorientation as a function of angular scale of smoothing. Blue contourrepresents interaction energy of +1.0 kcal/mol; red contour representsinteraction energy of −1.0 kcal/mol.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230378&req=5

fig2: Smoothing kernelsand effect of smoothing on interaction potentials.(a) Plots of the smoothing kernels wtrans(γij) and worient(χij) given in eqs 4 and 6 for smoothing scaleγ0 = χ0 = 60°. (b) Contourplots of interaction energy between peptide-bond fragments of identicalorientation as a function of angular scale of smoothing. Blue contourrepresents interaction energy of +1.0 kcal/mol; red contour representsinteraction energy of −1.0 kcal/mol.
Mentions: Because thesmoothing kernels wtrans and worient are solutions to the diffusionequation in their respective spaces, this smoothing procedure canbe interpreted as allowing the Boltzmann probability, exp(−βU), to diffuse along the angular and orientationalcoordinates. The angular scales γ0 and χ0 control the extent of this diffusion and therefore the degreeof translational or orientational smoothing. For γ0 = χ0 = 0, no smoothing takes place and the interactionenergy is equivalent to that given by the atomistic force field, withrelatively small errors that come from the finite resolution of thetable. In the limit as γ0 → ∞ and χ0 → ∞, all variation in the interaction energywith the angular coordinates (θ, ϕ, ϕ′, θ′,ψ′) is eliminated, and the interaction potential becomesa spherically symmetric potential, dependent only on the interfragmentdistance r. Thus, by adjusting the values of γ0 and χ0, and constructing tables accordingly,we can obtain a continuous range of protein force fields, rangingfrom a united-atom force field all the way to a MARTINI-like coarse-grainedmodel with spherical “beads” centered on the centerof mass of each fragment. Figure 2b shows thistransformation, and a plot of the kernel functions wtrans(γ) and worient(χ) for γ0 = 60° and χ0 = 60° is shown in Figure 2a.

Bottom Line: For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations.Chem.Theory Comput.2006, 2, 656-666).

View Article: PubMed Central - PubMed

Affiliation: Department of Computational and Systems Biology, University of Pittsburgh , Pittsburgh, Pennsylvania 15213, United States.

ABSTRACT
Many commonly used coarse-grained models for proteins are based on simplified interaction sites and consequently may suffer from significant limitations, such as the inability to properly model protein secondary structure without the addition of restraints. Recent work on a benzene fluid (Lettieri S.; Zuckerman D. M.J. Comput. Chem.2012, 33, 268-275) suggested an alternative strategy of tabulating and smoothing fully atomistic orientation-dependent interactions among rigid molecules or fragments. Here we report our initial efforts to apply this approach to the polar and covalent interactions intrinsic to polypeptides. We divide proteins into nearly rigid fragments, construct distance and orientation-dependent tables of the atomistic interaction energies between those fragments, and apply potential energy smoothing techniques to those tables. The amount of smoothing can be adjusted to give coarse-grained models that range from the underlying atomistic force field all the way to a bead-like coarse-grained model. For a moderate amount of smoothing, the method is able to preserve about 70-90% of the α-helical structure while providing a factor of 3-10 improvement in sampling per unit computation time (depending on how sampling is measured). For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations. For a β hairpin, secondary structure is also preserved, albeit for a narrower range of the smoothing parameter and, consequently, for a more modest improvement in sampling. We have also applied the new method in a "resolution exchange" setting, in which each replica runs a Monte Carlo simulation with a different degree of smoothing. We obtain exchange rates that compare favorably to our previous efforts at resolution exchange (Lyman E.; Zuckerman D. M.J. Chem. Theory Comput.2006, 2, 656-666).

No MeSH data available.


Related in: MedlinePlus