Free-energy calculations - Theoretical Biophysics Group

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Reaction coordinate–based free-energy calculations Hydrophobic hydration 56 SHIRTS ET AL. (2003) Translocation of a single methane molecule across a water–air interface, using unconstrained MD and the average force exerted along ξ, the direction normal to the aqueous interface. The free energy difference between the tail–ends of the PMF yields the hydration free energy: +2.4±0.4 kcal/mol (exp. +2.0 kcal/mol). FEP creation and annihilation of methane in vacuum and in water. 1.02 ns forward and reverse simulations. ∆G hydr = +2.5±0.4 kcal/mol. This agrees nicely with the recent estimate of +2.44 kcal/mol, based on a 73.2 ns simulation. 56 Chris Chipot Free-energy calculations
Reaction coordinate–based free-energy calculations Measuring the error associated to an ABF calculation Midpoint rule: ∆A −∆ξ p 〈Fξ〉ξi i=1 Average and variance of the force over the reaction pathway: ⎧ ⎪⎨ ⎪⎩ µ = 〈Fξ〉ξ = 1 σ p 1 〈Fξ〉ξi = p p i=1 p µi i=1 2 = 1 p σ p i=1 2 2 i + (µ − µi) Fluctuation on the free-energy difference: 〈|∆A − ∆A| 2 〉 = (∆ξ) 2 p ni nj 1 〈(F ninj i,j=1 k=1 l=1 i ξ,l − µ)(Fi ξ,k − µ)〉 (∆ξ) 2 p p σ N i=1 2 i + (µ − µi) 2 2 p2 + 2σ N κ Standard deviation: 57 σ∆A ∆ξ σ (1 + 2κ)1/2 N1/2 57 RODRIGUEZ-GOMEZ ET AL. (2004) Chris Chipot Free-energy calculations
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Free-energy calculations Measuring
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Free-energy perturbation calculatio
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Substitute where Free-energy pertur
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Substitute where Free-energy pertur
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P(∆U ) 2.4 2.0 1.6 1.2 0.8 P (∆
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(a) 2.4 P(∆U ) 2.0 1.6 1.2 0.8 P
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(a) 2.4 P(∆U ) 2.0 1.6 1.2 0.8 P
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