Free-energy calculations - Theoretical Biophysics Group

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Reaction coordinate–based free-energy calculations A backdrop on potential of mean force calculations ξ and {x} are not independent variables: Pξ = |J| exp[−βU(q; ξ)] dq exp[−βT(px)]dpx Derivative of the probability distribution with respect to ξ: dPξ dξ = × exp[−βU(q; ξ)] exp[−βT(px)] dpx The kinetic contribution vanishes in dA(ξ)/dξ: dA(ξ) dξ ∂U(q; ξ) −β|J| + ∂ξ ∂|J| dq ∂ξ = − 1 1 exp[−βU(q; ξ β Pξ ∗ )] δ(ξ ∗ − ξ) × −β|J| ∂U(q; ξ∗ ) + ∂ξ ∂|J| dq dξ ∂ξ ∗ Chris Chipot Free-energy calculations
Reaction coordinate–based free-energy calculations A backdrop on potential of mean force calculations Back transformation into Cartesian coordinates: dA(ξ) dξ = − 1 1 exp[−βU(x)] δ[ξ(x) − ξ] β Pξ × −β ∂U(x) 1 ∂|J| + dx ∂ξ |J| ∂ξ The derivative of the free energy with respect to the order parameter may be expressed as a sum of configurational averages at constant ξ: 50 50 CARTER ET AL. (1989); CHIPOT, POHORILLE (2007) dA(ξ) dξ = ∂U(x) − ∂ξ ξ 1 ∂ ln |J| := −〈Fξ〉ξ β ∂ξ ξ Chris Chipot Free-energy calculations
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Free-energy calculations Measuring
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Foreword Free-energy differences ca
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Free-energy perturbation calculatio
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6 JORGENSEN, RAVIMOHAN (1985) 7 SIM
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8 WIDOM (1963) Free-energy perturba
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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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11 HUMMER ET AL. (1996) 12 HÜNENBE
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15 KIRKWOOD (1935) Free-energy pert
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16 PEARLMAN, KOLLMAN (1989) Free-en
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Free-energy calculations - Theoretical Biophysics Group

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