Free-energy calculations - Theoretical Biophysics Group

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33 BEUTLER ET AL. (1994) 34 ZACHARIAS ET AL. (1994) Free-energy perturbation calculations “Alchemical transformations” Solution: Modification of the parametrization of the van der Waals term in the potential energy function that governs the interaction of an appearing, or disappearing, atom, i, with an unaltered one, j: 33 U vdW ij (rij; λ) = 4 ɛij λ n × ⎧ ⎪⎨ 1 ⎪⎩ αvdW (1 − λ) 2 62 rij + σij − 1 αvdW (1 − λ) 2 ⎪⎬ 6 rij + ⎪⎭ σij Or equivalently, 34 U vdW ⎡⎛ (rij; λ) = 4ɛij(1 − λ) ⎣⎝ σ2 ij r2 ⎞6 ⎛ ⎠ − ⎝ ij + αλ σ2 ij r2 ⎞3 ⎠ ij + αλ ⎤ ⎦ Possibility to scale interactions with different schedules. Chris Chipot Free-energy calculations ⎫
Free-energy perturbation calculations “Alchemical transformations” 1 Build the topologies representative of state 0 and state 1, and establish an exclusion list to prevent atoms that are not common to 0 and 1 from interacting. 2 Generate an ensemble of configurations that are representative of the reference state, λ. 3 For each configuration, evaluate the potential energy using the reference state Hamiltonian, U(x; λ). 4 Repeat the same calculations using the Hamiltonian of the target state. 5 For each configuration, evaluate the potential energy difference. 6 Compute the ensemble average 〈exp {−β [U(x; λ + ∆λ) − U(x; λ)]}〉 λ , from which the free energy difference ∆A = A(λ + δλ) − A(λ) can be derived. 7 Increment λ and go to stage 2. Chris Chipot Free-energy calculations
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