# FreeE - Free Energy Calculation in MD Simulation Basic...

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Free Energy Calculation in MD Simulation

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Basic Thermodynamics Helmoholtz free energy A = U – TS + Σ μ i N i dA = w rev (reversible, const N V T) eq (22.9) Gibbs free energy G = U + PV – TS + Σ μ i N i = H – TS + Σ μ i N i dG = w nonPV (reversible, const N P T) U internal energy P Pressure μ i Chemical potential V Volume T Temperature S Entropy dS = dq/T S = k B ln W
Implication of Free Energy A ↔ B K eq = [A]/[B] K eq = exp (-ΔG 0 /RT) ΔG 0 = -RT ln K eq ΔG = ΔG 0 + RT ln Q ΔG > 0 Unfavorable ΔG = 0 ΔG < 0 Favorable

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Statistical Mechanics System can be described using Hamiltonian H(p 1 ,p 2 ,......... p N , r 1 , r 2 ,....... r N ) Different ensemble (fixed system quantities) - Canonical ensemble (N,V,T) - NPT ensemble
Statistical Mechanics

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Common Free Energy Type Solvation Free Energy / Transfer Free Energy Binding Free energy Confomational Free Energy
Calculating Free Energy Experimentally - probabilities of finding the system at given states ΔG = -RT ln (P 1 /P 0 ) - reversible work of moving the system between two states Computationally - pobability - reversible work → more efficient

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Probability Method ( Brute Force ) Ergodic hypothesis time average = ensemble average ΔG = -RT ln (P 1 /P 0 ) Is this true? In general, NO! - sampling time is too short computationally - hard to sample every state of the system For system state of zero sampling, P A = 0 ΔG 0 → A = ∞ A = lim t ∞ 1 t A t dt = 1 M M A i =⟨ A
Alanine Dipeptide

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Accurate calculations of absolute free energy is nearly impossible due to insufficient sampling in a finite length and time scale simulation. Need different methods to estimate free energy. Common method
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## This note was uploaded on 12/13/2010 for the course GENETIK 12 taught by Professor Atillabasar during the Spring '10 term at Istanbul Technical University.

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FreeE - Free Energy Calculation in MD Simulation Basic...

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