Free perturbation-umbrella sampling

Major DT, Gao J (2007) An integrated path integral and free-energy perturbation-umbrella sampling method for computing kinetic isotope effects of chemical reactions in solution and in enzymes. J Chem Theory Comput 3 949—960... 

FEP/US Free energy perturbation/umbrella sampling Hevb EVB Hamiltonian... 

Integrated Path Integral-Free Energy Perturbation/ Umbrella Sampling (PI-FEP/UM) Method for Computing KIEs... 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

Umbrella sampling method, see Free energy perturbation method... 

One weakness of this treatment, however, is that it neglects entropic contributions. Entropic contributions were considered in the free energy profiles (FEP) calculated earlier using umbrella sampling [58] and Monte Carlo Free energy Perturbation [59], both using a QM/MM scheme and the AMI Hamiltonian for the QM part. Our group used the same SIESTA DFT-based QM/MM method described above... 

The PMF as a function of Xs is determined by a coupled free energy perturbation and umbrella sampling technique.5,14,16,41 The computational procedure follows two steps, although they are performed in the same simulation. The first is to use a reference potential rp to enforce the orientation polarization of the solvent system along the reaction path. A convenient choice of the reference potential, which is called mapping potential in Warshel s work,13,14,16,42 is a linear combination of the reactant and product diabatic potential energy ... 

In considering fluids, a variety of approaches have been used to compute entropy and free energy a free-volume method,111-112 thermodynamic perturbation theory,113-116 thermodynamic integration,117-121 umbrella sampling,122-124 and a Monte Carlo recursion method.125-126 The entropy of association of two protein molecules in water has also been computed.127... 

The concept of potential of mean force (PMF) was introduced by Kirkwood in 1935 [31], which is now the central of the reactions in the macromolecule simulation. To obtain reliable and accurate PMFs or free energy surfaces, two methods have been generally used in the simulations, i.e., free energy perturbation [32], umbrella sampling [33]. In this work, all of free energy surfaces are generated based on umbrella sampling. 

In simulations, an alternative to perturbation theory is umbrella sampling. It is used to connect the two configurations of interest (e.g., a protein plus a bound ligand in solution versus a protein in solution and a free ligand in solution see Fig. 10(b)) by an appropriate configurational coordinate. Since the calculations correspond exactly to those used with a reaction coordinate in activated dynamics (Chapt. IV.E) we do not repeat the description of the umbrella sampling method.,70a... 

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