Approximate free energy simulations

In equation (13), a and /J are empirical scaling parameters derived by fitting experimental data for a series of inhibitors [274-276] ub and b refer to the 

The advantages of LIA over the classical (TP and TI) free energy simulation methods are (i) the absolute binding free energies are computed (AF instead of AAF), (ii) the intermediate hybrid states are eliminated and only the end-points are sampled, and (iii) a physical path is used between the initial and the final states which prevents the X goes to end-points catastrophe problem. However, a certain degree of empiricism is associated with the model, and in fact, somewhat different values for the scaling parameters a and P have been derived by various authors [274-276]. 

Also providing free energy estimates, the free energy derivatives formalism [287-289] is based on the following equation  

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There now exist several methods for predicting the free energy associated with a compositional or conformational change.7 These can be crudely classified into two types "exact" and "approximate" free energy calculations. The former type, which we shall discuss in the following sections, is based directly on rigorous equations from classical statistical mechanics. The latter type, to be discussed later in this chapter, starts with statistical mechanics, but then combines these equations with assumptions and approximations to allow simulations to be carried out more rapidly. 

The second term in Equation 41 is constant and may be estimated using free energy simulation or semi-empirical methods. When the ligands are similar and the entropy terms associated with the restraining potential are expected to cancel, the second term can be approximated by an internal energy difference... 

Van Gunsteren, W.F., Beutler, T.C., Praternali, F., King, P.M., Mark, A.E., Smith, P.E. Computation of free energy in practice Choice of approximations and accuracy limiting factors, in Computer Simulations of Biomolecular Systems, Vol 2, W.F. van Gunsteren, P.K. Weiner and A.J. Wilkinson, eds. Escom, Leiden (1993) 315-348. 

A linear dependence approximately describes the results in a range of extraction times between 1 ps and 50 ps, and this extrapolates to a value of Ws not far from that observed for the 100 ps extractions. However, for the simulations with extraction times, tg > 50 ps, the work decreases more rapidly with l/tg, which indicates that the 100 ps extractions still have a significant frictional contribution. As additional evidence for this, we cite the statistical error in the set of extractions from different starting points (Fig. 2). As was shown by one of us in the context of free energy calculations[12], and more recently again by others specifically for the extraction process [1], the statistical error in the work and the frictional component of the work, Wp are related. For a simple system obeying the Fokker-Planck equation, both friction and mean square deviation are proportional to the rate, and... 

Gerber, P. R., Mark, A. E., van Gunsteren, W. F. An approximate but efficient method to calculate free energy trends by computer simulation Application to dihydrofolate reductase-inhibitor complexes. J. Comp. Aid. Mol. Desgn 7 (1993) 305-323... 

Modem understanding of the hydrophobic effect attributes it primarily to a decrease in the number of hydrogen bonds that can be achieved by the water molecules when they are near a nonpolar surface. This view is confirmed by computer simulations of nonpolar solutes in water [15]. To a first approximation, the magnimde of the free energy associated with the nonpolar contribution can thus be considered to be proportional to the number of solvent molecules in the first solvation shell. This idea leads to a convenient and attractive approximation that is used extensively in biophysical applications [9,16-18]. It consists in assuming that the nonpolar free energy contribution is directly related to the SASA [9],... 

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