Ilja V. Khavrutskii, PhD
2007-present, Research Associate with Prof. J. Andrew McCammon, HHMI/UCSD/CTBP, La Jolla, CA
2004-2007, Research Associate with Prof. Charles L. Brooks III, TSRI/CTBP, La Jolla, CA
1998 MSc, Novosibirsk State University and The Boreskov Institute of Catalysis, Novosibirsk, Russia
Since April 2004, I have been developing new methods that would help us study rare events in large molecules of interest to biology. My primary interests in this area are enzyme catalysis, allosteric regulations, protein folding, ligand binding and small molecule transport through various channels. Structural descriptions of any of the involved transformations without the corresponding free energy information are likely to be very limited. Thus, I devote special attention to ways of computing accurate free energies of these transformations.
Recently, we have developed a novel method to compute minimum free energy reaction or more generally transition path ensembles along with the corresponding free energy profiles in molecular systems with arbitrary many dimensions (Khavrutskii et al., JCP V125, N17, p174108 (2006); first draft in May 2006). I named this method Harmonic Fourier Beads. Since the first HFB publication, the method has evolved substantially and now provides a complete solution to the transition path ensemble problem with the help of free energy gradient in both Cartesian and generalized coordinates. The Cartesian version of the HFB method is called the Gradient-Augmented Harmonic Fourier Beads (JCP; first draft in Aug 2006). Very recently we have extended the method capabilities to include centers-of-mass of groups of atoms in addition to atomic positional restraints. This variant of the method is called Generalized Gradient-Augmented Harmonic Fourier Beads method or gga-HFB for short (Khavrutskii et al., JCP V127, N12, p124901 (2007); first draft in Feb 2007). Gga-HFB allows to study permeation of small molecules through membranes and various channels. The latest development extends the applicability of the gga-HFB method to generalized (non)linear reactive coordinate spaces. In this variant a proper Jacobian correction is required to get at the correct PMF (Khavrutskii et al., JCP V128, N4, p044106 (2008); first draft in Aug 2007).
Unlike many other methods, the HFB method family is histogram-, Jacobian- (only the Cartesian version), metric tensor-, and reaction coordinate-free. I would like to stress one more time that when using reaction coordinates other than Cartesian in umbrella sampling simulations with Cartesian MD propagators (default) and unbiasing your results with either wheighted histogram analysis method (WHAM) or gga-HFB, it is absolutely essential to apply a proper Jacobian correction.
It gives me special pride that the HFB method also solves an important mathematical problem of locating saddle points on various energy surfaces by using convex optimization techniques, thus avoiding the use of expensive second derivatives calculations. The best part is that gga-HFB is guaranteed to find all the saddle points and all the intermediates present in the path between a given reactant and product and independently provides highly accurate energy profiles.
Although, I derived the unbiased free-energy gradient or the mean force theorem independently, I would like to acknowledge that a similar equation, yet histogram-based, was derived from a slightly different perspective earlier by Prof. Johannes Kästner and Prof. Walter Thiel (see their "Umbrella Integration" papers in JCP). However, an even earlier derivation of the moment-based free energy gradient (as the one used in gga-HFB) has been provided by Prof. Attila Szabo (see G. Hummer and A. Szabo in Acc. Chem. Res. V 38, pp 504-513 2005, eq. 38 there). The free-energy gradient theorem could be used to optimize a single molecule and might become useful in the context of flexible ligand docking. It is also worth mentioning that instead of MD one can use Monte Carlo simulations that are tipically employed when the gradient of the potential function is not available or cannot be computed.
I am currently working on a few pages to describe the use of the HFB method in various applications, including simple PMF calculations. You should see some tutorials on using the HFB with CHARMM and NAMD in the near future.