Small molecule binding to T4-lysozyme L99A

Overview

In this tutorial, free energy calculations will be used to calculate the relative binding free energy of two simple ligands, benzene and phenol to the T4-lysozyme mutant L99A. Free energies will be computed by using the thermodynamic integration facilities of the sander program. A modified van-der-Waals equation (softcore potentials) are used to ensure smooth free energy curves.
This tutorial assumes familiarity with Linux-systems, the basic workings of the Amber package and knowledge on how to run MD simulations using sander.
The tutorial is intended for users of Amber10, since the input conventions for TI have changed over different versions, earlier Amber versions cannot be used for this example. For an introduction to TI in previous versions, tutorials on calculating pKa values (here) or solvation free energies (here) are available.
This tutorial is intended to give users an example on how a free energy calculation might be performed in principle using the Amber software suit. They do not necessarily provide the optimal choice of parameters or methods for the particular application area.

Biochemical Background

1.8 Å resolution X-ray structure of T4 lysozyme L99A with cocrystallized benzene in red (picture generated by vmd and povray)

Lysozyme is a 14.4 kilodalton enzyme (EC 3.2.1.17) that destroys bacteria by hydrolyzing the polysaccharide component of the cell wall. It is abundant in a number of secretions, such as tears or in the cytoplasmic granules of the polymorphonuclear neutrophils. It is also found in high concentration in e.g. egg white. As one of the earliest enzymes crystallized to obtain a high resolution X-ray structure (see Blake et. al, Nature 1965 761-763), it is referenced in 1036 pdb database entries. In this example we will use the X-ray structure of bacteriophage T4 lysozyme (see pdb entry here) into which an artificial cavity suitable for the binding of small non-polar molecules was introduced by single aar point mutation (See Eriksson et al., Nature 1992, 371-373). The binding affinities of several small molecules to this enzyme have been determined, making it a good model system for the study of protein-ligand binding. Benzene is bound in the lipophilic cavity with a &Delta GBind of -5.2 kcal/mol, while the more polar phenol does not bind at all. It is assumed that no major conformational changes of the protein occur upon binding and that the binding site is free of water molecules in the absence of a bound ligand.

Thermodynamic cycle and Method

TI calculations compute the free energy difference between two states A and B by coupling them via a parameters &lambda that serves as an additional, nonspatial coordinate. This &lambda formalism allows the free energy difference between the states to be computed as:







In this equation, V(&lambda) is the &lambda -coupled potential function that corresponds to V(A) for &lambda =0 and V(B) for &lambda =1. The integration is carried out over the average of the &lambda derivative of the coupled potential function at given &lambda values. Since this integration can only rarely be performed analytically, an integration scheme is used in which simulations at different discrete &lambda point or "windows" are performed and the value of the integral is calculated numerically. A benefit of TI calculations is that several indipendent MD simulations at fixed &lambda values need to be performed, allowing for effcient parallelization and the subsequent addition of additional &lambda windows to improve accuracy.
Since Thermodynamic Integration calculations calculate the free energy difference between two systems of different chemical constitution (e.g. a benzene and a phenol molecule in this example) for which no experimental verification is available, a thermodynamic cycle similar to the one depicted on the right must be used to connect the result from a series of TI calculations to pysical observables. Processes A and B represent the binding of two different ligands to a protein, while processes C and D are transformations from one ligand to the other while it is bound to the protein (C) or simply solvated in water (D). Since &Delta G_C-&Delta G_D = &Delta G_A-&Delta G_B, TI calculations can be used to compute relative binding free energies, making them useful tools in drug design or lead optimization applications.
Different and more elaborate thermodynamic cycles can be constructed to obtain other thermodynamic quantities, e.g. solvation free energies or absolute binding free energies. A general assumption in all TI calculations is that the system does not undergo significant conformational changes during the transformation, otherwise MD simulations will most likely not sample enough phase space for converged results. Other free energy techniques can be used if free energies from conformational changes need to be computed.

This tutorial will continue with a description of how to set up the parameter and input files here