Towards Accurate Free Energy Calculations in Ligand Protein-Binding Studies

Current Medicinal Chemistry, 2010, 17, 767-785 767 Towards Accurate Free Energy Calculations in Ligand Protein-Binding Studies Thomas Steinbrecher1 and Andreas Labahn*,2 1BioMaps Institute, Rutgers University, 610 Taylor Rd., 08854 Piscataway, NJ 2Institut für Physikalische Chemie, Universität Freiburg, Albertstr. 23a, 79104 Freiburg, Germany Abstract: Cells contain a multitude of different chemical reaction paths running simultaneously and quite independently next to each other. This amazing feat is enabled by molecular recognition, the ability of biomolecules to form stable and specific complexes with each other and with their substrates. A better understanding of this process, i.e. of the kinetics, structures and thermodynamic properties of biomolecule binding, would be invaluable in the study of biological systems. In addition, as the mode of action of many pharmaceuticals is based upon their inhibition or activation of biomolecule targets, predictive models of small molecule receptor binding are very helpful tools in rational drug design. Since the goal here is normally to design a new compound with a high inhibition strength, one of the most important thermodynamic properties is the binding free energy G0. The prediction of binding constants has always been one of the major goals in the field of computational chemistry, because the ability to reliably assess a hypothetical compound's binding properties without having to synthesize it first would save a tremendous amount of work. The different approaches to this question range from fast and simple empirical descriptor methods to elaborate simulation protocols aimed at putting the computation of free energies onto a solid foun- dation of statistical thermodynamics. While the later methods are still not suited for the screenings of thousands of compounds that are routinely performed in computational drug design studies, they are increasingly put to use for the detailed study of protein ligand interactions. This review will focus on molecular mechanics force field based free energy calculations and their application to the study of protein ligand interactions. After a brief overview of other popular methods for the calculation of free energies, we will describe recent advances in methodology and a variety of exemplary studies of molecular dynamics simulation based free energy calculations. Keywords: Protein-ligand binding, free energy calculations, thermodynamic integration, molecular dynamics, computer aided drug design, virtual screening. 1. INTRODUCTION [6]. Without disregarding other possible action mechanisms such as nucleic acid binding drugs [7, 8], therapeutic anti- A cell's metabolism consists of thousands of chemical re- bodies [9] or other pharmacologically active molecules, we actions running in parallel. The ability to run and regulate will define 'drug-design' in this article as the art of finding these complex biochemical networks to maintain homeosta- small organic molecules with acceptable toxicological and sis and reproduce is not only essential for but can be put ADME (absorption, distribution, metabolism and excretion) forward as the very definition of a living organism [1]. Mo- properties that are active, i.e. binding with a high affinity, lecular recognition plays a critical role almost everywhere in towards a given drug target. this process [2]. Enzymes rely on their ability to tightly and specifically bind their substrates and cofactors to provide efficient catalysis, cellular signalling cascades are initiated by small molecule messenger recognition and the activity and expression of proteins is regulated by such a multitude of biomolecule binding phenomena that even a most basic survey of them is a daunting endeavour [3, 4]. Here, we will focus on protein-ligand binding, where Fig. (1). A minimal model of competitive inhibition where a recep- ligand stands for any small organic molecule with 'drug-like' tor R can either bind a ligand L to form the complex C or an inhibi- properties [5]. Such interactions are of particular interest tor I. All binding is reversible to form noncovalent complexes. The because the bulk of drug action mechanisms involves the binding strength of L and I is given by their binding constants KD binding of a pharmaceutical compound to a protein target and KI, respectively. Another important property of a promising drug compound, apart from the free enthalpy of binding, is its aqueous *Address correspondence to this author at the Institut für Physikalische solubility. This property is important for e.g. a compound’s Chemie, Universität Freiburg, Albertstr. 23a, 79104 Freiburg, Germany; Tel: +49(761)203-6188; Fax: +49(761)203-6189; suitability for oral uptake and its membrane permeability and E-mail: [email protected] the development of many early drug candidates is cancelled 0929-8673/10 $55.00+.00 © 2010 Bentham Science Publishers Ltd. 768 Current Medicinal Chemistry, 2010 Vol. 17, No. 8 Steinbrecher and Labahn due to insufficient solubility [10]. Theoretical methods to dependent on the conditions under which the inhibition predict solubilities for new compounds are an equally impor- measurement was conducted and experimental data should tant part of computational drug design (for recent reviews be interpreted with this consideration in mind. see [11, 12]). Drug design has evolved significantly from the trial-and- From a thermodynamical perspective, the simplest possi- error approach of earlier times [14]. Modern rational drug ble model for ligand binding is the reversible association of a design starts from a well characterized target, preferably with ligand and receptor molecule to form a noncovalent 1:1 structural information from X-ray crystallography. Hundreds complex. The most important thermodynamic quantities de- of macromolecular drug targets are known today and analy- scribing the binding process are the corresponding standard sis of the human genome suggests that there may be thou- 0 Gibbs binding free energy G Bind and the standard associa- sands more to be discovered [15]. Against the selected target 0 1 tion constant K A : a collection of candidate molecules is tested. Such a chemical library can either be one of the standardized sets of thou- k L R on C sands of drug-like molecules that pharmaceutical companies + k off maintain [16, 17] or be specifically built by means of combi- natorial chemistry for the target in question [18]. High GBind = RT ln K A throughput screening (HTS) techniques are then used to find 1 k [C] active compounds within the set and once promising lead K = = on = (1) A K k [L][R] molecules are identified, their binding affinity and pharma- D off cological properties are improved through chemical optimi- in which L, R and C stand for a ligand, free receptor and zation until a promising drug candidate is produced [19]. complex, kon and koff are rate constants and KA is the complex During this optimisation process from early hit to drug can- association constant. Its inverse, the complex dissociation didate molecule, the compound's binding strength will in- constant KD is the most widely used measure for a ligand's crease by several orders of magnitude, typically from a lower binding strength. Binding processes can in reality be much micromolar to below nanomolar KD. more complicated than the simple model given here, due to While the experimental elucidation of all relevant ther- effects like oligomerisation of receptors, multiple binding modynamic quantities for receptor binding of a ligand is sites, allosteric effects, irreversible covalent binding or possible [20], it is rarely done in practice. A quantitative in- multistep kinetics to name only a few. Nevertheless, charac- vitro determination of a lead compound's KD, using large terizing the activity of a ligand by a single KD constant is amounts of time and biochemical sample material, would be common, even when the binding kinetics are not fully under- prohibitively expensive but of limited usefulness to predict stood. its later in-vivo properties. Therefore, especially in the early When the ligand in question acts as a competitive inhibi- HTS stage of drug development, qualitative assays are used tor I to a second ligand L binding the same receptor, as in to give a fast hit-or-miss assessment of binding affinity. This Fig. (1), its affinity is often given not as an inhibition con- approach is plagued by generating large numbers of false stant KI but as an IC50 value. This is the inhibitor concentra- positive 'hits' [21] and may miss important thermodynamic tion at which the receptor occupancy is 50% of what it would or kinetic properties [22]. On the experimental side, the be in the absence of inhibitor. The inhibition constant KI and emergence of reliable microcalorimetry methods might help IC50 value are related via the Cheng-Prusoff equation [13]: to make the measurement of a ligand's full thermodynamic profile more of a standard technique in the future [23, 24]. []L0 Alternatively, the tools of computational chemistry can be IC = K 1+ (2) 50 I used as additional filters for chemical libraries and to gener- K D ate supporting data through every step of the drug design where [L0] and KD are the initial concentration and dissocia- process [25]. tion constant of the competing ligand L. The derivation of Virtual or 'in silico' screening techniques aim at predict- equation 2 assumes that ligand and inhibitor are added in ing the binding strengths or complex structures of new excess of protein and that they bind reversibly and ligands from available data, empirically optimized models or stoichiometrically to the same single binding site on the re- physico-chemical first principles [26, 27, 28]. The appeal of ceptor. If the assay in question was conducted with a ligand studying novel compounds without the need to actually syn- concentration far below its K , then K and IC are approxi- D I 50 thesize them first was apparent early on in the development mately equal. Since the two values are proportional, the same of computational chemistry and has led to a broad and lively relative (but not absolute) binding free energies for a set of field of study [29].

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