Markov State Models in Drug Design

Abstract

Starting from the lock-and-key model [1], models of ligand–target binding have been extended to acknowledge the role of conformational flexibility. In current models, the targets are assumed to fluctuate between several different confor- mations. In the conformational selection model [2], one of these conformations is the active state, i.e. the conformation which is assumed in complex with the ligand. e ligand then “selects” this conformation from the ensemble and stabi- lizes it by forming a complex. By contrast, in the induced-fit model [3], the active conformation is not sampled by the apo-target. Instead, the receptor and the lig- and form an unspecific encounter complex. is weak complex then triggers a conformational rearrangement in the receptor, which leads to the fully formed complex. While examples of mechanisms have been found [4–7], most binding processes fall somewhere in between these two extremes. e conformational selection and the induced-fit model neglect the confor- mational dynamics of the ligand, which is justified if the ligand is either rigid or its dynamics is fast compared to the dynamics of the target. However, this is not always a valid assumption. In particular, peptides and peptidomimetics exhibit a complex and often slow conformational dynamics. It is increasingly recognized that the flexibility of the target and the ligand and their mutual inter- action are crucial factors in the ligand-binding process. us, to systematically vary the thermodynamic and kinetic properties of a drug molecule, not only bind- ing affinities but also dynamics need to be taken into account. Experimentally, it is difficult to characterize the full conformational ensem- ble and its dynamics. However, an increase in computer power combined with improved algorithms has rendered molecular dynamics (MD) simulations as use- ful tools in structure-based drug design [8]. With progress in distributed com- puting [9], special purpose computers [10], and graphics processing unit (GPU) devices [11], trajectories of several tens in microseconds are now accessible on a routine basis. A visual inspection of these trajectories is sometimes not feasible, due to the shear size of the data set, and almost always unrewarding, because it does not yield a quantitative description of the system.1 While statistical analyses of the trajectory for the stationary properties of the system have been used routinely for decades, methods which yield a model of the dynamics have matured only recently. Markov State Models (MSMs) [12–17], in which the dynamics is approx- imated as a Markovian jump process between distinct microstates, are the most widely used dynamic models. MSMs have been used to improve ensemble dock- ing, to optimize a specific conformation in a ligand, to identify cryptic allosteric sites, and to characterize ligand-binding processes as well as inactive-to-active transitions in signaling proteins. We do not aim at a comprehensive survey of the literature on this subject, nor do we focus on specific results. Our goal is to explain the different ways in which MSMs can be helpful in structure-based design.