Dr. Richard Feynman, recipient of the 1965 Nobel Prize of Physics said “If we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it’s that all things are made of atoms, and that everything that living thing can do can be understood in terms of the jigglings and wigglings of atoms”. Indeed, proteins are flexible biomolecules and standard molecular docking or pharmacophore studies as reported in Chapter 2 and 3, do not account for these dynamic properties , even if hybrid techniques exist (soft-docking, rotamer libraries, protein conformations ensemble 1-6). The historical model of the “lock-and-key”, proposed by Emil Fischer for drug-target, is nowadays replaced by two dynamic events, the so-called induced-fit and conformational selection, making the ligand binding process a “hand-and-glove” mechanism (Box 2 7, 8).
Crystallographic or NMR structures of a same protein are able to convincingly demonstrate proteins loop motions and dynamic events upon ligand binding, as shown for HDAC8 17-20. But the extensive working time they require have led to the development of alternative methods such as computational techniques able to simulate such a dynamic behavior. Whereas crystals are static samples among the whole configuration portfolio a protein can adopt, NMR structures can give an idea of the most abundant conformation of a system in solution. Molecular dynamics (MD) simulations have thus been developed to fill the gap between these techniques. MD simulations were first developed in the 1970’s 21, 22. The overall purpose of this method is to mimic the conditions in which a biomolecular system is exposed in vitro (pH, solvent, etc.) They simulate the time-dependent atomic motions of a macromolecule (proteins, nucleic acids, carbohydrates) and its surrounding water molecules according to the Newton’s law of motion. In classical MD, atoms are considered as solid spheres and their covalent bonds are modeled through virtual springs. The energy resulting from covalent interactions (chemical bonds, angles, dihedrals) is estimated through a sinusoidal function (Box 2). The non-bonded forces arise in the molecular system, due to van der Waals interactions, are estimated through the Lennard-Jones 6-12 potential, and the Coulomb’s law. The Particle Mesh Ewald (PME) method is usually employed to treat long-ranged electrostatic interactions (Box 3). Altogether, these parameters describe the atomic forces that govern molecular dynamics and all contribute to the force field (Box 2).
MD simulations are usually conducted in four stages: preparation of the initial coordinates (missing atoms, atom types, charges, solvent and minimizations steps), heating stage (gradual scaling to the desired temperature), system equilibration stage (density convergence, structure relaxation), and production stage (structural and energetic data collection). During the simulation, all atoms of the modeled system are moved in a series of short time steps (usually 2 fs). At each step, forces applied on atoms are computed according the chosen force field, and both atomic position and velocity of the evolving system are updated. This process is repeated to finally provide a continuous atomic trajectory
Box 2. General concepts
Induced-fit effect. Conformational changes of the protein upon ligand binding.
Force field. Mathematical expression of the forces (energies) governing the dynamics of a molecular system. They are estimated through:
E.g. used for MD simulations of molecular systems: CHARMM
9-11, AMBER 12-14 and GROMOS 15. Figure and equation are adapted from Durrant J.D. et al.16.
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that can then be analyzed and visualized. The simulation duration is of great importance depending on which kind of molecular event one would like to sample, from ligand binding to allosteric motions, from nanosecond- (106 time steps) to millisecond-long (1012 time steps) MD simulations. But the longer (and more complex) the simulation, the higher the computer cost, and so is the time necessary to compute and to analyze the large amount of data thus produced.
The questions asked in MD simulations have become, these past ten years, more and more complex, on biomolecular systems that have also grown size and complexity, requiring extensive MD simulation time and computational cost. In parallel, the sustained development of graphic processing units (GPUs), being an integral part of personal computers, were continuously increasing the computational power and memory of calculations, because of the high demand in electronics industry.
In 2012, the use of GPUs was implemented into MD algorithms to allow the MD data collection in a fastest way, therefore facilitating the access to complex biomolecular systems simulations 13, 14.
Structure-based drug design is a very active field to assist the early drug discovery process, as solved bound and unbound protein structures are getting more and more available. The recent editorial article from Current Topics in Medicinal Chemistry (January 2017) is a good demonstration of the enthusiasm around this field 27. MD simulations coupled to molecular docking have already demonstrated their efficacy through the discovery of raltegravir, which was the first-in-class HIV-integrase inhibitor approved by the FDA 28-30. Indeed, multiple conformations of the viral protein were generated through MD simulations, revealing a transient groove, adjacent to the originally active site.
In this chapter, molecular docking followed by MD simulations, are used in an attempt to get insights into the potential plasticity of the very recent HDAC6 protein structure solved by crystallography. A flexible behavior of the catalytic domain 2 (CD2) was suspected, regarding the narrow pocket volume of the crystallographic structure and the reported HDAC6-selective bulky inhibitors 31. Simulations are conducted using AMBER12 (Assisted Model Building with Energy Refinement 12-14). In these simulations, the catalytic zinc ion was considered as a non-bonded entity and
Box 3. Molecular Dynamics parameters, algorithms and analysis
Periodic boundary conditions, PME and water boxes. Electrostatic interactions (EI) have longer range than van der Waals interactions, that decrease rapidly with distance and that can hence be limited by a cutoff without introducing significant error in calculations (truncated Lennard-Jones potential). EI are longer than half the box distance in which the protein is solvated, and atoms located at the edge would be in contact with the surrounding vacuum. To avoid this artificial situation, periodic boundary conditions are employed: the system is virtually surrounded by replicas of itself in all directions so that one atom that exists on one side of the box will wrap to the other side of the box. The periodic water box hence created must be large enough to avoid the solvated molecule to interact with its periodic images. This will make the system look like an infinite one. Several water boxes exist for explicit-solvent simulations, but the most used is the TIP3P model in which the water molecule is considered as a rigid triangular entity. Ambermd.org accessed September 21st 2017, gromacs.org accessed September 21st 2017 23-26.
SHAKE. Algorithm used to constrain the covalent bond involving hydrogen atoms. Allows to use a time-step simulation of 1.5 - 2 fs 8.
NPT/NVT ensembles. During MD simulation, experimental conditions are simulated (pressure P, temperature T, number of atom N, solvent). These factors are controlled through statistical mechanics ensembles: isothermal-isobaric (NPT) or isothermal-isovolumic (NVT). NPT is the most commonly used.
RMSD/RMSF. Root Mean Square Deviation/Fluctuation. Measure the average deviation (Å) of atoms in 3D space from reference positions (e.g. from the initial position prior to the production phase of MD simulations). If RMSD < 2 Å, then the 2 positions are considered identical in this study. RMSF is a more specialized deviation: it gives the average fluctuations of an entire residue, or its side chain, along the MD simulation.
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modelled by introducing external force field parameters 32. Trajectories are analyzed using Ambertools 12 and the key influence of several loops and residues motion, together with solvent-mediated effects, are highlighted. Results are provided in the section 4.2, experimental details in the section 4.7 and supplementary information are given in the section 4.8.
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4.2 Unravelling the structural elements governing the selective inhibition of HDAC6 by