1	Drug-Receptor Binding Computational Chemistry --- Molecular Mechanics --- Quantum Mechanics --- Molecular Dynamics etc. Docking Force-field Based 3D-QSAR Free-energy Perturbations
2	Computational Chemistry Methods classical mechanics, a.k.a. molecular mechanics, a.k.a. force fields quantum mechanics --- semi-empirical models --- Hartree-Fock models --- density functional models --- Moeller-Plesset models
3	Molecular Mechanics I the molecule is represented by a set of atoms connected by springs bond lengths, angles, and dihedral angles in relaxed molecules have ‘optimal’ magnitudes (averages of those found in most molecules)
4	Molecular Mechanics II any deviation from the equilibrium state increases the energy according to simple functions --- for bond lengths --- for bond angles --- for dihedrals - in aromatic rings electrostatic and van der Waals interactions
5	Molecular Mechanics III the overall energy of a system (one molecule or several interacting molecules) is calculated as the sum of all contributions the energy is a function of bond lengths, angles, torsion angles, and distances between atoms this function can be minimized - corresponding bond lengths, angles, torsion angles, and distances characterize optimal geometry of the system
6	Molecular Mechanics IV force field – form of the functions and values of the parameters many force fields available, developed for --- organic molecules (MM2, MM3) --- proteins (CHARMM, OPLS, Amber) --- ligand-protein interactions (MMFF4) specific developments --- polarizability --- directional hydrogen bonds (Vedani…) --- organometallic complexes (SIBFA…)
7	Quantum Mechanics I interactions between electrons and nuclei are described molecular geometry in terms of minimum energy arrangements of nuclei background – Schrödinger equation exact solution – available just for hydrogen – defines wavefunctions (s, p, d… orbitals) the square of the wavefunction defines electron density – measured in x-ray experiments
8	Quantum Mechanics II Born-Oppenheimer approximation – electron moves much faster than nuclei; nuclei fixed and SE only for electrons Hartree-Fock approximation – multi-electron wavefunction expressed as the product of single-electron wavefunctions LCAO approximation – molecular orbitals are expressed as a linear combinations of atomic orbitals (prescribed basis functions)
9	Hartree-Fock Methods (ab initio) the approximations result in Roothaan-Hall equations solved iteratively until self-consistency problem – the electrons are treated as independent; their movement causes more repulsion than is actually present electron correlation – coupling of movements of electrons methods have been developed to account for electron correlation – additional cost
10	Hartree-Fock Methods: Semi-empirical consider valence electrons only the basis set reduced to minimal representation parameterizations are based on reproducing a wide variety of experimental data, including --- equilibrium geometries --- heats of formation --- dipole moments --- ionization potentials frequently used models AM1 and PM3 incorporate essentially the same approximations but differ in their parameterization
11	Density Functional Models I based on the Hohenberg-Kohn theorem: “The minimal energy of a collection of electrons under the influence of an external (Coulombic) field is a unique ‘functional’ (a function of a function) of the electron density.” the energy includes many of the same components as the Hartree-Fock energy, but provides explicit account of electron correlation in the form from the exact (numerical) solution of a many-electron gas of uniform density
12	Density Functional Models II different density functional models available, the names are formed of the last name initials of authors the simplest method --- SVWN (Slater, Vosko, Wilk, Nusair) other methods --- BP (Becke, Perdew) --- BLYP (Becke, Lee, Yang, Parr) --- B3LYP (the same authors) for similar cost as Hartree-Fock methods, they provide better descriptions
13	Moeller-Plesset Models account for many-electron effects based on a perturbation expansion of the energy --- the first level: Hartree-Fock energy --- the second level: MP2 --- higher level MP3, MP4 are impractical most expensive method
14	Basis Sets functions describing molecular orbitals in --- Hartree-Fock, --- Density Functional, and --- Moller-Plesset models Gaussian-type functions used most frequently --- a polynomial in the Cartesian coordinates (x,y,z) followed by an exponential in r² the coefficients determined by the fit to exponential Slater-type orbitals (STO)
15	Selecting a Method
16	Computational Time I used molecule – morphine computational demands depend on --- the method --- basis set times are relative to the Hartree-Fock method with the 3-21G basis set symbols --- (a) too short to measure --- (b) standard
17	Computational Time II
18	Molecular Dynamics I simulates dynamics of a molecular system of known composition by solving the Newton equation to calculate the forces F, an energy function is needed essentially, any method can be used depending upon the size and expected changes of the system and available computational resources in drug design, force fields are used as energy functions because the analyzed systems are large (drug-receptor complexes, bilayers)
19	Molecular Dynamics II the set of equations is integrated numerically initial velocities are assigned to reflect temperature of the system the time steps must by rather short – picoseconds many cycles needed to simulate 1-nanosecond event
20	Langevin Dynamics based on a stochastic differential equation two terms were added to the Newton equation --- friction term (proportional to velocity) --- random forces (kicks of the solvent molecules if they are not explicitly represented) the time steps can be longer and the system coarser than in MD
21	Monte Carlo Simulation this method does not calculate forces to determine the motion of the system instead, the motion is generated by random jumps (conformations are crossing the barriers without feeling them) only the overall energy is calculated no time-dependent quantities can be derived, just equilibrium (thermodynamic) properties the state of the system is based on Boltzmann distribution of energies
22	Estimating Ligand-Receptor Interactions
23	Drug Design for Known Receptors receptor structure can be obtained --- experimentally (x-ray, NMR) --- from sequence, by homology modeling or threading for a receptor of known structure, the ligand binding can be examined by a variety of methods differing in quality and speed --- docking - approximate and fast --- de novo design - intermediate --- force-field based 3D-QSAR - intermediate --- binding free energy calculations – precise & slow free energy perturbation – very slow, LR - faster
24	Docking I in silico screening tool meant to provide rapid selection of structures that will bind to a receptor two interrelated aspects --- docking the structure into the receptor cavity --- predicting the binding energy using a scoring function the first method – DOCK (Kuntz, 1982) --- both receptor and ligand are treated as rigid
25	Docking II flexible ligand in rigid binding site – the problem becomes combinatorially demanding various techniques used to sample the vast space of possible solutions (FRED is exhaustive) --- fast shape matching (DOCK, Eudock) --- incremental construction (FlexX, Hammerhead) --- TABU search (ProLead, SFDock) --- simulated annealing (AutoDock 2.4) --- genetic algorithms (GOLD, Gambler) --- Lamarckian genetic algorithms (AutoDock 3.0) --- Monte Carlo simulations (MCDock, Dockvision, QXP) --- distance geometry (Dockit)
26	Docking III Future directions: flexible receptors so that induced fit can be incorporated solvent effects improvement in scoring functions coordination interactions with metals for metalloproteins (incorporated in the latest version of FlexX)
27	Docking Illustration – DOCK: Step 1
28	Docking Illustration – DOCK: Step 2
29	Docking Illustration – DOCK: Step 3
30	Docking Illustration – DOCK: Step 4
31	Docking Illustration – DOCK: Step 5
32	de novo Design instead of taking pre-generated structures and evaluate them for binding, a new structure can be ‘grown’ inside the binding site approaches are similar --- LUDI (Bohm, Accelrys) --- BUILDER (UCSF, Kuntz) --- CombiBUILD (UCSF, Kuntz) --- SMoG (Small Molecular Growth) – deWitte, Harvard --- SPROUT (SimBioSys)
33	de novo Design Illustration – BUILDER: Step 1 identify the zones of interest – places of interactions --- 1: positive charge --- 2: hydrophobic --- 3: negative charge
34	de novo Design Illustration – BUILDER: Step 2a fill the zones of interest with appropriate fragments
35	de novo Design Illustration – BUILDER: Step 2b fill the zones of interest with appropriate fragments
36	de novo Design Illustration – BUILDER: Step 2c fill the zones of interest with appropriate fragments
37	de novo Design Illustration – BUILDER: Step 3 fragments are paired down to the crucial characteristics identified for each zone of interest
38	de novo Design Illustration – BUILDER: Step 4 bridge the fragments to form a composite molecule
39	de novo Design Illustration – BUILDER: Step 5 minimize the energy of the composite molecule (methotrexate reproduced)
40	Force-field Based 3D-QSAR the drug-receptor interaction energy is calculated using appropriate force field the receptor is dissected in fragments (amino acids or larger fragments) the binding energies for individual fragments are weighted using MLR or PLS to account for the effects like variations in dielectric constants… two approaches published --- FF-3D-QSAR (Anton Hopfinger, Chicago) --- COMBINE (Rebecca Wade, Heidelberg)
41	Ensemble-Based Approaches Free-energy Perturbation Approach --- the most precise and most expensive approach to calculate the binding energy --- based on thermodynamic cycles and gradual morphing of known ligand into a new ligand Partitioning methods - to become practical, several approximations were introduced --- the overall energy can be written as the sum of electrostatic, van der Waals, and desolvation contributions (characterized through SASA – solvent-accessible surface area) --- ensemble averages describe the situation well --- the methods are under development
42	Linear Response Methods LR – one of the most frequently used (software Liaison) Authors Aquist, Jorgensen (1994-1995) --- D difference between bound and free ligands --- á ñ denotes ensemble averages of energies obtained by force-field-based MD simulation not suitable for bonds that are not described well by force fields (e.g. coordination bonds) --- the two leftmost terms can be replaced by QM energy of the time-averaged structure
43	QMMM LR Method Docking with the poses selected using metal binding parameters QM/MM geometry optimization MD with classical force field with restrained zinc binding group Single point QM/MM energy on the time-averaged structures Correlation using Linear Response approximation: