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Structure based design - modelling

Structure based design - modelling. Thirty years ago all molecular models were ‘physical’ ones The explosive growth in computing power has led to the upsurge in computer aided molecular modelling (CAMM) via theoretical (mathematical) models)

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Structure based design - modelling

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  1. Structure based design -modelling

  2. Thirty years ago all molecular models were ‘physical’ ones The explosive growth in computing power has led to the upsurge in computer aidedmolecular modelling (CAMM)via theoretical (mathematical) models) Initially applied to the modelling of protein and DNA biomolecules the area has widened considerably since the early 70’s History (1)

  3. Ease of construction of computer based molecular models A wide variety of molecular model display styles due to computer aided molecular graphics Atomic positions form the basis for calculations Two main types of calculation Quantum Mechanical and Molecular Mechanical Computer Models (2)

  4. To obtain data that cannot be easily (or rapidly) obtained from experiment To help rationalise experimental data To test ideas and design best experiments Why model ? (3)

  5. Single molecules (drugs and targets) Molecular properties including accessible geometries (conformational properties) Assemblies of molecules (drug target complexes) Drug/protein (receptor) interactions determination of binding energies and hence to indicate most likely sites of interaction Reactions of molecules - transition states (sometimes within biomolecular systems particularly enzymes) Areas of application (4)

  6. These QM methods rely on the Schrödinger equation, • H = E • Pros • Chemically accurate • Can calculate electronic properties (electron distribution, bond strengths, orbital occupancy etc) • Cons • Expensive to run (routinely limited to ~ 100 atoms) • Often output difficult to interpret Quantum Mechanical modelling (QM) (5)

  7. These methods treat molecules as simple ‘ball and spring models’, molecular mechanics (MM) working under Newtonian physical law • Inexpensive to run (even on biomolecular complexes) • An adaptation of MM can be used to simulate molecular motion at > 0 K (Molecular Dynamics (MD)). Allows motion to evolve over a period of time, coordinate changes monitored • Energy minimisation (w.r.t. geometry) may be performed for both QM and MM techniques (and even interfaced together!) Molecular Mechanics (MM) (6)

  8. The molecular mechanics or force field method. Molecular mechanics (MM) is a mathematical formalism which attempts to reproduce molecular geometries, energies and other features by adjusting bond lengths, bond angles and torsion angles in attempt to restore them to ideal equilibrium values from their constructed model molecular environment. The molecular model parameters are dependent on the hybridisation of the atoms and their bonding environment. Molecular Modelling - MM (7)

  9. Rather than utilising quantum physics, the method relies on the laws of classical Newtonian physics and experimentally derived parameters to calculate geometry as a function of a total molecular potential energy. The general form of the force field equation is Etot = ∑ Ebond + ∑ Eang + ∑ Edih+ ∑ EvdW + ∑ Eelec Molecular Modelling - MM (8)

  10. Etot = ∑ Ebond + ∑ Eang + ∑ Edih+ ∑ EvdW + ∑ Eelec Etot is the total potential energy (Etot) which is defined as the difference in energy between the collection of atoms and their connectivity in a ‘real molecule’ as compared to an ideal molecule. Ebond, the energy resulting from deforming a bond length from its natural value, is calculated using Hooke's equation for the deformation of a spring (e.g. Ebond = k(r - ro)2 where k is the force constant for the bond, ro is the equilibrium bond length and r is the current bond length). Molecular Modelling - MM (9)

  11. Eang, the energy resulting from deforming a bond angle from its natural value, is also calculated from Hooke's Law Edih is the energy which results from altering the dihedral or torsion angle from a ‘natural low energy’ arrangement EvdW is the energy arising from van der Waal non-bonded interactions and Eelec is the energy arising from Coulombic forces between charged atoms. Molecular Modelling - MM (10)

  12. Molecular Modelling - MM (11)

  13. The form of Hooke’s Law curve for bond extension and compression Molecular Modelling - Bond movements (12)

  14. The form of Hooke’s Law curve for valence bond angle extension and compression Molecular Modelling - Angle movements (13)

  15. The form of curve for dihedral angle changes from a minimum Molecular Modelling - Dihedral Angle (14)

  16. The form of curve for non-bonding changes from a minimum value (both vdW and Coulombic) Molecular Modelling - Non-Bonding (15)

  17. A generic MM algorithm • Build initial drug and/or target biomolecular structure • (atomco-ordinates from x-ray or NMR data or 2D file or 3D fragment library) • Assign atom characteristics • (atom typing, partial atomic charge, non-bonding characteristics etc) • Construct force field • (parameterisation, bond lengths, angles from ‘look up’ tables) • Search for minimum energy structure(s) Molecular Modelling - MM calculations (16)

  18. H3 (HO) O1 (OT) H4 (HA) C1 (CT) H1 (HA) H2 (HA) Molecular Modelling - atom typing (17) ATOM C1 CT 0.033 ATOM H1 HA 0.052 ATOM H2 HA 0.052 ATOM H4 HA 0.052 ATOM O1 OT -0.398 ATOM H3 HO 0.209 BOND C1 H1 BOND C1 H2 BOND C1 H4 BOND O1 H3 BOND O1 C1 IC H1 C1 O1 H3 1.38 94.44 148.09 94.04 0.95 IC H2 C1 O1 H3 0.79 135.38 28.02 94.04 0.95 IC H4 C1 O1 H3 1.25 100.43 -126.36 94.04 0.95 Atom name/ atom type/partial charge Bonding sequence IC = internal coordinates of a group of four atoms H1 C1 O1 H3 1.38 (H1 C1 bond length) 94.44 (H1 C1 O1 bond angle) 148.09 (H1 C1 O1 H3 dihedral angle 94.04 (C1 O1 H3 bond angle) 0.95 (O1 H3 bond length)

  19. Molecular Modelling - atom typing (18) Parameter lookup table for methanol (MeOH) created by CHARMM (Chemistry at Harvard Molecular Mechanics), a molecular mechanics software package. The following list contains all parameters that were sent to CHARMm Created on Tue Nov 25 14:35:59 2003 Bonds: Atom Types Distance (Å) Force (kcal mol-1/Å) ------------------------------------------------------------------------ HA-CT 1.09 340.0 CT-OT 1.405 375.0 HO-OT 0.948 505.0 Angles: Atom Types Angle (degree) Force (kcal mol-1/degree) ------------------------------------------------------------------------ HA-CT-HA 107.8 33.0 HA-CT-OT 108.0 55.0 HO-OT-CT 106.7 59.0 Dihedral angles: Atom Types Dihedral (degree) Multiplicity. Force (kcal mol-1/degree) ------------------------------------------------------------------------------------------------------ HA-CT-OT-HO 0.0 3 0.05 X-CT-OT-X 0.0 3 0.25 X refers to a general substituent

  20. Where do force field parameters come from ? The ability of a forcefield to model molecular properties depends crucially on the quality of the parameter set. These parameters are optimised to reproduce experimental data (structure, vibrational properties) from well characterised molecules. It is then assumed that they can be used to model related systems. This assumption represents the most important weakness with MM calculations. Molecular Modelling - Parameters (19)

  21. How may initial force field parameters obtained and verified ? • Data gatherers • X-ray crystallography - electron densities, atom positions • Infrared spectroscopy - bond lengths and angles and their strengths • NMR - conformational analysis (torsional barriers) • Data checkers • NMR - movement (dynamics), conformations, relative orientation, molecular proximities (NOE) • Extensive QM Ab initio calculations Molecular Modelling - Parameters (20)

  22. What are parameters ? • Taking bond stretching (to r) as an example, k (the force constant, a specifier of bond strength) is required for each bonded atom pair in a molecular species, as is an equilibrium bond length (ro) • Similarly there are other atom-dependent parameters in the other functions (angles, torsions etc). Molecular Modelling - Parameters (21)

  23. Problems • Constructing a force field for a molecule when ‘non-standard’ atoms types are present (encountering ‘odd’ chemistry) • Potentiallylengthy calculations (searching for a minimum energy) • Ensuring you find a global minimum Molecular Modelling - MM calculations (22)

  24. E Local minimum Global minimum • Problems • Ensuring you find a global minimum - atomic positions are iteratively adjusted until the molecular geometry is optimised and the molecular potential energy is minimised Molecular Modelling - MM calculations (23)

  25. Molecular Modelling - Finding a minimum (24) An exhaustive search - Generate all possible arrangements of atoms and minimise the entire set. Assume a resolution of 30° , number of conformations = (360/30)6 = 2,985,984, if minimisation takes 1 second of CPU per conformation, time = ~ 1 month ! A coarse resolution of 60 ° would take 13 hours. Other approaches may be used.

  26. Molecular dynamics - simulation (MD) Mimics nature - give molecule thermal energy and watch it move (solving Newton’s equations of motion) x(t+t) = x(t) + v(t). t v(t+t) = v(t) + (f . t)/m Co-ordinates x and velocities (v) are updated every t seconds, where m is the mass of the particle, f is the force acting on the particle. Molecular Modelling - Conformational searching - MD - simulation (25)

  27. The approach ‘saves’ selected conformations at certain time periods for minimisation and examination. • Advantages • covers ‘conformational space’ quicker than an exhaustive search • allows viewing of dynamical nature of a system • Drawbacks • may be time consuming in complex systems • jumps energy barriers slowly • sometimes difficult to analyse results quantitatively Molecular Modelling - Conformational searching - MD - simulation (26)

  28. Molecular dynamics - simulated annealing • Give molecule thermal energy and watch it evolve over an appropriate period of time to sample the available ‘conformation space’ then cool the system down to 0K by taking the thermal energy away. • Advantages • This should generate the global minimum. Molecular Modelling - Conformational searching - Molecular dynamics - annealing (27)

  29. Random methods - Monte Carlo approach • Basic protocol • 1. introduce random change into molecule • 2. Re-minimise and save new structure • 3. pick a saved structure to re-input into 1 • 4. Iterate until a stop condition is reached • Advantages • Random methods - sample readily accessible conformations of small molecules rapidly Molecular Modelling - Conformational searching - Monte Carlo (28)

  30. E http://userweb.port.ac.uk/~bantingl/1MPHA325/Butane.mov Molecular Modelling - MD and MM simulation of eclipsed n-butane (29)

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