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Introduction to Amber

Introduction to Amber. The theory and practice of biomolecular simulations using the Amber suite of programs. Dr. Vladislav Vassiliev NCI National Facility, The Australian National University, ACT 0200, Canberra, Australia. February 2011. Presentation Outline. Introduction to Amber 12

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Introduction to Amber

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  1. Introduction to Amber The theory and practice of biomolecular simulations using the Amber suite ofprograms Dr. Vladislav Vassiliev NCI National Facility, The Australian National University, ACT 0200, Canberra, Australia February 2011

  2. Presentation Outline Introduction to Amber 12 Hands-on • Setting up a standard Amber MD Run • Building non-standard Residues • QM/MM: Using Amber-Gaussian Interface • QM/MM: Using Amber inbuilt QM methods

  3. What is AMBER? Assisted Model Building with Energy Refinement AMBER

  4. What is Amber? “Amber” refers to two things: 1) a set of molecular mechanical force fields for the simulation of biomolecules 2) a package of molecular simulation programs (about 50 ) which includes source code and demos The current version of the code is Amber version 12, which is distributed by UCSF (University of California, San Francisco) subject to a licensing agreement Amber Home Page:http://ambermd.org/

  5. What is Amber • Amber is distributed in two parts: • AmberTools12andAmber 12: • AmberTools12could be used without Amber12, but not vice versa • AmberTools12 currently consists of several independently developed packages that work well by themselves, and with Amber itself • Amber 12 centered around the sander and pmemd simulation programs and continues to be licensed as before, under a more restrictive license (Academic/non-profit/government: $400. Industrial (for-profit): $20,000 for new licensees, $15,000 for licensees of Amber 10).

  6. AmberTools

  7. AmberTools • AmberToolsis released under the GNU General Public License (GPL) • A few components are included that are in the public domain or which have other,open-source, licenses. • AmberToolsis distributed in source code format, and must be compiled in order to be used. One needs C, C++, and fortran compilers to compile the AmberTools programs. • The source code of AmberTools could be obtained here: http://ambermd.org/AmberTools-get.html

  8. Versions of Amber

  9. AMBER Home • Have a look at the Amber Home Page: http://ambermd.org/

  10. Amber Main References A general overview of the Amber codes: D.A. Case, T.E. Cheatham, III, T. Darden, H. Gohlke, R. Luo, K.M. Merz, Jr., A. Onufriev, C. Simmerling, B. Wang and R. Woods. The Amber biomolecular simulation programs. J. Comput. Chem. 26, 1668-1688 (2005) An overview of the Amber protein force fields, and how they were developed: W. Ponder and D.A. Case. Force fields for protein simulations. Adv. Prot. Chem. 66, 27-85 (2003). E. Cheatham, III and M.A. Young. Molecular dynamics simulation of nucleic acids: Successes, limitations and promise. Biopolymers 56, 232-256 (2001).

  11. What is Amber? “Amber” is a software package for modelling of Large Molecular Systems

  12. Why Do We Need A Special Treatment for Large Molecular Systems? Or, Why Do We Need Amber?

  13. Quantum Chemistry Methods Provide a Rigorous Description of Molecular Systems They solve Schrödinger equation And they are generally applicable: But… they are very time consuming…

  14. To Treat Large Molecular Systems We Need to Reduce the Complexity of the System Molecular Mechanics is a non-quantum mechanical technique for treating Large Molecular Systems As a result Molecular Mechanics methods are thousands times faster than Quantum Chemistry methods

  15. Molecular Mechanics vs Quantum Mechanics

  16. Force Fields The potential energy equations to calculate the energy in Molecular Mechanics methods and the parameters/constants used in the equations are known as a Force Field There are many force fields designed for different purposes. QVBMM SIBFA UFF MM2, MM3, MM4 COSMOS-NMR AMBER DRF90 PIPF OPLS MMFF ECEPP/2 CFF ENZYMIX GROMACS CHARMm X-Pol CVFF QCFF/PI GROMOS AMOEBA CHARMM

  17. Amber Force Field The total Energy in Amber force field consists of • bonded terms relating to atoms linked by covalent bonds and • nonbonded terms describing the long-rangeelectrostatic and van der Waals interactions: Etotal = Ebonded + Enonbonded

  18. Amber Force Field: Bonded Terms The bonded Energy in Amber force field consists of bond stretching, angle bending, and torsion terms: Ebonded = Estretch + Ebend + Etorsion

  19. Amber Force Field: Bond Stretching Amber force field treats covalent bonds between atoms as springs (Hooke's Law, F = -kx) where Kr is the empirical stretching force constant, r is the actual bond length and req is the “natural” (empirical) bond length

  20. Amber Force Field: Bond Stretching

  21. Amber Force Field: Angle Bending Amber force field treats angles that are bonded to the same central atomas springs (Hooke's Law, F = -kx) where Kθ is the empirical bending force constant, θ is the actual bond angle and θeq is the “natural” (empirical) bond angle

  22. Amber Force Field: Angle Bending

  23. Amber Force Field: Torsion Energy Torsion Energy: torsional (dihedral) angle rotation between atoms that are vicinal (bonded to adjacent atoms) to each other where Vn is the barrier to free rotation for the “natural” bond, n is the periodicity of the rotation (number of cycles in 360°), φ is the torsion angle and γis the angle where the potential passes through its minimum value

  24. Amber Force Field: Torsion Energy

  25. Amber Force Field: Nonbonded Terms The nonbonded Energy terms in Amber force field describe the long-range electrostatic and van der Waals interactions: Enonbonded = Eelectrostatic + EvdW

  26. Amber Force Field: Electrostatic Energy The Electrostatic Energy in the Amber force field represents the pair-wise sum of the electrostatic energies of all possible interacting non-bonded atoms i and j: where qi and qj are the point charges on atoms, Rij is the interatomic distance and ε is the dielectric constant

  27. Amber Force Field: van der Waals Energy The van der Waals Energy in the Amber force field represents the pair-wise sum of the van der Waals energies of all possible interacting non-bonded atoms i and j: where the Aij and Bij parameters control the depth and position (interatomic distance) of the potential energy well for a given pair of non-bonded interacting atoms and Rij is the interatomic distance

  28. Amber Force Field - Empirical Parameters

  29. Where Do Empirical Parameters Come From?

  30. Parameter Derivation:Partial Charges In AMBER: Partial atomic charges are static Quantum chemical methods (B3LYP/ccpVTZ//HF/6-31G**) are used to generate an electrostatic potential (ESP) around a molecule on the spheric grid 3) RESP (Restrained Electrostatic Potential) Method is used to derive the partial charges QM = ab initio, DFT, semi-empirical Connolly Connolly

  31. Parameter Derivation: Van der Waals Parameters It is the most difficult part… 1) Optimizing van der Waals parameters to reproduce the experimental or high-level Quantum Chemical data Could be computationally expensive 2) Optimizing van der Waals parameters through the Monte Carlo or MD simulations to reproduce the experimental properties of bulk solvent (density, etc.). For example, OPLS van der Waals parameters Could be computationally expensive 3) Reusing existing van der Waals parameters for similar atom types from the same or other force field The simplest approach

  32. Parameter Derivation:Bond and Angle Interactions reqandθeq come either from experimental data (X-ray, neutron diffraction) or Quantum Chemical calculations (geometry optimization) KrandKθforce constants are usually optimized to reproduce the vibration frequencies calculated using high-level Quantum Chemical methods. Or (the simplest approach) KrandKθforce constants could be derived from the existing bond/angle parameters for similar bond/angle types from the same or other force field

  33. Parameter Derivation:Dihedral Angle Interactions Vn,n, and γare derived to reproduce the rotational profile from the high-level Quantum Chemical calculations. Or (the simplest approach) Vn,n, and γcould be derived from the existing dihedral angle parameters for similar dihedral angle types from the same or other force field J.Wang et al., Development and testing of a general amber force field, Journal of Computational Chemistry, 25 (2004), 1157

  34. Force Fields in Amber 12 J.Wang et al., Development and testing of a general amber force field, Journal of Computational Chemistry, 25 (2004), 1157

  35. Force Fields in Amber 12 Lipid11: A modular lipid force field A new modular force field for the simulation of phospholipids and cholesterol designed to be compatible with the other pairwise additive Amber force field J.Wang et al., Development and testing of a general amber force field, Journal of Computational Chemistry, 25 (2004), 1157

  36. Other Force Fields in Amber: Inclusion of Polarization Non-additive" force fields based on atom-centered dipole polarizabilities can also be used. These add a "polarization" term to what was given above where μi is an induced atomic dipole. In addition, charges that are not centered on atoms, but are off-center (as for lone-pairs or "extra points") can be included in the force field.

  37. Other Force Fields in Amber: AMOEBA (Atomic MultipoleOptimized Energetics for BiomolecularApplications) • Atomic Multipoles: The model uses a polarizable atomic multipole description of electrostatic interactions. Multipoles through the quadrupole are assigned to each atomic center based on a distributed multipole analysis (DMA) derived from large basis set molecular orbital calculations at the MP2/aug-cc-pVTZ level and the experimental geometry of the gas-phase monomer. • Polarization is treated via self-consistent induced atomic dipoles. Atomic dipole polarizabilities can be derived from an empirical fit to experimentally known molecular polarizabilities. The induced dipole at each atomic site is computed as where αi is the atomic polarizability and Ei,α is the sum of the fields generated by both permanent multipoles and induced dipoles

  38. Other Force Fields: AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) • The functional forms for bond stretching and angle bending were taken from the MM3 force field: • A Urey-Bradley functional form was chosen for the stretch-bend term:

  39. Other Force Fields: AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) • Repulsion-Dispersion. The buffered 14-7 potential has been applied to model pairwise additive vdW interactions where εij is the potential well depth, ρij= Rij/R0ij with Rij as the i-j separation and R0ijthe minimum energy distance. n = 14, m = 7, δ = 0.07, γ=0.12. The combining rules are: • The buffered 14-7 function yields a repulsive region softer than the Lennard-Jones 6-12 function but steeper than typical Buckingham exp-6 formulations. • The buffered 14-7 form was found to outperform Lennard-Jones and Buckingham potentials in simultaneously reproducing gas phase ab initio results and liquid thermodynamic properties of noble gases and a series of diatomic species.

  40. What we can do with Amber?

  41. Molecular Dynamics Simulations The Molecular Dynamics simulation method is based on Newton’s second law or the equation of motion, F=ma, where F is the force exerted on the particle, m is its mass and a is its acceleration • Integration of the equations of motion then yields a trajectory that describes the positions, velocities and accelerations of the particles as they vary with time. From this trajectory, the average values of properties can be determined.

  42. MD: Melting of Ice

  43. Human carboxyl esterasecomplexed with morphine

  44. MD: Translocation of DNA This movie shows the electrophoretically-driven translocation of a 58-nucleotid DNA strand through the transmembrane pore of alpha-hemolysin

  45. Molecular Dynamics: Amber MD Workhorses SANDER - Simulated Annealing with NMR-Derived Energy Restraints PMEMD - Particle Mesh EwaldMolecular Dynamics PMEMD is up to 55% faster than SANDER SANDER GPU PMEMD

  46. Molecular Dynamics: What Are Current Simulation Capabilities? Time scales of biological processes Femtosecond (fs) = 10-15 second Picosecond (ps) = 10-12 second Nanosecond (ns) = 10-9 second Microsecond (μs) = 10-6 second

  47. Molecular Dynamics Trajectory Molecular Dynamics Simulation Time Snapshots Snapshots of Representative Structures Molecular dynamics trajectory is a file containing snapshots of the simulated system

  48. For each Snapshot Amber Saves Structure and Energy Decomposition Energy Decomposition for each snapshot is written in the form: NSTEP = 100 TIME(PS) = 10.200 TEMP(K) = 297.23 PRESS = -1257.4 Etot = -73238.8859 EKtot = 18131.6434 EPtot = -91370.5294 BOND = 654.2822 ANGLE = 1929.4666 DIHED = 775.1417 1-4 NB = 817.8912 1-4 EEL = 4242.6763 VDWAALS = 9440.1805 EELEC = -109230.1680 EHBOND = 0.0000 RESTRAINT = 0.0000 EKCMT = 7732.1695 VIRIAL = 16916.4636 VOLUME = 338304.5955 Density = 0.9012 Ewald error estimate: 0.1550E-03 ------------------------------------------------------------------------------ Snapshots of Representative Structures

  49. Plotting Molecular Dynamics Properties Equilibration step allows atoms and molecules to find more natural positions with respect to one another Equilibration step MD Phase During the MD Phase molecular properties (structures, energies, etc.) are accumulated for future analysis

  50. Not all system properties reach equilibrium at the same time

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