Overview of Amber Force Fields and Solvation Models

The classical (mechanics) Force Fields are designed as ball-and-stick models, describing atomic interactions Torsion angles Are 4-body Angles Are 3-body Bonds Are 2-body Non-bonded pair

Forces between atoms: vdW interactions r Lennard-Jones potential This is a pair-wise potential: It depends on two atoms. Where do ε and σ come from? Combinations rules Warning: Charmm combination rules are DIFFERENT!

Torsions are special ! : they DO NOT represent physics. They are simply useful terms designed to FIT to high level ab- initio data. They are fitted to E(torsional angle) QM -E(torsional angle, torsional term=0) QM !

Non-Bonded Parameter Requirements The common AMBER force fields are ‘pairwise additive’ – Therefore non-bonded parameters are only dependent on a single atom type and not on ‘pairs’ or atoms. Each atom requires: – Mass – RESP Charge in electrons. – VDW Parameters (Well depth and intersection)

Transferable Force Fields Force field is designed to be transferable Minimize the number of atom types. Parameterization is based on units (Amino Acids or DNA Bases)

Common AMBER Force Field Sets (Never say just ‘Amber force field’! ff14. Newest, recommended force field. ff12SB: is an update of ff10 and seeks to robustly calibrate the dihedrals for the backbone and side chains for proteins which builds upon 99SB: recalibration of backbone potentials for proteins by Carlos Simmerling/Adrian Roitberg (SB) [Recommended] (>1800 citations as of May 2014) ff99bsc0 and chi.OL3 for nucleic acids and updated ion paramaters Uses the basis of the Cornell et al 1994 for topology and electrostatics, bond stretch and angle deformation and VDW parameters

Common AMBER Force Field Sets (Never say just ‘Amber force field’!) Lipid 14: Modular force field for phospholipids. 03ua: united atom extension of 03. GAFF: General Amber Force Field (J Wang) - Amber force field developed for general ligands.

Other supported force fields Extra point extensions to Amber force fields. CHARMM (AMBERTools 14 [Chamber]) Amoeba GLYCAM-06 and GLYCAM-06EP: carbohydrates and lipids GAFF Lipid: Alternate Lipid Force Field Various QM Hamiltonians (PM3, AM1, MNDO, RM1, PM3/PDDG, MNDO/PDDG, PM3CARB1, SCC-DFTB)

Force Field Charge Models RESP (Restrained electrostatic potential)-based – FF94, FF96, FF99, FF99SB, FF12SB, FF14SB  HF/6- 31G* – FF03, FF03UA  QM Continuum solvent (PCM dielectric=2) – FF02, FF02EP  B3LYP/cc-pVTZ//HF/6-31G* (Method is iterative to obtain specific dipole moment) Do NOT change the QM theory used for the ESP charge calculation!

Unpublished data for FF14SB. Courtesy of Dr. Carlos Simmerling Stony Brook University Energies

J-couplings

S 2 order parameters

Options for solvation models 1. Disregards solvation 2. Approximate finite solvent drop 3. Explicit periodic solvent (“more” expensive) 4. Implicit solvent bad: Surface tension effect

Explicit Solvent Models Triangulated Water Models (MUST BE USED WITH SHAKE, looks weird, it is correct) – TIP3P (Transferable intermolecular potential with 3 points) – TIP4P / TIP4PEW – TIP5P – SPC Flexible Water Models – SPC/FW (Requires 1fs time step) Polarizable Water Models – POL3 Other Solvents (Non-polarizable) – Methanol – Chloroform – N-MethylAcetamide (NMA) – 8M Urea - Water Mixture

Implicit Solvent Models Poisson Boltzmann (PB) Accurate but generally too slow for MD Generalized Born (GB) 7 different models / parameterizations available. IGB=1,2,3,4,5,7,8 (where did 6 go?) All have advantages and disadvantages, you must read the original articles and follow up applications. IGB=5 or 8 are generally considered most reliable. Tips for using implicit solvent Avoid using a cut off (  set cut = 999.0) Use langevin dynamics (ntt=3) Implicit solvent is not always faster than explicit solvent ; cross-over is approximately 1,000 solute atoms.

Motivation (for implicit solvation) Model a macromolecule in realistic surroundings for - Rational Drug Design - Ligand Docking - Functional Studies - Protein Folding - Macromolecular Interactions - pKa calculations - etc...

Solvation Free Energy Macromolecules are charged, polar, irregular objects Δ G Solv Δ G elec, int Δ G elec Δ G cavity

Explicit solvent pro con accurate large systems standard approach boundary artifacts

Continuum approximation Coulomb‘s Law for point charges only: In vacuum, ε=1. In water, ε=78.5 In water, the interaction between two charges is roughly 1/80 smaller than in vacuum. What is ε? It is an attempt to represent the effect of the solvent, without putting the solvent ! Water ‘shields’ the charges, by making them less visible to each other at a given distance. It comes from electronic polarization of each water molecule PLUS water movement. ++

Simple implicit solvent models For spherical particles ! Born equation (1920): Onsager Dipole Model +  =1  =80 +  =1  =80   If only particles were spherical, the world would be easier to understand...

The value of epsilon matters very little after it is large enough. The free energy difference between epsilon 1 and 2 is already half of that from 1 to infinity !

Poisson Boltzmann Equation (linearized) Contains ionic contributions The Gold standard of continuum models but hard (expensive) to solve Widely applied: Delphi, pbsa... grid-based solutions are practical Used for when the molecule is not spherical, and the charge distribution is not homogeneous.

Generalized Born models Fast and analytical (good for MD) vacuum energysolvation contribution The functional form for f GB (r) is chosen to get the proper limits as r  0 and r  infinity. There is no real physical basis for this formuale, except to try to use a simple model to understand a complex shape.

The Born radii - indicates how shielded an atom is from solvent - depends on the surrounding geometry - two extreme cases: single atom:  =r Atom completely buried:  =R molecule - recomputed at every step (according to an empirical formula)

Advantages of Implicit Solvent -In principle, lower computational cost. In reality, maybe not. - no need for water equilibration (it amounts to assuming infinitely fast water relaxation when the protein structure changes) - improved sampling (no water viscosity) - no periodic boundary artifacts - easier free energy calculations

Disadvantages of Implicit Solvent - empirical formula, additional layer of parametrization - no structural role for water molecules (H-Bonds) - no diffusion properties - wrong timescales for e.g. loop motions (can be ‘fixed’ via a friction coefficient) - no standardization, evolving algorithms and parameters