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Atomic and molecular models for macromolecular structure Molecular Modeling Molecular Mechanics / Force Fields • Computational model • Atomic framework for macromolecular structure • Full quantum mechanics is not possible • Classical forces between atoms • Minimize energy to obtain structure Force Field • CHARMM, OPLS, GROMOS, AMBER • Each atom has – Position, charge, mass, perhaps polarizability – Radius, Bonding accounted for in energy function • Account for bonding and non-covalent interactions: Etotal Ebonded Enonbonded Bonding and Nonbonding Interactions • Bonded interactions have simple constraints for configuration in 1D, 2D, and 3D Ebonded Ebonds Eangles Edihedrals • Non-covalent or through space Enonbonded Eelectrostatic Evan derWaals Erepulsion • Sometimes extra terms ܧ௫௧ • • • • • Dipole-Dipole Hydrogen Bonds -conjugation Anharmonicity Fixing problems… The Force Field Potential Energy Rmin + repulsion (r-12) http://amit1b.wordpress.com/computational-biophysics/ Parameterization • Force Fields are Empirical or Semi-Empirical • Empirical: Parameterized to match experiment – – – – Thermodynamic data (Hform) Dipole moments Known molecular structure Vibrational frequencies • Semiempirical: – Parameterized from ab initio calculations • Self-consistent analysis of data SPC/E water (Simple Point Charge Extended) • Point charges for O, H • Lennard-Jones Potential http://www1.lsbu.ac.uk/water/water_models.html Examples of other models • “Knowledge Based” statistical models – Free energy drawn from known statistics: F = -kT lnP – For instance: Statistically determined angles. QM/MM (Quantum Mechanics/Molecular Mechanics) • For study of processes where quantum mechanical effects are crucial (i.e. enzymatic catalysis) • Divide space into two regions Quantum and Classical Spaces interact mechanically and electrostatically: Classical (MM) Quantum (QM) H H QM H MM H QM / MM Coarse Grained Models • Cross-over from atomic to physical models • Beads with springs – 1-6 for amino acids – Beads for proteins • Multiscale models