791_ak_lecture3

791_ak_lecture3 - 7.91 Amy Keating How do we use...

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How do we use computational methods to analyze , predict , or design protein sequences and structures? Theme: Methods based on physics vs. methods based on our accumulated empirical knowledge of protein properties 7.91 Amy Keating
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For a molecular simulation or model you need: 1. A representation of the protein 2. An energy function 3. A search algorithm or optimizer
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Covalent Potential Energy Terms U Covalent = U bond + U angle bond + U dihedral improper + U torsion 2 U bond = 1 k b ( b b 0 ) bonds 2 2 U angle bond = 1 k θ ( θ−θ ) angles bond 2 0 U dihedral improper = 1 dihedrals improper 2 k Φ ( Φ Φ 0 ) U torsion = 1 k φ [1 + cos( n φ− δ )] torsions 2 Brooks et al., J. Comput. Chem . 4 : 187-217 (1983) 2
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Non-Covalent Potential Energy Terms U Non-covalent = U vdW + U elec Lennard-Jones potential 12 ij ij r B 6 ij ij r C B ij U vdW = 12 C ij i ; j r ij r ij 6 “accurate” approximate q i q j U elec = Coulomb’s law i ; j ε r ij
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The potential energy surface is a 3N-6 dimensional space. For a protein, we assume a single native-structure minimum. There are many local minima, and some may be close in energy to the global minimum. E n e r g y X
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Sampling the Potential Energy Surface Energy minimization “downhill” search, generally to nearest local minimum can be used to relax structures might be useful to define local changes due to mutation Normal mode analysis defines “characteristic motions”, which are distortions about a local minimum structure orders motions “easy” (low frequency) to “hard” (high) Molecular dynamics movie of motion at given temperature (300 K) equivalent to statistical mechanical ensemble Monte Carlo/Simulated Annealing Describe properties of the landscape and thermodyanmic parameters without simulating how the molecular actually moves
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Energy Minimization Conformational Space, R Potential Energy, U(R) X-ray structure X Iterative procedures; terminate when reach tolerance, such as small ( F i = −∇ r U ) i gradient Poor initial structure leads r i + 1 = r i + δ F i to poor local minimum Multiple minimum problem ONLY FINDS LOCAL MINIMA!
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Uses of simple minimization 1. The “minimum perturbation approach” to modeling a mutation Assume structure of single-site mutant is close to known wild-type structure Find stable conformations for mutant side chain in context of wild-type protein Use energy minimization to relax candidate structures (all degrees of freedom) Shih, Brady, and Karplus, Proc. Natl. Acad. Sci. USA 82 : 1697–1700 (1985); hemagglutinin Gly to Asp mutation modeled accurately 2. Relieving strain before analyzing the energy of an experimental or predicted structure 3. Structure building and refinement when solving structures using X-ray crystallography or NMR
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This note was uploaded on 11/11/2011 for the course BIO 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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791_ak_lecture3 - 7.91 Amy Keating How do we use...

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