Normal modes of proteins sometimes correspond to biologically relevant motions shearing"or hinging"conformational changes are common in enzymes Can compare structure changes computed from Nma with alternate conformations observed experimentally. frequently a low-frequency mode describes the change(but it may not be the lowest energy mode) NMa is a way to get an idea about motion from a static structure
Normal modes of proteins sometimes correspond to biologically relevant motions • “shearing” or “hinging” conformational changes are common in enzymes • Can compare structure changes computed from NMA with alternate conformations observed experimentally. Frequently a low-frequency mode describes the change (but it may not be the lowest energy mode) • NMA is a way to get an idea about motion from a static structure
Molecular Dynamics Simulations Simulate motions of molecules as a function of time Collect short movie"of protein"swimming"in solution Can use the simulation to compute Average structure( at given temperature, 7) Atomic fluctuations (at 7) Thermodynamic quantities(temperature dependent) 声, (t+a)=r()+n(t+c/2) (t+/2)=v(t-/2)+( Verlet leap frog algorithm
Molecular Dynamics Simulations • Simulate motions of molecules as a function of time – Collect short “movie” of protein “swimming” in solution • Can use the simulation to compute: – Average structure (at given temperature, T) – Atomic fluctuations (at T) – Thermodynamic quantities (temperature dependent) m ∂ 2 xi Fi Fi = mi ai ai = = − ∇iU i ∂ t2 mi G G r (t + δt) = r ( t) + δ G tv t ( + δt /2) G v (t + δt /2) = G v (t − δt /2) + δt G a ( t) Verlet “leap frog” algorithm
Running a molecular dynamics simulation Minimize initial coordinates Assign random starting velocities from Maxwell-Boltzmann distribution 1/2 风() 2mhT/ exp/m,L 2kT Use small time step to integrate Newton's equations of motion (1 fs =1 x 10-15 sec is typical) Equilibration (running dynamics until system equilibrates) Production dynamics(useful dynamics at a desired temp
Running a Molecular Dynamics Simulation • Minimize initial coordinates • Assign random starting velocities from Maxwell-Boltzmann distribution 1/2 2 ⎞ p( vi) = ⎜ ⎛ mi ⎟ ⎞ exp⎜⎜ ⎛− mivi ⎟ ⎟ ⎝ 2 πkT ⎠ ⎝ 2kT ⎠ • Use small time step to integrate Newton’s equations of motion (1 fs =1 x 10-15 sec is typical) • Equilibration (running dynamics until system equilibrates) • Production dynamics (useful dynamics at a desired temp)
Sampling conformational space using Monte Carlo Monte Carlo randomly samples configurations rather than simulating how the molecule would actually move in time 1. Begin with a random ( energy-minimized ) conformation 2. Evaluate the energy Eo 3. Make a random conformational change ( e.g. rotation around a bond) 4. Evaluate the new energy =E 5. DECISION if e< Eo ACCEpt the move, set E0= E go to 3 if E>E0 ANd if exp[(E-E0)kT]> random# then accept the move, set eo=e go to 3 else reject the move go to 3 6. Proceed for an arbitrary amount of time The acceptance criterion is such that the conformations generated sample the boltzman distribution
Sampling conformational space using Monte Carlo Monte Carlo randomly samples configurations, rather than simulating how the molecule would actually move in time. 1. Begin with a random (energy-minimized) conformation 2. Evaluate the energy = E0 3. Make a random conformational change (e.g. rotation around a bond) 4. Evaluate the new energy = E’ 5. DECISION: if E’ < E0 ACCEPT the move, set E0 = E’, go to 3 if E’ > E0 AND if exp[-(E’-E 0)/kT] > random # then ACCEPT the move, set E0 = E’, go to 3 else reject the move, go to 3 6. Proceed for an arbitrary amount of time The acceptance criterion is such that the conformations generated sample the Boltzman distribution