Transcript Molecular Dynamics

X-PLOR
XPLOR minimizes the hybrid energy function
Ehybrid = Echem = wexpEexp
where Echem could be
a molecular dynamics force field
(CHARMM, AMBER, OPLS/AMBER)
a modified geometric force field
Engh/Huber, PROLSQ, PARALLHDG
and Eexp would be derived from Xray data or NMR data
Minimization Methods
Powell’s conjugate gradient minimization
Molecular dynamics
numerical solution of Newtons equations of motion
with temperature variation simulated annealing
Rigid body dynamics
Rigid body minimization
With respect to the coordinates or some other
properties (occupancies temperature factors)
Step 1: define topology
(chemical (primary) structure)
topology @TOPPAR:topallhdg.pro end
segment
name= “ “
chain
@TOPPAR:tophpep19.pro
sequence Ala Ala end
end
end
write structure output=diala.psf end
stop
Calculate Energies
To minimize we need
PSF file (Structure)
structure @diala.psf end
energy parameters
parameter @TOPPAR:parallhdg.pro end
starting coordinates
XPLOR PDB format
coor @diala.pdb end
mini powell nstep=50 end
write coor output=dialamin.pdb end
stop
Energy Function
Molecular Dynamics
Molecular dynamics is the numerical solution of Newton’s
equations of motion
Fi = mi ai = mi d2xi/dt2 = d/dxi ETOTAL
second order differential equation
masses mi are defined in topology file
ETOTAL is the XPLOR energy function force field in parameter file
and experimental terms
Verlet Dynamics
The Verlet algorithm is derived from a linear
approximation it is very simple and very stable
xi(t+h) = xi(t) + vi(t) h + ½ ai h2
xi(t-h) = xi(t) - vi(t) h + ½ ai h2
Add (using Fi=aimi)
xi(t+h) = 2xi(t) - xi(t–h) + Fi(t) h2/ mi
velocities are calculated by
vi(t) = ½ h (xi(t+h) - xi(t-h))
Langevin Dynamics
XPLOR can calculate Langevin dynamics
mi d2xi/dt2(t) = -gradxi E + [ fi(t) ]- mibi dxi/dt(t)
in addition to Newton equation friction terms
fi is a random force on atom i
mibi dxi/dt(t)
is a velocity dependent friction term with friction
constant bi and is used as temperature control
T Control
Temperature control temperature coupling
Berendsens method for Langevin dynamics
with adjustable friction coeffcient and zero random force
bi = bi0 ( T0/T -1)
if T >T0 bi is positive -> cooling
if T<T0 bi is negative -> heating
Dynamics is initialized with random vi s drawn from a
Boltzmann distribution
Slow Cooling
A slow cooling script
…
evaluate ($bath = 1000)
vector do (vx = $bath) (all)
vector do (vy = $bath) (all)
vector do (vz = $bath) (all)
while ($bath > 50) loop cool
evaluate ($bath = $bath - $tempstep)
dynamics verlet
nstep=1000 time=0.005
iasvel=current
tcoup=true tbath=$bath
nprint=$nstep iprfrq=$ntrfrq
end
end loop cool
…
Strategy
Annealing Schedule
Evdw: LJ or hard sphere
repulsive potential
E(NOE)
E(NOE)
14
12
E
10
8
asymptote k(r-rupper)
6
constant force
4
2
harmonic region (r-rupper)2
0
0
2
4
flat bottom
[rlower –rupper]
6
Rij
8
10
12
Series1
More Energy Terms
The Result – a Bundle
Assessing the Quality of NMR Structures
Number of experimental constraints
RMSD of structural ensemble (subjective!)
Violation of constraints
Molecular energies
Comparison to structure database: PROCHECK
Compactness of Structure, Hydrophobic Burial
Back-calculation of experimental parameters
Ramachandran Quality