1
Dinamica Molecular
y el
modelamiento de
macromoleculas
2
Historical Perspective







1946 MD calculation
1960 force fields
1969 Levinthal’s paradox on protein folding
1970 MD of biological molecules
1971 protein data bank
1998 ion channel protein crystal structure
1999 IBM announces blue gene project
3
Proteins
 Polypeptide chains made up of amino acids or residues
linked by peptide bonds
 20 aminoacids
 50-500 residues, 1000-10000 atoms
 Native structure believed to correspond to energy minimum,
since proteins unfold when temperature is increased
4
Proteins: Local Motions
 0.01-5 AA, 1 fs -0.1s
 Atomic fluctuations
• Small displacements for substrate binding in enzymes
• Energy “source” for barrier crossing and other activated processes
(e.g., ring flips)
 Sidechain motions
• Opening pathways for ligand (myoglobin)
• Closing active site
 Loop motions
• Disorder-to-order transition as part of virus formation
5
6
Levinthal paradox
 Proteins simply can not fold on a reasonable time scale (Levinthal
paradox; J. Chem. Phys., 1968, 65: 44-45)
• Each bond connecting amino acids can have several (e.g., three)
possible states (conformations). A protein of, say, 101 AA could exist
in 3100 = 5 x 1047 conformations. If the protein can sample these
conformations at a rate of 1013/sec, 3 x 1020/year, it will take 1027
years to try them all. Nevertheless, proteins fold in a time scale of
seconds.
7
Proteins: Rigid-Body Motions
 1-10 AA, 1 ns – 1 s
 Helix motions
• Transitions between substrates (myoglobin)
 Hinge-bending motions
• Gating of active-site region (liver alcohol dehydroginase)
• Increasing binding range of antigens (antibodies)
8
Quantum Mechanical Origins
 Fundamental to everything is the Schrödinger equation

Nuclear coordinates
• H  i
t
• wave function ( R, r , t )
Electronic coordinates
• H = Hamiltonian operator
H  K  U   2 m  i2  U
• time independent form
H   E
 Born-Oppenheimer approximation
• electrons relax very quickly compared to nuclear motions
• nuclei move in presence of potential energy obtained by solving
electron distribution for fixed nuclear configuration
it is still very difficult to solve for this energy routinely
• usually nuclei are heavy enough to treat classically
9
Force Field Methods
 Too expensive to solve QM electronic energy for every
nuclear configuration
 Instead define energy using simple empirical formulas
• “force fields” or “molecular mechanics”
 Decomposition of the total energy
Neglect 3- and
higher-order terms
U (r N )  i u (1) (ri )  i  j i u (2) (ri , r j )  i  j i  k  j u (3) (ri , r j , rk ) 
Single-atom energy
(external field)
Atom-pair contribution
3-atom contribution
 Force fields usually written in terms of pairwise additive
interatomic potentials
• with some exceptions
10
Conformation optimization for molecular
interaction
Molecular Mechanics Approach:
11
Energy minimisation
 Calculation of how atoms should move to minimise TOTAL potential energy
 At minimum, forces on every
atom are zero.
 Optimising structure to remove strain & steric clashes
 However, in general finds local rather than global minimum. Energy barriers are
not overcome even if much lower energy state is possible ie structures may be
locked in. Hence not useful as a search strategy.
12
Energy minimisation
 Potential energy depends on many parameters
 Problem of finding minimum value of a function with >1 parameters. Know value of
function at several points.
 Grid search is computationally
not feasible
 Methods
• Steepest descents
• Conjugate gradients
13
Molecular Dynamics: Introduction
Newton’s second law of motion
14
Molecular dynamics
 F=ma
 F is calculated from molecular mechanical potential.
 Model conformational changes.
 Calculate time-dependent properties (transport properties).
15
Molecular Dynamics: Introduction
We need to know
The motion of the
atoms in a molecule, x(t)
and therefore,
the potential energy, V(x)
Molecular Dynamics: Introduction
How do we describe the potential energy V(x) for a
molecule?
Potential Energy includes terms for
Bond stretching
Angle Bending
Torsional rotation
Improper dihedrals
16
17
Molecular Dynamics: Introduction
Potential energy includes terms for (contd.)
Electrostatic
Interactions
van der Waals
Interactions
18
Molecular Dynamics: Introduction
To do this, we should know
at given time t,
 initial position of the atom
x1
 its velocity
v1 = dx1/dt
 and the acceleration
a1 = d2x1/dt2 = m-1F(x1)
19
Molecular Dynamics: Introduction
The position x2 , of the atom after time interval t would be,
x2  x1  v1t
and the velocity v2 would be,
1
v2  v1  a1t  v1  m F ( x1)t  v1  m
1 dV
dx
x 1 t
20
Molecular Dynamics: Introduction
In general, given the values x1, v1 and the potential energy
V(x), the molecular trajectory x(t) can be calculated, using,
xi  xi 1  vi 1t
1 dV ( x)
vi  vi 1  m
xi1 t
dx
21
How a molecule changes during MD
22
The Necessary Ingredients
 Description of the structure: atoms and connectivity
 Initial structure: geometry of the system
 Potential Energy Function: force field
AMBER
CVFF
CFF95
Universal
23
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
24
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
25
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
26
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
27
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
28
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
29
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
Mixed terms
30
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
Mixed terms
31
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
Mixed terms
- + - + Attraction
32
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
+ - + - Attraction
Mixed terms
33
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 Ustr stretch
 UvdW van der Waals
 Ubend bend
 Uel electrostatic
 Utors torsion
 Upol polarization
 Ucross cross
+ - + - Attraction
Mixed terms
+
-
34
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 UvdW van der Waals
 Ustr stretch
Attraction
u(2) + - +  Uel electrostatic + +
u(2) -
 Ubend bend
 Upol polarization
 Utors torsion
 Ucross cross
u(N)
Mixed terms
++
-
35
Contributions to Potential Energy
 Total pair energy breaks into a sum of terms
U (r N )  U str  U bend  U tors  U cross  U vdW  U el  U pol
Intramolecular only
Repulsion
 UvdW van der Waals
 Ustr stretch
Attraction
u(2) + - +  Uel electrostatic + +
u(2) -
 Ubend bend
 Upol polarization
 Utors torsion
 Ucross cross
u(N)
Mixed terms
+
-
36
Modeling Potential energy
dU
U(r) 
 U(req )  dr
1 d 2U
(r  req ) 
2
2
dr
r req
(r  req ) 2
r req
n
1 d 3U
1
d
U
3

(r  req ) ....
3 dr r r
n! dr n
eq

(r  req ) n
r req

37
Modeling Potential energy
0
0 at minimum
2
1dU
dU
U(r)  U(req ) 
(r  req ) 
2
2
dr
dr r req
1 d 2U
U(r) 
2 dr 2

r req
1
(r  req )  kAB (r  req ) 2
2
2
r req
(r  req ) 2
38
Stretch Energy
 Expand energy about equilibrium position
o
U (r12 )  U (r12
)
define
dU
dr
r ro
o
(r12  r12
)
d 2U
dr 2
(neglect)
o 2
(r12  r12
) 
r ro
minimum
o 2
U (r12 )  k (r12  r12
)
harmonic
Morse
 Model fails in strained geometries
• better model is the Morse potential

U (r12 )  D 1  e
dissociation
energy

 r12 2
Energy (kcal/mole)
250
200
150
100
50
0
force constant
-0.4
-0.2
0.0
0.2
0.4
Stretch (Angstroms)
0.6
0.8
39
Bending Energy

 Expand energy about equilibrium position
dU
d 2U
o
U ( )  U ( ) 
(   ) 
d   o
d 2
(   o ) 2 
o
define
(neglect)
  o
minimum
U ( )  k (   o ) 2
harmonic
• improvements based on including higher-order terms
 Out-of-plane bending
U ( c )  k ( c  c o )2
u(4)
c
40
Torsional Energy
 Two new features
f
• periodic
• weak (Taylor expansion in f not appropriate)
 Fourier series
U (f )   n 1U n cos(nf )
• terms are included to capture appropriate minima/maxima
depends on substituent atoms
– e.g., ethane has three mimum-energy conformations
• n = 3, 6, 9, etc.
depends on type of bond
– e.g. ethane vs. ethylene
• usually at most n = 1, 2, and/or 3 terms are included
41
Van der Waals Attraction
 Correlation of electron fluctuations + - +  Stronger for larger, more polarizable molecules
• CCl4 > CH4 ; Kr > Ar > He
 Theoretical formula for long-range behavior
att
U vdW
C
8

O
(
r
)
6
r
 Only attraction present between nonpolar molecules
• reason that Ar, He, CH4, etc. form liquid phases
 a.k.a. “London” or “dispersion” forces
-+ -+
42
Van der Waals Repulsion
 Overlap of electron clouds
 Theory provides little guidance on form of model
 Two popular treatments
inverse power
rep
U vdW
typically n ~ 9 - 12
A
rn
rep
U vdW
exponential
Ae Br
two parameters
 Combine with attraction term
• Lennard-Jones model
A C
U  12  6
r
r
Exp-6
10
U  Ae Br 
LJ
Exp-6
8
20
a.k.a. “Buckingham” or “Hill”
6
x10
3
15
10
Beware of anomalous
Exp-6 short-range
attraction
4
Exp-6 repulsion is
slightly softer
2
5
0
0
2
4
6
8
C
r6
1.0
1.2
1.4
1.6
1.8
2.0
43
Electrostatics 1.
 Interaction between charge
inhomogeneities
 Modeling approaches

• point charges


• point multipoles
 Point charges
• assign Coulombic charges to several
points in the molecule
• total charge sums to charge on
molecule (usually zero)
• Coulomb potential
U (r ) 
1.0
0.5
0.0
qi q j
-0.5
4 0r
-1.0
very long ranged
Lennard-Jones
Coulomb
1.5
1
2
3
4
44
Electrostatics 2.
 At larger separations, details of charge distribution are less
important
 Multipole statistics capture basic features
  i qiri
• Dipole
Q  i qiriri
• Quadrupole
• Octopole, etc.
  0, Q  0
Vector

Tensor
      0, Q  0

 Point multipole models based on long-range behavior
• dipole-dipole
udd  
1 2
r
3


3(ˆ1  rˆ )(ˆ 2  rˆ )  ( ˆ1  ˆ 2 )
Q
Q
• dipole-quadrupole
udQ 
3 1Q2 
ˆ 2  rˆ )2  1  2( ˆ1  ˆ 2 )(Qˆ 2  rˆ ) 
ˆ
ˆ
(


r
)
5(
Q
1

2 r4 


• quadrupole-quadrupole
uQQ 
3 Q1Q2 
2
2
2
2 2
1

5
c

5
c

2
c

35
c
c2  20c1c2c12 
1
2
12
1
5


4 r
Axially
symmetric
quadrupole
45
Polarization
 Charge redistribution due to influence of surrounding
molecules
++
+
• dipole moment in bulk different
from that in vacuum
 Modeled with polarizable charges or multipoles
 Involves an iterative calculation
• evaluate electric field acting on each charge due to other charges
• adjust charges according to polarizability and electric field
• re-compute electric field and repeat to convergence
 Re-iteration over all molecules required if even one is moved
46
Polarization
ind  E
Approximation

ind ,i  E i
Ei  
ji

q j rij
rij3
ij 

  3 
3rij 1


r
r
ij

ji ij 
rij
Electrostatic field does not include contributions
from atom i
47
Common Approximations in Molecular Models
 Rigid intramolecular degrees of freedom
• fast intramolecular motions slow down MD calculations
 Ignore hydrogen atoms
• united atom representation
 Ignore polarization
• expensive n-body effect
 Ignore electrostatics
 Treat whole molecule as one big atom
• maybe anisotropic
 Model vdW forces via discontinuous potentials
 Ignore all attraction
 Model space as a lattice
• especially useful for polymer molecules
Qualitative
models
48
Molecular Dynamics: Introduction
Equation for covalent terms in P.E.
 k (l  l )   k    
Vbonded ( R) 
l
0
bonds


2
2
0
angles
k (   0 ) 2 
impropers
 A [1  cos(nf  f )]
n
torsions
0
49
Molecular Dynamics: Introduction
Equation for non-bonded terms in P.E.
Vnonbonded( R) 

i j
rijmin 12
rijmin 6
qi q j
( ij [(
)  2(
) ]
rij
rij
4 r  0 rij
An overview of various motions in proteins (1)
Motion
Spatial extent (nm)
Log10 of
characteristic time
(s)
Relative vibration of bonded
atoms
0.2 to 0.5
-14 to –13
Elastic vibration of globular
region
1 to 2
-12 to –11
Rotation of side chains at
surface
0.5 to 1
-11 to –10
Torsional vibration of buried
groups
0.5 to 1
-14 to –13
50
An overview of various motions in proteins (2)
Motion
Spatial Extent
(nm)
Log10 of characteristic
time (s)
Relative motion of different globular
regions (hinge bending)
1 to 2
-11 to –7
Rotation of medium-sized side chains
in interior
0.5
-4 to 0
Allosteric transitions
0.5 to 4
-5 to 0
Local denaturation
0.5 to 1
-5 to 1
Protein folding
???
-5 to 2
51
52
A typical MD simulation protocol
 Initial random structure generation
 Initial energy minimization
 Equilibration
 Dynamics run – with capture of conformations at regular
intervals
 Energy minimization of each captured conformation
53
Essential Parameters for MD
(to be set by user)
 Temperature
 Pressure
 Time step
 Dielectric constant
 Force field
 Durations of equilibration and MD run
 pH effect (addition of ions)
54
STARTING DNA MODEL
55
DNA MODEL WITH IONS
56
DNA in a box of water
57
SNAPSHOTS
58
Protein dynamics study
 Ion channel / water channel
 Mechanical properties
• Protein stretching
• DNA bending
Movie downloaded from theoreticla biophysics group, UIUC
59
Molecular Interactions
water-water interaction
U ww ( X i , X j )  U LJ (rij )  U HB ( X i , X j )
van der Waals’ term
 
U LJ ( rij )  4 LJ  LJ
r

 ij
Hydrogen bonding term
12




  LJ

 r
 ij




6




3
U HB ( X i , X j )   HBG( rij  rHB )  G(ik  uij  1)G( jl  uij  1)
k ,l 1
G( x )  exp(  x / 2 2 )
2
ion-water interaction
U iw ( X i , X j )  U LJ ( rij )  U charge ( X i , X j )
,
U charge ( rij )  zi z j  HB 
exp( rij )
rij
60
61
Average number of hydrogen bonds within the first water shell around an ion
62
63
Solvent dielectric models
QiQ j
V
rij
Effetive dielectric constant

eff r  r 
r 1
rS
2
S  0.15Å1 ~ 0.3Å1
2

 2rS  2 erS
64
Introduction to Force Fields
•Sophisticated (though imperfect!)
mathematical function
•Returns energy as a function
of conformation
It looks something like this …
U(conformation) = Ebond + Eangle + Etors + Evdw + Eelec+ …
65
Why do we need force field?
 Force field and potential energy surface.
• Changes in the energy of a system can be considered as movements on a
multidimentional surface call the “energy surface”. Force is the first derivative of
the energy.
 In molecular mechanics approach, the dimension of potential surface is 3N, N is
number of particles.
 The probability of the molecular system stay in certain conformations can be
calculated if the underlying potential is known.
66
Three types of force field
 Quantum mechanics (Schrodinger equation for electrons),
usually deal with systems with less than 100 atoms.
 Empirical force field: molecular mechanics (for atoms), can
be used for systems up to millions of atoms.
 Statistical potential (flexible), no restriction.
67
Source of FF components
•Geometrical terms: bond, angle, torsion
& vdw parameters come from
empirical data.
•Electrostatic charges: two problems arise
 no exp.data for charges
 basis underlying molec. model
68
Molecular mechanical force field





Potential is the summation of the following terms :
Bond stretching,
Angle bending,
Torsion rotation,
Non-bonded interactions
• Vdw interaction,
• Electrostatic interaction.
 (Hydrogen bonds).
 (Implicit solvent).
 …
69
Figures are taken from NIH guide of molecular modeling
70
71
72
non-bonded terms
73
Common empirical force fields
Class I
CHARMM
CHARMm (Accelrys)
AMBER
OPLS/AMBER/Schrödinger
ECEPP (free energy force field)
GROMOS
Class II
CFF95 (Biosym/Accelrys)
MM3
MMFF94 (CHARMM, Macromodel, elsewhere)
UFF, DREIDING
74
Assumptions
 Hydrogens often not explicitly included (intrinsic hydrogen
methods)
• “Methyl carbon” equated with 1 C and 3 Hs
 System not far from equilibrium geometry (harmonic)
 Solvent is vacuum or simple dielectric
75
Assumptions:
Harmonic Approximation
8.35E-28
8.35E-28
8.35E-28
8.35E-28
8.35E-28
1.4E-18
8.35E-28
8.35E-28
1.2E-18
8.35E-28
8.35E-28
1E-18
8.35E-28
8.35E-28
8.35E-28
8E-19
8.35E-28
8.35E-28
6E-19
8.35E-28
8.35E-28
4E-19
8.35E-28
8.35E-28
2E-19
8.35E-28
8.35E-28
8.35E-28
0
8.35E-28
0
8.35E-28
8.77567E+14
20568787140
2.03098E-18
1.05374E-18
8.77567E+14Potential
20568787140
1.77569E-18
Empirical
for Hydrogen
Molecule9.66155E-19
8.77567E+14
20568787140
1.54682E-18
8.82365E-19
8.77567E+14
20568787140
1.34201E-18
8.02375E-19
8.77567E+14
20568787140
1.15913E-18
7.26185E-19
8.77567E+14
20568787140
9.96207E-19
6.53795E-19
8.77567E+14
20568787140
8.51451E-19
5.85205E-19
8.77567E+14
20568787140
7.23209E-19
5.20415E-19
8.77567E+14
20568787140
6.09973E-19
4.59425E-19
8.77567E+14
20568787140
5.10362E-19
4.02235E-19
8.77567E+14
20568787140
4.2311E-19
3.48845E-19
8.77567E+14
20568787140
3.47061E-19
2.99255E-19
8.77567E+14
20568787140
2.81155E-19
2.53465E-19
8.77567E+14
20568787140
2.24426E-19
2.11475E-19
8.77567E+14
20568787140
1.75987E-19
1.73285E-19
8.77567E+14
20568787140
1.35031E-19
1.38895E-19
8.77567E+14
20568787140
1.0082E-19
1.08305E-19
8.77567E+14
20568787140
7.26787E-20
8.15147E-20
8.77567E+14
20568787140
4.99924E-20
5.85247E-20
8.77567E+14
20568787140
3.22001E-20
3.93347E-20
8.77567E+14
20568787140
1.87901E-20
2.39447E-20
8.77567E+14
20568787140
9.29638E-21
0.5
1
1.5
2
2.5
31.23547E-20
3.5
8.77567E+14
20568787140
3.29443E-21
4.56475E-21
4
76
Assumptions:
Harmonic Approximation
d 2U
dx 2
 6.45 10 2
x0
kg
k
2
s
HO    k  m 2
kg
k
s2  6.215 1014 Hz
 


1.67 1027 kg
6.45 10 2



 9.8911013 Hz  3.30 10 3 cm 1 (Exp : 4.395 10 3 cm 1 )
2
77
Brief History of FF
78
Force Field classification
1.-
with rigid/partially rigid geometries
ECEPP, …
2.-
without electrostatics
SYBYL, …
3.-
simple diagonal FF
Weiner, GROMOS, CHARMm, OPLS/AMBER, …
4.-
more complex FF
MM2, MM3, MMFF, …
79
Comparison of the simple diagonal FF
Force Field
Electrostatics
van der Waals
CHARMm
empirical fit to quantum
mechanics dimers
empirical (x-ray,
crystals)
GROMOS
empirical
empirical (x-ray,
crystals)
OPLS/AMBER
empirical (Monte Carlo
on liquids)
empirical (liquids)
Weiner
ESP fit (STO-3G)
empirical (x-ray,
crystals)
Cornell
RESP fit (6-31G*)
empirical (liquids)
80
Transferability
 AMBER (Assisted Model Building Energy Refinement)
• Specific to proteins and nucleic acids
 CHARMM (Chemistry at Harvard Macromolecular
Mechanics)
• Specific to proteins and nucleic acids
• Widely used to model solvent effects
• Molecular dynamics integrator
81
Transferability
 MM? – (Allinger et. al.)
• Organic molecules
 MMFF (Merck Molecular Force Field)
• Organic molecules
• Molecular Dynamics
 Tripos/SYBYL
• Organic and bio-organic molecules
82
Transferability
 UFF (Universal Force Field)
• Parameters for all elements
• Inorganic systems
 YETI
• Parameterized to model non-bonded interactions
• Docking (AmberYETI)
83
MMFF Energy
 Electrostatics (ionic compounds)
• D – Dielectric Constant
• d- electrostatic buffering constant
Eelectrostatic 
qi q j
DRij  d 
n
84
MMFF Energy
 Analogous to Lennard-Jones 6-12 potential
• London Dispersion Forces
• Van der Waals Repulsions
EVDW


 1.07 R

  ij 
*

 Rij  0.07 Rij 

*
ij
7
*7


 1.07 Rij

 2
 7
7
*
R

0
.
07
R


ij
 ij

The form for the repulsive part has no physical basis and is
for computational convenience when working with large
macromolecules. K. Gilbert: Force fields like MM2 which
is used for smaller organic systems will use a Buckingham
potential (or expontential) which accurately reflects the
chemistry/physics.
85
Pros and Cons
 N >> 1000 atoms
 Easily constructed
 Accuracy
 Not robust enough to describe
subtle chemical effects
• Hydrophobicity
• Excited States
• Radicals
 Does not reproduce quantal
nature
Simple Statistics on
MD Simulation
 Atoms in a typical protein and water
simulation
32000
 Approximate number of interactions in force
calculation
109
 Machine instructions per force calculation 1000
 Total number of machine instructions
1023
 Typical time-step size
10–15 s
 Number of MD time steps
1011 steps
 Physical time for simulation
10–4 s
 Total calculation time (CPU: P4-3.0G ) days 10,000
86
87
Hardware Strategies
 Parallel computation
• PC cluster
• IBM (The blue gene), 106 CPU
 Massive distributive computing
• Grid computing (formal and in the future)
• Server to individual client (now in inexpensive)
Examples: SETI, folding@home, genome@home
protein@CBL
88
# publications/year mentioning FF used to model proteins