Transcript Force Fields - BIDD - National University of Singapore

SMA5233
Particle Methods and Molecular Dynamics
Lecture 3: Force Fields
A/P Chen Yu Zong
Tel: 6516-6877
Email: [email protected]
http://bidd.nus.edu.sg
Room 08-14, level 8, S16
National University of Singapore
Force Fields
• A force field (also called a forcefield) refers to the functional form and
parameter sets used to describe the potential energy of a system of
particles (typically but not necessarily atoms). Force field functions
and parameter sets are derived from both experimental work and
high-level quantum mechanical calculations. "All-atom" force fields
provide parameters for every atom in a system, including hydrogen,
while "united-atom" force fields treat the hydrogen and carbon atoms
in methyl and methylene groups as a single interaction center.
"Coarse-grained" force fields, which are frequently used in long-time
simulations of proteins, provide even more abstracted
representations for increased computational efficiency.
• The usage of the term "force field" in chemistry and computational
biology differs from the standard usage in physics. In chemistry
usage a force field is defined as a potential function, while the term is
used in physics to denote the negative gradient of a scalar potential.
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Molecular Mechanics Force Fields:
Functional Forms
The basic functional form of a force field encapsulates both bonded terms
relating to atoms that are linked by covalent bonds, and nonbonded
(also called "noncovalent") terms describing the long-range
electrostatic and van der Waals forces. The specific decomposition of
the terms depends on the force field, but a general form for the total
energy can be written as
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
The stretching energy
equation is based on
Hooke's law. The "kb"
parameter controls the
stiffness of the bond
spring, while "ro"
defines its equilibrium
length.
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
The stretching energy
equation is based on
Hooke's law. The "kb"
parameter controls the
stiffness of the bond
spring, while "ro"
defines its equilibrium
length.
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
The bending energy
equation is also based
on Hooke's law
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
The bending energy equation is also based on Hooke's law
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
The torsion energy
is modeled by a
simple periodic
function
Why?
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
Torsion energy as a
function of bond
rotation angle.
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
The non-bonded energy
accounts for repulsion,
van der Waals attraction,
and electrostatic
interactions.
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
• van der Waals attraction
occurs at short range, and
rapidly dies off as the
interacting atoms move apart.
• Repulsion occurs when the
distance between interacting
atoms becomes even slightly
less than the sum of their
contact distance.
• Electrostatic energy dies out
slowly and it can affect atoms
quite far apart.
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
Types of Hydrogen Bond:
N-H … O
N-H … N
O-H … N
O-H … O
Can be modeled by
•
•
•
VdW+electrostatic (AMBER)
Modified Linard-Jones (CHARM)
Morse potential (Prohofsky/Chen)
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
Complete Energy Function:
p2
1
1
2
2
H 
 
k r (r  req ) 
k
(



)



eq
atoms 2m
bond  stretch 2
bond  angle bending 2
vn
[1  cos(n   )]

2

bond  rotation
 [V (1  e
H bond
0
 [V (1  e
S bond
 a ( r  r0' ) 2
)  V0 ] 

non bonded
 a ( r  r0' ) 2
)  V0 ] 
0
[
Aij
12
ij
r

Bij
6
ij
r

qi q j
 ij rij
]
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
Concept of energy
scale is Important
for molecular
Modeling
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
Concept of energy scale is Important for molecular modeling
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Molecular Mechanics Force Fields:
Parameterization
• In addition to the functional form of the potentials, a force field typically
defines a set of parameters for each of a number of atom or particle types
that correspond to different atoms and bonding patterns in commonly
simulated molecules.
• The parameter set includes values for atomic mass and partial charge for
individual atoms, and equilibrium bond lengths and angles for pairs,
triplets, and quadruplets of bonded atoms.
• Preparation for a molecular dynamics simulation involves assigning an
atom or particle type to each atom or particle in the molecules of interest.
• Although many molecular simulations involve biological macromolecules
such as proteins, DNA, and RNA, the parameters for given atom types are
generally derived from observations on small organic molecules that are
more tractable for experimental study and quantum calculation.
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Popular molecular mechanics force fields:
Classical
AMBER (Assisted Model Building and Energy Refinement) - widely used for
proteins and DNA
CHARMM - originally developed at Harvard, widely used for both small molecules
and macromolecules
CHARMm - commercial version of CHARMM, available through Accelrys
CVFF - also broadly used for small molecules and macromolecules
GROMACS - The force field optimized for the package of the same name
GROMOS - A force field that comes as part of the GROMOS (GROningen
MOlecular Simulation package), a general-purpose molecular dynamics
computer simulation package for the study of biomolecular systems.
GROMOS force field (A-version) has been developed for application to
aqueous or apolar solutions of proteins, nucleotides and sugars. However, a
gas phase version (B-version) for simulation of isolated molecules is also
available
OPLS-aa, OPLS-ua, OPLS-2001, OPLS-2005 - Members of the OPLS family of
force fields developed by William L. Jorgensen at Yale Department of
Chemistry.
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ECEPP/2 - free energy force field
Popular molecular mechanics force fields:
Second-generation
CFF - a family of forcefields adapted to a broad variety of organic compounds,
includes forcefields for polymers, metals, etc.
MMFF - developed at Merck, for a broad range of chemicals
MM2, MM3, MM4 - developed by Norman L. Allinger, for a broad range of
chemicals
Reactive force fields
ReaxFF - reactive force field developed by William Goddard and coworkers. It is
fast, transferable and is the computational method of choice for atomistic-scale
dynamical simulations of chemical reactions.
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Molecular Mechanics Force Fields:
Basic Interactions and Their Models
Sources of force parameters:
Bonds, VdW, Electrostatic (for amino acids, nucleotides only):
• AMBER: J. Am. Chem. Soc. 117, 5179-5197
• CHARMM: J. Comp. Chem. 4, 187-217
H-bonds (Morse potential):
• Nucleic Acids Res. 20, 415-419.
• Biophys. J. 66, 820-826
p2
1
1
H 
 
k r (r  req ) 2 
k (   eq ) 2 

atoms 2m
bond  stretch 2
bond  angle bending 2
vn
[1  cos(n   )]

2

bond  rotation
 [V (1  e
H bond
0
 [V (1  e
S bond
 a ( r  r0' ) 2
)  V0 ] 

non bonded
 a ( r  r0' ) 2
)  V0 ] 
0
[
Aij
12
ij
r

Bij
6
ij
r

qi q j
 ij rij
]
Electrostatic parameters of organic molecules need to be
computed individually by using special software (such as
Gaussian)
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Molecular Mechanics Force Fields:
Atom Types
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields:
Atom Types and Standard Parameters
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields: Atom Partial Charge
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields: Atom Partial Charge
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Molecular Mechanics Force Fields: Atom Partial Charge
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields: Atom Partial Charge
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields: Atom Partial Charge
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields: Bond Parameters
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Molecular Mechanics Force Fields: Bond Parameters
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Molecular Mechanics Force Fields: Bond Parameters
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Molecular Mechanics Force Fields:
Bond and Non-Bonded Parameters
AMBER: J. Am. Chem. Soc. 117, 5179-5197
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Water Models
A recent review listed 46 distinct
models, so indirectly indicating their
lack of success in quantitatively
reproducing the properties of real
water.
They may, however, offer useful
insight into water's behavior.
Some of the more successful
simple models are illustrated in the
picture
Models types a, b and c are all
planar whereas type d is almost
tetrahedral
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Water Models
Lennard-Jones potential
Buckingham potential
Shown right is the Lennard-Jones
potential for the SPC/E model (solid red
line). The σ parameter gives the
molecular separation for zero
interaction energy. The minimum
energy (-ε) lies 12% further at σx21/6 Å.
Also shown (dotted blue line) is an
equivalent Buckingham potential (σ
3.55 Å, ε 0.65 kJ mol-1, γ 12.75);
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Water
Models
A recent review
listed 46
distinct models,
so indirectly
indicating their
lack of success
in quantitatively
reproducing
the properties
of real water.
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Water Models
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Coarse-Grain Force Fields:
Basic Interactions and Their Models
•
A polymer chain is modeled using N+1 beads connected by elastic joints
in a three-dimensional space. Each bead represents one or more amino
acid or nucleotide. The motion of the ith bead follows the underdamped
Langevin equation with a leapfrog algorithm:
m is the mass of a bead, and ui is the vector tangential to the chain. gi(t)
is the Gaussian white noise and obeys the fluctuation-dissipation
theorem:
z0 and zn represent friction coefficients for motion parallel and normal to
the chain, respectively. We set zn =L at 1<i<N-1 and zn=z0 at i=0,N
J. Chem. Phys. 114, 7260-7266 (2001)
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Coarse-Grain Force Fields:
Basic Interactions and Their Models
Uintra = Ubond+ Ubend+ Unonbond
J. Chem. Phys. 114, 7260-7266 (2001)
Ubond is the bonded potential, Ubend is
the bending potential, and Unonbond
represents the non-bonded interaction
energy terms.
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