Transcript Fundamentals of molecular modeling. - BIDD

LSM3241: Bioinformatics and
Biocomputing
Lecture 6: Fundamentals of Molecular Modeling
Prof. Chen Yu Zong
Tel: 6516-6877
Email: [email protected]
http://bidd.nus.edu.sg
Room 07-24, level 7, SOC1,
National University of Singapore
Structural organization of a molecule
Three features:
• Configuration (atom
organization).
• Conformation (atom
spatial arrangement).
• Shape (Surface
landscape, steric
packing)
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Structural organization of a molecule
I. Configuration:
• The organization of atoms and chemical bonds.
• Change of configuration requires breaking of bonds.
Switch between H and NH2 requires bond breaking.
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Structural organization of a molecule
An important aspect of configuration is chirality
• Chirality defines the property of mirror image.
The image on the right is an mirror image of the one at left.
• If mirror image is not the same as the original, the
compound is called chiral.
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Structural organization of a molecule
Example of chiral and non-chiral compound:
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Structural organization of a molecule
II. Conformation:
• Determined by the spatial positions of its constituent
atoms.
• Inter-convertible without breaking and making bonds
Rotatable bond
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Protein structure and conformation change:
Movie Show:
Drug Binding
Induced
Conformation
Change in Protein
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Structural organization of a molecule
III. Shape
• Steric packing (what part of space is covered by the
compound).
• Surface features (cavities, grooves where other
molecules can bind to).
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Protein Surface Determines Its Interaction with
Other Molecules:
Protein-Protein Interaction
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Protein Surface Determines Its Interaction with
Other Molecules:
Protein-DNA Interaction
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Protein Surface Determines Its Interaction with
Other Molecules:
Protein-RNA Interaction
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Protein Surface Determines Its Interaction with
Other Molecules:
Protein-Drug Interaction
Mechanism of
Drug Action:
A drug interferes with
the function of a
disease protein by
binding to it.
This interference
stops the disease
process
Drug Design:
Structure of disease
protein is very useful
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Atomic motions in a molecule
• Atoms are not rigidly
positioned.
• External and internal
forces can induce
atomic motions.
• Some motions have
chemical effect.
Movie Show:
Protein transient opening for ligand
or drug binding and dissociation:
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Atomic motions in a molecule
The effect of motions
are described by
energy:
Energy measures the
ability to do work.
Motion is associated
with energy.
Movie Show:
Protein transient opening for ligand
or drug binding and dissociation:
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Types of Energy
Kinetic energy -- motional energy
Kinetic energy is related to the speed and mass of a moving object. The higher the
speed and the heavier the object is, the bigger work it can do.
Potential Energy -- "positional" energy.
Water falls from higher ground to lower ground. In physics such a phenomenon is
modeled by potential energy description:
Objects move from higher potential energy place to lower potential energy place.
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Potential Energy Description of Molecular Motions
A molecule changes from higher potential energy form to lower potential energy
form.
Potential energy is determined by inter-molecular, intra-molecular, and
environmental forces
The total energy of motions is:
Energy = Stretching Energy + Angle Bending Energy +Torsion Energy +
Non-Bonded Interaction Energy
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Molecular Modeling:
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 Modeling:
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 Modeling:
Basic Interactions and Their Models
The bending energy
equation is also based
on Hooke's law
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Molecular Modeling:
Basic Interactions and Their Models
The bending energy equation is also based on Hooke's law
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Molecular Modeling:
Basic Interactions and Their Models
The torsion energy
is modeled by a
simple periodic
function
Why?
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Molecular Modeling:
Basic Interactions and Their Models
Torsion energy as a
function of bond
rotation angle.
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Molecular Modeling:
Basic Interactions and Their Models
The non-bonded energy
accounts for repulsion,
van der Waals attraction,
and electrostatic
interactions.
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Molecular Modeling:
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 Modeling:
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 Modeling:
Basic Interactions and Their Models
Complete Energy Function:
p2
1
1
2
2
H 
 
k r (r  req ) 
k
(



)



eq
atoms2m
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 Modeling:
Basic Interactions and Their Models
Concept of energy
scale is Important
for molecular
Modeling
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Molecular Modeling:
Basic Interactions and Their Models
Concept of energy scale is Important for molecular modeling
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Molecular Modeling:
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 

atoms2m
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 Modeling:
Modeling Method I: Conformation search:
Change each torsion angle: Phi -> Phi+dphi
Subsequent change of atom positions: xi -> xi+dxi; yi -> yi+dyi; zi -> zi+dzi
Energy is changed: E -> E +dE
Each set of torsion angles corresponds to a conformation.
Find sets with lower energy
All possible states can be explored
H
p2
1
1
 
k r (r  req ) 2 
k (   eq ) 2 


atoms2m
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 Modeling:
Modeling Method II: Energy minimization:
H
p2
atoms
Force guided approach:
1
1
k r (r  req ) 2 
k (   eq ) 2 

2
bond  stretch
bond  anglebending 2
 2m  
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
rij12

Bij
rij6

qi q j
 ij rij
]
Initialize:
Change atom position: xi -> xi+dxi
Compute potential energy change:
V -> V +dV
Determine next movement:
Force: Fxi=-dV/dxi; Fyi=-dV/dyi; Fzi=-dV/dzi
Atom displacement: dxi=C*Fxi
New position: xi=xi+dxi
Energy minimization can only go down hill. Why?
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Summary of Today’s lecture
• Structural organization of a molecule.
• Basic interactions and models
• Modeling methods (conformation search, energy
minimization)
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