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CZ5225 Methods in Computational Biology
Lecture 7: Protein Structure and
Structural Modeling
Prof. Chen Yu Zong
Tel: 6874-6877
Email: [email protected]
http://xin.cz3.nus.edu.sg
Room 07-24, level 7, SOC1, NUS
August 2004
Protein Structural Organization
Proteins are made from just 20 kinds of amino acids
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Protein
Structural
Organization
Protein has four
levels of structural
organization
3
Protein Structure Determines Its Interaction with
Other Molecules:
Protein-Protein Interaction
4
Protein Structure Determines Its Interaction with
Other Molecules:
Protein-DNA Interaction
5
Protein Structure Determines Its Interaction with
Other Molecules:
Protein-RNA Interaction
6
Protein Structure 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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Protein Structure and Motions:
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
8
Protein structure and motions:
Movie Show:
Drug Binding
Induced
Conformation
Change in Protein
9
Protein structure and motions:
Movie Show:
Protein transient
opening for ligand or
drug binding and
dissociation:
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Protein structure: Lowest Free Energy State
Modeling of Protein
Structure in Different
Environment:
Finding the global
minimum free energy
state
Question:
1. No. of possible
conformations of a protein.
2. Computing cost for
searching these
conformations
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Structural 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.
12
Structural 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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Structural Modeling:
Basic Interactions and Their Models
The bending energy
equation is also based
on Hooke's law
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Structural Modeling:
Basic Interactions and Their Models
The bending energy equation is also based on Hooke's law
15
Structural Modeling:
Basic Interactions and Their Models
The torsion energy
is modeled by a
simple periodic
function
Why?
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Structural Modeling:
Basic Interactions and Their Models
Torsion energy as a
function of bond
rotation angle.
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Structural Modeling:
Basic Interactions and Their Models
The non-bonded energy
accounts for repulsion,
van der Waals attraction,
and electrostatic
interactions.
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Structural 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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Structural Modeling:
Basic Interactions and Their Models
Hydrogen Bond:
N-H … O
N-H … N
O-H … N
O-H … O
Modeled by
VdW+electrostatic
Modeled by More potential
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Structural Modeling:
Basic Interactions and Their Models
Complete Hamiltonian:
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
]
Structural Modeling:
Basic Interactions and Their Models
Concept of energy
scale is Important
for molecular
Modeling
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Structural Modeling:
Basic Interactions and Their Models
Concept of energy scale is Important for molecular modeling
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Structural 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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Energy Landscape
for DNA Base Flipping Movement
Phys. Rev. E62, 1133-1137 (2000).
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Structural Modeling:
Basic Interactions and Their Models
From structure (x,y,z coordinates) to energy function:
rij=sqrt((xi-xj)**2+(yi-yj)**2+(zi-zj)**2)
cos(theta_i)=(xj-xi)*(xk-xi)+(yj-yi)*(yk-yi)+(zj-zi)*(zk-zi))/(rij*rik)=
Aij*Aik+Bij*Bik+Cij*Cik
cos(phi)=[(Aik*Bkl-Bik*Akl)*(Aik*Bij-Bik*Aij)+
(Akl*Cik-Ckl*Aik)*(Aij*Cik-Cij*Aik)+
(Bik*Ckl-Cik*Bkl)*(Bik*Cij-Cik*Bij)]/(Pi*Pk)
Pi=sin(theta_i)
Pk=sin(theta_k)
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
Homework: derive or find formula for  [V (1  e
Xi=x(r,theta,phi) etc.
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
]
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Structural Modeling:
Basic Interactions and Their Models
Structural Modeling Method I:
Conformation search:
Phi -> Phi+dphi
xi -> xi+dxi; yi -> yi+dyi; zi -> zi+dzi
E -> E +dE
All possible states can be explored
Conformation space
Energy landscape
H
p2
1
1
k r (r  req ) 2 
k (   eq ) 2 

2
2
bond  stretch
bond  anglebending
 2m  
atoms
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
]
Q: Can you write a simple
conformation search program?
27
Structural Modeling:
Basic Interactions and Their Models
Structural Modeling Method II:
Energy minimization:
General methods in Numerical Recipes
H
p2
1
1
k r (r  req ) 2 
k (   eq ) 2 

2
bond  stretch
bond  anglebending 2
 2m  
atoms
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
]
Force guided approach:
Initialize: xi -> xi+dxi
Compute potential energy change:
V -> V +dV
Determine next movement:
Fxi=-dV/dxi; Fyi=-dV/dyi; Fzi=-dV/dzi
dxi=C*Fxi
new xi=xi+dxi
Energy minimization can only go down hill. Why?
28
Structural Modeling:
Basic Interactions and Their Models
H
Structural Modeling Method III:
Molecular Dynamics Simulation:
p2
1
1
 
k r (r  req ) 2 
k (   eq ) 2 


2
m
2
2
atoms
bond  stretch
bond  anglebending
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
]
• Time-dependent motion trajectory based on laws
of classical physics.
• Advantage: "Accurate" dynamics.
• Disadvantage: Short-time event only.
• Application: "All purpose", most widely used
approach.
Curr. Opin. Struct. Biol. 6, 232 (1996).
Detailed description of MD general theory
29
Structural Modeling:
Basic Interactions and Their Models
Structural Modeling Method III:
Molecular Dynamics Simulation:
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
]
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Molecular Dynamics Simulation
Challenge: Time-scale gap
Bio-events: 10-3~10s
MD: 10-6s on 200-node parallel computer for 30aa peptide
Gap: Need to increase computing speed by >>1000
Time-saving techniques in development:
Technique
Speed-up factor
Reduction of degrees of freedom
Parallelization
Multiple time-step integration
Deformation of interaction potential or
increase space dimension
Scaling of system parameters (T, mass, etc)
Efficient search of nearest neighbors
Miscellaneous tricks (Newton's 3rd law etc)
up to 100
10~100
10~
10~
3~
3
2
Curr. Opin. Struc. Biol. 7, 181 (1997)
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CZ5225 Methods in Computational Biology
Assignment 2
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