CZ5225 Methods in Computational Biology Lecture 4-5: Protein Structure and Structural Modeling Prof....
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CZ5225 Methods in Computational BiologyCZ5225 Methods in Computational Biology
Lecture 4-5: Protein Structure and Lecture 4-5: Protein Structure and Structural ModelingStructural Modeling
Prof. Chen Yu ZongProf. Chen Yu Zong
Tel: 6874-6877Tel: 6874-6877Email: Email: [email protected]@nus.edu.sghttp://xin.cz3.nus.edu.sghttp://xin.cz3.nus.edu.sg
Room 07-24, level 7, SOC1, NUSRoom 07-24, level 7, SOC1, NUSAugust 2004August 2004
22
Protein Structural OrganizationProtein Structural Organization
Proteins are made from just 20 kinds of amino acids
33
Protein Protein Structural Structural OrganizationOrganization
Protein has four levels of structuralorganization
44
Protein Structure Determines Its Interaction with Protein Structure Determines Its Interaction with Other Molecules:Other Molecules:
Protein-Protein InteractionProtein-Protein Interaction
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Protein Structure Determines Its Interaction with Protein Structure Determines Its Interaction with Other Molecules:Other Molecules:
Protein-DNA InteractionProtein-DNA Interaction
66
Protein Structure Determines Its Interaction with Protein Structure Determines Its Interaction with Other Molecules:Other Molecules:
Protein-RNA InteractionProtein-RNA Interaction
77
Protein Structure Determines Its Interaction with Protein Structure Determines Its Interaction with Other Molecules:Other Molecules:
Protein-Drug InteractionProtein-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
88
Protein Structure and Motions:Protein Structure and Motions:
Protein-Drug InteractionProtein-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
99
Protein structure and motions:Protein structure and motions:
Movie Show:
Drug Binding Induced Conformation Change in Protein
1010
Protein structure and motions:Protein structure and motions:
Movie Show:
Protein transient opening for ligand or drug binding and dissociation:
1111
Protein structure: Lowest Free Energy StateProtein structure: Lowest Free Energy State
Modeling of Protein Structure in DifferentEnvironment:
Finding the global minimum free energy state
Question:
1. No. of possible conformations of a protein.
2. Computing cost for searching these conformations
1212
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic 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.
1313
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic 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.
1414
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
The bending energy equation is also based on Hooke's law
1515
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
The bending energy equation is also based on Hooke's law
1616
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
The torsion energy is modeled by a simple periodic function
Why?
1717
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
Torsion energy as a function of bond rotation angle.
1818
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
The non-bonded energy accounts for repulsion, van der Waals attraction, and electrostatic interactions.
1919
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic 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.
2020
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
Hydrogen Bond:
N-H … ON-H … NO-H … NO-H … O
Modeled by VdW+electrostatic
Modeled by More potential
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
Complete Hamiltonian:
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
2222
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
Concept of energyscale is Important for molecular Modeling
2323
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
Concept of energy scale is Important for molecular modeling
2424
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic 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
Electrostatic parameters of organic molecules need to be computed individually by using special software (such as Gaussian)
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
2525
Energy Landscape Energy Landscape for DNA Base Flipping Movementfor DNA Base Flipping Movement
Phys. Rev. E62, 1133-1137 (2000).
2626
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic 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)
Homework: derive or find formula forXi=x(r,theta,phi) etc.
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
2727
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
Structural Modeling Method I:
Conformation search:
Phi -> Phi+dphixi -> xi+dxi; yi -> yi+dyi; zi -> zi+dziE -> E +dE
All possible states can be exploredConformation spaceEnergy landscape
Q: Can you write a simple conformation search program?
2828
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
Structural Modeling Method II:Energy minimization:
General methods in Numerical Recipes
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/dzidxi=C*Fxinew xi=xi+dxi
Energy minimization can only go down hill. Why?
2929
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
Structural Modeling Method III:Molecular Dynamics Simulation:
• 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
3030
Structural Modeling: Structural Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models
bondednon ijij
ji
ij
ij
ij
ijrra
bondH
bondS
rra
rotationbond
n
eqbendinganglebond
eqrstretchbondatoms
r
r
B
r
AVeV
VeVn
v
krrkm
pH
][])1([
])1([)]cos(1[
2
)(2
1)(
2
1
2
61202)(
0
02)(
0
222
'0
'0
Structural Modeling Method III:Molecular Dynamics Simulation:
3131
Molecular Dynamics SimulationMolecular Dynamics SimulationChallenge: 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 up to 100
Parallelization 10~100Multiple time-step integration 10~
Deformation of interaction potential orincrease space dimension
10~
Scaling of system parameters (T, mass, etc) 3~Efficient search of nearest neighbors 3
Miscellaneous tricks (Newton's 3rd law etc) 2
Curr. Opin. Struc. Biol. 7, 181 (1997)
3232
CZ5225 Methods in Computational Biology Assignment 2Assignment 2