Download Lect 11: Receptor Ligand Binding, Energy Minimization and docking

LSM2104/CZ2251
Essential Bioinformatics and Biocomputing
Protein Structure and
Visualization (3)
Chen Yu Zong
[email protected]
6874-6877
LSM2104/CZ2251
Essential Bioinformatics and Biocomputing
Lecture 11
Receptor Ligand Binding, Energy Minimization
and docking concepts
Structural Modelling
1. Receptor-Ligand Interactions
2. Energy description of structures
3. Structure optimization by energy minimization
4. Receptor-ligand docking
Protein-Protein Interaction
Protein-Protein interaction:
Surface contact, shape complementarity
Intermolecular forces:
Van der Waals, hydrogen bonding, electrostatic force
Hydrogen Bond
Types of Hydrogen Bond:
N-H … O
N-H … N
O-H … N
O-H … O
V
r
Protein-DNA Interaction
Protein-DNA
interaction:
• DNA recognition by
proteins is primarily
mediated by
certain classes of
DNA binding
domains and motifs
Protein-RNA Interaction
Protein-RNA
interaction:
• RNA recognition by
proteins is primarily
mediated by
certain classes of
RNA binding
domains and motifs
Protein-Ligand Interaction
Ligand Binding:
A small molecule
ligand normally binds
to a cavity of a protein.
Why?
Effect of Binding:
Activate, inhibit,
being metabolized or
transported by,
the protein
Protein-Ligand Interaction
Ligand Binding:
A small molecule
ligand normally binds
to a cavity of a protein.
Why?
Effect of Binding:
Activate, inhibit,
being metabolized or
transported by,
the protein
Protein-Ligand Interaction
Ligand Binding:
A small molecule
ligand normally binds
to a cavity of a protein.
Why?
Effect of Binding:
Activate, inhibit,
being metabolized or
transported by,
the protein
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
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
Example of Binding Induced Shape Change
Example 2: Induced Fit of Hexokinase (blue)
Upon Binding of Glucose (red).
Note that the active site is a pocket within the enzyme.
Energy Description
Energy is needed to make things or objects change:
Movement, Chemical reaction, Binding, Dissociation, Structural Change,
Conformational change etc.
Why Energy Description for molecular structure?
•
Structure determination (“evolution” of a structural-template into the
correct structure)
•
Binding induced shape change (binding sometimes induces shape
change, one of the mechanisms for the interference of the function of a
molecule by another)
•
Protein motions (proteins undergo internal motions that have implications
such as the switch between active and in-active state)
Energy Description
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.
Potential Energy Description of
Protein Structure “Evolution”
• 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
• Protein structural “evolution” can be performed by systematic variation
of the atom positions towards the lower energy directions. This
procedure is called “structure optimization” or “energy minimization”
Energy Minimization for Structural Optimization
• Protein structure “evolution” can be performed by systematical variation
of the atom positions towards the lower energy directions. This
procedure is called “structure optimization” or “energy minimization”
Potential Energy Surface (PES)
A force field defines for each molecule a unique PES.
Each point on the PES represents a molecular conformation
characterized by its structure and energy.
Energy is a function of the coordinates.
(Next) Coordinates are function of the energy.
CH 3
energy
CH3
CH 3
coordinates
Goal of Energy Minimization
A system of N atoms is defined by 3N Cartesian coordinates or 3N6 internal coordinates. These define a multi-dimensional potential
energy surface (PES).
• Minima (stable conformations)
• Maxima
• Saddle points (transition states)
energy
A PES is characterized by
stationary points:
Goal of Energy Minimization
• Finding the stable conformations
coordinates
Classification of Stationary Points
1st Derivative
0
0
0
Type
Minimum
Maximum
Saddle point
2nd Derivative*
positive
negative
negative
20.0
16.0
energy
transition state
12.0
8.0
local minimum
4.0
global minimum
0.0
0
90
180
270
360
coordinate
*
Refers to the eigenvalues of the second derivatives (Hessian) matrix
Minimization Definitions
Given a function:
f  f ( x1 , x2 , x3  x3 N )
Find values for the variables for which f is a minimum:
f
0
xi
2 f
0
2
xi
Functions
• Quantum mechanics energy
• Molecular mechanics energy
Variables
• Cartesian (molecular mechanics)
• Internal (quantum mechanics)
Minimization algorithms
• Derivatives-based
• Non derivatives-based
A Schematic Representation
Starting geometry
 Easy to implement; useful for well defined structures
 Depends strongly on starting geometry
Population of Minima
Active Structure
Most populated minimum
Global minimum
Most minimization method can only go downhill and so locate
the closest (downhill sense) minimum.
No minimization method can guarantee the location of the
global energy minimum.
No method has proven the best for all problems.
A General Minimization Scheme
Starting point x0
Minimum?
No
Calculate
xk+1 = f(xk)
yes
Stop
Two Questions
Where to go (direction)?
How far to go (magnitude)?
f(x,y)
This is where we want to go
How Far To Go? Until the Minimum
Line search in one dimension
• Find 3 points that bracket the minimum
(e.g., by moving along the lines and
recording function values).
• Fit a quadratic function to the points.
• Find the function’s minimum through
differentiation.
• Improved iteratively.
Arbitrary Step
Real function
Cycle 1: 1, 2, 3
Cycle 2: 1, 2, 4
3
1
2
• xk+1 = xk + lksk, lk = step size.
• Increase l as long as energy reduces.
• Decrease l when energy increases.
4
5
Steepest Descent
Where to go?
• Parallel to the force (straight downhill): Sk = -gk
How far to go?
• Line search
• Arbitrary Step
Steepest Descent: Example
f ( x, y)  x  2 y
2
 2x 
g  
4y
2
Sk   g k
Starting point: (9, 9)
15
Cycle 1:
Step direction: (-18, -36)
Line search equation: y  2 x  9
Minimum: (4, -1)
10
Cycle 2:
Step direction: (-8, 4)
Line search equation:
-5
5
0
-10
y  0.5 x  1
Minimum: (2/3, 2/3)
-15
-15
-10
-5
0
5
10
15
Steepest Descent:Overshooting
SD is forced to make 90º turns between subsequent steps (the
scalar product between the (-18,-36) and the (-8,4) vector is 0
indicating orthogonality) and so is slow to converge.
Why Ligand-Protein Docking?
Molecular recognition is a central phenomenon in biology
• Enzymes  Substrates
• Receptors  Signal inducing ligands
• Antibodies  Antigens
Classifying docking problems in biology
• Protein-ligand docking
– Rigid-body docking
– Flexible docking
• Protein-protein docking
• Protein-DNA docking
• DNA-ligand docking
Ligand-Protein Docking
• Proteins  Drugs
• Proteins  Natural Small Molecule Substrates
The Molecular Docking Problem
Given two molecules with 3D conformations in
atomic details:
• Do the molecules bind to each other? If yes:
• How does the molecule-molecule complex looks like?
• How strong is the binding affinity?
Structures of protein-ligand complexes
• X-ray (PDB: 30,179 entries from X-ray
crystallography, NMR and neutron diffraction)
• NMR
Importance of the protein 3D structures
• Resolution < 2.5Å
• Homology modeling problematic
Basic Principles
The association of molecules is based on interactions
• H-bonds, salt bridges, hydrophobic contacts, electrostatic
• Very strong repulsive (VdW) interactions on short distances.
Association interactions are weak and short ranged.
• Strong binding implies surface complementarity.
Most molecules are flexible.
Docking Concept
Representation of a Cavity
HIV-1 Protease
Generation of Cavity Model
X-ray structure of HIV protease
Molecular surface model at active site
Active site filled with spheres. Sphere centers become potential locations for
ligand atoms.
Ligand-protein docking concept
Ligand-protein .docking concept
Ligand-Protein Docking Concept
Checking Chemical Complementarity in
Ligand-Protein Docking
Potential Energy Between Ligand and Protein:
•
A ligand with sufficiently low ligand-protein potential energy is considered as
a drug candidate
•
Chemical database can be searched to find which chemical molecules can
be docked to a disease protein with sufficiently low ligand-protein energy
Summary

Receptor-ligand binding

Energy minimization for structural
optimization

Receptor-ligand docking concept