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CZ5225 CZ5225 Modeling and Simulation in Biology Modeling and Simulation in Biology
ProteinsProteins
Chen Yu Zong [email protected]
6874-6877
Mechanism of Protein function
Protein sequence-structure-function relationship
Protein structure determines its functionFunction of Proteins is determined
by their four level structures
Primary - Sequence of amino acids
Secondary - Shape of specific region along chain mostly through H-bonding
Tertiary - 3 Dimensional structure of globular protein through molecular folding
Quaternary - Combination of separate polypeptide and prosthetic group. Aggregation and prosthetic.
1. Primary structure
The general formula for α-amino acid. 20 different R groups in the commonly occurring
amino acids.
Proteins are polymers of a set of 20 amino acids.20 amino acids = building units.
Chiral Centerasymmetric carbon
The CORN method for L isomers: put the hydrogen towards you and read off CO R N clockwise around the Ca This works for all amino acids.
All naturally occurring amino acids that make up proteins are in the L conformation
Classification of 20 R groups
Aliphatic residues
Aromatic residues
Acidic
Basic
Charged residues
Negatively charged
Positively charged
Polar residues
Side chain = H IminoC
CC
CC
The unique couple
H
Through hydrolysis reactions, amino acids are connected through peptide bond to form a peptide/protein.
H2N CH C
CH3
OH
O
NH
CH C
CH2
OH
O
SH
H
H2N CH C
CH3
O
NH
CH C
CH2
OH
O
SHAmide
Ala Val
+ H2O
Structure of peptide bonds
• Key features:– 1. Planar
– 2. Rigid due to partial double bond character.
– 3. Almost always in trans configuration.
– 4. Polar. Can form at least two hydrogen bonds.
2. Secondary structure
Local organization mainly involving the protein backbone:
-helix,
-strand (further assemble into -sheets)
turn and interconnecting loop
The (right-handed) -helix
• First structure to be predicted (Pauling, Corey, Branson: 1951) and experimentally solved (Kendrew et al. 1958) – myoglobin
• Turn: 3.6 residues• Pitch: 5.4 Å/turn • Rise: 1.5 Å/residueHydrogen
bond
i+4
i+8
i
+
-
The -sheet
• Side chains project alternately up or down
strand
Turn Structures
Loop structures
3.1. -hairpins
3.2. -corners
3.3. Helix hairpins
3.4. The corner
3.5. Helix-turn-helix
4. Tertiary structure– secondary structure
elements pack into a compact spatial unit
– “Two methods now available to determine 3D structures of proteins: X-ray crystallography and Nuclear MagneticResonance (NMR)
Mad cows disease and the Prion protein
Protein mis-folding can cause diseases
Prion protein-------Memory?
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 … ON-H … NO-H … NO-H … O
r
V
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 moleculeligand normally binds to a cavity of a
protein. Why?
Effect of Binding:Activate, inhibit, being metabolized ortransported by, the protein
Protein-Ligand Interaction
Ligand Binding: A small moleculeligand normally binds to a cavity of a
protein. Why?
Effect of Binding:Activate, inhibit, being metabolized ortransported by, the protein
Protein-Ligand Interaction
Ligand Binding: A small moleculeligand normally binds to a cavity of a
protein. Why?
Effect of Binding:Activate, inhibit, being metabolized ortransported 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 ofProtein 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.
ener
gy
coordinates
CH3
CH3
CH3
Goal of Energy Minimization
A system of N atoms is defined by 3N Cartesian coordinates or 3N-6 internal coordinates. These define a multi-dimensional potential energy surface (PES).
A PES is characterized by stationary points:
• Minima (stable conformations)• Maxima• Saddle points (transition states)
Goal of Energy Minimization• Finding the stable conformations
ener
gy
coordinates
Classification of Stationary Points
0.0
4.0
8.0
12.0
16.0
20.0
0 90 180 270 360
transition state
local minimum
global minimum
ener
gy
coordinate
TypeMinimum MaximumSaddle point
1st Derivative000
2nd Derivative*positivenegativenegative
* Refers to the eigenvalues of the second derivatives (Hessian) matrix
Minimization Definitions
0
ixf
02
2
ixf
Given a function:
Find values for the variables for which f is a minimum:
),,( 3321 Nxxxxff
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
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.
Global minimum
Most populated minimum
Active Structure
A General Minimization Scheme
Starting Point x0
Minimum?
Calculate New Pointxk+1 = f(xk)
Stopyes
No
Two Questions
f(x,y)
Where to go (direction)?
How far to go (magnitude)?
This is where we want to go
How Far To Go? Until the Minimum
Real function
Cycle 1: 1, 2, 3
Cycle 2: 1, 2, 4
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• xk+1 = xk + ksk, k = step size.• Increase as long as energy reduces.• Decrease when energy increases. 4
3
21
5
Where to go?• Parallel to the force (straight downhill): Sk = -gk
How far to go?• Line search• Arbitrary Step
Steepest Descent
Steepest Descent: Example
-15 -10 -5 0 5 10 15
-15
-10
-5
0
5
10
15441
361289
169225
12181
4925
91
Starting point: (9, 9)
Cycle 1:Step direction: (-18, -36)Line search equation:Minimum: (4, -1)
Cycle 2:Step direction: (-8, 4)Line search equation:
Minimum: (2/3, 2/3)
92 xy
15.0 xy
22 2),( yxyxf
y
xg
4
2kk gS
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