CZ5225 Modeling and Simulation in Biology Modeling and Simulation in Biology Proteins Chen Yu Zong [email protected] 6874-6877.

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