Modeling Proteins at an Oil / Water Interface

Chemistry 699.08Final Presentation

Patrick BrunelleDecember 13, 2001

Why care about oil / water interfaces?

• Proteins can have different biological effects, depending on their conformation.

• Some proteins have the ability of penetrating the membrane of cells, thus, participating in the cell functions.

• This can also be a problem (virus are a good example).

What are the theories available?

• Absorption of a polymer on a flat surface (Singer, 1948).

• Absorption of a flexible, high molecular weight, polymer on an impenetrable solid surface (Silbergberg, 1962).Extension to proteins:

• Dickinson’s Model (E. Dickinson and S.R. Euston, Adv. Colloid Interfaces Sci., 1992, 42, 89)

• Anderson’s Model (R.E. Anderson, V.S. Pande and C.J. Radke, J. Chem. Phys., 2000, 112, 9167)

Dickinson’s Model - Purpose

Dickinson used his model to get an understanding of the conformation of milk proteins at the interface between an oil droplet and water.

Beta-casein could be consider as a near random chain of 209 amino acids.

For this study, beta-casein was chosen because of its abundance in milk.

Dickinson’s Model - Basics

Monte-Carlo Algorithm is used on a tetrahedral lattice, where each amino acid occupies on lattice site.

The bottom half of the lattice is occupied by water molecules and the top half is occupied by “oil” molecules.

But how to define the hamiltonian of the system???

Dickinson’s Model - Basics

Dickinson’s Model - Hamiltonian

The Hamiltonian is defined as follows:

• All the amino acids are classified in 4 categories: • polar (p)• non-polar (np)• positively charged (c+)• negatively charged (c-)

• There is no interaction between the solvent molecules.

• There is no interaction between two amino acids.

So, the Hamiltonian is the sum of the interaction energies of the amino acids with the two different type of solvents.

Dickinson’s Model - Interaction Energies

E(np,oil)E(p,oil)E(c+,oil)E(c-,oil)

+0.5-1.0-10.0-10.0

E(np,aq)E(p,aq)E(c+,aq)E(c-,aq)

-1.00.0+5.0+5.0

Adsorption Energy (KT)

AdsorptionEnergy (KT)

E(np,aq/oil) = -E(np,oil/aq)E(p,aq/oil) = -E(p,oil/aq)E(c+,aq/oil) = -E(c+,aq/oil)E(c-,aq/oil) = -E(c-,aq/oil)

-1.00.0+10.0+10.0

Solvent Change (KT)

Dickinson’s Model - Simulation

• The simulation is run for 5 x 106 steps to reach equilibration.

• And sampling is done at every 5 x 103 steps for a total of 20 x 106 steps.

• This model seems to agree with the CRISP procedure (neutron diffraction experiment). The CRISP procedure gave a maximum extension of the protein in aqueous phase of 12nm and the modeling shows 12nm.

Anderson’s Model - Purpose

Improve from Dickinson’s model

Anderson’s Model - Basics

• The Hamiltonian is defined by using the matrix of Miyazawa and Jernigan.(Macromolecules, 1985, 18, 534)

• A octahedral lattice is used.

Anderson’s Model - Model Protein

FVHTGELYNAKTKGRIMQAESPRVLDS

The model peptide is 27 amino acids long and is known to fold to one specific conformation. The folding process is also very fast. (It folds and unfolds in 3.24 x 107 Monte Carlo steps, in bulk water)

Anderson’s Model - Hamiltonian

H s r B r rI I IJ I JI J

N

({ } , { } ) ( ),

= 1 neighbouring amino acids

= 0 otherwise

Bij is the matrix element of amino acid i and j from the matrix of Miyazawa and Jernigan.

The solvents are approximated:water is taken as histidineoil is taken as glycine

BUT

Anderson’s Model - Temperature Controlled

T=T*/Tm*

The simulation is run at 0.94T which has been shown to have 50% of the protein in the folded state and 50% unfolded.

Anderson’s Model - Partition Function

Z z Q z z Q Qcon f con f

con f

( , ) ( ) ( )

(x) = 1 for x=0(x) = 0 otherwise

40 000 conformations are used.

Each simulation is run for about 2 x 109 steps.

Anderson’s Model - Bias Potential

V z z b ( ) 2=6.67

“Biased” free energy: F z Q T Z z Q' ( , ) ln ( , )

Free Energy: F z Q T Z z Q z z b( , ) ln ( , ) ( ) 2

Anderson’s Model - Enthalpy

E z Q

z z Q Q E

Mp

con f con f p con fC on f

M

( , )

( ) ( ) ,

E z Q

z z Q Q E

Mt

con f con f t con fC on f

M

( , )

( ) ( ) ,

Anderson’s Model - Entropy

TSt = Et - F

p z QW z Q

W z Qii

ii

( , )( , )

( , )

S z Q p z Q p z Qp i ii

( , ) ( , ) ln ( , )

Ss = St - Sp

Anderson’s Model - Sample

Anderson’s Model - Results

• Based on the simulation, the entropy increases during the adsorption.

• However, the strongest driving force is the reduction of the unfavourable interaction between the oil and the water layer that is reduced by the presence of the protein.

• Anderson recommends the use of this model for “short” single domain proteins (50 to 70 amino acids).