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Modeling Proteins at an Oil / Water Interface
Chemistry 699.08
Final Presentation
Patrick Brunelle
December 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.
For this study, beta-casein was chosen because of its
abundance in milk.
Beta-casein could be consider as a near random chain of
209 amino acids.
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
Adsorption
Energy (KT)
E(np,oil)
E(p,oil)
E(c+,oil)
E(c-,oil)
+0.5
-1.0
-10.0
-10.0
Adsorption
Energy (KT)
E(np,aq)
E(p,aq)
E(c+,aq)
E(c-,aq)
-1.0
0.0
+5.0
+5.0
Solvent Change (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)
-1.0
0.0
+10.0
+10.0
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
N
H ({sI },{rI }) 

I ,J
BIJ  (rI  rJ )
) = 1 neighbouring
amino acids
) = 0 otherwise
Bij is the matrix element of amino acid i and j
from the matrix of Miyazawa and Jernigan.
BUT
The solvents are approximated:
water is taken as histidine
oil is taken as glycine
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
conf
 z) (Qconf  Q)
conf
*(x) = 1 for x=0
*(x) = 0 otherwise
Each simulation is run for about 2 x 109 steps.
40 000 conformations are used.
Anderson’s Model - Bias Potential
V   ( z  zb )
“Biased” free energy:
Free Energy:
2
"=6.67
F '( z, Q)   T ln Z ( z, Q)
F ( z, Q)   T ln Z ( z, Q)   ( z  zb ) 2
Anderson’s Model - Enthalpy
M
  (z
E p ( z, Q) 
conf
Conf
M
M
  (z
E t ( z, Q) 
 z) (Qconf  Q) E p ,conf
conf
 z) (Qconf  Q) E t ,conf
Conf
M
Anderson’s Model - Entropy
TSt = Et - F
pi ( z, Q) 
Wi ( z, Q)
 W ( z , Q)
i
i
S p ( z, Q)    pi ( z, Q) ln pi ( z, Q)
i
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).