Chemistry Reference
In-Depth Information
7.3.2 The HP Model with an Attractive Surface
We have also examined the behavior of several HP sequences when a surface is
introduced. As an example we have performed Wang-Landau simulations for a
rather short sequence, a 48mer, in a 3D space both with and without a surface field.
In our simulations, one of the 48mers proposed in [
19
] was used (also see Table
7.1
).
It is merely an artificial sequence originally designed to test folding algorithms and
so it might not have direct correspondence to real proteins. We have compared the
results obtained from it with those from other HP sequences and found that this
48mer has already captured general behaviors. Nevertheless, it should be noted that
the details of the properties still vary from sequence to sequence.
Common inorganic substrates include metals (Ag, Au, Pd, Pt), oxides (CaCO
3
,
Cr
2
O
3
,Fe
2
O
3
,SiO
2
, ZnO) or semiconductors (GaAs, ZnS). Their adsorption prop-
erties are so well studied that polypeptide sequences can even be tailor-made to
bind with a particular material [
51
]. Substrates made with different materials have
various surface properties. When a protein interacts with a substrate, its surface can
be attractive, neutral, or repulsive to different amino acids due to, for examples, the
presence of charges, acidity (or basicity), and hydrophobicity. Handling charges or
acidity is beyond the scope of the HP model, but we can still take the hydrophobicity
of the surface into account and identify three types of attractive surface fields for the
HP model. The first surface attracts both hydrophobic (H) and polar (P) monomers
with the same magnitude. The second one is hydrophobic, i.e., it only attracts H
monomers. The third one is polar, i.e., it only attracts P monomers. Here, we only
consider the first type of surface for illustrative purpose.
In the absence of a surface field the 48mer folds into a compact globule as shown
in Fig.
7.4
. With the peripheral polar monomers surrounding a hydrophobic core,
this structure maximizes the number of H-H bond pairs so as to attain the minimum
energy
E
min
=−
34. Equivalently, 34 H-H bond pairs are formed. The simulation
found the lowest energy and its corresponding states without difficulties, and the
density of states was determined in the energy range
.
In the limiting case where the surface attraction is infinite, on the other hand, the
HP polymer is completely attached to the surface and forms a 2D structure that is
very different from the 3D native state. Figures
7.5
and
7.6
show two typical ground
state structures of energy
E
min
=−
[−
34
,
0
]
21 (i.e., there are 21 H-H bonds). The density
of states was also determined with energies ranging from zero down to this ground
state energy. A hydrophobic “core” is still observed in this case, but it does not
remain as intact as in the case of the 3D free space. Figure
7.5
represents some con-
figurations that still retain marginally the single hydrophobic core, although it has
to be forced into a 2D structure. Some configurations might have the hydrophobic
core broken into pieces as seen in Fig.
7.6
. This suggests that with the presence of a
strong attractive surface field, a protein would be deformed into a shape that is very
different from its native one. Whether the protein in an adsorbed condition would
still retain its function is not guaranteed.
After obtaining the density of states, the specific heat is then calculated. In
Fig.
7.7
, the two-step acquisition of the ground state is again observed as for the
