Biology Reference
In-Depth Information
upon interacting with proteins and, on the other hand, the residual mismatch due to
any incomplete adaptation to the membrane in order to avoid highly energetic or un-
favorable contacts, that is, hydrophobic-hydrophilic contacts. The purpose of this
section is to illustrate how to assess such hydrophobic mismatch, in particular for
the simulation of GPCR-membrane complexes.
The consideration of the membrane as an elastic continuum medium has been
widely used (
Choe, Hecht, & Grabe, 2008; Huang, 1986; Mondal et al., 2011;
Nielsen et al., 1998
) for the quantification of membrane remodeling due to the as-
sembly of TM proteins. This continuummedium deforms according to several forces
specified by means of empirical moduli that depend on the composition of the mem-
brane. The free energy cost of such deformation is described to second order as a
surface integral,
(
!
)
d
O
2
þ
2
ð
2
u
2
u
1
2
K
a
d
0
K
c
@
x
2
þ
@
@
u
@
u
4
u
2
DG
def
¼
þ
y
2
C
0
þ a
@
@
@
x
@
y
O
where
K
a
and
K
c
stand for the compression-extension and the splay distortion mod-
uli, respectively;
C
0
stands for the monolayer spontaneous curvature and
for the
surface tension;
O
represents the membrane area; and
u
stands for the deformation
function per bilayer leaflet, which is defined locally as
a
1
2
dx
ux
ðÞ¼
;
y
ð
ðÞ
;
y
d
0
Þ
without assuming a radial symmetry and where
d
(
x
,
y
) and
d
0
are the local thickness
and the bulk bilayer thickness, respectively.
The conventional elastic models, which have been devoted to the study of
membrane-single TM helix systems, assume a radial symmetry of the system
(
Huang, 1986; Nielsen & Andersen, 2000; Nielsen et al., 1998; Owicki &
McConnell, 1979; Owicki, Springgate, & McConnell, 1978
). The usual procedure
to assess these systems starts with a self-consistent minimization of the
G
def
with
regard to the deformation function
u
and based on several initial boundary conditions
(i.e.,
u
at the membrane-protein boundaries,
u
△
0 at the unperturbed
regions of the membrane, etc.). Therefore, only a few pieces of information are
needed to complete the assessment. In this line, a recent implementation enables
the inclusion of asymmetries in the description of a membrane-protein boundary
of singly charged TM segments (
Choe et al., 2008
). However, an adequate applica-
tion of the elastic continuum theory to membrane-GPCR systems requires a more
detailed description of that boundary due to the anisotropic character of the mem-
brane deformation at the membrane-protein contour. Nowadays, this issue has been
solved since the deformation function
u
and the necessary boundary conditions can
be obtained from MD trajectories. However, the deformation function
u
obtained
from MD simulations has been claimed to be too noisy for an accurate evaluation
of
DG
def
(
Mondal et al., 2011
). Thereby, the combination of MD with continuum
elastic models has made possible the accurate study of the remodeling of the
!
0 and
r
u
!
