Simulating G Protein-Coupled Receptors in Native-Like Membranes: From Monomers to Oligomers - Methods in Cell Biology - page 74

membrane due to the GPCR insertion. This philosophy is conceived in a recent
model known as three-dimensional continuum MD (3D-CTMD) ( Mondal et al.,
2011 ). The 3D-CTMD model is a generalization of conventional continuum models
( Huang, 1986; Nielsen et al., 1998; Owicki &McConnell, 1979; Owicki et al., 1978 )
that allows for the consideration of radial asymmetries, needed for systems with sev-
eral TM segments such as GPCRs. In addition, the 3D-CTMD model is able to go
beyond the assumption of strong hydrophobic coupling ( Huang, 1986; Nielsen &
Andersen, 2000; Nielsen et al., 1998; Owicki & McConnell, 1979; Owicki et al.,
1978 ), which assumes a total alleviation of the residual mismatch.
The 3D-CTMD model has been implemented in the recently developed
CTMDapp software that provides a user-friendly interface ( http://memprotein.
org ) . The input required by the CTMDapp is an equilibrated MD trajectory file con-
taining those atoms used for measuring membrane thickness (i.e., P or C2 atoms). As
for most membrane-protein simulation analyses, the membrane normal needs to be
previously aligned to the z -axis, whereas reference coordinates, or zero point, must
be set to the center of mass of the protein. The initial step of the procedure consists in
the calculation of the MD-averaged deformation profile u out of the time-averaged
leaflets fitted in a grid ( Fig. 4.3 ). Thereafter, the CTMDapp asks the user for a
PDB file containing the coordinates of the protein at any point of the simulation
in order to accurately define membrane-protein boundaries. At this point, the bound-
ary conditions needed for the optimization procedure are already created. Once the
user sets the aforementioned empirical moduli according to the composition of
the membrane, the setup is finished and the optimization procedure starts. To check
the convergence of the calculation, several extraiterations can be requested after the
optimization procedure is finished. Then, the self-consistently optimized deforma-
tion profile u and DG def are finally obtained ( Fig. 4.3 ). The preparation of all inputs
needed in this pipeline can be straightforwardly performed by a visualization
software such as VMD.
The complete adaptation of the membrane in order to avoid unfavorable lipid-
protein contacts is not always possible. In particular, this adaptation is nearly
unreachable for complex TM proteins such as GPCR-membrane systems. GPCRs
are proteins with a minimum of seven adjacent TM segments of different lengths.
The complete alleviation of hydrophobic-hydrophilic contacts for all segments
would likely need a huge amount of energy devoted to severe local deformations
of the membrane. Thereby, the so-called residual mismatch is the remaining set
of unfavorable interactions occurring due to hydrophobic-hydrophilic contacts in
the equilibrated protein-membrane system.
According to the aforementioned continuum formulation, the penalty energy
due to the membrane-protein remodeling and the residual mismatch should be op-
timal in the equilibrium state of the system. Only recently, the quantification of the
residual mismatch in GPCR-membrane systems has been performed ( “Interactions
of the cell membrane with integral proteins,” n.d.; Mondal et al., 2011; Mondal,
Khelashvili, Shi, & Weinstein, 2013 ) by determining the accessible surface area
involved in unfavorable hydrophilic-hydrophobic (i.e., exposed surface area)