MOLECULAR MODELING AND MOLECULAR MECHANICS 169
complex^26 (PDB: 1RIE) were used for equilibrium bond lengths, angles, and
torsional angles. A method similar to that used for calculating the heme charge
distribution (Gaussian - 94 at the Hartree – Fock level with a 3 - 21G basis set),
with further manipulation to include 4 - methyl - imidazole (representing histi-
dine) and a methylthiolate (representing cysteine), resulted in a charge distri-
bution set for the [Fe 2 S 2 ] cluster presented in Table 2 of reference 22. Any
missing force constants for the [Fe 2 S 2 ] cluster and for his and cys groups were
derived from existing parameters for similar structures in CHARMM22 and
CHARMM19 force fi elds.
The protein structure was prepared in the following manner. Atomic coor-
dinates from the cytochrome bc 1 complex from chicken heart mitochondria
(PDB: 1BCC and 3BCC) were used with hydrogen atom coordinates added
using the HBUILD feature of X - PLOR.^27 The bc 1 complex structure with
stigmatellin bound at the Q 0 site (see Section 7.6.2 and Figure 7.30 , PDB:
3BCC) was used to build a model in which the reduced [Fe 2 S 2 ] cluster is in
the proximal position (closer to heme b L , its redox partner in cytochrome bc 1 ).
The hemes b L , b H , and c 1 were modeled in their oxidized forms by assigning
the appropriate charge distributions to each. Stigmatellin was then removed
from the model. (Figures 1 and 2 of reference 22 illustrate the heme and [Fe 2 S 2 ]
cluster positions clearly.) The resulting structure, comprised of 32,310 atoms,
was refi ned by 500 steps of energy minimization of hydrogen atoms, followed
by 1500 steps of minimization of all atoms.
Next, water molecules were placed in the protein following a modifi ed
procedure of the software program DOWSER.^28 After use of the HBUILD
routine and an additional 500 steps of energy minimization, 121 water
molecules were selected and refi ned into the structure in 500 more energy
minimization steps. This fi nal cytochrome bc 1 complex, including internal water
molecules, was used in further modeling. The reference 22 researchers also
modeled a lipid bilayer to mimic the in vivo position of cytochrome bc 1 in a
membrane bilayer. A 3 - Å layer of solvent water was energy - minimized into a
120 - Å × 155 - Å × 35 - Å box; also, the protein, in its membrane bilayer, was posi-
tioned in the water solvent box so that the lipid bilayer was bounded by a
solvent layer on either side. Additional solvent was modeled to interact with
the protein surrounding heme c 1. Figure 6 of reference 22 visualizes the fi nal
model.
Now the model can be subjected to the steered molecular dynamics simula-
tion (SMD). The researchers applied external forces generating a torque to
induce rotation of the mobile head of the ISP about its rotation axis as
described in the initial algorithm. In the SMD simulation, the forces were
exerted on theα - carbon atoms of the ISP residues 73 – 196. As the forces are
applied, the system must overcome potential energy barriers, such as the
breaking of a hydrogen bond between the ISP and another subunit. Peaks are
generated that correspond to the energy minima along the ISP rotation path.
The SMD trajectory was analyzed by calculating the torque applied to each
of the restrainedα - carbon atoms relative to the assumed axis of rotation and