Bridging the Gap Between Theory and Experiment to Derive a Detailed Understanding of Hammerhead Ribozyme Catalysis - Progress in Molecular Biology and Translational Science - page 47

3.3.1 Free-energy profile
To shed light on the HHR reaction mechanisms of the phosphorylation and
protonation steps in which the binding mode of Mg 2 þ continuously
changes, we explicitly simulated the enzymatic reactions by generating a
series of six 2D PMF or free-energy profiles. Three of these 2D PMFs
were combined to form a course-grained 3D PMF (the coarse-grained
third dimension representing the coordinate associated with the Mg 2 þ -
binding mode).
Before the QM/MM simulations, we first performed classical MD sim-
ulations (i.e., the whole system was described by an MM force field) to fur-
ther equilibrate the entire system for more than 1 ns from the structure
which had already been equilibrated for more than 2 ns in the previous clas-
sical MD simulations. 75,76 Next, a series of umbrella samplings 127 using
QM/MM MD simulations were carried out to span the entire range of
the 2D or 3D reaction coordinates.
3.3.2 Enhanced sampling efficiency
Harmonic biasing potentials along each reaction coordinate were applied
with a force constant ranging between 20 and 45 kcal/mol/ ˚ 2 in accordance
with different regions of the configuration samplings. The choices of the
force constants and the number of windows were made to ensure sufficient
overlap of the probability distributions with neighboring windows. Follow-
ing the initial 1 ns equilibration in classical MD simulations, each window
was further equilibrated with the QM/MM potential for more than 5 ps
after the system was equilibrated in the adjacent windows. Subsequently,
a 10 ps of QM/MM configuration sampling was performed in each
window.
3.3.3 Weighted histogram analysis method
Finally, the weighted histogram analysis method 128,129 was used to generate
unbiased PMFs as a function of different sets of reaction coordinates by com-
bining all the sampled configurations. All the configurations were collected
at every MD time step in a bin size of 0.1 ˚ except for the third reaction
coordinate in the 3D PMF. In the 3D PMF, configurations along z 3 were
collected in a bin size of 0.4 ˚ at every time step. After determining the
MFEP from the 2D PMF profiles, we simulated a series of 1D PMFs follow-
ing the MFEP, in which 100 ps sampling was performed in each window
and the bin size of collecting configurations is 0.01 ˚ .