Biomedical Engineering Reference
In-Depth Information
t
,
Np
Pt
, “Current time”
……
C
l
, t
l
C
i
, t
i
C
j
, t
j
C
k
, t
k
Fig. 4
Schematic for the O(1) sorting approach of collision events by Paul. The linear array of
length N
g
corresponds to the time interval •t . The array is head-tail connected for repeated usage.
A pointer indicates the current time t
c
in units of •t =N
g
. Each collision time is inserted into the
array with respect the current time: ŒP
t
C
.t
t
c
/=.•t =N
g
/% N
g
. An element can hold more than
one event connected by a simple linked list. The next collision is obtained by advancing the pointer
until an occupied array is encountered, and choosing the event with the shortest collision time. By
carefully select •t and N
g
, the number of events in each element is small and the next collision can
be found by a simple bubble sort
within this time window are linked by a simple “linked list.” The next collision is
obtained by moving the current time pointer forward to the first nonempty element,
within which the soonest collision can be found by a simple “bubble sort” approach
if the number of events within each element is small. One can define •t and N
p
in
such a way that the number of events within each element is small.
We find that
when the system is large
.
10
5
to
10
6
atoms/,
sorting takes a significant amount of
CPU time (
20
%
of total computation time). In this case, Paul's sorting approach
greatly reduces the percentage of CPU time for sorting from
20
%
to only 1-2%
.
Therefore, by carefully selecting the size of the fine grid, reducing the number
of unnecessary square-root calculations, and adopting an O(1) sorting algorithm,
DMD simulation efficiency can be greatly improved over the traditional approach
[
9
,
36
], allowing for the simulation of biomolecular systems with realistic models
and force fields. Next, we describe recent developments in the DMD force field and
high-resolution molecular models
3
Development of DMD Force Field for Biomolecules
3.1
Hydrogen Bonds
The hydrogen bond interaction is the driving force for secondary structure for-
mation in proteins and nucleotides. In contrast to the model used in continuous
MD simulations, hydrogen bond interactions cannot be modeled as dipole-dipole
interactions in DMD simulations. Liu and Elliot [
39
,
40
] first proposed a hydrogen
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