56
A. Jayaraman et al.
All systems are first equilibrated for 10
8 time steps followed by a 10
7 time step
production run in which data is collected every 100,000 time steps. Also, for each
simulation of a given CLP sequence and fixed reduced temperature T
* , three trials
are performed with different initial conditions (i.e., positions and velocities of CLP
beads).
To quantify the hybridization state of the CLP triple helix, we define the ensemble
average fraction of inter-strand glycine (G) triplets that are intact, f intact . An interstrand G triplet refers to three G BB beads that are all part of separate strands and
are located at the same relative position along the triple helix. For example, the first
G BB bead in each CLP strand would constitute the first G triplet. Next, the triplet
is counted as intact if the maximum distance among all G BB beads is less than 3σ.
Therefore, a plot of f intact vs. reduced temperature, T
* , would describe the melting
curve of a given sequence, with the melting temperature defined as f intact = 0.5. A
f intact of 1.0 would correspond to a fully hybridized triple helix while a value of 0.0
would correspond to a fully melted triple helix. We also calculate the diameter of the
triple helix at every triplet along the triple helix; we do this by first calculating the
center of mass of a triplet of BB beads and denoting the maximum pairwise distance
between the triplet center of mass and each BB bead in a given triplet as the radius
of the triple helix at that triplet. Finally, we define the end-to-end distance of a CLP
strand as the magnitude of the vector connecting terminal BB beads along each CLP
strand. For all results (i.e., melting curves, end-to-end distances and diameters), error
bars show the standard deviation obtained from three trials.
3.4 Key Results
To investigate whether our CG model captures the correct, experimentally observed
melting trends, we perform simulations of (POG) n where n = 6, 7, 8, 12 and
14 to investigate the effect of CLP length on CLP melting. We also incorporate amino acid substitutions of the canonical (POG) triplet by including (PKG)
and (DOG) triplets for the following CLP sequences: (PKG) 4 (POG) 4 (DOG) 4
and (PKG) 4 (POG) 6 (DOG) 4 . Furthermore, we explore the effect of charge imbalances on CLP melting by performing simulations of (PKG) 3 (POG) 7 (DOG) 4 and
(PKG) 4 (POG) 7 (DOG) 3 . For all uncharged CLP sequences excluding (POG) 12 and
(POG) 14 , simulations are performed in a reduced temperature range from T
*
= 3.0 to
T
*
= 5.5. For (POG) 12 and (POG) 14 , simulations are performed in a reduced temperature range of T
*
= 3.0 to T
*
= 6.0. Also, for all charged CLP sequences (i.e.,
sequences containing K or D), simulations are performed in a reduced temperature
range of = 3.0 to T
*
= 5.0. These temperature ranges allow us to sample hybridized
and melted states of the CLP triple helix.
In Fig. 7, we show the CLP melting curves for both neutral and charged CLPs
and in Table 1. As shown in Fig. 7a and in Table 1, the melting temperature, T m , of
a CLP triple helix consisting strictly of (POG) repeat units increases as the length
of the peptide is increased from (POG) 6 to (POG) 14 . These results agree with the
A. Jayaraman et al.
All systems are first equilibrated for 10
8 time steps followed by a 10
7 time step
production run in which data is collected every 100,000 time steps. Also, for each
simulation of a given CLP sequence and fixed reduced temperature T
* , three trials
are performed with different initial conditions (i.e., positions and velocities of CLP
beads).
To quantify the hybridization state of the CLP triple helix, we define the ensemble
average fraction of inter-strand glycine (G) triplets that are intact, f intact . An interstrand G triplet refers to three G BB beads that are all part of separate strands and
are located at the same relative position along the triple helix. For example, the first
G BB bead in each CLP strand would constitute the first G triplet. Next, the triplet
is counted as intact if the maximum distance among all G BB beads is less than 3σ.
Therefore, a plot of f intact vs. reduced temperature, T
* , would describe the melting
curve of a given sequence, with the melting temperature defined as f intact = 0.5. A
f intact of 1.0 would correspond to a fully hybridized triple helix while a value of 0.0
would correspond to a fully melted triple helix. We also calculate the diameter of the
triple helix at every triplet along the triple helix; we do this by first calculating the
center of mass of a triplet of BB beads and denoting the maximum pairwise distance
between the triplet center of mass and each BB bead in a given triplet as the radius
of the triple helix at that triplet. Finally, we define the end-to-end distance of a CLP
strand as the magnitude of the vector connecting terminal BB beads along each CLP
strand. For all results (i.e., melting curves, end-to-end distances and diameters), error
bars show the standard deviation obtained from three trials.
3.4 Key Results
To investigate whether our CG model captures the correct, experimentally observed
melting trends, we perform simulations of (POG) n where n = 6, 7, 8, 12 and
14 to investigate the effect of CLP length on CLP melting. We also incorporate amino acid substitutions of the canonical (POG) triplet by including (PKG)
and (DOG) triplets for the following CLP sequences: (PKG) 4 (POG) 4 (DOG) 4
and (PKG) 4 (POG) 6 (DOG) 4 . Furthermore, we explore the effect of charge imbalances on CLP melting by performing simulations of (PKG) 3 (POG) 7 (DOG) 4 and
(PKG) 4 (POG) 7 (DOG) 3 . For all uncharged CLP sequences excluding (POG) 12 and
(POG) 14 , simulations are performed in a reduced temperature range from T
*
= 3.0 to
T
*
= 5.5. For (POG) 12 and (POG) 14 , simulations are performed in a reduced temperature range of T
*
= 3.0 to T
*
= 6.0. Also, for all charged CLP sequences (i.e.,
sequences containing K or D), simulations are performed in a reduced temperature
range of = 3.0 to T
*
= 5.0. These temperature ranges allow us to sample hybridized
and melted states of the CLP triple helix.
In Fig. 7, we show the CLP melting curves for both neutral and charged CLPs
and in Table 1. As shown in Fig. 7a and in Table 1, the melting temperature, T m , of
a CLP triple helix consisting strictly of (POG) repeat units increases as the length
of the peptide is increased from (POG) 6 to (POG) 14 . These results agree with the