Behaviour of velocities
in
protein folding events
Aldo Rampioni, University of Groningen
Leipzig, 17th May 2007
Plan of the talk
• Questions that we want to address
• System studied: the ß-heptapeptide
• Definition of folding event
• Methodology used for the analysis
• Results of the analysis
• Final remarks
Questions that we want to address:
Do velocities show any correlation or
cooperative behaviour during the
protein folding event?
Can this information be used to detect
when the folding event occurs?
Imagine being an amino-acid…
ß-heptapeptide
• Small peptide  fast
simulations
• 50 ns sufficient to generate
an equilibrium distribution
(multiple folding-unfolding
events  good statistics)
Figures from Daura, X et al.
PROTEINS: Struc. Func. Gen. 34 (1999)
Simulation conditions
Ten 50-ns MD simulations were performed using:
•
GROMACS 3.2.1 software package
•
force field GROMOS96 43a1
•
The end groups were protonated -NH3+ and –COOH
•
Solvent: methanol (962 molecules) [model B3 in J.Chem.Phys.112 (2000)]
•
Temperature 340 K
•
Time step of 2fs
•
Twin-range cutoff of 0.8/1.4 nm for all non-bonded interactions
•
Initial structure: helical fold (shown in figure)
Five 100-ns MD simulations:
Same conditions as above, but starting from an unfolded conformation
Definition of folding event
(first trial)
We used a criterion of similarity (RMSD) to group
different structures (cluster algorithm) and build a
dynamics on grapho. It is natural to define “folding
event” each jump to the cluster representative of
the folded structure.
Cluster algorithm
1
Structures were extracted
from the trajectories at
regular time intervals for
analysis
4
The structure with the highest
number of neighbours was the
centre of the first cluster.
2
For each pair of structures
the RMSD was calculated
after fitting the backbone
atoms of residues 2 to 6.
3
Using the criterion of similarity
of two structures RMSD<cutoff,
the number of neighbours for
each of the structures in the
initial pool was determined.
5
All the structures belonging
to
this
cluster
were
removed from the pool.
6
This process was iterated until all
structures were assigned to a
cluster.
Choice of the cutoff
Cluster analysis over 50 ns
Cluster number
Time interval 10 ps
(5000 frames)
Time interval 50 ps
(1000 frames)
1
2824
567
2
354
66
3
323
65
4
182
21
5
91
15
Number of cluster with
a population > 0.4%
19
21
Central structures of the five most populated clusters
3-2
1-1
2-3
Blue time
interval 10 ps
Red time
interval 50 ps
4-4
5-5
Time series of cluster
Transitions among the 5 most
populated clusters over 50 ns
1
2*
3*
4
5
1
0/0
155/33
0/0
0/0
62/17
2*
157/36
0/0
0/0
0/0
0/0
3*
0/0
0/0
0/0
0/0
0/0
4
0/0
0/0
0/0
0/0
0/0
5
62/16
0/0
0/1
0/1
0/0
The total number of transitions among all clusters is 1224/322
* After switching 2 and 3 in the cluster numbering of the set got using 50 ps time interval
Limits of this definition
• The representative structure of cluster
number 2 and 5 are very close to the
folded structure, i.e. the jump from those
clusters to the cluster number 1 is the last
step of different folding paths
• How to consider jumps to cluster number
1 followed by an immediate jump out?
Definition of folding event
(second trial)
We simply used a criterion of similarity (RMSD) to
the folded structure, introducing two thresholds:
below the lower one we consider the peptide folded,
above the higher we consider the peptide unfolded.
We define “folding event” every time the RMSD pass
from values higher than the upper threshold to
values lower than the bottom threshold.
Definiton of folding event
VF: n<3
F: 2<n<7
S: 7<n
According to this definition we extracted from 1 s
simulation:
49 VERYFAST folding events
42 FAST folding events
40 SLOW folding events
These events have been aligned choosing as t0 the
last time the RMSD is above the higher threshold
Methods
j = 1,…,N denotes the atom coordinate
k = 1,…,T denotes the time
i = 1,…,M denotes the trajectory
is the ith trajectory
is a slice of the matrix at time k
the average is over the trajectories
Covariance
matrix
at time k
Time
autocovariance
Covariance matrices of the velocities
of the backbone atoms
between t0-500 and t0+500 ps
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
RMSD
RGYR
PC1
PC2
CV1
CV2
RMSD RGYR
PC1
PC2
CV1
CV2
If
the
principal
components
of
motions in cartesian space do not
correlate with the order parameter
(RMSD), there is no hope to see
something looking at velocities in
cartesian space
Thus we chose to investigate some
internal degree of freedom such as
torsional angles
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Acknowledgments
28th of April, Zlotoryja, Poland
Dr. Tsjerk Wassenaar, University of Utrecht, The Netherlands
Prof. Alan Mark, University of Queensland, Australia
A particular thank to Drs. Magdalena Siwko now…in Rampioni!!!