Behaviour of velocities in protein folding events

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Behaviour of velocitiesinprotein folding events

• Aldo Rampioni, University of Groningen
• Leipzig, 17th May 2007

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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

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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

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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)
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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
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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.
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Cluster algorithm
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Choice of the cutoff
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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 gt 0.4 19 21
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Central structures of the five most populated
clusters
Blue time interval 10 ps Red time interval 50 ps
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Time series of cluster
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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
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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?

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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.
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Definiton of folding event
VF nlt3
F 2ltnlt7
S 7ltn
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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
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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
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Covariance matrices of the velocities of the
backbone atoms between t0-500 and t0500 ps
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RMSD
RGYR
PC1
PC2
CV1
CV2
RGYR
PC1
PC2
CV2
RMSD
CV1
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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
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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 nowin
Rampioni!!!