Behaviour of velocitiesin

protein folding events

Aldo Rampioni, University of GroningenLeipzig, 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…

• Small peptide fast simulations

• 50 ns sufficient to generate an equilibrium distribution (multiple folding-unfolding events

good statistics)

ß-heptapeptide

Figures from Daura, X et al.PROTEINS: Struc. Func. Gen. 34 (1999)

Simulation conditions

• 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)

Ten 50-ns MD simulations were performed using:

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

4The structure with the highest number of neighbours was the centre of the first cluster.

1Structures were extracted from the trajectories at regular time intervals for analysis

2

For each pair of structures the RMSD was calculated after fitting the backbone atoms of residues 2 to 6. 6

This process was iterated until all structures were assigned to a cluster.

3Using the criterion of similarity of two structures RMSD<cutoff, the number of neighbours for each of the structures in the initial pool was determined.

5All the structures belonging to this cluster were removed from the pool.

Choice of the cutoff

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 15Number of cluster with

a population > 0.4%19 21

Cluster analysis over 50 ns

Central structures of the five most populated clusters

1-1

2-3

3-2

4-4

5-5

Blue time interval 10 psRed time interval 50 ps

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

* After switching 2 and 3 in the cluster numbering of the set got using 50 ps time interval

The total number of transitions among all clusters is 1224/322

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

Methodsj = 1,…,N denotes the atom coordinatek = 1,…,T denotes the timei = 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

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Covariance matrices of the velocities

of the backbone atomsbetween t0-500 and t0+500 ps

CV2

RMSD

RGYR

PC1

PC2

CV1

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 aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Prof. Alan Mark, University of Queensland, Australia

Acknowledgments

Dr. Tsjerk Wassenaar, University of Utrecht, The Netherlands

A particular thank to Drs. Magdalena Siwko now…in Rampioni!!!

28th of April, Zlotoryja, Poland