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…

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 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 4 The structure with the highest number of neighbours was the centre of the first cluster. 1 Structures 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. 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.

Choice of the cutoff

Cluster numberTime interval 10 ps (5000 frames) Time interval 50 ps (1000 frames) Number of cluster with a population > 0.4% 1921 Cluster analysis over 50 ns

Central structures of the five most populated clusters Blue time interval 10 ps Red time interval 50 ps

Time series of cluster

Transitions among the 5 most populated clusters over 50 ns 12*3*45 10/00/0155/330/00/00/00/062/17 2*157/360/00/00/00/00/00/00/00/0 3*0/00/00/00/00/00/00/00/00/00/0 40/00/00/00/00/00/00/00/00/00/0 562/160/00/00/10/10/10/10/00/0 * 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<7S: 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 t 0 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 t and t ps

CV2 RMSD R GYR PC1 PC2 CV1 RMSD R GYR PC1PC2 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

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