Generation, comparison and merging of pathways Generation, comparison and merging of pathways between protein conformations: Gating in K-between protein conformations: Gating in K-

channelschannels**

Angela Enosh1, Barak Raveh1,3, Ora Schueler-Furman3, Dan Halperin1 and Nir Ben-Tal21 School of Computer Science, Tel-Aviv University, Israel 2 Department of Biochemistry, Tel-Aviv University, Israel 3 The Hebrew University, Hadassah Medical School, Israel

*accepted for publication in Biophys. J.

Faster Alternative to Molecular

Dynamics? Molecular dynamics is used to predict molecular motion based on first principle physics, but it is slow and cannot generate a very large number of pathways, hence a faster alternative is needed.

Algorithms for Predicting Motion in KcsA

A Putative Three-Phase Secure Mechanism (I) unlock(I) unlock (II) open(II) open (III) relock(III) relock

Robotic Motion Planning

Industrial robot arm: joints, links and degrees of freedom (e.g. elbow)

Peptide chain: joints, links and degrees of freedom ()

From Robotics to Biology:From Robotics to Biology:

Rapidly-exploring Random Trees (RRT): Rapidly-exploring Random Trees (RRT): finding your way among obstaclesfinding your way among obstacles

Pathway Optimization

Similarity of Molecular Pathways – Similarity of Molecular Pathways – String MatchingString Matching

Pathways Hybridization: optimal pathway Pathways Hybridization: optimal pathway from suboptimal segmentsfrom suboptimal segments

Finding ShortcutsChoosing among sub-optimal alternatives

(a) An intracellular perspective of the KcsA channel in its closed conformation (grey cartoon), with the location of the C-alpha atom of residue V155 along the pathway marked in spacefill. The optimal pathway comprises the following phases: Brownian motion (grey), Phase I where the closed conformation is unlocked (cyan), Phase II where the gate opens (purple) and Phase III where the channel is locked in its open conformation (red).

(b) The energy profile of the pathway. The pathway from the closed conformation to the (model-structure of the) open conformation (step 23) involves crossing an energy barrier (step 12) which is a transition step between phases I and II.

(c,d) HOLE analysis along the pathway. (c) The magnitude of the radius along the pore-axis (Z). The green and red curves were obtained using the open and closed conformations, and the blue curves correspond to intermediate conformations (d) The green and red curves mark the changes of the pore radius at Z=35Å and Z=23Å along the pathway, congruently. The black curve marks the changes in the pore radius at the minimal constriction. It is noteworthy that the depth of the minimal constriction along the Z-axis changes along the motion pathway.

Integration into Rosetta Modeling Package Rosetta is a comprehensive framework for different molecular modeling tasks which enhances state of the art energy function, optimization and sampling protocols.

Ion Channels GatingIon Channels Gating

gate openinggate opening

A general framework for generating and optimizing A general framework for generating and optimizing collision-free and low-energy motion pathwayscollision-free and low-energy motion pathways between protein between protein conformations while considering a wide range of degrees of freedom involved in the motionconformations while considering a wide range of degrees of freedom involved in the motion..

(a)

Gate region

(c)

Rad

ius

Selectivity filter

Z-axis

(b)

Trajectory step

Phase I Phase II Phase III

En

ergy

Rad

ius

Phase II Phase IIIPhase I

Trajectory step

(d)

extracellular

membrane

(a) (b)

90o 90o

(a) The X-ray crystal structure of KcsA in its closed state was taken as the initial conformation.(b) A model-structure of the open conformation of KcsA, derived from the known X-ray structure of KvAP, was taken to be the goal conformation. The four monomers of the KcsA are colored blue, pink, pale cyan and cyan.

http://vertrees.org/ by Jason Vertrees

Transmembrane proteins form pumps & channels that control transport of ions and metabolites across the membrane. One of the challenging tasks is to define the molecular details of these protein’s mechanisms.

Biggin, P. C. and M. S. Sansom (2002) Biophys J. 83:1867-1876.Enosh, A., S. J. Fleishman, N. Ben-Tal and D. Halperin (2007) Bioinformatics 23:e212-e218.

Kirillova, S., J. Cortes, A. Stefaniu and T. Simeon (2008) Proteins 70:131-143.Shimizu, H., M. Iwamoto, T. Konno, A. Nihei, Y. C. Sasaki and S. Oiki (2008) Cell 132:67-78.

Shrivastava, I. H. and I. Bahar (2006) Biophys. J. 90:3929-3940.Tikhonov, D. B. and B. S. Zhorov (2004) Biophys J. 87:1526-1536.

Problem Definition