Automated computation of a low energy pathway for the complex conformational switch of Ras p21.

Frank Noe, Fabian Ille, Jeremy C. Smith & Stefan Fischer*

Proteins, vol. 59, p. 534-544 (2005).


The computation of Minimum Energy Paths (MEP) in proteins is an approach for gaining insight into conformational transitions that are too slow to be observed with unconstrained molecular dynamics simulations.  MEPs have the advantage to provide the energy barrier of the rate-limiting step(s), allowing to discriminate between different paths.
Finding low-energy MEPs for complex transitions, involving rearrangements of the backbone fold or the repacking of buried side-chains, was hitherto unfeasible in a reliable manner. This problem is solved by combining a new procedure for generating an initial guess of the path with the Conjugate Peak Refinement (CPR) method.
CPR is robust method that can find MEPs for transitions with hundreds of saddle-points along the path. It does so by refining an initial guess of the path, for instance the linear interpolation between the Cartesian coordinates of the reactant and product conformations.  In complex transitions, such a simple initial path is likely to lead to unphysical behavior, like the crossing of bonds. We avoid such behavior by building an initial path based on a combination of interpolations in Cartesian and internal coordinates. This allows complex MEPs between given reactant and product states to be found rapidly and automatically, in a manner unbiased by external driving constraints.
The approach is tested on the conformational switch in Ras-p21. This conformational transition involves some partial unfolding and re-folding, a process for which a multitude of pathways are likely to co-exist and for which a single MEP is not a meaningful description. However, this transition requires some sterically demanding re-arrangements, thus exercising the ability of a method to find low-energy pathways free of structural aberrations.  The present approach successfully achieves this, since a path is found with a rate-limiting barrier of only 24 kcal/mol.
The two end-states:  Ras p21 is a crucial signaling-protein involved in regulating cell reproduction. Upon hydrolysis of the bound GTP, the protein undergoes a transition from its GTP-bound form ("reactant", in yellow) to its GDP-bound form ("product", in red).  The predominantly mobile regions are the switch I and switch II elements.  The gray region is very similar in the two states, and thus can be held fixed during the computation of the path. Methods to identify MEPs rely on the local optimization of an initially guess for the path. With most initial guesses, these optimization techniques tend to get stuck in local solutions, producing paths with unrealistically high energy barriers. Such paths typically include unphysical transition-states, like the interpenetration of bonds (here of an Arg and a Thr side-chain, top panel), or the passage of a water molecule through an aromatic ring (bottom panel).


To obtain an initial guess that can be optimized to a MEP with low barriers, we used a combined interpolation technique, interpolating the coordinates of backbone atoms in Cartesian and the coordinates of side-chain atoms in internal coordinates. In addition, the side-chain bonds are shrunken in the initial path, resulting in miniature side-chains which are unlikely to produce clashes or interpenetrations in the initial path. These unnaturally short bonds expand to their normal size in the course of CPR's optimization procedures.

After the first CPR refinement, the MEP involves no structural deformations, but its rate-limiting energy barrier is still high (~100 kcal/mol).
To reduce this, CPR is run again between local minima adjacent to high barriers. The new path sections thus produced replaced the old ones. Following this strategy, a MEP with a rate-limiting barrier of less than 40 kcal/mol is found.  Repeating this procedure yields a path with a rate-limiting barrier of only 24 kcal/mol. Enthalpic barriers in the order of 20-40 kcal/mole can be compensated by entropic effects, thus it is possible that a realistic pathway has been identified.  The final path has more than 100 transition-states (saddle-points), due to the large number of local rearrangements that are necessary for side-chain re-orientations and for backbone re-folding, each of which involves at least one saddle-point.

Molecular movies:

Showing the motion of the backbone, as it unfolds and then re-folds the two Switch regions.
The reactant (green) and product (red) structures are shown throughout the movie to get a feeling of the structural progress (yellow). One can distinguish phases of the transition:  A) Unfolding of the Helix in Switch II, B) conformational change of Switch I, C) conformational change of Switch II. The Mg++ is shown as green sphere, the GDP as balls&sticks.
Download the movie , 1.7Mb

Showing the motion of the side-chains, which one after the other undergo their own re-orientation.
Side-chains are colored according to their instantaneous energy: brighter colors correspond to higher energies (Dark blue: energy <= 0White: energy >= 30).
The energy assigned to each residue at each frame is computed by its self-energy plus half the interaction energy with all other residues (i.e. these energies add up to the total potential energy).  The difference between this energy in a given frame and in the end-states gives the instantaneous energy.
Download the movie , 3.5Mb.
Same movie, but very fast, 2Mb.

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