The low energy reactant and product conformations
of a reaction or conformational change can be thought to be located at
the bottom of two "basins" on a surface representing the energy landscape
of the macromolecule. The path that connects these two basins by
traveling along the "valleys" of the surface and going over the "passes"
(which are saddle-points on the surface and correspond to the transition
states) is commonly referred to as the **minimum energy path (MEP),**
also known as the intrinsic path (because it is close to the average over
the most probable paths).

Many methods for finding the minimum energy path have been proposed.
One method that is robust and fast enough to find
paths in macromolecules is called **Conjugate Peak Refinement (CPR)**.

The contour lines show the two-dimensional energy landscape of a hypothetical molecule (with minima at R, I, P). An

Each CPR-cycle (cycles are numbered in blue) automatically adds a path
intermediate (**.**) to the highest-energy region
of the path (the '**peak**') and optimizes it by a conjugate minimization
(**->**) so that it lies closer to the bottom of the energy-valley (**X**).
This new point is then incorporated into the path by the two adjacent interpolation
segments (**- - -**). Repeating this heuristic procedure
yields a final path (**--**) that follows
the valley of the energy surface and goes through the exact **saddle-points**
(S1 ,S2), close to the minimum energy path
(shown in green).

The real energy surface of a protein is very high-dimensional and has
many MEPs. On such surfaces, an alternative outcome of a CPR-cycle
is the **removal** of the highest path-intermediate (**X**) from
the path, which is then rebuild between the adjacent intermediates (this
is a very frequent outcome for a CPR-cycle, but cannot be shown here, since
it does not happen on simple 2D-surfaces). The advantage of removal/rebuilding
is that high energy barriers are often circumvented early during the path-refinement,
resulting in final paths with **globally lower** barriers.

CPR finds the minimum energy path **without applying any constraint**
to drive the reaction. It does so by starting from an initial guess
of the path, to which it adds a sufficient number of intermediate conformations
and optimizing them until they lie in the "valleys" and until the highest-energy
conformers coincide with the saddle-points.

The resulting intrinsic path constitutes a **smooth 'movie' **of
the process, even though every atom is allowed to move independently.
It shows only the motions that are essential to the transition, unlike
trajectories created by other methods used to accelerate slow conformational
changes, such as targeted molecular dynamics.

Because no artificial strain is created, CPR yields meaningful and easily
interpretable **energy barriers** along the path. The latter is
what distinguishes CPR from methods that determine pathways by some form
of coordinate-driving. In these, the transition-states often are
not identified reliably and thus the energy barriers along the paths are
not known, making it difficult to assess the probability of a path.

To find MPE with low barriers for very complex conformational transitions
in proteins, it is not always possible to use an initial path built by
simple linear interpolation in Cartesian coordinates (as in the Figure
above). Using more sophisticated interpolations and other procedures
to **generate the initial path** has allowed to solve that problem,
as described for the conformational
transition in Ras p21.

CPR is a deterministic method, in the sense that it always optimizes
the same initial path into the same final path. **To find different
and better paths** is achieved by varying the initial path. This
has been described for the search of chloride-transfer
paths in halorhodopsin.

Go to Home of S. Fischer