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Worked example: Adenylate kinase (1AKE-4AKE)
Here is an example (fraction of contacts plot), where the trajectory obtained with our local implementation of UMMS (see Morphing section) is also presented.
It is clear that the UMMS trajectory is a linear interpolation between states 1 and 2, while the MinPath trajectory is much more complex, and avoids high energy regions.
This again concernes adenylate kinase with elastic spring constants of 0.1 kcal/Mol/Angstr^2 for both sides.
Because the calculation is very rapid, it is possible to investigate the role of each residue in the transition path and its kinetic constant through a "perturbation analysis".
The principle is the following: for each residue, in turn, the ENM is modified so that the residue under consideration receives a stronger elastic constant (k->100k) in its interactions with all its neighbours. Then the trajectory is calculated and the Energy E# of the transition state recorded. Finally, a plot of E# vs residue number is produced in a Pertubation plot.
This is similar in spirit to the phi-value plots used in folding transition analysis and should be useful to experimentalists who can systematically mutate each residue, in turn, into Ala and measure the new kinetic constant of the transition.
Some remedies have been proposed for this: see Marakagis and Karplus (2005) and Best and Hummer (2005) in the Ref. section.
However, we think that the relative value of the transition state energy (see perturbation plot above) contains relevant information to engineer mutations in a protein design experiment to modulate the rate of an enzyme-catalyzed chemical reaction involved in a metabolic cycle or not.
In addition, we have found that:
1. The Maragakis and Karplus model will indeed decrease the energy at the transition state by exactly epsilon, the parameter of the model. But its value is arbitrary.
2. The Mixing temperature of Hummer's model will need to be set to a very high value (3000K) to observe an effect in the energy of the transition state. Its exact value is also arbitrary.
Here are the results for Adenylate kinase in the same conditions than Maragakis and Karplus (2005), namely cutoff=8 Angstroms, K1=0.02 and K2=0.0067 kcal/Mol/Angstroms^2.
Transition state file.
Full Trajectory file.
Page last modified 17:48 September 28, 2007.