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Worked example: Adenylate kinase (1AKE-4AKE)

  • A Q1 vs Q2 plot will also be produced in postscript format, where Q1 is the fraction of contacts as in the initial state, and Q2 the fraction of contacts as in the final state, for each point along the trajectory.
    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.
  • If needed, a Q1-specific - Q2-specific vs Q-common plot can also be built, upon request. This kind of plot reveals possible unfolding during the transition (see Okasaki et al., 2006).
  • An interesting quantity to plot is the Q1-specific or Q2-specific plot as a function of time. It behaves very much like an order parameter because its sudden decrease (increase) occurs precisely at the transition state. See the attached plot.
  • The Elastic Energy during the transition can be calculated. The attached energy plot demonstrates that MinActionPath generates a trajectory with less elastic energy than UMMS linearly interpolated one (see curve pink+green vs blue+red curve).
    This again concernes adenylate kinase with elastic spring constants of 0.1 kcal/Mol/Angstr^2 for both sides.
  • The question of the robustness of the trajectory with respect of the k1/k2 ratio, i.e. the elastic constants for both sides of the reaction, is of interest. Here is a Q1 vs Q2 plot for adenylate kinase and k2/k1=5, k1=k2 and k1/k2=2.
  • The influence of the Delta_E parameters can also be systematically investigated. Here is a Q1 vs Q2 plot for DeltaE=-3, 0 and +3 kcal/Mol.
  • In addition to the trajectory in Pymol format, the total action Stot and the energy of the transition state (measured with respect to the energy of the left -initial- state) are given in the output.
    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.
  • We are aware that the Transition State Energy may be overestimated by the model we use (ENM for each of the 2 states). In particular, there is a cusp form of the energy plot at the transition point, that does not make much physical sense.
    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.

  • Recently, we updated the code to be able to tackle full-atom models.
    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.
    Log file.
    Transition state file.
    Full Trajectory file.

  •   Marc Delarue http://lorentz.dynstr.pasteur.fr
    Page last modified 17:48 September 28, 2007.