Supplemental Material to:
Effect of Divalent Cations on the Structure of the Antibiotic Daptomycin
Steven W. Ho1≠, David Jung2≠, Jennifer R. Calhoun3≠, James D. Lear3≠, Mark Okon1, Walter R.P. Scott1, Robert E.W. Hancock2, and Suzana K. Straus1*
1 Department of Chemistry, University of British Columbia, 2036 Main Mall, Vancouver, B.C., Canada, V6T 1Z1
2 Department of Microbiology and Immunology, University of British Columbia, 232B -2259 Lower Mall, Vancouver, B.C., Canada, V6T 1Z4
3 Department of Biochemistry & Biophysics, University of Pennsylvania, School of Medicine, 422 Curie Boulevard, Philadelphia PA 19104-6059
≠ Authors contributed equally to this work
* to whom correspondence should be addressed: Department of Chemistry,
University of British Columbia,
2036 Main Mall, Vancouver,
B.C., Canada, V6T 1Z1
tel: (604) 822-2537
fax: (604) 822-2157
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Keywords: daptomycin, Ca2+binding, Mg2+ binding, analytical ultracentrifugation, molecular dynamics simulation, NMR, Nuclear Overhauser Enhancement (NOE)
Molecular Dynamics Refinement Protocol
NOE-derived interatom distance upper and lower bounds were introduced into a simulation using the GROMOS96 NOE refinement potential energy functions as defined in (Scott et al. 1999):
(1)
where is the actual interatom distance between atom i and j, is the force constant, and the potential energy terms are harmonic close to , the reference distance, and become linear for larger deviations i.e. for and for the attractive and repulsive cases, respectively.
Both the time-averaged (Torda and van Gunsteren 1991) and instantaneous NMR refinement techniques were applied. Briefly, in time-averaged refinement, the refinement potential acts on a time-weighted average of a given interatom distance rather than on its instantaneous value. This technique has been shown to better account for conflicting NOE distance constraints due to protein mobility than instantaneous refinement (Nanzer et al. 1995). The time-weighting is biased towards recently sampled configurations:
,(2)
where is the relaxation time. The choice of in formula (1) and are interdependent; here we choose =1ps and = 400 N (Nanzer et al. 1995).
In order to quantify the extent of deviation of a simulated structure from experimental NOE derived distances, an average relative NOE violation was calculated:
(3)
where ND is the total number of distance restraints and the other parameters are as defined above.
The degree of mobility during a simulationwas quantified by calculating the root mean squared (RMS) positional fluctuation of atomic positions in the trajectory. This RMS is defined as:
(4)
where N is the total number of atoms in molecule, Ncfg is the total number of configurations in a trajectory, and is the average position of atom i in the trajectory. A superposition using Cαatoms as a reference was employed.
Finally, the conformational specificity was characterized in terms of the structural spread encountered during the simulation. This was determined using a clustering algorithm, which partitions S, the sequence of all conformations xi, i=1...N that are encountered during a simulation, into a sequence of subsets (clusters) each containing similar conformations. The double difference matrix distance metric DAB was chosen to measure the difference between any two conformations A and B
(5)
where N is the number of atoms considered in the distance measurement (in this case, all Cα’s) and dijA,B is the scalar interatomic distance of two considered atoms i and j within the same structure. This measure was chosen over the more widespread R.M.S. positional deviation distance measurement, because it obviates the need for a rigid-body superposition of structures which can lead to misleading results for very different conformations. Two conformations are considered to be similar, and thus neighbors, if DAB is below 1.5 Å.
References
Nanzer AP, van Gunsteren WF, Torda AE (1995) Parametrization of Time-Averaged Distance Restraints in Md Simulations. Journal of Biomolecular Nmr 6:313-320
Scott WRP, Hunenberger PH, Tironi IG, Mark AE, Billeter SR, Fennen J, Torda AE, Huber T, Kruger P, van Gunsteren WF (1999) The GROMOS biomolecular simulation program package. Journal of Physical Chemistry A 103:3596-3607
Torda AE, van Gunsteren WF (1991) The Refinement of Nmr Structures by Molecular-Dynamics Simulation. Computer Physics Communications 62:289-296