Efficient determination of low-frequency normal modes of large protein structures by cluster-NMA

The structure-function relationship is critical to understanding the biologically relevant functions of protein structures. Various experimental techniques and numerical modeling methods, normal mode analysis (NMA) in particular, have been employed to gain insight into this relationship. Experimental methods are often unable to provide all the desired information and comprehensive modeling techniques are often too computationally expensive. The authors build upon and optimize their cluster normal mode analysis (cNMA) tool, which uses embedded rigid-bodies and harmonic potentials to capture the biologically significant, low-frequency, oscillations of protein structures. cNMA represents atomic details with a scalable number of degrees-of-freedom, which can be chosen independent of structure size. This representation overcomes the otherwise quadratic order memory requirements and cubic order computational complexity associated with traditional all-atom NMA. cNMA is two orders of magnitude faster than traditional all-atom NMA when clustering by residue (very high resolution) and in the more traditional application using a fixed number of clusters, cNMA computationally scales as O(n), which is two orders of complexity faster than all-atom NMA. cNMA is presented and very large example structures with up to 10(6) atoms are analyzed on a notebook PC in the time scale of minutes/hours. The resulting mode shapes help identify biologically significant, conformational pathways.