Mahalanobis distance correlation: A novel approach for quantitating changes in multidimensional NMR spectra in biological applications

We present here a novel protocol for quantitating changes in the NMR spectra, which is based on Mahalanobis statistics. In a two dimensional NMR spectrum, the various peaks are taken to represent a distribution, and the two chemical shifts along the orthogonal axes and the peak intensities constitute three observables. All these observables vary in a correlated manner. Taking account of these, the Mahalanobis distance (MD) reflects the distance of any chosen peak from the centre of the distribution. For quantitating changes in a particular spectrum (say A) with N peaks (altered protein NMR spectrum) with respect to a reference spectrum (say B) with M peaks (original protein NMR spectrum), a composite spectrum with N + M peaks is generated. A one-to-one correspondence between N MD values considering all the N peaks in A and the same N peaks in the composite spectrum (A + B) is calculated. The MD distance of corresponding peaks in two different distributions can be correlated to assess the changes in the spectra during the course of a biological phenomenon, or as a result of biomolecular interactions. We have demonstrated these ideas, first, using the ¹H-¹⁵N HSQC spectrum of Ubiquitin, and then application of these has been demonstrated for monitoring progression of fibrillation of the protein α-Synuclein, in absence and presence of safranal, a known inhibitor of fibrillation of the protein. The method is in general applicable to multidimensional NMR spectra, does not require extensive data collection, and allows quantitative assessment of spectral changes via a single parameter. We believe that the method will have wide ranging applications to monitor many biological phenomena, and will also be useful in an industrial environment for mass comparison of molecules in a rapid manner.