Scaling in biological nuclear magnetic resonance spectral distributions

A statistical analysis of the distribution of the eigenvalues of the chemical shift interaction as detected by nuclear magnetic resonance (NMR) spectroscopy in large biological systems is presented in the light of random matrix theory. A power law dependence is experimentally observed for the distribution of the number of eigenvalues, N, of the shielding hamiltonian with epsilon i less than or equal to E as a function of the energy E. From this cumulative distribution of energy levels, N(E), we also obtain a density of states rho(E). The exponent of the energy variation of N(E) and rho(E) are correlated with the dimensionality of the molecular system. A crossover in the values of the exponents is found in passing from low to higher energy in the spectra. Our method classifies and reduces the chemical shift data base of proteins and also demonstrates a degree of regularity in seemingly irregular spectral patterns