Title: Dynamic long distance correlations in bio-macromolecules                                                                                                                                                                                                                                                                                                                                                        Abstract : Bio-macromolecules show long distance intra-molecular coupling. Microscopic understanding of such long distance coupling is a fundamental challenge in understanding their functions. A weak statistical covariance has been observed between functional distant residues as far as 15 A0 involved in molecular binding via recognition in ubiquitin, a protein associated with protein degradation in cells. The statistical covariance is the correlation of the variables at a given instance of time. The correlation should hold in time till the binding partners mutually diffuse to come in proximity to participate in binding events. This leads us to examine the dynamic cross correlation from simple mathematical model and compare the results to the functionally important but distant residues in ubiquitin via detailed Molecular Dynamics (MD) simulations. The mathematical analysis shows that the cross-correlation functions show a peak at low frequencies and an algebraic tail with a universal exponent for large frequencies. The MD data supports qualitatively these features of the cross-correlation functions. Based on detailed analysis of dynamically correlated pairs we provide the evidence for existence of path of correlated degrees of freedom among functionally important but spatially separated residues. The generality of our analysis suggests that similar mechanism of correlation via dynamic fluctuations should be operative in bio-macromolecules in general.