Large macromolecular assemblies are often important for biological processes in cells. Allosteric communications between different parts of these molecular machines play critical roles in cellular signaling. Although studies of the topology and fluctuation dynamics of coarse-grained residue networks can yield important insights, they do not provide characterization of the time-dependent dynamic behavior of these macromolecular assemblies. Here we develop a novel approach called Perturbation-based Markovian Transmission (PMT) model to study globally the dynamic responses of the macromolecular assemblies. By monitoring simultaneous responses of all residues (>8,000) across many (>6) decades of time spanning from the initial perturbation until reaching equilibrium using a Krylov subspace projection method, we show that this approach can yield rich information. With criteria based on quantitative measurements of relaxation half-time, flow amplitude change, and oscillation dynamics, this approach can identify pivot residues that are important for macromolecular movement, messenger residues that are key to signal mediating, and anchor residues important for binding interactions. Based on a detailed analysis of the GroEL-GroES chaperone system, we found that our predictions have an accuracy of 71-84% judged by independent experimental studies reported in the literature. This approach is general and can be applied to other large macromolecular machineries such as the virus capsid and ribosomal complex.