It has been an established idea in recent years that protein is a physiochemically connected network. Allostery, understood in this new context, is a manifestation of residue communicating to remote parts in a molecule, and hence a rising interest to identify communication pathways within such a network. Recently, we have developed the timedependent linear response theories (td-LRTs), which shown to well interpret the ligand photodissociation relaxation dynamics of myoglobin. In this article, we applied the td-LRT with impulse force to investigate the allostery on an enzyme system -the dihydrofolate reductase (DHFR), which catalyze the hydride transfer (HT) reaction -the reduction of dihydrofolate (DHF) to tetrahydrofolate (THF) using the cofactor nicotinamide adenine dinucleotide phosphate (NADPH). We developed a connection matrix to record the counts of mechanical signals propagating through donor-acceptor pairs launched from the active sites with the td-LRT. Through the connection matrix, the communication score (CS) of each residue is assigned, which quantify how often the signals propagate through a residue in its most accessible way. The sites with high CS are termed "intramolecular communication centers (ICCs)", which were shown to be highly conservative. Furthermore, we showed that the HT rate reduction by a single residue mutation is highly correlated with its CS. Especially, the mysterious 200-fold HT rate reduction of the distal mutation G121V from kinetic isotope effect experiment is well described by our model with its ultra-high CS which means the G121 participating on the signal propagation process most frequently. On the other hand, several mutants: G67V, S148A and W133F causing minor HT rate reduction were described by its low CS, which means fewer signals through those sites. We proposed that the fold of HT rate reduction for a given mutant is an exponential function of its CS, which suggests that the dynamics signal propagation in the wild type play a background role to facilitate the HT quantitatively.