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In this paper, we consider a molecular relay channel in which signal molecules are transmitted by a sender of communication, propagated, amplified, removed in the channel, and sensed by the receiver of communication that decodes the signal molecules. To understand and characterize the communication capacity of the molecular relay channel, we develop an information communication model that consists of the transmitter, channel, and receiver. Mutual information is used to quantify the amount of information that is transferred from the transmitter through the channel to the receiver. The method employed and results presented in this paper may help elucidate design principles of biological systems as well as help in the design and engineering of synthetic biological systems from the perspective of information theory.