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Signal processing is an integral part of cell biology. The associated algorithms are implemented by signaling pathways that cell biologists are just beginning to understand and characterize. Our objective in the context of signal processing is to understand these algorithms and perhaps emulate them in other contexts such as communication and speech processing. Towards this end, the paper proposes a new framework for modeling cellular signal processing using interacting Markov chains. The model is presented and preliminary results that validate it are given. Specifically, the example of the mitogen activated protein kinase cascade is examined and model predictions are compared to experimental findings. The model is consistent with the key properties of the cascade, i.e. ultrasensitivity, adaptation, and bistability.