We discuss the problem of the evolution of the cellular communication system from the RNA world to progenote to the modern cell. Our method analyses syntactical structure of molecular fossils in the non-coding regions of DNA within the information-processing gene model developed earlier. We concluded that sequence-specific binding is an ancient communication process with its origin in the RNA world. Moreover, we illustrate. our viewpoint using four evolution snapshots from the first RNA segments, some 4.1 billion years ago, to the first cell, 3.8 billion years ago.