A mechanistic model of discrete one-dimensional arrays of autocrine cells interacting via diffusible signals is investigated. Under physiologically relevant assumptions, the model is reduced to a system of ordinary differential equations for the intracellular variables, with a particular, biophysically derived type of long-range coupling between cells. Exact discrete traveling wave and static kink solutions are obtained in the model with sharp threshold nonlinearity. It is argued that the considered mechanism may be used extensively for transmission of information in tissues during homeostasis and development.