Biochemical networks can respond to temporal characteristics of time-varying signals. To understand how reliably biochemical networks can transmit information we must consider how an input signal as a function of time--the input trajectory--can be mapped onto an output trajectory. Here we estimate the mutual information between input and output trajectories using a Gaussian model. We study how reliably the chemotaxis network of E. coli can transmit information on the ligand concentration to the flagellar motor, and find the input power spectrum that maximizes the information transmission rate.