  Living cells are continually exposed to environmental signals that vary in
time. These signals are detected and processed by biochemical networks, which
are often highly stochastic. To understand how cells cope with a fluctuating
environment, we therefore have to understand how reliably biochemical networks
can transmit time-varying signals. To this end, we must understand both the
noise characteristics and the amplification properties of networks. In this
manuscript, we use information theory to study how reliably signalling cascades
employing autoregulation and feedback can transmit time-varying signals. We
calculate the frequency-dependence of the gain-to-noise ratio, which reflects
how reliably a network transmits signals at different frequencies. We find that
the gain-to-noise ratio may differ qualitatively from the power spectrum of the
output, showing that the latter does not directly reflect signaling
performance. Moreover, we find that auto-activation and auto-repression
increase and decrease the gain-to-noise ratio for all of frequencies,
respectively. Positive feedback specifically enhances information transmission
at low frequencies, while negative feedback increases signal fidelity at high
frequencies. Our analysis not only elucidates the role of autoregulation and
feedback in naturally-occurring biological networks, but also reveals design
principles that can be used for the reliable transmission of time-varying
signals in synthetic gene circuits.
