Accurate encoding and decoding by single cells: amplitude versus frequency modulation

TL;DR

This paper compares amplitude and frequency modulation in cellular signaling, showing bursty signaling (FM) is more accurate for single receptors with fast dynamics, while amplitude modulation (AM) is more accurate with multiple receptors.

Contribution

It introduces a simple model to analyze the accuracy of AM and FM in cellular signaling, revealing conditions favoring each mechanism and suggesting biological reasons for FM usage.

Findings

Burst signaling is more accurate than continuous signaling for fast receptor dynamics.

AM is always more accurate than FM in multi-receptor systems.

Cells may use FM for reasons other than accuracy, such as coordination or threshold mechanisms.

Abstract

Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.