Accurate Encoding and Decoding by Single Cells: Amplitude Versus Frequency Modulation

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.

Entangled signal pathways can both control expression stability and induce stochastic focusing

“…For eukaryotic cells, due to the asymmetry of transition rates, the average off‐state dwell time is always longer than the average on‐state dwell time . This means that in contrast to AM, FM has more advantages because it can make the gene expression more stable, which is consistent with the previously reported results .…”

“…We point out that the EM essentially belongs to the frequency modulation (FM) strategy since it regulates the gene expression (refer to (Eqn 1)) by modulating the off-state dwell time, whereas the IM to the amplitude modulation (AM) strategy since it regulates the gene expression by changing the on-state dwell time [44][45][46][47][48]. The combination of the results in Fig.…”

Systematic Characterization of Dynamic Parameters of Intracellular Calcium Signals

“…It is well established that a diverse amount of biochemical processes can be amplitude- and/or frequency-modulated (Adachi et al, 1999; Micali et al, 2015). To analyse such oscillatory data, the fast Fourier transform (FFT) is commonly used, which allows for the conversion of a signal from its time domain, into the frequency domain.…”

Know the Single-Receptor Sensing Limit? Think Again

“…For example, to implement maximum likelihood in the fast unbinding limit a receptor should only signal upon a ligand-binding event as illustrate in Fig. 3 b (thin arrows), rather than continuously signaling while ligand is bound (see [ 26 ] for further discussion). How can the cell achieve such short and well-defined signaling durations?…”