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.
Highlights
Cells are exposed to changing environmental conditions and need to respond to external stimuli with high accuracy, e.g. to utilize nutrients and to avoid lethal stresses [1, 2]
Information, can generally be transmitted either by amplitude (AM) or frequency (FM) modulation, as used, for example, in the transmission of radio waves since the 1930s. Both types of modulation are known to play a role in biology with amplitude modulation (AM) conventionally associated with signaling and gene expression, and frequency modulation (FM) used to reliably transmit electrical signals over large distances between neurons
We propose a simple model of signaling by receptors with subsequent gene regulation, implementing both AM and FM in different types of biological pathways
Summary
Cells are exposed to changing environmental conditions and need to respond to external stimuli with high accuracy, e.g. to utilize nutrients and to avoid lethal stresses [1, 2]. To represent (encode) chemicals in the environment, either ligand-bound receptors trigger chemical signals or ion channels allow entry of secondary messengers These in turn activate transcription factors (TFs), which regulate target-protein production (decoding). The conventional view is that the level of signaling within the cell directly encodes the external stimuli, with consequent gradual changes in the nuclear TF concentrations. This is effectively an amplitude modulation (AM) mechanism [3,4,5,6,7,8,9,10]. Recent single-cell experiments show pulsating signals [3, 11,12,13,14] and bursty entry of TFs into the nucleus [3, 10, 15,16,17], in close analogy to frequency modulation (FM). (Note that, there is no modulation of an underlying carrier wave as in radio broadcasting [18], the AM/FM terminology is commonly used in quantitative biology [10, 15].) several hypotheses have been put forward, the benefits and detrimental effects of either type of response remain largely unclear
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