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Allosteric proteins as logarithmic sensors

Significance Biological sensory systems have the capacity to respond to signals over a broad range of intensities, be it vision in animals or signal transduction in cells. Such a broad response range is thought to be mediated by the system’s ability to sense signal logarithmically. We seek to understand the implementation of logarithmic sensors in cells. We find that a pervasive class of proteins, those that are allosterically regulated, have dynamics that facilitate response on a logarithmic (as opposed to absolute) scale, allowing sensitive response across a broad range of signal. Many sensory systems, from vision and hearing in animals to signal transduction in cells, respond to fold changes in signal relative to background. Responding to fold change requires that the system senses signal on a logarithmic scale, responding identically to a change in signal level from 1 to 3, or from 10 to 30. It is an ongoing search in the field to understand the ways in which a logarithmic sensor can be implemented at the molecular level. In this work, we present evidence that logarithmic sensing can be implemented with a single protein, by means of allosteric regulation. Specifically, we find that mathematical models show that allosteric proteins can respond to stimuli on a logarithmic scale. Next, we present evidence from measurements in the literature that some allosteric proteins do operate in a parameter regime that permits logarithmic sensing. Finally, we present examples suggesting that allosteric proteins are indeed used in this capacity: allosteric proteins play a prominent role in systems where fold-change detection has been proposed. This finding suggests a role as logarithmic sensors for the many allosteric proteins across diverse biological processes.