A biochemical logarithmic sensor with broad dynamic range

Abstract

Sensory perception often scales logarithmically with the input level. Similarly, the output response of biochemical systems sometimes scales logarithmically with the input signal that drives the system. How biochemical systems achieve logarithmic sensing remains an open puzzle. This article shows how a biochemical logarithmic sensor can be constructed from the most basic principles of chemical reactions. Assuming that reactions follow the classic Michaelis-Menten kinetics of mass action or the more generalized and commonly observed Hill equation response, the summed output of several simple reactions with different sensitivities to the input will often give an aggregate output response that logarithmically transforms the input. The logarithmic response is robust to stochastic fluctuations in parameter values. This model emphasizes the simplicity and robustness by which aggregate chemical circuits composed of sloppy components can achieve precise response characteristics. Both natural and synthetic designs gain from the power of this aggregate approach.

Mathematical modeling and analysis of mitochondrial retrograde signaling dynamics

“…The interactions among retrograde proteins and the translocation of Rtg1p/Rtg3p are assumed to obey the law of mass action ( Voit et al., 2015 ; Reyes et al., 2022 ; King et al., 2021 ), and the total concentration of each protein was regarded as conserved. To connect retrograde proteins with mitochondrial damage, the activation of Rtg2p was modeled using the Hill equation with the sum of mitochondrial damage ( Frank, 2018 ). The purpose of applying Hill equation is to summarize the cascading effect on sensing mitochondrial damage, such as ROS-induced ROS release ( Chowdhury et al., 2020 ).…”