A biochemical logarithmic sensor with broad dynamic range.

Steven A Frank

doi:10.12688/f1000research.14016.1

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-Menton 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.

Highlights

I present a simple biochemical circuit that logarithmically transforms input signals. This circuit adds the outputs of several reactions that follow standard mass action Michaelis-Menton kinetics
Simple mass action kinetics often follows the Hill equation with k = 1, which corresponds to classical MichaelisMenton kinetics[2]
Prior studies have emphasized that a Hill equation response can act as a logarithmic sensor[3,4]

Summary

Introduction

I present a simple biochemical circuit that logarithmically transforms input signals. This circuit adds the outputs of several reactions that follow standard mass action Michaelis-Menton kinetics. The biochemical kinetics may follow the commonly observed Hill equation response, which includes Michaelis-Menton kinetics as a special case. This sensor has high dynamic range, responding logarithmically across many orders of magnitude. The aggregate nature of this circuit provides robustness to parameter variations. Aggregate sensor design may explain the commonly observed high dynamic range of logarithmic biological responses and may provide a useful tool for synthetic biology

Results and discussion

Frank SA