Proofreading systems of multiple stages for improved accuracy of biological discrimination

The phenomenal accuracy of biological discrimination is due in many cases to specific proofreading mechanisms. We have previously developed a macroscopic theory of such mechanisms and applied it to the case of single-stage proofreading. In this article we apply the theory to systems with multiple stages of proofreading. A specific relationship between improved accuracy due to proofreading and the associated energy cost is given. This is a macroscopic relationship that must be satisfied regardless of the details of the underlying mechanisms. Five factors in the design of such systems are shown to influence their overall accuracy: (1) initial discrimination, (2) number of proofreading stages, (3) proofreading discrimination of each stage, (4) distribution of proofreading effort among the stages, and (5) total energy expended for proofreading. We show that there is an optimal distribution of proofreading effort that, for a given degree of accuracy, minimizes the energy cost of proofreading. We also provide a simple physical interpretation of this minimum condition. These results are used to examine proofreading in two experimental systems for which there is appropriate data available in the literature: the valyl-tRNA synthetase catalyzed misacylation of tRNA^Val with threonine and the isoleucyl-tRNA synthetase catalyzed misacylation of tRNA^Ile with valine. The correlation between the magnitude of a discrimination factor and the size of the corresponding enzymatic cavity is discussed.