The Problem with Double Reciprocal Plots

Raymond      S. Ochs

Abstract

The double-reciprocal, or Lineweaver-Burke plot appears in virtually every treatment of enzyme kinetics and enzyme inhibition from the textbook level to research papers and monographs. It is also widely used in research to extract kinetic parameters, such as the Vmax, Km, and Ki values. It has long been recognized that in the process of taking reciprocals, the very worst data are emphasized; the smallest numbers have the most influence. Various graphical and later analytical (non-linear regression) solutions have been proposed over the years, but the double reciprocal plot remains the standard for pattern recognition of the three principal forms of reversible enzyme inhibition: competitive, uncompetitive, and non-competitive. However, a separate problem coexists with double reciprocal plots that is seldom mentioned: they are strongly anti-intuitive. Few people are adept at thinking in double-reciprocal space, that is, how an inverse substrate concentration might affect an inverse velocity. This is compounded by the fact that the double reciprocal plots, reduced to pattern recognition, allow no interpretation at all. Corresponding cartoon diagrams used to indicate how inhibition might occur are misleading. Combined with the fact that few investigators use the correct kinetic constants in analyzing enzyme inhibition, it is not surprising that very few scientists have a sound understanding of any inhibition form other than competitive – and that one is only evident because of common experience with the idea. In this contribution, I demonstrate the meanings of the intercepts of the double reciprocal plot by showing the mapping to direct velocity-substrate plots. In addition, I present different model drawings to extend understanding of modes of reversible inhibition. Reliance on double reciprocal plots to extract kinetic constants themselves is a mathematical error; reliance on the patterns themselves is an intuitive error. Overcoming these provides a simple, yet fundamental understanding of all forms of reversible enzyme inhibition.

Keywords: Lineweaver-Burke, double reciprocal, uncompetitive inibition, Lineweaver-Burke plot, enzyme inhibition, kinetic mechanisms, reciprocal transformation, monographs, competitive inhibition, uncompetitive inhibition, slope effect, intercept effect, ping-pong mechanism, active site, Kinetic data, inositol phosphatase, lithium action, pH transform, Ohm's law, Kirchoff's Law, resistors, anthropomorphic notion