Abstract

Classical enzyme kinetic theories are summarized and linked with modern discoveries here. The sequential catalytic events along time axis by enzyme are analyzed at the molecular level, and by using master equations, this writing tries to connect the microscopic molecular behavior of enzyme to kinetic data (like velocity and catalytic coefficient k) obtained in experiment: 1/k = t equals to the sum of the times taken by the constituent individual steps. The relationships between catalytic coefficient k, catalytic rate or velocity, the amount of time taken by each step and physical or biochemical conditions of the system are discussed, and the perspective and hypothetic equations proposed here regarding diffusion, conformational change, chemical conversion, product release steps and the whole catalytic cycle provide an interpretation of previous experimental observations and can be testified by future experiments.

Highlights

  • Some of the basic theories of biochemistry come from chemistry [1,2,3], which deals with small molecules most of the time

  • The master equations here provide a framework for the analysis of catalytic kinetics of enzymes, relationships between catalytic efficiency, catalytic rate/velocity, the amount of time taken by each step and physical/biochemical conditions of the system at diffusion, conformational change, chemical conversion, product-release steps and for the whole catalytic cycle will be discussed at each individual section, and all the essential steps are linked together by master equations

  • If we’d like a catalytic coefficient to reveal the properties of the enzyme and the physical and chemical conditions of the system, like the pressure, the temperature, the viscosity, density, etc., it should have nothing to do with substrate concentration, enzyme concentration, or enzyme–substrate complex concentration

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Summary

Introduction

Some of the basic theories of biochemistry come from chemistry [1,2,3], which deals with small molecules most of the time. The catalytic process includes the traditionally defined chemical-transformation step (which may include multiple sub-steps itself), and other related physical, biophysical or biochemical catalytic steps, for instance, diffusion, enzyme–substrate recognition or binding, conformational change and product-release steps [6] This is the case for chemical reactions as well as biochemical reactions catalyzed by enzymes. If any of these “trivial” steps take time to accomplish, it will affect the overall catalytic rate and cannot be ignored if accuracy is required. Catalytic step, enzyme, catalysis and catalytic cycle in the following discussion mean to refer to those related to biochemical reactions in homogeneous stable aqueous solution catalyzed by enzymes, unless stated otherwise.

The First Special Assumption and General Assumption
Master Equations
The Second Assumption
The Third Assumption
Diffusion Process
Substrate-to-Product Chemical Conversion Step
Product-Release Step
10. Explanations to Master Equations
Findings
12. Summary and Perspectives
Full Text
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