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Mathematical Description of the Enzymatic Activity of Proteins with Ionizable Groups Exhibiting Deviations from the Henderson-Hasselbalch Equation

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Abstract

The ionization equilibrium implied in the calculation of the specific activity is classically described through the Henderson-Hasselbalch equation. An extension for the description of anomalous ionization profiles using the Hill equation is presented in this communication. The proposed framework was applied to the description of the specific enzymatic activity curve as a function of pH of five enzymes presenting different ionization states in their active site. The developed equation improves the description of relative enzymatic curves that deviate from the bell curve predicted by the application of the Henderson-Hasselbalch equation, regardless of the ionization scheme related to the active site.

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Availability of Data and Material

Not applicable.

Code Availability

VBA codes of spreadsheet macros used to calculate activity curves are available from the corresponding author upon request.

Abbreviations

a :

Relative enzymatic activity

\({A}_{j}\) :

Ionizable group j in non-protonated form

\({A}_{j}^{+}\) :

Ionizable group j in protonated form

k :

Active configuration of the active site

n :

Number of ionizable groups in the active site

N :

Number of experimental points

z k :

Net charge of the active site in configuration k

\({\alpha }_{j}\) :

Fraction of ionized groups j

\({\beta }_{j}\) :

Parameter in Hill's Eq. (3)

\({\varepsilon }_{jk}\) :

Charge of group j in configuration k

\({\nu }_{j}\) :

Charge of group j in its ionized state

π :

Specific enzymatic activity

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Acknowledgements

PAPF gratefully thanks Prof. Dr. John M. Prausnitz (University of California, Berkeley, USA) for the invaluable discussions on the subject. Thanks are due also to Prof. Dr. Pol Tijskens (Wageningen University, The Netherlands) and Prof. Dr. Ralf Greiner (Max Rubner-Institut, Karlsruhe, Germany) for sharing their data on the activity of phytase from Klebsiella terrigena.

Funding

This study received financial support through grant 2012/23860–2, Sao Paulo Research Foundation (FAPESP), and grant 305747/2020–7, from the National Council for Scientific and Technological Development (CNPq).

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Authors and Affiliations

  1. Chemical Engineering School, University of Campinas, Av. Albert Einstein, 500, Campinas, SP, 13083-852, Brazil

    Luis Fernando Mercier Franco

  2. Department of Chemical Engineering, Engineering School, University of Sao Paulo, Av. Prof. Lineu Prestes, 580, Bl. 20, Sao Paulo, SP, 05508-000, Brazil

    Pedro de Alcantara Pessoa Filho

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  1. Luis Fernando Mercier Franco
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  2. Pedro de Alcantara Pessoa Filho
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Contributions

Conceptualization: L. F. M. F. and P. A. P. F.; methodology: L. F. M. F. and P. A. P. F.; formal analysis: P. A. P. F.; funding acquisition: P. A. P. F.; investigation: P. A. P. F.; software: P. A. P. F.; writing—original draft: P. A. P. F.; writing—review and editing: L. F. M. F. and P. A. P. F.

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Correspondence to Pedro de Alcantara Pessoa Filho.

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Franco, L.F.M., Pessoa Filho, P.d.A. Mathematical Description of the Enzymatic Activity of Proteins with Ionizable Groups Exhibiting Deviations from the Henderson-Hasselbalch Equation. Appl Biochem Biotechnol 194, 1221–1234 (2022). https://doi.org/10.1007/s12010-021-03700-y

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