Symmetry reduction from D2 tetramer to C2 dimer: group-theoretic and thermodynamic modeling of enzyme catalytic efficiency
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Symmetry reduction from D2 tetramer to C2 dimer: group-theoretic and thermodynamic modeling of enzyme catalytic efficiency

Tianyi Qiu 1*
1 Bethany Lutheran College
*Corresponding author: vqiu@blc.edu
Published on 4 November 2025
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AORPM Vol.4 Issue 3
ISSN (Print): 3029-0899
ISSN (Online): 3029-0880
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Abstract

A mathematical framework is presented to quantify the relationship between quaternary-structure symmetry, free energy, and catalytic efficiency during the transition from aD2-symmetric tetramer to aC2-symmetric dimer, exemplified with LDHA. The approach constructs explicitD2representations on subunit and interface feature spaces, derives projection operators to decompose operators and data into irreducible-representation components, and computes symmetry-resolved free-energy differences via Gaussian/statistical and harmonic/Hessian methods. Connections to kinetics are made through transition state theory with channel degeneracy. Reproducible algorithms and a workflow for mapping FoldX outputs into irrep-resolved diagnostics and efficiency predictions are provided.

Keywords:

symmetry reduction, group representation, enzyme catalytic efficiency, free energy, LDHA

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Qiu,T. (2025). Symmetry reduction from D2 tetramer to C2 dimer: group-theoretic and thermodynamic modeling of enzyme catalytic efficiency. Advances in Operation Research and Production Management,4(3),1-34.

References

[1]. Gallian, J. A. (1990). Contemporary abstract algebra. New Delhi: Cengage Learning.

[2]. Fulton, W., & Harris, J. (2013). Representation theory: a first course (Vol. 129).Springer Science & Business Media.

[3]. Conway, J. B. (2019). A course in functional analysis (Vol. 96).Springer.

[4]. Horn, R. A., & Johnson, C. R. (2012). Matrix analysis. Cambridge University Press.

[5]. Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T. N., Weissig, H., ... & Bourne, P. E. (2000). The protein data bank.Nucleic Acids Research, 28(1), 235–242.

[6]. Berman, H. M., Henrick, K., Kleywegt, G., Nakamura, H., & Markley, J. (2012). RCSB PDB.Nucleic Acids Research, 40(D1), D445–D452.

[7]. Truhlar, D. G., Garrett, B. C., & Klippenstein, S. J. (1996). Current status of transition-state theory.The Journal of Physical Chemistry, 100(31), 12771–12800.

[8]. Tinkham, M. (2003). Group theory and quantum mechanics. Courier Corporation.

References

[1]. Gallian, J. A. (1990). Contemporary abstract algebra. New Delhi: Cengage Learning.

[2]. Fulton, W., & Harris, J. (2013). Representation theory: a first course (Vol. 129).Springer Science & Business Media.

[3]. Conway, J. B. (2019). A course in functional analysis (Vol. 96).Springer.

[4]. Horn, R. A., & Johnson, C. R. (2012). Matrix analysis. Cambridge University Press.

[5]. Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T. N., Weissig, H., ... & Bourne, P. E. (2000). The protein data bank.Nucleic Acids Research, 28(1), 235–242.

[6]. Berman, H. M., Henrick, K., Kleywegt, G., Nakamura, H., & Markley, J. (2012). RCSB PDB.Nucleic Acids Research, 40(D1), D445–D452.

[7]. Truhlar, D. G., Garrett, B. C., & Klippenstein, S. J. (1996). Current status of transition-state theory.The Journal of Physical Chemistry, 100(31), 12771–12800.

[8]. Tinkham, M. (2003). Group theory and quantum mechanics. Courier Corporation.

Cite this article

Qiu,T. (2025). Symmetry reduction from D2 tetramer to C2 dimer: group-theoretic and thermodynamic modeling of enzyme catalytic efficiency. Advances in Operation Research and Production Management,4(3),1-34.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

About volume

Journal: Advances in Operation Research and Production Management

Volume number: Vol.4
Issue number: Issue 3
ISSN: 3029-0880(Print) / 3029-0899(Online)

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