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Correlated Parameter Fit of Arrhenius Model for Thermal Denaturation of Proteins and Cells

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Abstract

Thermal denaturation of proteins is critical to cell injury, food science and other biomaterial processing. For example protein denaturation correlates strongly with cell death by heating, and is increasingly of interest in focal thermal therapies of cancer and other diseases at temperatures which often exceed 50 °C. The Arrhenius model is a simple yet widely used model for both protein denaturation and cell injury. To establish the utility of the Arrhenius model for protein denaturation at 50 °C and above its sensitivities to the kinetic parameters (activation energy E a and frequency factor A) were carefully examined. We propose a simplified correlated parameter fit to the Arrhenius model by treating E a, as an independent fitting parameter and allowing A to follow dependently. The utility of the correlated parameter fit is demonstrated on thermal denaturation of proteins and cells from the literature as a validation, and new experimental measurements in our lab using FTIR spectroscopy to demonstrate broad applicability of this method. Finally, we demonstrate that the end-temperature within which the denaturation is measured is important and changes the kinetics. Specifically, higher E a and A parameters were found at low end-temperature (50 °C) and reduce as end-temperatures increase to 70 °C. This trend is consistent with Arrhenius parameters for cell injury in the literature that are significantly higher for clonogenics (45–50 °C) vs. membrane dye assays (60–70 °C). Future opportunities to monitor cell injury by spectroscopic measurement of protein denaturation are discussed.

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Notes

  1. Alternatively, the correlated parameter approach (Eq. 6) can also be re-written as \( k = \exp ( - C)\exp \left[ {\frac{{E_{\text{a}} }}{R}\left( {\frac{1}{316} - \frac{1}{T}} \right)} \right] \), where 316 K (or 43 °C) can be considered as the reference temperature derived from past measurements (Fig. 1).

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Acknowledgment

This project was financially supported by the National Institute of Health (NIH) R01-CA07528. W.F.W. performed work in Minnesota and Hannover for this project and was supported in part by funding from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) for the Cluster of Excellence REBIRTH (From Regenerative Biology to Reconstructive Therapy). Z.Q was supported by an Interdisciplinary Doctoral Fellowship and Doctoral Dissertation Fellowship. J.C.B. was supported by McKnight Professorship and Carl and Janet Kuhrmeyer Chair in Mechanical Engineering. J.A.P. received partial support for his investigations from the T.L.L. Temple and O-Donnell Foundations, and from Transonic/Scisense Inc. We thank Dr. Neil Wright for his insightful comments.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota, 111 Church St. SE, Minneapolis, MN, 55455, USA

    Zhenpeng Qin, Saravana Kumar Balasubramanian & John C. Bischof

  2. Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, USA

    John C. Bischof

  3. Department of Urologic Surgery, University of Minnesota, Minneapolis, MN, USA

    John C. Bischof

  4. Institute of Multiphase Processes, Leibniz Universität Hannover, Hannover, Germany

    Willem F. Wolkers

  5. Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, USA

    John A. Pearce

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  1. Zhenpeng Qin
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  2. Saravana Kumar Balasubramanian
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  3. Willem F. Wolkers
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Correspondence to John C. Bischof.

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Associate Editor Agata A. Exner oversaw the review of this article.

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Qin, Z., Balasubramanian, S.K., Wolkers, W.F. et al. Correlated Parameter Fit of Arrhenius Model for Thermal Denaturation of Proteins and Cells. Ann Biomed Eng 42, 2392–2404 (2014). https://doi.org/10.1007/s10439-014-1100-y

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