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Reply to Kang and Brooks: Comment on the calculations in protein thermodynamics

  • Anthony A. Kossiakoff
    Correspondence
    To whom correspondence should be addressed:Dept. of Biochemistry and Molecular Biology, University of Chicago, 900 E 57th St., Chicago, IL 60637. Tel.:773-702-9257; Fax:773-702-0439
    Affiliations
    From the Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637

    Institute for Biophysical Dynamics, Gordon Center for Integrative Science, Chicago, Illinois 60637
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  • Somnath Mukherjee
    Affiliations
    From the Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637
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  • James R. Horn
    Affiliations
    Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, Illinois 60115
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Open AccessPublished:April 06, 2018DOI:https://doi.org/10.1074/jbc.RL118.002471
      This is a response to a letter by Kang and Brooks (
      • Kang J.
      • Brooks K.V.
      Comment on the calculations in protein thermodynamics.
      ).
      In their comments, Kang and Brooks (
      • Kang J.
      • Brooks K.V.
      Comment on the calculations in protein thermodynamics.
      ) purport to have identified several errors in the isothermal calorimetry (ITC) data used to calculate the thermodynamic cycle described in Table 2 of our paper (
      • Mukherjee S.
      • Griffin D.H.
      • Horn J.R.
      • Rizk S.S.
      • Nocula-Lugowska M.
      • Malmqvist M.
      • Kim S.S.
      • Kossiakoff A.A.
      Engineered synthetic antibodies as probes to quantify the energetic contributions of ligand binding to conformational changes in proteins.
      ). However, we disagree with this assertion because it does not consider the standard deviations that are inherent in the experimental data and which are reported in the table. The values for ΔG0, ΔH0, and ΔS0 possess uncertainty. Thus, calculations of ΔG0 from ΔH0 and −TΔS0 values, as suggested by Kang and Brooks, would be prone to additional and unnecessary error since the −TΔS0 values were calculated from ΔG0 and ΔH0, which originate from experimentally derived parameters. For example, calculation of the ΔG0 from its enthalpic and entropic components for the interaction between maltose-binding protein (MBP) and sAB-11M with 1 mm maltose is (−14 ± 2) + (2 ± 2) = −12 ± 3 kcal/mol, which has larger error, as expected, but remains equivalent to the experimentally derived ΔG0 value (−11.4 ± 0.1 kcal/mol).
      We agree that equivalent energetic paths of a thermodynamic cycle must remain true regardless of path. When calculations were necessary, such as the determination of ΔS0, appropriate uncertainty was accounted for and suitably indicated at the end of the calculation (
      • Harris D.C.
      Quantitative Chemical Analysis.
      ). The thermodynamic parameters have been rounded to present the final values with appropriate significant figures. Consequently, the thermodynamic values cannot be subjected to additional calculations without including the associated error in the calculations. For example, the energetic relationship for two equivalent paths along the cycle can be calculated, such as path A:TΔS0Maltose: MBP + TΔS0MBP: sAB-11M in 1 mm maltose, and path B: TΔS0MBP: sAB11M + TΔS0Maltose: MBP in 5-fold molar excess sAB-11M. Using the data presented in Table 2, path A = (10.4 ± 0.1) + (−2 ± 2) = 8 ± 2 kcal/mol and path B = (6 ± 2) + (2 ± 1) = 8 ± 2 kcal/mol, which observes the expected equality within the limits of the accuracy of the measurements.
      With regard to the other comment by Kang and Brooks, we thank them for pointing out a typographical error in Fig. 5 and Table 2. We had made the correction in the final version that has been published (
      • Mukherjee S.
      • Griffin D.H.
      • Horn J.R.
      • Rizk S.S.
      • Nocula-Lugowska M.
      • Malmqvist M.
      • Kim S.S.
      • Kossiakoff A.A.
      Engineered synthetic antibodies as probes to quantify the energetic contributions of ligand binding to conformational changes in proteins.
      ).

      References

        • Kang J.
        • Brooks K.V.
        Comment on the calculations in protein thermodynamics.
        J. Biol. Chem. 2018; 2935062
        • Mukherjee S.
        • Griffin D.H.
        • Horn J.R.
        • Rizk S.S.
        • Nocula-Lugowska M.
        • Malmqvist M.
        • Kim S.S.
        • Kossiakoff A.A.
        Engineered synthetic antibodies as probes to quantify the energetic contributions of ligand binding to conformational changes in proteins.
        J. Biol. Chem. 2018; 293 (29321208): 2815-2828
        • Harris D.C.
        Quantitative Chemical Analysis.
        9th Ed. W.H. Freeman and Company, New York, NY2016