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Planck-Benzinger Thermal Work Function: Thermodynamic Characterization of the Carboxy-Terminus of p53 Peptide Fragments

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Abstract

The thermodynamic parameters for six p53 carboxy-terminus peptide fragments as determined by analytical ultracentrifugal analysis were compared over the experimental temperature range of 275–310 K to evaluate the Gibbs free energy change as a function of temperature, ΔG o(T), from 0 to 400 K using our general linear third-order fitting function, ΔG o(T) = α + βT 2 + γT 3. Data obtained at the typical experimental temperature range are not sufficient to accurately describe the variations observed in the oligomerization of these p53 fragments. It is necessary to determine a number of thermodynamic parameters, all of which can be precisely assessed using this general third-order linear fitting function. These are the heat of reaction, innate temperature-invariant enthalpy, compensatory temperatures and the thermodynamic molecular switch occurring at the thermal set point. This methodology can be used to distinguish the characteristic structure and stability of p53 carboxy-terminal fragments or other p53 mutants. It should be used for the thermodynamic characterization of any interacting biological system.

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Abbreviations

K :

Kelvin, one degree on the absolute temperature scale

T m :

Melting temperature at which ΔH o(T m ) and TΔS o(T m ) intersect and the ΔG o(T m ) value reaches zero

T h :

Harmonious temperature at which ΔH o(T h ) and TΔS o(T h ) intersect and the ΔG o(T h ) value reaches zero

T s :

Thermal set point

\( T_{{C_{p} }} \) :

Temperature at which ΔC o p (T) value reaches zero

IMSL:

International mathematical subroutine library

S :

Entropy

H :

Enthalpy

A :

Helmholtz free energy

ΔG o(T):

Gibbs free energy change as a function of temperature

ΔW o(T):

Heat flux term

ΔW o(T) = ΔH o(T 0) − ΔG o(T):

Planck-Benzinger thermal work function

ΔH o(T 0):

Innate temperature-invariant enthalpy

φ:

Effective free energy from the partition function

K eq :

Equilibrium constant

ΔC p (T)(+) → ΔC p (T)(−):

Thermodynamic molecular switch at which the Gibbs free energy of reaction reaches a true negative minimum, changing in sign from positive to negative

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Acknowledgments

I wish to thank Dr. Ettore Appella, of the Laboratory of Cell Biology, National Cancer Institute, National Institutes of Health, for providing us the samples of six p53 fragments for the sedimentation equilibrium measurements.

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Correspondence to Paul W. Chun.

Appendix

Appendix

How the basic laws of thermodynamics apply to life processes

The general linear third-order fitting function we have developed obeys the basic laws of thermodynamics. It is unique in that it can and should be applied to any interacting biological system.

  1. I.

    The first law of thermodynamics: Conservation of the internal energy of the body

    • Food intake (to maintain the internal energy of body) = Heat generated +Work (exercise)—Julius Robert Mayer, Turbingen University (1838).

  2. II.

    The second law of thermodynamics: Equilibrium conditions needed to maintain life processes.

    $$\Delta G^{o}(T_{S})(-)_{{{\text{minimum}}}} = \Delta H^{o}(T_{S})(-)\,{\text{at}}(T_{S})\quad{\text{where}}\,T\Delta S^{o} = 0 $$

    Life begins at the thermal set point, (T S ).

  3. III.

    The third law of thermodynamics:

    • At the point where TΔS o ≠ 0 you can no longer maintain the negative Gibbs free energy minimum at (T S ) essential to life processes. Entropy increases to the point that the system breaks down, and life ceases.

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Chun, P.W., Lewis, M.S. Planck-Benzinger Thermal Work Function: Thermodynamic Characterization of the Carboxy-Terminus of p53 Peptide Fragments. Protein J 29, 617–630 (2010). https://doi.org/10.1007/s10930-010-9286-9

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