Thermodynamic descriptors, profiles and driving forces in membrane receptor-ligand interactions

Abstract

Extension of the (isothermal) Gibbs–Helmholtz equation for the heat capacity terms (ΔC_p) allows formulating a temperature function of the free (Gibbs) energy change (ΔG). An approximation of the virtually unknown ΔC_p temperature function enables then to determine and numerically solve temperature functions of thermodynamic parameters ΔH and ΔS (enthalpy and entropy change, respectively). Analytical solutions and respective numeric procedures for several such approximation formulas are suggested in the presented paper. Agreement between results obtained by this analysis with direct microcalorimetric measurements of ΔH (and ΔC_p derived from them) was approved on selected cases of biochemical interactions presented in the literature. Analysis of several ligand-membrane receptor systems indicates that temperature profiles of ΔH and ΔS are parallel, largely not monotonic, and frequently attain both positive and negative values within the current temperature range of biochemical reactions. Their course is determined by the reaction change of heat capacity: temperature extremes (maximum or minimum) of both ΔH and ΔS occur at ΔC_p = 0, for most of these systems at roughly 285–305 K. Thus, the driving forces of these interactions may change from enthalpy-, entropy-, or enthalpy-entropy-driven in a narrow temperature interval. In contrast, thermodynamic parameters of ligand-macromolecule interactions in solutions (not bound to a membrane) mostly display a monotonic course. In the case of membrane receptors, thermodynamic discrimination between pharmacologically defined groups—agonists, partial agonists, antagonists—is in general not specified and can be achieved, in the best, solely within single receptor groups.

Keywords::

• Membrane-coupled receptors
• thermodynamics/ligand-receptor interaction
• thermodynamic descriptors
• heat capacity change
• agonism/antagonism
• enthalpy/entropy change

Acknowledgements

The critical reading and comments to this article by Dr. Paul Pliska, Dr. Vojtêch Spiwok and Professor Gerd Folkers are gratefully acknowledged.

Declaration of interest

The author declares no conflict of interest.

Notes

¹ΔH and ΔS may appear constant usually only in “highly” exothermic or endothermic chemical reactions but scarcely in ligand-macromolecule interactions in which mainly weak bonds are reshaped.

²http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html

³http://www.mathworks.com/access/helpdesk/help/techdoc/ref/interp1.html

⁴http://www.systat.com/products.aspx

⁵SYSTAT commands (as text files) for computation of thermodynamic descriptors and some additional criteria from T, ΔG data sets can be required by the author.

⁶http://www.upa.pdx.edu/IOA/newsom/da1/ho_posthoc.doc