Calculation of the apparent pKa for the CO2 hydration reaction in turtle blood. Empirical equations relating pKa to pH, Temperature, Na+, protein conc, and ionic strength and CO2 solubility coefficient to temperature.

Description

   Hydration of CO2 yields HCO3- via the reaction:
         CO2 + H2O <-> H2CO3 <-> HCO3- + H+ <-> (CO3)2- + 2H+. 
Acid–base physiologists traditionally simplify the reaction by omitting the H2CO3 term
and lumping all ionic CO2 species into the HCO3- term. The simplified reaction forms
the basis for the familiar Henderson–Hasselbalch equation of the CO2–HCO3- buffer
system:
         pH = pKa + log( [HCO3-]/(alphaCO2*PCO2) ), 			
where alphaCO2 is the solubility coefficient relating [CO2] and PCO2 (partial pressure of CO2) 
using Henry’s Law. The apparent pK (pKa) in this equation lacks a rigorous thermodynamic 
definition. Instead, it is an empirical factor relating pH, the product of alphaCO2 and PCO2, 
and the apparent [HCO3-] (i.e. the sum of all ionic CO2 species). 
   alphaCO2 and pKa are sensitive to the temperature, pH and/or the ionic strength of the
reaction medium. alphaCO2 and pKa of normal mammalian blood plasma have been well    
defined over a range of temperatures and pH values (e.g. Severinghaus, 1965; Siggaard-
Andersen, 1974; Reeves, 1976). These mammalian values are commonly used in
analyses of the acid–base status of non-mammalian species, despite evidence that such
practices can produce misleading results (Nicol et al. 1983). As an alternative, Heisler
(1984; erratum in Heisler, 1986) developed complex equations for alphaCO2
(mmol/(L*mmHg)) (1 mmHg = 133.22Pa) and pKa that are purported to be generally 
applicable to aqueous solutions (including body fluids) between 0 and 40°C and
incorporate the molarity of dissolved species (Md), solution pH, temperature (T, °C),
sodium concentration ([Na+], mol/L), ionic strength of nonprotein ions (I, mol/L) and 
protein concentration ([Pr], g/L). 
   pKa and alphaCO2 data were acquired from sea turtle plasma and compared to an empirically 
derived pKa equation and to two CO2 solubility equations: one adapted from Heisler 1986 
and the other from Christmas and Bassingthwaighte 2017.					

Figure: (top) pKa as a function of temperature and pH. Each line represents the pKa at a different temperature, in increments of 10 degrees celsius. The four circles represent experimentally measured values in sea turtle plasma. (bottom) CO2 solubility coefficient, alphaCO2, (ml oxygen per ml of plasma per atmosphere) as a function of temperature (celsius). Red circles are sea turtle plasma measurements from Stabenau 1993. Black line is alphaCO2 equation adapted from Heisler, 1986 and red line is alphaCO2 equation from Christmas and Bassingthwaighte, 2017.

Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.