Long chain fatty acid binding to human plasma albumin

Description

   All constants and intermediate variables have been declared private,
   with the exception of the parameters and variables pertaining to
   Palmitate (P). Commenting the word private in the model will restore 
   them to the input and output display on the runtime menu.
   
   The variables nu_bar_XX are the ratios of the average number of moles of
   fatty acid bound per mol of albumin.

   The independent variable in this model is c, the molar concentration of 
   the unbound fatty acid in the aqueous phase.

   The suffix a indicates that the equilibrium constants were calculated
   using corrections for unbound fatty acid association in the albumin
   solution.

   the nu_bar functions are suffixed L(Laureate), M(Myristate), Ma(Myristate_a),
   P(Palmitate) Pa(Palmitate_a), S(Stearate), Sa(Stearate_a), O(Oleate), and
   LO(Linoleate).


Calculate 
nu_bar =
( 
       K1 * c 
 + 2 * K1 * c^2  * K2 
 + 3 * K1 * c^3  * K2 * K3 
 + 4 * K1 * c^4  * K2 * K3 * K4 
 + 5 * K1 * c^5  * K2 * K3 * K4 * K5 
 + 6 * K1 * c^6  * K2 * K3 * K4 * K5 * K6 
 + 7 * K1 * c^7  * K2 * K3 * K4 * K5 * K6 * K7 
 + 8 * K1 * c^8  * K2 * K3 * K4 * K5 * K6 * K7 * K8 
 + 9 * K1 * c^9  * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 
+ 10 * K1 * c^10 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 * K10 
+ 11 * K1 * c^11 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 * K10 * K11 
+ 12 * K1 * c^12 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 * K10 * K11 * K12
)
 /
( 
   1 
 + K1 * c
 + K1 * c ^ 2 * K2 
 + K1 * c ^ 3 * K2 * K3 
 + K1 * c ^ 4 * K2 * K3 * K4
 + K1 * c ^ 5 * K2 * K3 * K4 * K5
 + K1 * c ^ 6 * K2 * K3 * K4 * K5 * K6 
 + K1 * c ^ 7 * K2 * K3 * K4 * K5 * K6 * K7
 + K1 * c ^ 8 * K2 * K3 * K4 * K5 * K6 * K7 * K8 
 + K1 * c ^ 9 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9
 + K1 * c ^ 10 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 * K10
 + K1 * c ^ 11 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 * K10 * K11
 + K1 * c ^ 12 * K2 * K3 * K4 * K5 * K6 * K7 * K8 * K9 * K10 * K11 * K12
 )

The calculation is shortened by defining T-variables recursively. See the code to
see how this is done.

Binding of fatty acids to human plasma albumin at 37o C:

Equations

None.

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.