The Mathematica Journal
Departments
Feature Articles
Columns
New Products
New Publications
Classifieds
Calendar
News Bulletins
Mailbox
Letters
Write Us
About the Journal
Staff and Contributors
Submissions
Subscriptions
Advertising
Back Issues
Home
Download this Issue

Additional Capabilities of BioEqCalc

Several additional classes of problems that BioEqCalc can solve are described in this section. As, in the previous sections, we continue to use the example of the ATP hydrolysis reaction although essentially any other biochemical reaction could have been used.

Example 5.

This example uses a (hypothetical) measured value of the apparent equilibrium constant [Graphics:../Images/index_gr_259.gif] and the function kReference[] to calculate the value of the equilibrium constant K for the chemical reference reaction

All of the parameters used by kReference[] have been defined previously with the exception of the following parameter.

[Graphics:../Images/index_gr_261.gif] [Graphics:../Images/index_gr_262.gif]

The calculated value K = 0.2946 for the chemical reference reaction (3) is identical to the value used initially (see Example 3).

[Graphics:../Images/index_gr_263.gif]
[Graphics:../Images/index_gr_264.gif]
[Graphics:../Images/index_gr_265.gif]

Example 6.

In this example, the aim is to calculate the standard molar transformed enthalpy of reaction [Graphics:../Images/index_gr_266.gif]. The module uses the relationship:

Here, R is the gas constant (8.31451 J [Graphics:../Images/index_gr_268.gif] [Graphics:../Images/index_gr_269.gif]) and P is pressure. This calculation is done with the function transHx[]. Here is the only parameter which has not yet been defined.

[Graphics:../Images/index_gr_270.gif] [Graphics:../Images/index_gr_271.gif]

The calculated value of [Graphics:../Images/index_gr_272.gif] is in excellent agreement with the value [Graphics:../Images/index_gr_273.gif] obtained previously by Alberty and Goldberg [13].

[Graphics:../Images/index_gr_274.gif]
[Graphics:../Images/index_gr_275.gif]

Example 7.

This example demonstrates the calculation of the change in binding of the [Graphics:../Images/index_gr_276.gif] ion, [Graphics:../Images/index_gr_277.gif], accompanying the biochemical reaction (3) at [Graphics:../Images/index_gr_278.gif], [Graphics:../Images/index_gr_279.gif], [Graphics:../Images/index_gr_280.gif], and [Graphics:../Images/index_gr_281.gif]. The function uses the relationship:

Note that temperature, ionic strength, and the values of [Graphics:../Images/index_gr_283.gif] are held constant in calculating the derivative. This calculation uses the function Binding[]. Most of the parameters have been defined previously. Here are the additional ones needed.

[Graphics:../Images/index_gr_284.gif] [Graphics:../Images/index_gr_285.gif]
[Graphics:../Images/index_gr_286.gif] [Graphics:../Images/index_gr_287.gif]
[Graphics:../Images/index_gr_288.gif] [Graphics:../Images/index_gr_289.gif]
[Graphics:../Images/index_gr_290.gif] [Graphics:../Images/index_gr_291.gif]

In this case, the index of [Graphics:../Images/index_gr_292.gif] is 3 and [Graphics:../Images/index_gr_293.gif]. The index of [Graphics:../Images/index_gr_294.gif] is 11 and [Graphics:../Images/index_gr_295.gif]. The result [Graphics:../Images/index_gr_296.gif] was obtained by Alberty and Goldberg [13].

[Graphics:../Images/index_gr_297.gif]
[Graphics:../Images/index_gr_298.gif]

Example 8.

Similarly, we now wish to calculate the change in binding [Graphics:../Images/index_gr_299.gif] at [Graphics:../Images/index_gr_300.gif], [Graphics:../Images/index_gr_301.gif], [Graphics:../Images/index_gr_302.gif], and [Graphics:../Images/index_gr_303.gif]. This problem is analogous to Example 7 except that the roles of [Graphics:../Images/index_gr_304.gif] and [Graphics:../Images/index_gr_305.gif] are reversed. The result [Graphics:../Images/index_gr_306.gif] was obtained by Alberty and Goldberg [13].

[Graphics:../Images/index_gr_307.gif]
[Graphics:../Images/index_gr_308.gif]

Example 9.

We now wish to calculate the calorimetric enthalpy [Graphics:../Images/index_gr_309.gif]. This calculation uses the relationship [14]

where [Graphics:../Images/index_gr_311.gif] is the standard molar enthalpy of ionization of the buffer at the specified ionic strength and temperature. [Graphics:../Images/index_gr_312.gif] is obtained by first using the function adjustH[] to calculate the values of [Graphics:../Images/index_gr_313.gif] for the chemical reactions in the system to the specified temperature and ionic strength. All of the other parameters used by adjustH[] have been defined. The ionization of Tris buffer is reaction 13 in the list of chemical reactions (see Example 3) and therefore the parameter bufferIndex is set equal to 13. The value of [Graphics:../Images/index_gr_314.gif] was calculated in Example 7 and [Graphics:../Images/index_gr_315.gif] in Example 8.

[Graphics:../Images/index_gr_316.gif]
[Graphics:../Images/index_gr_317.gif]

Example 10.

This example demonstrates the calculation of the standard molar enthalpy of reaction [Graphics:../Images/index_gr_318.gif] for the chemical reference reaction (3). This calculation uses the function hReference[]. The parameter Hmeas is the (hypothetically) measured value [Graphics:../Images/index_gr_319.gif] of [Graphics:../Images/index_gr_320.gif] which, in this case, is [Graphics:../Images/index_gr_321.gif]. The other variables have already been defined. The function hReference[] displays the calculated values of [Graphics:../Images/index_gr_322.gif], [Graphics:../Images/index_gr_323.gif], and of [Graphics:../Images/index_gr_324.gif] for the chemical reference reaction (3). The calculated value of [Graphics:../Images/index_gr_325.gif] for this chemical reference reaction is in agreement with the value [Graphics:../Images/index_gr_326.gif] given in Example 3.

[Graphics:../Images/index_gr_327.gif]
[Graphics:../Images/index_gr_328.gif]
[Graphics:../Images/index_gr_329.gif]
[Graphics:../Images/index_gr_330.gif]
[Graphics:../Images/index_gr_331.gif]
[Graphics:../Images/index_gr_332.gif]
[Graphics:../Images/index_gr_333.gif]
[Graphics:../Images/index_gr_334.gif]

Example 11.

This example demonstrates application to a system consisting of the following three biochemical reactions:

Here, G6P is glucose 6-phosphate and AMP is adenosine [Graphics:../Images/index_gr_337.gif]-monophosphate. The system is described by 20 reactions and 29 species. Although more complex than the previous examples, the principles are the same.

[Graphics:../Images/index_gr_338.gif]
[Graphics:../Images/index_gr_339.gif]
[Graphics:../Images/index_gr_340.gif]
[Graphics:../Images/index_gr_341.gif]
[Graphics:../Images/index_gr_342.gif]
[Graphics:../Images/index_gr_343.gif]
[Graphics:../Images/index_gr_344.gif]
[Graphics:../Images/index_gr_345.gif]
[Graphics:../Images/index_gr_346.gif]
[Graphics:../Images/index_gr_348.gif]
[Graphics:../Images/index_gr_349.gif]
[Graphics:../Images/index_gr_350.gif]
[Graphics:../Images/index_gr_351.gif]
[Graphics:../Images/index_gr_352.gif]
[Graphics:../Images/index_gr_353.gif]
[Graphics:../Images/index_gr_354.gif]
[Graphics:../Images/index_gr_355.gif]
[Graphics:../Images/index_gr_356.gif]
[Graphics:../Images/index_gr_357.gif]
[Graphics:../Images/index_gr_358.gif]
[Graphics:../Images/index_gr_359.gif]
[Graphics:../Images/index_gr_360.gif]
[Graphics:../Images/index_gr_361.gif]
[Graphics:../Images/index_gr_362.gif]
[Graphics:../Images/index_gr_363.gif]
[Graphics:../Images/index_gr_364.gif]
[Graphics:../Images/index_gr_365.gif]
[Graphics:../Images/index_gr_366.gif]
[Graphics:../Images/index_gr_367.gif]
[Graphics:../Images/index_gr_368.gif]

Example 12.

It is also possible to perform equilibrium calculations on systems of biochemical reactions without any knowledge of the ionic equilibria. For example, if one knows the values of [Graphics:../Images/index_gr_369.gif] for the biochemical reactions (7), (8), and (9), one can use ionicEquilib[] to solve the chemical equilibrium equations. The values of the apparent equilibrium constants [Graphics:../Images/index_gr_370.gif] are taken to be the values calculated in Example 11. The values of [Graphics:../Images/index_gr_371.gif] and [Graphics:../Images/index_gr_372.gif] have been set to zero so that the values of [Graphics:../Images/index_gr_373.gif] are independent of temperature. The global parameter ideal must be set equal to Y so that all activity coefficients and the activity of water are set equal to unity. The parameter Istr can be set to any value and the behavior will still be ideal (see output below). The calculated molalities of the biochemical reactants are in agreement with those obtained in Example 11.

[Graphics:../Images/index_gr_374.gif]
[Graphics:../Images/index_gr_375.gif]
[Graphics:../Images/index_gr_376.gif]
[Graphics:../Images/index_gr_377.gif]
[Graphics:../Images/index_gr_378.gif]
[Graphics:../Images/index_gr_379.gif]
[Graphics:../Images/index_gr_380.gif]
[Graphics:../Images/index_gr_382.gif]
[Graphics:../Images/index_gr_383.gif]
[Graphics:../Images/index_gr_384.gif]
[Graphics:../Images/index_gr_385.gif]
[Graphics:../Images/index_gr_386.gif]
[Graphics:../Images/index_gr_387.gif]
[Graphics:../Images/index_gr_388.gif]
[Graphics:../Images/index_gr_389.gif]


Converted by Mathematica      

[Article Index] [Prev Page][Next Page]