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Hydrolysis of Adenosine [Graphics:../Images/index_gr_133.gif]-triphosphate

Example 3.

We are now in a position to consider a typical example of an overall biochemical reaction, namely the hydrolysis of ATP to adenosine [Graphics:../Images/index_gr_134.gif]-diphosphate (ADP) and orthophosphate:

As before, the system of reactions must be specified in terms of the pertinent species.

[Graphics:../Images/index_gr_136.gif]
[Graphics:../Images/index_gr_137.gif]
[Graphics:../Images/index_gr_138.gif]

As in the previous examples, one must provide the necessary data for the function reactions[].  However, instead of directly inputting the parameters reactants, ntprime, and pseudo one can use the function makeInputBR[] to obtain these parameters. Here are the parameters needed by makeInputBR[].

[Graphics:../Images/index_gr_139.gif] [Graphics:../Images/index_gr_140.gif]
[Graphics:../Images/index_gr_141.gif] [Graphics:../Images/index_gr_142.gif]

The function makeInputBR[] returns the parameters reactants, ntprime, and pseudo. Therefore, it should be used before using the function reactions. In this example, there is only one overall biochemical reaction. However, four pseudoisomer groups are specified, one for each biochemical reactant (including [Graphics:../Images/index_gr_143.gif]).

[Graphics:../Images/index_gr_144.gif]
[Graphics:../Images/index_gr_145.gif]
[Graphics:../Images/index_gr_146.gif]
[Graphics:../Images/index_gr_147.gif]
[Graphics:../Images/index_gr_150.gif]
[Graphics:../Images/index_gr_151.gif]
[Graphics:../Images/index_gr_152.gif]
[Graphics:../Images/index_gr_153.gif]
[Graphics:../Images/index_gr_154.gif]
[Graphics:../Images/index_gr_155.gif]
[Graphics:../Images/index_gr_156.gif]
[Graphics:../Images/index_gr_157.gif]
[Graphics:../Images/index_gr_158.gif]
[Graphics:../Images/index_gr_159.gif]

Again, ionicEquilib[] can be used to calculate the molalities of the species, the ionic strength, and the mole fractions of the species within the pseudoisomer groups. In this example the values of the activity coefficients [Graphics:../Images/index_gr_160.gif], the activity of the water [Graphics:../Images/index_gr_161.gif], the transpose of the stoichiometric number matrix [Graphics:../Images/index_gr_162.gif], and the transpose of the apparent stoichiometric number matrix [Graphics:../Images/index_gr_163.gif] are also displayed.

[Graphics:../Images/index_gr_164.gif]
[Graphics:../Images/index_gr_165.gif]
[Graphics:../Images/index_gr_166.gif]
[Graphics:../Images/index_gr_167.gif]
[Graphics:../Images/index_gr_168.gif]
[Graphics:../Images/index_gr_169.gif]
[Graphics:../Images/index_gr_170.gif]
[Graphics:../Images/index_gr_172.gif]

The apparent equilibrium constant [Graphics:../Images/index_gr_173.gif] for the overall biochemical reaction can now be calculated by using the function apparentEqX[]. The output that is displayed also includes the total molalities of the biochemical reactants, the values of [Graphics:../Images/index_gr_174.gif] for the constrained species ([Graphics:../Images/index_gr_175.gif] and [Graphics:../Images/index_gr_176.gif] in this example), the temperature T, and the ionic strength I. All of the parameters needed by apparentEqX[] have already been obtained.

[Graphics:../Images/index_gr_177.gif]
[Graphics:../Images/index_gr_178.gif]
[Graphics:../Images/index_gr_179.gif]
[Graphics:../Images/index_gr_180.gif]
[Graphics:../Images/index_gr_181.gif]
[Graphics:../Images/index_gr_182.gif]
[Graphics:../Images/index_gr_183.gif]
[Graphics:../Images/index_gr_184.gif]

To calculate the value of [Graphics:../Images/index_gr_185.gif] at [Graphics:../Images/index_gr_186.gif], we set Istr to that value.

[Graphics:../Images/index_gr_187.gif]
[Graphics:../Images/index_gr_188.gif]
[Graphics:../Images/index_gr_189.gif]
[Graphics:../Images/index_gr_190.gif]
[Graphics:../Images/index_gr_191.gif]
[Graphics:../Images/index_gr_192.gif]
[Graphics:../Images/index_gr_193.gif]
[Graphics:../Images/index_gr_194.gif]

Alberty and Goldberg [13] calculated the standard transformed Gibbs free energy [Graphics:../Images/index_gr_195.gif] for biochemical reaction (2), the hydrolysis of ATP(aq) to {ADP(aq) + orthophosphate(aq)}, at [Graphics:../Images/index_gr_196.gif], at [Graphics:../Images/index_gr_197.gif], [Graphics:../Images/index_gr_198.gif], and [Graphics:../Images/index_gr_199.gif]. We wish to see if we obtain the same value. To do this, we first obtain the values of the activity coefficients [Graphics:../Images/index_gr_200.gif] of [Graphics:../Images/index_gr_201.gif] (species 3) and of [Graphics:../Images/index_gr_202.gif] (species 11) from the parameter [Graphics:../Images/index_gr_203.gif] and then calculate the values of [Graphics:../Images/index_gr_204.gif] and [Graphics:../Images/index_gr_205.gif] that correspond to the respective values of [Graphics:../Images/index_gr_206.gif] and [Graphics:../Images/index_gr_207.gif]. These values are subsequently used in the parameter constpXa.

[Graphics:../Images/index_gr_208.gif]
[Graphics:../Images/index_gr_209.gif]
[Graphics:../Images/index_gr_210.gif]

The function apparentEqX[] is next used to calculate [Graphics:../Images/index_gr_211.gif] and then the function gibbsEnergy[] is used to calculate the standard transformed Gibbs free energy [Graphics:../Images/index_gr_212.gif]. Here are the parameters used by gibbsEnergy[].

[Graphics:../Images/index_gr_213.gif] [Graphics:../Images/index_gr_214.gif]
[Graphics:../Images/index_gr_215.gif]

[Graphics:../Images/index_gr_216.gif]
[Graphics:../Images/index_gr_217.gif]
[Graphics:../Images/index_gr_218.gif]
[Graphics:../Images/index_gr_219.gif]
[Graphics:../Images/index_gr_220.gif]
[Graphics:../Images/index_gr_221.gif]

Thus, the value calculated for [Graphics:../Images/index_gr_222.gif] is in excellent agreement with the result [Graphics:../Images/index_gr_223.gif] obtained by Alberty and Goldberg [13].


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