Page 384 - Thermodynamics of Biochemical Reactions

384 Mathematica Solutions to Problem

-0.403393 (-461.322 + 2.47897 LoglADP] - 2.47897 Log[ATP])
E +
-0.403393 (-458.027 + 2.47897 Log[ADP] - 2.47897 LOg[ATPI)
E t
Power[E, -0.403393 (-2202.84 + 2 (-1428.93 + 2.47897 Log[ADPI) -
2 (-2292.61 + 2.47897 Log[ATPI))I

TraditionalForm[gal

e -0.403393 (2.47897 log(ADP)-2.47897 log(ATP)-46 1.322) +
b? -0.403393 (2.47897 log(ADP)-2.47897 log(ATP)-4.58.027) +
a? -0.403393 (2 (2.47897 log(ADP)- 1428.93)-2 (2.47897 log(ATP)-2292.61)-2202.84)

Note that the first Exp and Log in gamma cancel so that the same result is obtained with

(gpfructosel6phos-2* (ggatp+8.31451* .29815*Log[ATP] )+2* (gpadp+8.31451* .29815*Log[ADPl) /
(8.31451*.29815)1
-0.403393 (-461.322 + 2.47897 LoglADP] - 2.47897 LOg[ATPI)
E
-0.403393 (-458.027 + 2.47897 Log[ADP] - 2.47897 LOg[ATPI)
E
Power[E, -0.403393 (-2202.84 + 2 (-1428.93 + 2.47897 LogLADPI) -
2 (-2292.61 + 2.47897 Log [ATPI ) ) 1

1
TraditionalForm [gamma2
e -0.403393 (2.47897 log(ADP)-2.47897 log(ATP)-461.322) +
b? -0.403393 (2.47897 10g(ADP)-2.47897 log(ATP)-458.027) +
-0.403393 (2 (2.47897 log(ADP)- 1428.93)-2 (2.47897 Iog(ATP)-2292.61)-2202.84)
&?
(c) The fundamental equation for G" shows that the amount of ATP bound by the pseudoisomer group is given by
nc(ATP) = 2lnF/2ln[ATP]
at constant [ADP]. There is a corresponding equation for ADP.

boundATP=D [Log [gamma2], Log [ATPI I
1.
E
( 0.403393 (-461.322 + 2.47897 Log[ADP] - 2.47897 LOg[ATP]) +
1.
0.403393 (-458.027 + 2.47897 Log[ADPl - 2.47897 LoglATP]) '
E
2. / PowerrE, 0.403393 (-2202.84 + 2 (-1428.93 + 2.47897 Log[ADPI) -
2 (-2292.61 + 2.47897 Log[ATPI))I) /
-0.403393 (-461.322 + 2.47897 LOglADPI - 2.47897 LOg[ATPI)
(E '
-0.403393 (-458.027 + 2.47897 Log[ADP] - 2.47897 LOg[ATPI)
E +
PowerLE, -0.403393 (-2202.84 + 2 (-1428.93 + 2.47897 Log[ADP]) -
2 (-2292.61 + 2.47897 Log[ATP]))I)