Page 317 - Thermodynamics of Biochemical Reactions

Chapter 5 Matrices in Chemical and Biochemical Thermodynamics

5.1 (a) Carry out the operations involved in equations 5.1-12 to 5.1-27 using MathematicaR. (b) Carry out the operations
involved in equations 5.1-22 to 5.1-26. (c) Calculate the amounts of the components C, H, and 0 for a system containing
one mole of each of the five species. (d) Calculate the amounts of the components CO, HI, and CH4 for the system contain-
ing one mole of each of the five species.

5.2 (a) Construct the conservation matrix for the hydrolysis of ATP to ADP in terms of species. (b) Calculate a basis for
the stoichiometric matrix from the conservation matrix and show that it is consistent with equations 5.1-28 to 5.1-31.

5.3 (a) Construct the conservation matrix A' for the hydrolysis of ATP to ADP in terms of reactants. (b) CafcuIate a basis
for the stoichiometric matrix from the Conservation matrix and show that it is consistent with ATP + H2 0 = ADP + P, .

5.4 The glutamate-ammonia ligase reaction is
glutamate + ATP + ammonia = glutamine + ADP + pi
It can be considered to be the sum of two reactions. (a) Write the stoichiometric number matrix for this enzyme-catalyzed
reaction and use NullSpace to obtain a basis for the conservation matrix.. (b) Write a conservation matrix that includes a
constraint to couple the two subreactions, and row reduce it to show that it is equivalent to the stoichiometric number matrix
obtained in (a).

5.5 Carry out the matrix multiplications in equation 5.4-4 for the three chemical reactions involved in the hydration of
fumarate to malate in the pH range 5 to 9.

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