Rate equations irreversible steps, 121-2 matrix

If, say, the third step is irreversible, its reverse coefficient X32 is zero. This coefficient appears in the second, negative term of the numerator of the rate equation, making it zero. It also appears in all matrix rows from the fourth on down, so that the products of the elements of these rows are zero. The denominator of the rate equation thus contains only three terms the products of the elements of the first three rows. These terms contain the forward coefficients of the steps from the fourth onward as common factors, and so does the numerator accordingly, these coefficients cancel and the rate equation is reduced to... 

The approximations in this section can be combined in many different ways. Significant further simplification may result. For example, for a cycle 8.34 with X as the macs and irreversible step X, + B — X2, the only remaining row of the Christiansen matrix is the second, and that row has but one single element, A qAq, (see reduced matrix 8.45). In this case, the rate equation reduces to... 

The overall reaction network results in ten-simultaneous equations which can be solved in a step-wise fashion due to the irreversible reactions. The matrix of rate constants is lower triangular involving 20 kinetic constants (plus deactivation function parameters). 

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