Regulatory Analysis of Branched Systems

In Section II it was shown that branched systems could be expressed as a set of quasi-linear fluxes and it was stated that these could be treated, at least for the analysis of control, as if they were linear. The following is a simple example of how this can be done. 

In this system there are three fluxes, J,and/j, such that/=(/ + Jh)-Factor X is a regulator of E2 and, since there is no direct feedback from E2 to El, X changesat the expense of Jy, leaving/unchanged. Thus, /, sjj is zero. 

The third equation derives from the flux balance, that isj = J + Jy, -, this canbe expressed as apower approximation,/ = fc/A/ [see Eq. (16)] and, since / is constant during the response to X, / / = k. [It should be noted that fc is a general constant term, so that fc(any constant) = k.] Thus, 

After rearranging this equation into the form, 

These functions describe the control of/, and/t by the concentration of X and three main conclusions follow. 

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