The effect of feedback on pathway transient response

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Abstract
The effect of variation of the rate of input of material on the transient behavior of metabolic pathways is examined. This reveals the existence of three transient times which make up the overall pathway transient. Two of these have been described previously and represent the times required for the accumulation of the free intermediate pool and the pool of enzyme-bound intermediate. They are state functions and as such are independent of the way in which the steady state was reached. The third is attributable to the variation in the rate of input of material to the pathway. It is dependent on three further factors. These are (a) the time required for the initial enzyme to reach its own steady state, (b) substrate depletion and (c) feedback. The description of the transient is: 1/VSS .cntdot. .intg.0VSS t .cntdot. dV0, where V0 represents the rate of input and VSS represents the steady-state flux. The transient time associated with the transition between steady-states is shown to be a simple function of the transients for the establishment of each steady state from rest and may be expressed as: .tau. = .tau.b - Va/Vb .cntdot. .tau.a, where Va and Vb refer to the fluxes in the two steady states and .tau.a and .tau.b represent the transient times for the establishment of each of the steady-states from rest. The total pathway transient may not be completely defined as: .tau. = 1/VSS .cntdot. .intg.0VSS t .cntdot. dV0 + .SIGMA.[I]/VSS + .SIGMA.[EI]/VSS, where summation over all intermediates, I, is implied. The significance of this to the analysis of pathway behavior is discussed with more general examples of pathway transient analysis.