CONTROL ANALYSIS OF PERIODIC PHENOMENA IN BIOLOGICAL-SYSTEMS

Principles of the control and regulation of steady-state metabolic sys tems have been identified in terms of the concepts and laws of metabol ic control analysis (MCA). With respect to the control of periodic phe nomena MCA has not been equally successful. This paper shows why in ca se of autonomous (self-sustained) oscillations for the concentrations and reaction rates, time-dependent control coefficients are not useful to characterize the system: they are neither constant nor periodic an d diverge as time progresses. This is because a controlling parameter tends to change the frequency and causes a phase shift that continuous ly increases with time. This recognition is important in the extension of MCA for periodic phenomena. For oscillations that are enforced wit h an externally determined frequency, the time-dependent control coeff icients over metabolite concentration and fluxes (reaction rates) are shown to have a complete meaning. Two such time-dependent control coef ficients are defined for forced oscillations. One, the so-called perio dic control coefficient, measures how the stationary periodic movement depends on the activities of one of the enzymes. The other, the so-ca lled transient control coefficient, measures the control over the tran sition of the system between two stationary oscillations, as induced b y a change in one of the enzyme activities. For forced oscillations, t he two control coefficients become equal as time tends to infinity. Ne ither in the case of forced oscillations nor in the case of autonomous oscillations is the sum of the time-dependent control coefficients ti me-independent, not even in the limit of infinite time. The sums of ei ther type of control coefficients with respect to time-independent cha racteristics of the oscillations, such as amplitudes and time averages , do fulfill simple laws. These summation laws differ between forced o scillations and autonomous oscillations. The difference in control asp ects between autonomous and forced oscillations is illustrated by exam ples.