Biological Oscillators: their Mathematical Analysis by Theodosios Pavlidis

By Theodosios Pavlidis

Organic Oscillators: Their Mathematical Analysis

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2 4 hours F I G . 3. Entrainment of the locomotor activity of a cockroach [Rob-2]. 2 33 CIRCADIAN RHYTHMS periodic regime is applied. We will discuss in detail the analytical and biological aspects of entrainment in Chapter 4. (2) P h a s e S h i f t s C a u s e d b y N o n r e p e t i t i v e S t i m u l i . 4 shows a change in the phase of the locomotor rhythm of a flying squirrel 5 I 10 «/> 15 20 9 ^ I 12 . I 16 ι I ι I . I 20 24 4 Time of day in hours i I 8 , I 12 FIG. 4. Phase shifting of the locomotor activity of a flying squirrel by a brief light pulse.

3) 54 3 PHASE SHIFTS AND PHASE RESPONSE CURVES T h e n the phase shift Q(x, S) caused by S applied at χ is defined as the phase difference P(x', y) if y e R(L). If y φ R(L), then the phase shift is undefined. , 1 0 min versus 2 4 hours), then the distinction between χ and x' is diminished and the phase shift could be defined as P ( x , y) without significant error. 5. , P ( x , z)]. Note that if χ φ L the above two definitions are meaningless since the effect of S may vary along an isochrone. Some generalizations about the shape of the phase response curves can be stated.

Indeed the simpler the organism the lesser the probability that the output of the circadian regulator will not be obscured by intermediate systems as much as it would in a higher-order organism. Also it is easier to study the effect of chemical agents on the clock. In a higher organism such agents may never reach the basic regulator because of the complex metabolic systems involved. 5 Biochemical Oscillators T h e study of chemical kinetics reveals that it is indeed possible to have sustained oscillations of the concentration of a chemical substance.

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