By B. Chance, etc.
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Extra resources for Biological and Biochemical Oscillators
The conjugated storage elements are the membrane itself (storing ions) and the chambers (storing volumes of solution). Figure 14b shows the characteristics and Figure 20 shows the excitation phenomenology, in the same manner as in Figure 15. 3. The "Ostwald-Lillie iron wire" in nitric acid is an example of an electrochemical nerve model which was proposed by Ostwald (21) and thoroughly studied 26 BIOCHEMICAL OSCILLATORS IONEXCHANGE MEMBRANE bistability tu refractory (TEORELL-model) Q-Um-φ n/10 NaCl n/ioo NaCl propagation Figure 20.
1967), "Oscillatory Processes in Biological and Chemical Systems," Moscow: "Nauka". A. M. (1961), Nature, 191, 457. Viniegra-Gonzalez, G. and Martinez, H. (1969), Proc. Biophys. Soc. Abstracts, 13, A210. , and Morales, M. (1969) unpublished results. Walter, C. (1969), Biophys. , ±9 863. Walter, C. (1970), J. Theoret. * 259. A. B. (1956), J. Chem. 221, 757. NOTE ADDED IN PROOF: The proofs of the relations presented in this paper are included in: G. D. thesis (Appendix of Part C ) , University of California at San Francisco.
2 ) . 2) A necessary condition for the existence of oscillations in this simple system is that the stationary solution should exist and should be locally instable. Thus, all sufficient conditions for local stability should be violated. The form of the sufficient condition for local instability (9) suggests that making the coefficients a^ unequal makes it more difficult to observe instabilities such as sustained oscillations. This is clearly shown when n β 3 (Fig. 3 ) , since it is obvious that the minimum number which M/a3 must exceed for instability to occur is obtained when the a^ are equal.
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