62
A. F. BARTHOLOMAY
References
1. BAILEY, N. T. J.: The Elements of Stochastic Processes, with Applications to
the Natural Sciences. New York: John Wiley 1964.
2. BARTHOLOMAY, A. F.: Bull. Math. Biophys. 20, 97 (1958).
3. - Bull. Math. Biophys. 20, 175 (1958); 21, 363 (1959).
4. - Bull. Math. Biophys. 22, 285 (1960).
5. - Biochemistry 1, 223 (1962).
6. - In: N. RASHEVSKY (Ed.), Physico-mathematical Aspects of Biology, p. 1.
New York: Academic Press 1962.
7. - IBM 6th Medical Symposium, cosponsored by Brookhaven National
Laboratory, Oct. 5-8, p. 325. New York: Poughkeepsie 1964.
8. - Bull. Math. Biophys. Special Issue 27, 235 (1965).
9. - (Abstract) in Proc. of the Third Ann. Symp. on Biomath. and Computer
Sc. in the Life Sciences. Houston, Tex.: 1, 1965.
10. - (Abstract) SIAM Review 8, 558 (1966).
11. -, Y. LI and E. FUGLISTER: (Abstract) - Abstracts of the Biophysical
Society 10th Annual Meeting, Feb. 23-25, 1966 p.27,. Boston Massachusetts, USA: 1966.
12. BHARUCHA-REID, A. T.: Elements of the Theory of Markov Processes and
Their Applications. New York: McGraw-Hill 1960.
13. DooB, J. L.: Trans. Amer. Math. Soc. 58,455 (1945).
14. GOODWIN, B. c.: Temporal Organization in Cells. New York: Academic
Press 1963.
15. GURLAND, J. (Ed.): Stochastic Models in Medicine and Biology. Madison:
Univ. of Wisconsin Press 1964.
16. HARRIS, T.E.: The Theory of Branching Processes. New Jersey: Prentice-Hall
1963.
17. LEVINE, H. D.: Proc. 9th International Congress of Internal Medicine, Amsterdam, Holland, Sept. 7-10, 1966. In: "Excerpta Medica International
Congress Series", No. 137, p. 429 (1966).
18. LONDON, W.: J. BioI. Chern. 241, 3008 (1966).
19. PENNYCUICK, S. W.: J. A. C. S. 48, 6 (1926).
20. RALEY, J. H., F. F. RUST and W. E. VAUGHAN: J. A. C. S. 70, 88 (1948).
21. SHEA, S. M.: Bull. Math. Biophys. 265 (1964).
22. - and A. F. BARTHOLOMAY: J. Theoret. BioI. 9, 389 (1965).
23. WADDINGTON, C. H.: The Strategy of the Genes. London: George Allen and
Unwin Ltd. 1957.
DisCIIssion
WALTER:
In relation to the suggestions that 81 (I) and 82 (I) are not separable:
1. In 1957 (or so) Dr. SCHNOLL (USSR) found large fluctuations of inorganic
phosphate liberated after a constant interval of hydrolysis of A TP catalyzed
by myosin. The fluctuations were reported to be much larger than the expected
experimental error. 2. Dr. J. A. CHRISTIANSEN suggested a few years ago in
"Advances in Enzymology" that enzyme catalyzed reactions might be synchronized. This would mean that enzyme reactions would not be strictly
continuous. If this suggestion is correct it would be important in relation to
the calculation of 81 (I) and 8 2 (I).
A. F. BARTHOLOMAY
References
1. BAILEY, N. T. J.: The Elements of Stochastic Processes, with Applications to
the Natural Sciences. New York: John Wiley 1964.
2. BARTHOLOMAY, A. F.: Bull. Math. Biophys. 20, 97 (1958).
3. - Bull. Math. Biophys. 20, 175 (1958); 21, 363 (1959).
4. - Bull. Math. Biophys. 22, 285 (1960).
5. - Biochemistry 1, 223 (1962).
6. - In: N. RASHEVSKY (Ed.), Physico-mathematical Aspects of Biology, p. 1.
New York: Academic Press 1962.
7. - IBM 6th Medical Symposium, cosponsored by Brookhaven National
Laboratory, Oct. 5-8, p. 325. New York: Poughkeepsie 1964.
8. - Bull. Math. Biophys. Special Issue 27, 235 (1965).
9. - (Abstract) in Proc. of the Third Ann. Symp. on Biomath. and Computer
Sc. in the Life Sciences. Houston, Tex.: 1, 1965.
10. - (Abstract) SIAM Review 8, 558 (1966).
11. -, Y. LI and E. FUGLISTER: (Abstract) - Abstracts of the Biophysical
Society 10th Annual Meeting, Feb. 23-25, 1966 p.27,. Boston Massachusetts, USA: 1966.
12. BHARUCHA-REID, A. T.: Elements of the Theory of Markov Processes and
Their Applications. New York: McGraw-Hill 1960.
13. DooB, J. L.: Trans. Amer. Math. Soc. 58,455 (1945).
14. GOODWIN, B. c.: Temporal Organization in Cells. New York: Academic
Press 1963.
15. GURLAND, J. (Ed.): Stochastic Models in Medicine and Biology. Madison:
Univ. of Wisconsin Press 1964.
16. HARRIS, T.E.: The Theory of Branching Processes. New Jersey: Prentice-Hall
1963.
17. LEVINE, H. D.: Proc. 9th International Congress of Internal Medicine, Amsterdam, Holland, Sept. 7-10, 1966. In: "Excerpta Medica International
Congress Series", No. 137, p. 429 (1966).
18. LONDON, W.: J. BioI. Chern. 241, 3008 (1966).
19. PENNYCUICK, S. W.: J. A. C. S. 48, 6 (1926).
20. RALEY, J. H., F. F. RUST and W. E. VAUGHAN: J. A. C. S. 70, 88 (1948).
21. SHEA, S. M.: Bull. Math. Biophys. 265 (1964).
22. - and A. F. BARTHOLOMAY: J. Theoret. BioI. 9, 389 (1965).
23. WADDINGTON, C. H.: The Strategy of the Genes. London: George Allen and
Unwin Ltd. 1957.
DisCIIssion
WALTER:
In relation to the suggestions that 81 (I) and 82 (I) are not separable:
1. In 1957 (or so) Dr. SCHNOLL (USSR) found large fluctuations of inorganic
phosphate liberated after a constant interval of hydrolysis of A TP catalyzed
by myosin. The fluctuations were reported to be much larger than the expected
experimental error. 2. Dr. J. A. CHRISTIANSEN suggested a few years ago in
"Advances in Enzymology" that enzyme catalyzed reactions might be synchronized. This would mean that enzyme reactions would not be strictly
continuous. If this suggestion is correct it would be important in relation to
the calculation of 81 (I) and 8 2 (I).