Biological and Biochemical Oscillators by B. Chance, etc.
By B. Chance, etc.
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7. , Mat. Sb. , 64, 193 (1948). 8. , Mat. Sb. 31, 73, 575 (1952). 9. , Russ. Math. Surveys, JJ8, 13 (1963). 10. , European J. Biochem. , 4^, 79 (1968). 11. , Z. Phys. , _72, 508 (1910). 12. , J. Am. Chem. , 1595 (1920). 40 STABILITY PROPERTIES OF METABOLIC PATHWAYS WITH FEEDBACK INTERACTIONS Gustavo Viniegra-Gonzalez Cardiovascular Research Institute University of California San Francisco Medical Center In the search for a basis of biochemical oscillations, various chemical schemes have already been considered.
3. D. Dissertation, University of Pennsylvania, Philadelphia (1968). 4. , Oeuvres, Vol. 1, Gauthier-Villars, Paris (1928). 5. de la Société Math, de Kharkow (1893). 6. , 24^, 1 (1901). 7. , Mat. Sb. , 64, 193 (1948). 8. , Mat. Sb. 31, 73, 575 (1952). 9. , Russ. Math. Surveys, JJ8, 13 (1963). 10. , European J. Biochem. , 4^, 79 (1968). 11. , Z. Phys. , _72, 508 (1910). 12. , J. Am. Chem. , 1595 (1920). 40 STABILITY PROPERTIES OF METABOLIC PATHWAYS WITH FEEDBACK INTERACTIONS Gustavo Viniegra-Gonzalez Cardiovascular Research Institute University of California San Francisco Medical Center In the search for a basis of biochemical oscillations, various chemical schemes have already been considered.
X* 4 K , x* . ), n n n-1 n-1' 1 1 If the source input level, v Q , is very low (vQ ^ V n ) or if its magnitude is moderate (vQ £ V n ) , but the affinity of E 0 for S n is much greater than the affinity of E n for its own substrate Sn(a~l'P ^ Ι ^ ) , then the degree of saturation of the last enzyme E^ will be very low (x* <^ K ) . , n-1), then the forward pathway will behave as a quasi-linear subsystem, because, according to (11), each forward velocity will be approximately proportional to each substrate concentration [v^ % (V i /K i )x i J.