926 CONCENTRATION FACTORS CHAP. 27 



able quantity of the enzyme Ea we can derive the following equations for the steady 

 state: 



/( k*K k* \ 



[l + KACO2] + ^' [CO2] + y^o) 



(27.40) P = n/c*KaAo[C02] /( 1 + K.iCO^] + p^ [CO2] + ^ ) 



The term proportional to A;;.[C02] in the denominator imposes on these carbon di- 

 oxide curves an "absolute ceiling" (i. e., a maximum rate independent of both [CO2] and 

 A;*, and thus of 7): 



(27.41) PStJ: = nA^eaE^Ao 



(The lower index refers to [CO2], the upper to I.) This obviously is n times the maximum 

 possible rate of carboxylation according to the mechanism (27.36 and 27.37).) 

 For relative saturation, as a function of [CO2], we obtain: 





[C02 



(27.42) P/(Pmax. -P) = '^.iiEt^L. 



1 + {k*IK.^l) 



and for half saturating carbon dioxide concentration: 



(27.43) „JC0,1 = i (i|, + 1)/ (1 + ^J 



which reduces itself to: 



(27.44) ,/JC02] = UK, 



for high A;* values (strong light), and to: 



(27.45) ,/JC02] = 1/ifa 



for low kr values (weak light). 



Depending on whether K& < Ke, or vice versa, 1/JCO2] will shift upwards or down- 

 wards with increasing light intensity. The initial slope of the curves (27.40) is: 



(07 An / rfP \ nktK^Ao 



^"^'■^^^ \d[C02])o 1 - AfAe'aE^ 



The reduction in rate caused by Ea deficiency is, by comparison of (27.40) with (27.8): 



K ^^ A'e[C02] + 1 



For saturating [CO2] values: 



(27-46a) ^ = VV+E!E^r:[C02] + l. 



(27.46b) /3 = 



V (' + sL) 



and is thus equal to 3^ for a light intensity k* — ^A^ea, which without enzyme deficiency 

 would have given the saturation value (equation 27.41). Generally, the saturation 



