SELF-NARCOTIZATION 1043 



and the half-saturating intensity: 



k,E,{k + 1) + 2A-,:Clilo 



(28.48) V/ = 



{g) Are Light Curves Hyperholicf 



2k*kCh]Q 



It will be noted that all the kinetic models used in this chapter lead to 

 quadratic equations for the rate of photosynthesis, P, as function of incident 

 light intensity, /; in other words, to hyperbolic light curves, P = /(/). 

 The imposition of a rate "ceiling," caused by limited supply of a reactant 

 or limited amount of an enzyme (in addition to a rate "roof," imposed by 

 the minimum number of quanta required to bring about the reaction) 

 changes the appearance of the light curves — for example, it can convert a 

 rectangular into a nonrectangular hyperbola— but in the mechanisms 

 discussed so far, general hyperbolical shape is preserved. 



A hyperbola is defined by three parameters. In our presentation of 

 light curves, the axis of abscissae, I, was parallel to one asymptote of the 

 hyperbola (the equation of the latter being P = p"''^^-)^ while the axis of 

 ordinates, P, was chosen so as to make P = at / = 0. One convenient 

 form of writing the equation of a hyperbola in this system of co-ordinates is: 



(28.48A) 



'"^ pmax. _ p \ ' pmax. / 



The three parameters in this equation are 70, the initial slope of the 

 curve, which is proportional to the maximum ciuantum yield of photo- 

 synthesis; i/J, the half-saturating light intensity; and P'"'^''-^ the limiting 

 rate in strong light. If the second term in parentheses vanishes, the equation 

 becomes: 



(28.48B) p^£:ip = p~J = coiist- X / 



which is the equation of a rectangular hyperbola. For the quadratic term 

 in (28. 48 A) to vanish, the following relation between the three parameters 

 must be fulfilled : 



E>max, 



(28.48C) 70 



W 



Several equations derived in chapters 27 and 28 for the light curves of 

 photosynthesis- — such as (28.29) — actually had the simplified form 

 (28.48B) ; however that was not always the case, as shown, e. g., by equa- 

 tion (28.42), which cannot be represented in the form (28.48B). 



Since 70 is not so easily measured as the other two parameters (in fact, 

 determination of 70 may be one aim of analytical representation of the light 



