578 Electronic Computers /3I :4 



Curve-fitting problems also arise in other fields associated with bio- 

 physics. One of these is the problem of finding the suitable rate con- 

 stants for enzyme-catalyzed reactions as discussed in Chapters 17 and 18. 

 Here, the rate constants are the parameters which are to be adjusted to 

 give curves which give the best fit to the experimental data. An 

 analog computer which does this calculation electronically was con- 

 structed at the Johnson Research Foundation at the University of 

 Pennsylvania. Its use will be described here as applied to the oxidation 

 by H 2 2 of a one-electron donor AH, when catalyzed by the enzyme 

 peroxidase (E). (This example is chosen for convenience of descrip- 

 tion.) 



The reaction scheme for this problem can be written 



e-p-p' x *+ p 



E +Sr~E-Sr 



p "IP' 



E-S z + AH-±E-S U + A 



E P -S n + AH ^ E + A + H 2 



where E is peroxidase and .Sis H 2 2 . The concentrations are represent- 

 ed by letters above the reactants. The intermediates are spectrophoto- 

 metrically distinct from the enzyme and from each other. 



The reaction scheme can be represented mathematically by the 

 differential equations 



j t = -k + x{e-p-p') + k^p 



■j. = -hap - k_p + k + x[e-p-p') 



dp' , 



-j- = l + ap — m + ap 



da , . 



-j- = —l + ap — m + ap 



