Slmulation of Enzyme Action on the Programmable Calculator
these assumptions can he validated by rigorously solving the cubic equation. Given the reaction B-+H20*HB+OH-
(1)
W. Gale Rhodes' and Donald W. Taylor, Jr. Whitman College Walla Walla, WA 99362
the equilibrium constant for the hydrolysis of the base is
The action of many simple enzymes is described by the Michaelis-Menten equations, which give accurate predictions of initial rates of enzymatic reactions at any substrate concentration and, with slight modification, in the presence of various types of inhibitors ( I ) . We have prepared a series of pocket calculator programs which provide realistic kinetic data for Michaelis-Menten enzymes in the presence of competitive, noncompetitive, and uncompetitive inhibitors, and in the inhibitor-free condition. The user stores the chnracteristicconstnnw K, and V,,,, and then inputs the concentration of inhihitor Ill. Subsequent successive inputs of concentration of substrate [S] result in calculation and display of initial reaction rates. The type of inhibition is determined by a small block of commands which can he altered without disturbing the rest of the program. An optional part of the program employs a pseudorandom number generator to introduce "experimental" variations in the output, with maximum percent variation chosen by the user. The Dromam will be useful to bothstudentsand facultv in elemen'tsr; biochemistry courses: Students can use the program as a simulation of enzvme action, in which the effects of changes in IS] or 111 can he ieadily ohserved,and comparisons between enzymes with different K, or V,,, can be made. Students c& also generate large quantities of kinetic data for graphical analysis in order to see how variations in the basic parameters of enzyme catalyzed reactions are reflected in Lineweaver-Burke or Eadie-Hofstee graphs. Faculty will find the nroerams . .. most useful as a source of realistic kinetic data for trst problems or classroom analysis. The author has found them especially useful for preparing individualized prohlems for take-home exams, since many sets of kinetic data, representine a \,arietv of uroblems ut essentiallv. equivalent diffi. culty, can'be generated in a short time. Programs CENZ. NONCENZ, U N C E N L H e w l e t t packaid HP-25 RPN, each program 39 statements, four comments, stack contents. Documentation includes listing and complete instructions on HP-25 program forms, listing of equations used in computations. Modification for other H P entails only insertion of labels. Program listing without documentation available for Texas Instruments SR-52 algebraic. Send one dollar cash or check made to Gale Rhodes, Chemistry Department, Whitman College, Walla Walla, WA 99362. Indicate type of calculator to be used. This paper was presented to the 34th Northwest Regional Meeting, American Chemical Society, June 1979.
(3) Equations (2) and (3) result from taking mass balance and charge balance into account without simplifying assumptions. Such a cuhic equation is normally solved by successive approximations, or more often, simplified to a quadratic or linear equation by the use of assumptions where possible. A systematic method for solving acid-base problems utilizes the Newton-Raphson minimization ( 2 ) technique, and is applicable with a programmable calculator. The technique utilizes the fact that the ratio of a function to its derivative, f(x)/f'(x), approaches zero as the correct value of x is approached. The minimization formula can he expressed as
A Simple Method for Solving Cubic Equatlons in Acid-Base Calculations P a u l B. Kelter a n d J a m e s D. C a r r Uniuersity of Nebraska Lincoln. NE 68588 Solving the cuhic equations encountered when calculating the pH of aqueous solutions of weak acids or bases is rarely accomplished. Instead, simplifying assumptions are commonly used. Teachine students to make such assumotions is challenging, but wgh the now common use of pocket calculators 'To whom correspondence should he addressed. 620 / Jwrnal of Chemical Education
Kb
[OH-l3
[OH-l2 - K, [HBI [OH1 = [B-] CB- - ([OH-] - Kd[OH-1)
+ Kb[OH-l2 - (K, + K&B-)
..
[OH-]
+ Kd
