Calculus HELP! Interpret the constant V and K. Evaluate the lim R(s) as s approa

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Calculus HELP!

Interpret the constant V and K. Evaluate the lim R(s) as s approaches infinity. Why is V the maximum production rate? Is there any value of [s] for which the production rate equals V? How does the shape of the graph of R change if V is increasing? If V is decreasing ?

72 Guided Projects Guided Project 12: Enzyme kinetics Topics and skills: Graphing, derivatives Enzymes are catalysts that facilitate the biochemical reactions that occur within all living organisms. O fundamental laws of enzyme kinetics was proposed by Lconor Michaelis and Maud Menten in 1913 has been supported by laboratory experiments and explained through mathematical modeling.1 Menten kinetics are used in many biological models. he ne of t . The law An enzyme molecule is designed to fit" another molecule called a substrate. The substrate (S) and enzyme (E) form an intermediate complex (ES), which then dissociates to form the final end-product of the reaction (P) and the original enzyme (which can be re-used: Figure I). An important question concerns the rate at which product molecules are formed. Under certain assumptions, Michelis-Menton kineties relates the rate of p to the amount of substrate present. roduction of P Enzyme + substrate Enzyme-substrate complex Figure I Enzyme+ product We let R be the rate of production of the final R product P and we let s be the concentration of the substrate initially present. Both s and P are measured in units such as micro-moles (uM), while R is measured in M/s. The Michaelis- Menton law says that 10 R(s)--Vs- K +s where V>0 and K> 0 are constants that are specific to each enzyme. Let K= 5 M and V= 1O HM/s and graph R as a function of s. 10 30 -5

Explanation / Answer

V is the maximum speed attainable, i.e. Vmax . and K is substrate concentration when V is half of the V maximum.
a) At high substrate concentration, when [S] approaches infinity ,it implies S is much greater than K,
In such case, R= V that is, the rate is maximal, independent of substrate concentration.
V is the maximum production rate as even with infinite substrate, rate cant not exceed V. Also, V saturates after a certain limit of S.
b) Production rate equals V for large concentrations of S as told above.
c) When V increases, The graph will have a higher height as the saturation now occurs at a lower concentration.
When V decreases , It implies a higher concentration of substrate to achieve this and so the Km of the enzyme will also be higher.

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