Question #c12d0
1 Answer
Jan 18, 2016
The generic enzyme reaction is:
#E + S stackrel(k_1)(rightleftharpoons)# #ES stackrel(k_2)(->) E + P#
#color(white)(aaaaa)^(k_(-1))# where:
#E# is free enzyme#S# is unbound substrate#ES# is the enzyme-substrate complex#P# is the product#k_1# is the rate constant for the forward reaction forming the#ES# complex#k_(-1)# is the rate constant for the reverse reaction forming the free enzyme and unbound substrate#k_2# is the rate constant for the reaction step that unbinds the enzyme and somehow forms the product. This may be multiple steps, and we don't necessarily know much about it right away.
MICHAELIS-MENTEN EQUATION
Your book should tell you something like this:
#color(blue)(v_0 = (k_2[E]_"tot"[S])/(K_M + [S]) = (v_max[S])/(K_M + [S]))# where:
#v_0# is the initial rate#[E]_"tot" = [E] + [ES]# #K_M# is the Michaelis constant (#(k_(-1) + k_2)/(k_1)# )#[S]# is the concentration of the substrate#v_max = k_2[E]_"tot"# is the maximum rate the reaction would reach, i.e. where#[S]# is large in a#v_0# vs.#[S]# plot
DOUBLE-RECIPROCAL/LINEWEAVER-BURK EQUATION
This is assuming without inhibitor. Naturally, double reciprocal literally means take the reciprocal of both sides.
#1/(v_0) = (K_M + [S])/(v_max[S])#
#color(blue)(1/(v_0) = (K_M)/(v_max)1/([S]) + 1/(v_max))#
Do take note, though, that the Lineweaver-Burk plot ought to be used more often for high concentrations of substrate than for low; at low
