Ch. 10: Kinetics, Inhibition, & Control

v

v = rate = k[S]

Km

the michaelis constant; [S] at ½ of vmax

vmax

maximal reaction velocity

kcat

catalytic constant; represented by vmax / [E]total; aka turnover number

plotting [P] vs time

initial slope is v0

plotting v0 vs [S]

slope = k = ∆v0/∆[S]

k

the rate constant; influence of temperature

v0

initial rate; rate when t = 0 & substrate concentration is highest

enzyme kinetics formula

E + S ←→ ES → E + P

k1

rate constant for E + S → ES; complex formation

k-1

rate constant for ES → E + S

k2

rate constant for ES → E + P; rxn & dissociation

rectangular hyperbola equation

y = ax / (b+x); a = asymptote of curve; b = a/2 or the point on the x axis where y is halfway to the aymptote

michaelis-menten equation

v0 = vmax[S] / (Km + [S])

in enzyme kinetics, the aymptote represents

vmax

in enzyme kinetics, ‘b’ represents

Km

in enzyme kinetics, the x-axis represents

substrate concentration

in enzyme kinetics, the y-axis represents

v0

Km interpretation

can be considered a measure of enzyme’s affinity for substrate; lower Km = tighter binding

2 things that affect Km

temperature, pH

typical Km range

10^-2 to 10^-5 molar

kcat represents

the # of rxn processes each active site catalyzes per unit time

below Km, v0 is

very sensitive to ∆[S]

above Km, v0

doesn’t change much in response to ∆[S] because the enzyme is approaching saturation

catalytic efficiency ratio

the ratio of kcat/Km; when kcat is high & Km is low, the enzyme is highly efficient

most efficient catalytic efficiency

10^8 to 10^9 M^-1 s^-1

diffusion-controlled limit

a reaction is catalyzed for virtually ever substrate binding

lineweaver-burk equation

a rearrangement of the michaelis-menten eqn

$$\frac{1}{v0}=\left(\frac{Km}{v\max}\right)\left(\frac{1}{\left\lbrack S\right\rbrack}\right)+\frac{1}{v\max}$$

kcat formula

kcat = vmax / [E]m total

acetylcholine

drives muscle contraction

acetylcholinesterase

allows muscles to release; needs to be very fast, so it has a low Km & a high kcat

digestive enzyme rate

relatively slow; digestive rxns are endothermic. high Km & low kcat

purpose of lineweaver-burk plot

allows measurement of Km & vmax

lineweaver-burk x-axis

1/[S]; [S] increases LEFT

lineweaver-burk y-axis

1/v0; v0 increases DOWN

lineweaver-burk x-intercept

-1/Km

lineweaver-burk y-intercept

1/vmax

lineweaver-burk slope

Km/vmax