Enzyme Kinetics

Lecture 4CHEM4421 2011

Michaelis-Menten kinetics model

Seminal work published in 1912 by Leonor Michaelis (1875–1949) and Maud Leonora Menten (1879–1960), a German man and a Canadian woman, cast light on the reasons why enzymes are so efficient.

Initial Velocity, vo

y = 0.2874x + 0.0251R2 = 0.9994

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

Time (min)

Ab

sorb

ance

(41

0nm

)

Slope of initial [P]/t at a particular [substrate] is a single point on the Michaelis-Menten graph

Linear (Reciprocal) Plots

The Lineweaver-Burk double-reciprocal plot, depicting extrapolations that allow the determination of the x- and y-intercepts and slope.

Lineweaver-Burk

A Hanes-Woolf plot of [S]/v versus [S], another straight-line rearrangement of the Michalelis-Menten equation.

Hanes-Woolf

You should use Hanes-Woolf, Eadie-Hofstee, or fit the hyperbolic curve (I do not think excel will do this, but Origin will)!

Demo

Different Types of Bi-Bi Reactions

Single displacement (sequential)randomordered

Double displacement (ping pong)

Single displacement Ordered: e.g., lactate dehydrogenase

Random: e.g., creatine kinase

Single-displacement bisubstrate mechanism

Single-displacement bisubstrate mechanism. Double-reciprocal plots of the rates observed with different fixed concentrations of one substrate (B here) are graphed versus a series of concentrations of A. Note that, in these Lineweaver-Burk plots for single-displacement bisubstrate mechanisms, the lines intersect to the left of the 1/v axis. Ks are dissocation constants for A and B as indicated in the superscript.

Random, single-displacement bisubstrate mechanisms where A does not affect B binding, and vice versa. Note that the lines intersect at the 1/[A] axis. (If [B] were varied in an experiment with several fixed concentrations of A, the lines would intersect at the 1/[B] axis in a 1/v versus 1/[B] plot.)

Random, single-displacement bisubstrate mechanism

Double displacement (ping – pong) reaction

Double-displacement (ping-pong) bisubstrate mechanisms are characterized by Lineweaver-Burk plots of parallel lines when double-reciprocal plots of the rates observed with different fixed concentrations of the second substrate, B, are graphed versus a series of concentrations of A.

Ping-pong bisubstrate mechanism

Temperature Dependence

V0,max(T)

T (oC)4020 30 50 60 70 80

Arrhenius kinetic behavior

proteindenaturation

pH dependence

V0

pH

pKa of reaction 1 ~ 4.0

pKa of reaction 2 ~ 9.0

2 124 6 8 10

max

low

Activity decreases due to lysine deprotonation

Activity decreases due to glutamate/aspartate protonation

Maximal activity range

More informative to plot Km and Vmax vs pH, which is most effected?

TM1667: glucose isomeraseBandlish et al. Biotech and Bioengineering, 80, 185 – 194 (2002)

glucose fructose

1U of enzyme activity is defined as that catalyzing the formation of 1 μmol product in 1 min Specific activity is the number of units per mg of protein

TM1155: glucose-6-phosphate dehydrogenase Hansen et al. FEMS Microbiology Letters, 216, 249 – 253 (2002)

TM1155: glucose-6-phosphate dehydrogenase

TM0343: 3-deoxy-D-arabino-heptulosonate 7-phosphate (DAHP) sythase

Wu et al., JBC, 278, 27525 – 27531 (2003)

TM0343: 3-deoxy-D-arabino-heptulosonate 7-phosphate (DAHP) synthase

TM1469: ATP-dependent glucokinaseHansen and Schönheit. FEMS Microbiology Letters, 226, 405 – 411 (2003)

TM1193: β-galactosidaseKim et al. J Appl Microbiol, 97, 1006 – 1014 (2004)

TM1520: Dihydrodipicolinate reductasePearce et al. J. Biochem, 143, 617 – 623 (2008)

TM1520: Dihydrodipicolinate reductase

TM0209: ATP-dependent 6-phosphofructokinaseHansen et al. Arch Microbiol, 177, 401 – 409 (2002)

Beyond Photometric Assays

• Many other ways to observe the activity of an enzyme over time– Fluorescence (photometric)– HPLC– NMR– O2 electrode assay– Radiographic assay– Gel assay