Lineweaver–Burk plot

In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of the Michaelis–Menten equation of enzyme kinetics, described by Hans Lineweaver and Dean Burk in 1934.

The double reciprocal plot distorts the error structure of the data, and is therefore not the most accurate tool for the determination of enzyme kinetic parameters. While the Lineweaver–Burk plot has historically been used for evaluation of the parameters, together with the alternative linear forms of the Michaelis–Menten equation such as the Hanes–Woolf plot or Eadie–Hofstee plot, all linearized forms of the Michaelis–Menten equation should be avoided to calculate the kinetic parameters. Properly weighted non-linear regression methods are significantly more accurate and have become generally accessible with the universal availability of desktop computers.

Definitions

The Lineweaver–Burk plot derives from a transformation of the Michaelis–Menten equation,

v

=

V

a

K

m

+

a

{\displaystyle v={\frac {Va}{K_{\mathrm {m} }+a}}}

in which the rate

v

{\displaystyle v}

is a function of the substrate concentration

a

{\displaystyle a}

and two parameters:

V

{\displaystyle V}

, the limiting rate, and

K

m

{\displaystyle K_{\mathrm {m} }}

, the Michaelis constant. Taking reciprocals of both sides of this equation it becomes as follows:

1

v

=

1

V

+

K

m

V

⋅

1

a

{\displaystyle {\frac {1}{v}}={\frac {1}{V}}+{\frac {K_{\mathrm {m} }}{V}}\cdot {\frac {1}{a}}}

Thus plotting

1

/

v

{\displaystyle 1/v}

against

1

/

a

{\displaystyle 1/a}

generates a straight line with ordinate (y) intercept

1

/

V

{\displaystyle 1/V}

, abscissa (x) intercept

−

1

/

K

m

{\displaystyle -1/K_{\mathrm {m} }}

and slope

K

m

/

V

{\displaystyle K_{\mathrm {m} }/V}

.

Applications

When used for determining the type of enzyme inhibition, the Lineweaver–Burk plot can distinguish between competitive, pure non-competitive and uncompetitive inhibitors. The various modes of inhibition can be compared to the uninhibited reaction.

Competitive inhibition

The apparent value of

V

{\displaystyle V}

is unaffected by competitive inhibitors. Therefore competitive inhibitors have the same intercept on the ordinate as uninhibited enzymes.