# Finding 1/V from absorbance in Lineweaver-burk plot

I’ve got six test-tubes with $0.5\ \mathrm{ml}+0.5\ \mathrm{ml}$ of 0.005 %, 0.0025 %, 0.00125 %, 0.000625 %, 0.0003125 % and 0.0003125 % starch and 4.2 pH phosphate buffer solution (2, 4, 8, 16, and 32-fold dilution of 1 % starch solution). 0.5 ml of beta-amylase was added to each test-tube, and heated (without sixth test-tube). Then the absorbance of each specimen was measured (sixth test-tube used as reference) in 530 nm wavelength.

I have to find the $K_\text{M}$ of β-amylase from Lineweaver–Burk graph. There is no problem with plotting $x$ points on graph (it’s just a reciprocal of substrate concentration). But how can I use absorbance data to find $V$ that I need to plot on $y$-axis?

Second, let me answer your question. The classical Lineweaver-Burke plot puts inverse reaction rate on the $y$ axis, i.e. $1/V$. Your question is how to find $V$ from absorbance data. The answer is, you don't need to. Let $A_i(t)$ be the absorbance data for tube $i$ as a function of time. What is $V_i(t)$ for that tube? We won't know unless you know the molar absorption coefficient of the substrate (or product -- I'm a little unclear from your question what you are hoping to detect by measuring $A_{\textrm{530 nm}}$). Assume that it is the product that is absorbing, and that it has a molar absorption coefficient of $\epsilon$ and that you are using a photometer with path length $L$. Then the reaction rate for the $i$th tube will be
$V_i(t)= \frac{1}{\epsilon L}\frac{dA_i(t)}{dt}$
This means take the slope of the absorbance measurement and divide it by $\epsilon$ and $L$ -- numbers you don't know -- to get $V$. But the key assumption is simply that $V \propto \frac{dA}{dt}$. Try making up any numbers you like for $\epsilon$ and $L$. Find $K_m$. Then make up new numbers and find $K_m$ again. Did the result change?