# Lowest Michaelis constant Km

I want to find a lower limit of the Michaelis constant for some evaluations of Michaelis-Menten enzyme kinetics. What is the lowest $K_m$ you ever encountered? Is there a theoretical limit?

• en.wikipedia.org/wiki/… Nov 23 '17 at 15:50
• The link does provide some examples, but no lower limit for k_m. Nov 24 '17 at 18:22
• It is generally believed that evolution places a theoretical limit on kcat/Km, but not necessarily on Km. I know of one reported Km in the nanomolar rnage (3.2 nM to be precise): aem.asm.org/content/85/13/e00438-19. There are probably others that are lower. Sep 23 '20 at 20:04
• Since the function under consideration is catalytic (accelerating the reaction rate), you might consider the natural rate of the reaction (in absence of enzyme) as setting a limit on kcat. From the diffusion limited on rate (as explained in an answer) and setting the off-rate kr to zero you can estimate a lower meaningful (theoretical) bound on Km. Sep 23 '20 at 20:45
• The other way to set an upper limit on kcat is by the lifetime of the enzyme. Most cellular proteins are degraded within hours or days. So you could set a conservative lifetime as 100 days and say that at least one turnover must happen (on average) within that time, so minimum kcat is 3 per year ~ $1\times 10^{-8}$ s$^{-1}$. Dividing by kf = 10^9 M-1s-1 gives a limit on Km of $10^{-17}$ M give or take a few orders of magnitude. Sep 24 '20 at 16:44

Take this generic reaction representing the Michaelis-Menten enzyme kinetic:

You can derive the Michaelis-Manten constant $$K_m$$:
(for derivation see https://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics)

The quasi-steady state hypothesis was used, therefore the rate of formation and breakdown of $$ES$$ are the same; this is a good approximation if the enzyme concentration is much less than the substrate concentration $$[S]$$ or $$K_m$$ or both. That means that $$K_m$$ can be extremely small (almost zero) and the Michaelis-Menten equation still be valid proven that the enzyme concentration is much less than $$[S]$$.

$$K_m$$ is very small if:
$$k_r$$ and $$k_{cat}$$ are both very small compared to $$k_f$$, thus if the complex $$ES$$ is formed very quickly compared to its breakdown.
In this case the reaction proceeds at its maximum velocity $$V_{max}=k_{cat}*E_0$$, with $$E_0=[ES]+[E]$$:

About the theoretical limit on how small $$K_m$$ can be there are two considerations:
First, $$k_f$$ cannot be cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate. This means that $$k_f$$ cannot be higher than $$10^9 s^{-1} M^{-1}$$ (ref.https://www.ncbi.nlm.nih.gov/books/NBK22430/#:~:text=This%20rate%20cannot%20be%20faster,s%2D1%20M%2D1.)
Second, $$k_{cat}$$ cannot be too small or the product $$P$$ formed is produced at a rate not suitable for the cell survival.

Generally, I haven't encountered $$K_m$$ smaller than $$10^{-6}M$$ in biological enzymes (e.g Triosephosphate isomerase, TPI) but possibly there are. In TPI, $$k_f$$$$10^9 s^{-1} M^{-1}$$, therefore $$k_r$$$$k_{cat}$$$$10^{3}s^{-1}$$ that is still quite high. It would be very interesting to know if there are enzymes with an even lower $$K_m$$. Very intresting question.

• Thank you, great answer! Sep 24 '20 at 12:55