Enzyme Kinetics

What is Michaelis-Menten kinetics?

Michaelis-Menten kinetics describes the rate of an enzyme-catalyzed reaction. The model outlines how an enzyme (E) reversibly forms an enzyme-substrate complex (ES), facilitating the conversion of substrate into product and regenerating the enzyme for further catalysis. This model introduces two key parameters: Vmax, the maximum reaction rate achieved when the enzyme is saturated with substrate, and Km (the Michaelis constant), which represents the substrate concentration at which the reaction rate is half of Vmax.

The model illustrates a hyperbolic curve where, initially, the reaction rate increases linearly with substrate concentration. However, as substrate increases, the enzyme becomes saturated and the rate of reaction approaches its maximum (Vmax), independent of further substrate increase. Michaelis-Menten kinetics provides a fundamental framework for understanding enzyme efficiency and activity.

Default Michaelis-Menten model

A hyperbolic curve useful for saturation binding experiments

The Michaelis-Menten model

In enzyme kinetic experiments, the Michaelis-Menten model is used to fit experimental data, obtained by measuring enzyme reaction rates across a range of substrate concentrations. From this fitting, crucial kinetic parameters like Km (the substrate concentration at half-maximal velocity) and Vmax (the maximum enzyme velocity) are determined.

The resultant curve is characteristic of a rectangular hyperbola, and the equation used to fit the Michaelis-Menten model is:

Saturation binding curve

Analogous to enzyme saturation with substrate, a saturation binding curve (or binding isotherm) illustrates the relationship between ligand concentration and the degree of receptor occupancy (or binding) in a biological system. As ligand concentration increases, more binding sites become occupied until the curve plateaus at a maximum level, signifying complete saturation.

The objective of a saturation binding experiment is to quantify the binding affinity, represented by the dissociation constant Kd (the ligand concentration at which half of the binding sites are occupied), and the maximum number of binding sites, Bmax.

Sound familiar? It should! The same mathematical equation that describes the saturation binding curve is identical in form to the Michaelis-Menten equation used for enzyme kinetics. A prime example of shared principles in biology.

Initializing parameters used during fitting

Rather than directly calculating parameters like linear models, non-linear regression employs an iterative process that starts with initial guesses and uses computational algorithms to progressively refine parameter values until the 'sum of squared residuals' is minimized."

While Graphmatik streamlines parameter auto-initialization with estimated good values, this process isn't infallible, especially when data is insufficient to fully capture the Michaelis-Menten curve.

As poor initial guesses can cause the algorithm to settle for a local minimum instead of the desired global minimum, manual adjustment of these initial values may be necessary to help Graphmatik find the best fit for your data.

Constraining the model

Graphmatik allows you to constrain or fix the upper bound (Vmax/Bmax) of the Michaelis-Menten or saturation binding curve, which can lead to a more accurate fit for undersampled datasets.

Interpolate from the curve

A Michaelis-Menten curve is most often used to measure an enzyme's affinity for its substrate (Km), where lower Km values indicate higher affinity and a lower substrate concentration needed to achieve Vmax

After fitting the Michaelis-Menten (or saturation binding) curve in Graphmatik, the Km (or Kd) will be reported as a parameter estimate inside the Analyze tab of the stats workspace alongside the estimate for Vmax (or Bmax).

But Graphmatik also makes it really easy to interpolate from the regression curve. After running an analysis, switch to the stats workspace and select the interpolate tab. A table will appear where you can enter values into X or Y columns.

Provide a value for X, and Graphmatik will interpolate the value for Y; enter a value for Y, and Graphmatik will estimate the corresponding value of X.

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