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advanced enzyme kinetics

by Georg F. Weber (Submitted: 11/16/2012)

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## WHAT IS IT?

This model demonstrates the kinetics of single-substrate enzyme-catalysis. The model allows users to visualize the reaction.

The standard equation for this reaction is shown below.

Kc Kr
E + S <=======> E-S <==----> E + P
Kd k-r

Here E represents Enzyme, S Substrate, E-S Enzyme-Substrate complex, and P product. The rate constants are Kc for complex formation, Kd for complex dissociation, Kr for catalysis, k-r for a reversible last step (K-r is typically much smaller than Kr). The first step in catalysis is the formation of the E-S complex. The rates of complex formation and dissociation are very fast because they are determined by collision and separation of the molecules. The next step is for the enzyme to catalyze the conversion of substrate to product. This rate is slower because the energy required for catalysis is much higher than that required for collision or separation. To be generically applicable, this model gives the option to set a reverse reaction rate k-r that is much lower than Kr.

In Michaelis-Menten kinetics, there is typically a fixed initial substrate concentration. This is a limited model of biology. Enzymes in situ often work under rhythmic substrate input. Therefore, this model has the option to activate and modify a sigmoidal input of substrate.

Enzyme catalysis can also be controlled using inhibitors. Inhibitors are molecules that are structurally similar to substrate molecules that can complex with the enzyme and interfere with the E-S complex formation. Subsequently, the kinetics of the reaction will be altered. The model demonstrates the effects of inhibitors on catalysis.

## HOW TO USE IT

Choose the values of Kc, Kd, kr, and K-r with appropriate sliders:
- Kc controls the rate at which substrates (green) and enzymes (red) stick together so that catalysis can occur
- Kd controls the rate at which they come unstuck
- Kr controls the rate of the forward reaction by which an enzyme (red) converts a substrate (green) to a product (blue)
-k-r controls the rate of the reverse reaction by which a product (blue) turns into a complex of enzyme (red) and substrate (green)

If you desire to model enzyme catalysis under the driving force of rhythmic substrate input set the driver switch to "on" and choose the values for drive-amplitude and drive-rate.

Having chosen appropriate values of the constants, press SETUP to clear the world and create a constant initial number of enzyme (red) molecules. Play with several different values to observe variable effects on complex formation and catalysis.

Press GO to start the simulation. A constant amount of enzyme (red) will be generated. The concentrations of substrate, complex, and product are plotted in the CONCENTRATIONS window. The rates of change per time unit in substrate, enzyme, and product are plotted in the RATES window.

Experiment with using the ADD-SUBSTRATE and ADD-INHIBITOR buttons to observe the effects of adding more molecules to the system manually as it runs. The default setting for Kr is 0, which means that no product (blue) will be generated unless you change Kr to a non-zero value.

Note that when complexes form they stop moving. This isn't intended to be physically realistic; it just makes the formation of complexes easier to see. (This shouldn't affect the overall behavior of the model.)

Inhibitors can be irreversible or reversible. That is, they can bind to an enzyme and never let go, or they can stick and fall off. Currently, the model simulates irreversible inhibitors.

## NETLOGO FEATURES

It is a little difficult to ensure that a reactant never participates in two reactions simultaneously. In the future, a primitive called GRAB may be added to NetLogo; then the code in the FORM-COMPLEX procedure wouldn't need to be quite so tricky.

## CREDITS AND REFERENCES

This model was developed by Georg F. Weber and Tom Carter from the NetLogo library model "Enzyme kinetics" written by Mike Stieff.

## HOW TO CITE

If you mention this model in a publication, the citations for the original model and for the NetLogo software are:
- Stieff, M. and Wilensky, U. (2001). NetLogo Enzyme Kinetics model. http://ccl.northwestern.edu/netlogo/models/EnzymeKinetics. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
- Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2001 Uri Wilensky.

![CC BY-NC-SA 3.0](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png)

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

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