Enzyme Catalyzation

Introduction

Chemical reactions between substances have different rates at which they happen, or in other words, differ in how many molecules of substrate S1 are turned into product P1 during a certain amount of time (with a unit of mol/s, for example). The basic reaction is described as follows:

S1->P1 

So basically, S1 becomes P1. But since humans and other living things have thousands of reactions happening all the time, how does the body avoid overproduction and uncontrollable reactions? Why do not all substrates immediately turn into product? The short answer is enzymes. The reaction of S1 into P1, without the presence of an enzyme, might have the rate of 1 mole per 100 hours, meaning that not much is happening. Adding an enzyme provides a new reaction path with a lower energy requirement. 

S1+E ⇌ ES -> P1+E

The enzyme can easily speed up the reaction by more than one million times the original rate, making S1 turn into P1 at a rate of about 3 mol/s or more. Controlling the amount of enzyme available to the substrate thus controls the reaction speed. The enzyme E binds the substrate and creates an enzyme-substrate complex, before progressing into product.

Explore the available scenarios by evaluating each cell in order. Evaluation is done by selecting a cell and pressing Shift+Enter.

In order to get the full experience of this example, you need the following:

Wolfram System Modeler; a free trial download is available at www.wolfram.com/system-modeler

The model that came in the same bundle as this notebook

For more information about Wolfram System Modeler, visit www.wolfram.com/system-modeler.

Initialize

Define the model name:

mmodel="EnzymeCatalysis";

Load the model:

Import[FileNameJoin[{NotebookDirectory[],"EnzymeCatalysis.mo"}]];

The Model

Check the model diagram:

SystemModel[mmodel,"Diagram"]

The red component with arrows represents the reactions and in which direction the reaction can flow. The first reaction has arrows in both directions (left and right), which means that it is reversible. An enzyme-substrate complex can therefore be produced and then break up again into enzyme and substrate, with no product being formed. More commonly of course, the reaction continues and results in enzyme and product. Once the product has been created, it cannot turn back into substrates, which can be seen through the irreversible reaction component. The non-enzymatic reaction is also irreversible.

Analysis

In order to analyze the model, a GUI for manipulating the concentrations of substrate and enzyme can be used.

Manipulate[
Grid[{{
SystemModelPlot[SystemModelSimulate[mmodel,<|"ParameterValues"->{"Sc0"->s,"Ec0"->e}|>,Method->{"CVODES"}],
"Substrate and product concentrations",
PlotRange->All,ImageSize->{360,300},Filling->Axis,PlotLegends->Placed[Automatic,Bottom],PlotLabel->"Concentration over time"],SystemModelPlot[SystemModelSimulate[mmodel,<|"ParameterValues"->{"Sc0"->s,"Ec0"->e}|>,Method->{"CVODES"}],
"Reaction rates",PlotRange-> All,ImageSize->{360,300},Filling->Axis,PlotLegends->Placed[Automatic,Bottom],PlotLabel->"Reaction rates"]
}}],
"Initial Conditions:",{{s,0.01,""},Row[{Pane["substrate",ImageSize->50],Slider[#1,{0,0.1,0.01},ContinuousAction->False],ToString[N[s]]<>" mol/l"}]&},{{e,0.0001,""},Row[{Pane["enzyme",ImageSize->50],Slider[#1,{0,0.001,0.0001},ContinuousAction->False],ToString[N[e]]<>" mol/l"}]&},FrameMargins->Small,SynchronousUpdating->False,
SynchronousInitialization->False]

In the plot that should appear, you see the concentration of the substrates and products of the reaction groups, as well as the derivatives of them. The sliders control the concentration of enzyme and substrate, allowing you to explore how the catalyzation affects the reaction rate. The states displayed are in the concentration unit of mol/l.

Terms and Conditions of Use

This domain example is an informational resource made freely available by Wolfram Research.

Use of This Example

• You may not use this example for any purpose that is unlawful or dangerous.
• You assume total responsibility and risk for your use of this example.
• You may not present this example with any alteration to its trade dress, trademarks, or design.

License

All content in this bundle is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. By accessing the content or using it in any way, you accept and agree to be bound by the terms of this license. If you do not agree to these Terms of Use, you may not use this content. Wolfram Research reserves the right to change, modify, add to, or remove portions of these Terms of Use at any time without notice. Please refer back to www.wolfram.com for the latest Terms of Use.

A summary of the licensing terms can be found at:
http://creativecommons.org/licenses/by-nc-sa/3.0

The full legal code can be found at: 
http://creativecommons.org/licenses/by-nc-sa/3.0/legalcode