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Modeling for Dummies

Modelling a metabolic pathway using Copasi

When first faced with the task of modelling a biological system, the concept might seem a bit daunting. This is why have decided to provide a comprehensive guide for creating a simple, yet applicable model of a metabolical pathway.

The model demonstrated in the examples below is a very simplified version of the carotenoid pathway that has been part of the metabolic engineering during this year’s project (fig.1).

The tools

While using MATLAB or a similar code-based inteface might allow for more customizable model, Copasi provides a more accesible platform. It runs on mostly anything, is free to use and provides a user friendly interface. It can be downloaded here http://www.copasi.org/tiki-index.php?page=download

What to consider:

• What do you know about the reaction?
  • Is the reaction reversible or irreversible?
    • Thermodynamically speaking, basically all metabolic reactions are reversible, and enzymes simply catalyze the progress towards equilibrium. However, this fact is often disregarded with the motivation that the product in intermediate steps never reaches concentrations high enough to affect the flow of equilibrium with any significance.^[1] The effect on the validity of the model from this assumption is still a a matter of discussion, but with limited data this might still be a good approach for an inital model.^[2]
  • What substrates are required?
  • What products are produced?
  • Are there any inhibitors?
  • What is known about the mechanism by which the enzyme catalyzes the reaction?
• What parameters are required?
  • This depends upon what reaction mechanism are used. In the following example we use Km, kcat, Ki as well as the concentrations of several key metabolites. Additionally, the stochiometry of each reaction is required.

The answer to these questions can best be found at databases such as KEGG or Brenda.

Additionally, one might want to consider what assumptions can be made and while still providing a functional model. Do you assume free diffusion within the cell? Will you account for degradation of enzymes and metabolites? What limitations does the cell’s central metabolism create for your specific pathway?

So, what about this specific model? For simplicity’s sake, we will make a few pretty hefty assumptions in the example below. We will assume that:

• All enzyme concentrations are constant and similar
• That there is no decay of metabolites and that all reactions are irreversible and follow simple Michaelis-Menten kinetics.
• That there is no additional flux of substrates after the beginning of the simulation. While unrealistic, this is to make the example more easy to follow.

From the links above we see that there are no inhibitors in our pathway to consider. The only metabolite concentrations above zero will be the the initial substrates IPP and FPP, and these levels are set to arbitrary but plausible values. The levels of FAD and FADH are assumed to be constant and abundant. In the table below is a compilation of all the parameters used in the example model if you should wish to replicate it.

Table 1: Enzyme parameters

Enzyme	kcat (1/s)	Km (mM)
CrtE	0.025	0.011 (FPP) 0.036 (IPP)
CrtB	0.0385	0.003
CrtI	0.00008	14.8
CrtY	0.0652	0.005

Table 2: Initial concentrations of metabolites <>

Metabolite	Concentration (M)
IPP	10-6
FPP	10-7
FAD	0.001
FADH	0.0001

All metabolites not listed are initially set to 0.

Setting up the model

Model

Here, you can assign a name and basic premises of your model.


Fig. 2. The main Model screen.

Model>Biochemical>Compartment

From this screen, you can set up a compartment for your reaction. By clicking on the compartment a more detailed interface becomes avaiable.

Fig. 3. The Compartment screen

Model>Biochemical>Reactions

This is where you can enter the reactions you wish to simulate. The syntax is simple:
= signifies a reversible reaction
-> signifies an irreversible reaction
; signifies the end of the reaction formula, given that it requires modifiers (enzymes, inhibitors etc.). Any compound listed afterwards will be treated as a reaction modifier. If there are no modifiers needed, this can be ignored.


Fig. 4. The Reactions screen.

Functions (Optional)

Copasi provides a wide selection of pre-set models. However, depending on the data available and the system being modeled, you might want to add your own function, as shown below.


Fig. 5. The function editor. Note that the variables are assigned accordingly in the menu below the function.

Model>Biochemical>Reactions

Selecting each reaction, a rate law can be defined and variables assigned. You can also enter values for the parameters.


Fig. 6. An individual reaction screen.

Model>Biochemical>Species

On this screen, the concentrations and properties of the metabolites and enzymes involved can be modified.


Fig. 7. The Species screen

Model>Biochemical>Parameter Overview

This is a screen that gives a bird’s eye-perspective of all parameters involved in your model, and gives you the option of changing the all values from one screen.


Fig. 8. The Parameter Overview screen.

Output

Copasi provides a number of output options that can be used to analyse your data. In this tutorial we will display some of the most basic functionalities required to analyse a metabolic pathay model.

Time course

As one might imagine, this tool allows for plotting mostly anything as a function of time. This can be useful for exmple predicting metabolite production under given circuimstances.

Tasks>Time Course>Output Assistant

In the example below we use it to display metabolite concentrations. This is done by selecting “Concentrations, Volumes, and Global Quantity Values” in the Output Assistant menu.


Fig. 9. The Output Assistant

Tasks>Time Course

In this window, you can define the duration and interval size of the plot. You can alo choose between several different deterministic and stochastic methods (in this example, a deterministic method is used)



Fig. 10. The main Time Course screen.


By clicking “Run”, one might recieve something like this:


Fig. 11. The plot of metabolite concentrations as a function of time recieved from a deterministic Time Course simulation.

Steady-state

This tool will simulates the flux of metabolites within the system when it has achieved euilibrium (in this case when the cell i in the steady-state growth phase).

Model>Biochemical>Species

The stedy-state simulation requres all metabolite conentrations at the first and last step of the pathway to be fixed. This can be done from the Species screen.


Fig. 12. Changing the species type.

Tasks>Steady-State

From this screen, you can alter and run the Steady-state simulation.



Fig. 13. The main Steady-State screen.

Tasks>Steady-State>Result

From this screen, the result of the simulation can be viewed.


Fig. 14. Results from the Steady-state analysis.

Looking forward

Having grasped the basics, one can now move on to new and greater things. For pedagogic purposes, the model in the examples above is simplified to a point where it’s applicability is questionable. A more complex versions of the same model can be found below, along with the model used in the tutorial

Simple model of the production of beta-carotene: Extended_carotenoid_model_uppsala.zip Expanded model, involving precursor steps to simulate more realistic influx of metabolites: Tutorial_model_Uppsala.zip

Handy links:

Copasi’s own documentation is always a good source of information: http://www.copasi.org/static/userguide.new/index.xhtml
Finding appropriate metabolite concentrations is not easy, and sometimes quite impossible without making your own measurements. However, Nature Chemical Biology provides a useful table of the most central components: http://www.nature.com/nchembio/journal/v5/n8/fig_tab/nchembio.186_T1.html

References:

[1]. R.M.T. Fleming, I. Thiele, H.P. Nasheuer, Biophysical Chemistry 145 (2009) 47–56:
Quantitative assignment of reaction directionality in constraint-based models of
metabolism: Application to Escherichia coli
http://thielelab.eu/documents/Papers/2009-Fleming-Quantitative%20assignment%20of%20reaction%20directionality%20in%20constraint-based%20models%20of%20metabolism%20Application%20to%20Escherichia%20coli.pdf
[2]. Mark G. Poolman et al., Plant Physiology 2009 November; 151(3): 1570-1581: A Genome-Scale Metabolic Model of Arabidopsis and Some of Its Properties
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2773075/