Simulating Enzymatic Pathways
Example software: COPASI

What are Enzymatic Pathways

Enzymatic pathways are a series of chemical reactions involving substrate and enzymes where the enzyme acts as a catalyst.

Biochemical Pathway Simulators

Goal of a biochemical pathway simulator is to predict the out come of cellular reaction based on the starting products (E.g. gene(s), protein(s), RNA, DNA, Enzymes etc.)
Can be used to predict the out comes of enzyme reactions
Examples of Simulators

COPASI
MATHLAB
Cell++
Cybercell
MesoRD
MCell
GEPASI
Smartcell

Developing the Model

The model begins with the basic kinetic enzyme model dSi/dt which is the difference in mass over the difference in time.


Figure 1. The basic enzymatic kinetic model.	Figure 2. Applying Vmax to the model.

From the basic model we can then build from there by adding stoichiometry, rate laws and differentical equations to the model. The addition of these other parameters adds complexity to the model.

Figure 2.

Construction of an exemplary kinetic model. A, Information about basic connectivities. B, Stoichiometric data adds numerical dependencies between the metabolites. C, Rate laws defining the reaction rate of each enzymatic step. D, Combining the stoichiometric data with the rate laws into a system of ODEs describing the change in metabolite concentrations over time.

Where Does the Data Come From

The data to input into the model is obtained from previously conducted experiments, realiable textbooks or databases.

Stochiometry = textbooks and databases
Rate law = dependent on stoichiometry and the mechanism of action of the enzyme
Vmax (maximum velocity) = Dependant on the concentration of the enzyme or more precisely the regulation of gene expression. In vivo measurement is required.
Km = literature

How an Ezymatic Pathway Model is Solved

The simulation works in a stepwise manner. Each equation is solved based on short time period. The final substrate and enzyme concentrations are collected and the equations are again updated. The process is repeated and the outcome is Dependant on the original parameters.

Figure 3.

Concentration time course in kinetic model with different parameter sets, exhibiting converging (A), diverging (B), and oscillatory behavior (C). Parameters are k₁ = k₂ = 1 and k₃ = 0.5 (A); k₁ = k₂ = 1 and k₃ = 1.5 (B); and k₁ = k₂ = k₃ = 1 (C). Units are arbitrary.

COPASI

COPASI based on GEPASI is a computer run program that simulates possible biochemical reactions. The website can be reached here.

Features: platform independant and user friendly (either graphic interface or command line)

How COPASI works: Models are developed by the user by inputing information into the model parameters. This information is gathered either by literature or from experimental data. The choices for the parameters are limited by the program.

Examples: Vmax, Km, Velocity

Output: The output is in the XML file format and contains a report file and output file. COPASI can also read files created in GEPASI and SBML.

Advantages:

Provides a estimation of the products produced by biochemical pathways, useful to preform before laboratory experiments
Useful tool to predict possible outcomes and reactions, especially useful when equipment and funds are limited

Disadvantages:

Time to search and prepare data
Errors that occur when developing the mathematical model
Models become too complex when multiple enzyme and substrates are used

Examples

Computer Simulated Calvin Cycle

Reference

Hoops, S. et. al. 2006. COPASI—a COmplex PAthway SImulator. Bioinformatics 22(24): 3067-3074.

Schallau, K. and Junker, B. 2010. Simulating Plant Metabolic Pathways with Enzyme-Kinetic Models. Plant Physiology 152 (4): 1763-1771.

Edelmira, V. et. al. 2009. Computer Simulation of the Dynamic Behavior of the Glutathione-Ascorbate Redox Cycle in Chloroplasts. Plant Physiology 149:1958-1969.