"
Team:Leicester/Modeling
From 2012.igem.org
Modeling
What are we modeling?
The aim of our project is to genetically modify a bacteria that can break down the polymer chains in expanded polystyrene (EPS). The result is a solution of monomer chains that can be extracted and used in the synthetic production of other useful chemicals, for instance Lactic Acid (C3H6O3). The computational model is going to be used to aid calculations predicting how much substrate (polymer chains) will be needed, how much product will be required to sustain the bacteria colony and how much product will be left over for other uses.
Why are we modeling?
By creating a computational model of a biological system, theoretical and experimental biologists are able to predict the outcomes and behaviour of a system for a set of input parameters. The results of the simulation can provide guidance to the success of the experiment for the tested input parameters before undertaking physically in the lab. The model built in our project will help determine the next steps in the project, for example to attempt to change the number of enzymes produced by the bacteria or modify how the enzyme behaves. The major advantages of developing and using a model in the project are that it can save time exploring an idea that had a high probability of failure and simultaneously save resources.
Enzyme Kenetics
Enzyme Kinetics is the processes by which chemical reactions are catalysed by enzymes. When we say that we aim to "genetically modify a bacteria that can degrade expanded polystyrene" what we really mean is that we aim to "create a chemical reaction catalysed by enzymes that can break down polystyrene polymer chains". The polymer chains in expanded polystyrene can be broken into monomers by industrial processes, however this involves the use of nasty chemicals.
The method adopted by bacteria to modify their environment, in order to obtain useful products, is the use of enzymes. Enzymes are biological molecules that have the ability to act as a catalyst in chemical reactions, in other words increase the rate of reaction. Enzymes have an active site that fits the substrate, like a "lock and key", once connected the enzyme performs the reaction. The Psuedmonas bacteria in our project secrete enzymes that break the polystyrene polymer in order to extract the carbon.
Above is a diagram illustrating an example of a substrate can be manipulated by the enzyme. The substrate collides with the active site of the enzyme to form a complex, the products are later released by the enzyme.
The formation of substrate to product via the use of enzymes can be described in the following expression:
Where:
E is the number of enzymes
S is the substrate concentration
ES is the enzyme-substrate complex
P is the product
k1 is the forward rate constant for enzyme-substrate formation
k-1 is the reverse rate constant for enzyme-substrate formation (the enzyme "drops" the substrate)
k2 is the forward rate constant for production formation from the enzyme-substrate complex and is assumed irreversible
The substrate concentration uses the units of molarity. A single monomer chain of polystyrene, known as styrene, has a molecular weight of 104.1 g/mol. In order to get one molarity solution, 104.1 grams in 1Litre of solvent. The average chain molecular weight is approximately 9.7685 x 106 g/mol, that's around 93, 838 styrene monomers per average chain. The active sites of the enzymes secreted by the bacteria can only fit the free ends of the polystyrene chain, so out of a 93, 838 long chain of styrene monomers, only 0.002% of the chain is available to the enzyme.
Also, it ought to be considered the method the enzyme will use to find the end of the chain. It can either collide with the polymer chain suspended in solution, and at part of the chain hold on and shuffle along to the end - similar to DNA splitting enzymes. The other method, with a chain suspended in solution, specifies at the enzyme can only start catalysing the reaction when colides with a free end only; a much more lengthly, although possibly more realistic, senerio.
Michaelis-Menton equation
The Michaelis-Menton equation is a model for single-substrate reaction and shall be used as a base for our model.
Where:
V0 is the initial veliocity of the reaction
Vmax is the rate of reaction when substrate is saturated
S is the substrate conerntration
Km is the substrate concerntration when the reaction rate is half the maximum and can be calculated using: k-1 + k2/k1
