NetLogo User Community Models
by Nicolas Descostes (Submitted: 11/26/2008)
WHAT IS IT?
‘The enzymes are important and essential components of biological systems, their function being to catalyse the chemical reactions that are essential to life. Without the efficient aid of the enzymes these chemical processes would occur at greatly diminished rates, or not at all’ (by Keith J. Laidler and Peter S. Bunting, 1973).
Basic mechanism of non allosteric enzymes:
E+S <-> ES -> P
This model is simulating action of ALLOSTERIC enzymes.
Allosteric enzymes bind small and physiologically important molecules by non covalent binding. These small regulatory molecules are called effectors.
There are different types of effectors:
The first part of the model is simulating the kinetics of allosteric enzymes with homotrophic effectors.
E+S1 <-> ES1 + S2 <-> ES1S2 -> P
is regulated by an affinity constant K, which enables to represent the change of affinity. Each combination induces also a change of conformation as it has been said before.
The second part of the model is simulating the action of effectors (inhibitors/activators) on the model (see cooperativity area).
The first part of the model is a theoretical one. It does not correspond to any "validated" models (Monod-Wyman-Changeux, Koshland-Némethy-Filmer, Association-dissociation model). The aim of this model is to make the user understand the main principles of allosteric enzymes kinetics by looking at different parameters. This 'non conventional' representation has been chosen because of the complexity of the models named above, but it represents most of ideas of these ones.
The model must be think in two parts wich are indepant. The first part enables to understand how an allosteric enzyme is working, the second enables to study the effect on effectors (activators/inhibitors) on the cooperativity.
HOW TO USE IT
The interface contains three main parts: THE SCREEN (in the center), THE RATE (on the left) AND THE AFFINITY (on the right) AREA.
________________________________The Screen Area________________________________:
________________________________The Rate Area________________________________:
E + S1 <-> ES1---------------> enzyme-substrate2 affinity slide:
Enables to chose the constant of the second reaction seen in the first part of this manual.
ES1 + S2 <-> ES1S2---------------> product-formation-constant slide:
Enables to chose the constant of the third reaction seen in the first part of this manual.
ES1S2 -> P---------------> substrate1_units slide:
Enables to fix the initial rate of substrate1.
---------------> substrate2_units slide:
Enables to fix the initial rate of substrate2.
---------------> enzyme_units slide:
Enables to fix the initial rate of enzyme.
Enable to follow the rate of each element of the system.
---------------> Frame number:
It ranges from 1 to 3. This enables to plot several times the rate curves without deleting the previous values. Hence, the user would be able to compare the rate variations when the paramaters are changed.
WARNING: It is not possible to plot two (or more) times (by resetup) using the same frame.
---------------> The Rate Plot:
Enables to visualize the different rate values using a graph. It is possible to clear it at any time using the "clear-rate-plot" button.
________________________________The Affinity Area________________________________
((V * (a ^ h)) / ((K.O.5 ^ h) + (a ^ h)))K is the value of the substrate concentration 'a' at which v = 0.5*V ie the velocity v is the half of the maximum velocity V.
---------------> Cooperativity slide:
Here Cooperativity is in fact the 'h' element in the equation. Cooperativity can be well estimated by the number of subunits the enzyme has. The slide enables to choose a positive or negative (between 0 and 1) cooperativity.
THINGS TO NOTICE/ THINGS TO TRY
->Enzymes/substrates, complex/substrate2 can combine only if they are close in space.
-> Notice the change of shape of each elements on the screen.
-> Notice S1-E-complex turtles and S1-E-S2-complex turtles are not moving on the screen to explicit transformations
-> Look at the different rates of each element at the beginning and at the end of the run. Try to pause the model at different moments to understand how an allosteric enzyme is working, by looking at the rate of each element.
-> Look at the rate plot. Link each curve with its rate monitor.
->Change the affinity slides and product formation values and look at the effect on the plot (Do not forget to not use the same frame two times). What is the relation between affinity constant and power of binding? Does a high affinity constant mean a strong binding?
-> Look at the values of the slides in the 'Rate Area', minimum and maximum. What does it means on a biological range?
->Change the initial rate of substrate1, substrate2 and enzyme. What are the effects? How the enzyme/substrate1/substrate2 concentration determines the speed of product formation? Look at it on the plot.
-> Start with only one substrate1, one substrate2 and one enzyme. Slow down the speed of the model and look at the mechanism of allostery.
-> An enzyme is made free each time a product is produced.
-> The cooperativity area is independant. The Rate and the Screen Area are linked.
-> The cooperativity study is a K-system. All curves are heading towards the same Vmax which has been set to 10. A V-system contains effectors that are changing the Vmax, that system has not been chosen because the modification of Vmax corresponds to a change of scale; hence, the information we would be able to obtain on the plot is not interesting.
-> Try to change the K value and cooperativity value. What are the difference between positive and negative cooperativity? What does a cooperativity of 1 mean? How does the plot look like with a such cooperativity? Could we use a cooperativity of 0?
EXTENDING THE MODEL
The main improvement we can do with this model is to adapt it to an existing theoretical one: the Monod, Wyman and Changeux model; the Koshland, Némethy and Filmer model; or the Association-dissociation model.
--------------> What could we do to create a Monod, Wyman and Changeux model?
********* What is this model?
Without any substrate or effectors, the enzyme tends to be in the conformation T. We can say that there is something like 99% of T-shaped enzymes at time 0. There are two ways of thinking the model of Monod-Wyman-Changeux: with the substrate and with the effectors. The most important thing is to think in mass attraction law and equilibrium:
********* What do we have to change in the current model?
Note the use of the 'frame-number system' and the 'pen-number system' makes the two functions 'update-rate-plot' and 'update-cooperativity-plot' not very efficient in the way of programming. A smarter solution could maybe be found to enable to plot several curves on the same screen.
Note the use of links and destruction of turtles with the 'die' procedure. The destruction/creation of turtles might consume more memory but the code is more efficient then with the use of hidden turtles.
-> Enzyme Kinetics
CREDITS AND REFERENCES
• Keith J. Laidler and Peter S. Bunting, the chemical kinetics of enzyme action, clarendon press, Oxford, 1973, P1.
• Robert K.Murray, Daryl K. Granner, Peter A. Mayes and Victor W. Rodwell, Harper’s Biochemistry, International edition, 24 edition, Prentice Hall International, p66
• Keitaro Hiromi, Kinetics of fast enzyme reactions theory and practice, A Halsted press book, Tokyo, 1979, p ix, p 3
• Athel Cornish-Bowden, fundamentals of enzyme kinetics, Portland Press Ltd, London, 1995, p 2, p 223, p228, p234
• B. I. Kurganov, Allosteric Enzymes, A Wiley-Interscience Publication, 1982, p4, p128
• Netlogo user manual, p1, p 34
• Brian Harvey, computer science logo style volume 1: intermediate programming, The MIT Press, Cambridge, Massachusetts, London, England, 1985
• ------------> This model has been created within the framework of the projet of Honors Year in Biology with Information Technologies at the University of the West of Scotland. It has been headed by Doctor Peter Birch. I want to thank him for his advices and his time spent to explain me the mechanisms of allostery.
• ------------> To refer to this model, please use: Descostes, N. (2008). NetLogo Allosteric Enzymes Kinetics model. University of the West of Scotland, Scotland.
• ------------> I will be very pleased if you could email-me if you are using this model for academic purposes. contact: firstname.lastname@example.org
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