Mass Action:

1
Today we will deal with two important Problems

• Law of Mass Action
• 2. Michaelis Menten problem.

Creating Biomodel in Vcell we will solve these
two problems
2
The Law of Mass Action (by Norwegian scientists
186479CCato M. Gulberg and Peter Waage) Cosider
this chemical reaction equation in which
reactants A and B react to give product AB.
A B ? AB The mass action law states
that if the system is at equilibrium at a given
temperature, then the following ratio is a
constant.
That is, the rate of a reaction is proportional
to the product of the active masses of the
reagents involved. This is the ideal law of
chemical equilibrium or law of mass action.
More explicitly....
3
In a chemical reaction --- AB
AB the "chemical affinity" or "reaction force"
between A and B did not just depend on the
chemical nature of the reactants, but also
depended on the amount of each reactant in a
reaction mixture. The affinity or the reaction
force between A and B kf A B Kf is
affinity constant.
kr
kf
forward reaction rate kf A B backward
reaction rate KrAB
At equillibrium forward reaction rate backward
reaction rate
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Now create a New Biomodel Document Consider the
case where A and B reacts to produce AB AB?AB.
Lets start with the following steps---

• Give name of the unnamed compartment
• Add specieses A,B and AB
• Set reaction
• Set Reaction Kinetic Editor
• Kinetic type Mass Action
• Put Value of Kf and Kr
• Save the Model with a name.

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• Go to Application ?New?Deterministic
• Name the Application (again we will be
• doing compartmental application) and OK.
• Put volume1 in Structure Mapping Text.
• Click Initial Condition Text and assign
• Value of A and B.
• Save the Model once again to View Math
• and to start Simulation.
• Note the Mathcomment,Which says Math
• Model is already generated by the software.

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We can view Math Equations or View VCMDL
Now click simulation Text to run the Simulation.
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See Results and play with the different
parameters by clicking Edit .
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Exercise Run Simulation with the following
parameter value---- Kf 1 , Kr 1, Ainit 1,
Binit 1
Check these two points. - Keep all parameters
the same as given on this slide, and start
increasing parameter Ainit. Make initial AB
zero. Is equilibrium reached faster? Does stable
AB concentration increase? Why? - Keep all
parameters the same as given on this slide, and
start increasing parameter kr. Make initial AB
zero. Is equilibrium reached faster? Does stable
AB concentration increase? Why?
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Keep all the parameters 1.0 and increase Ainit,
see the stable concentration of AB.
10
Increase Kr, see Equillibrium is reached faster.
At equillibrium, forward reaction rate
backward reaction rate
Go back to the equations to verify your results.
11
Michaelis-Menten Kinetics(by Leonor Michaelis
and Maud Menten in 1913 )
M-M kinetics approximately describes the kinetics
of the Enzyme. The most convenient derivation of
the MichaelisMenten equation, is obtained as
follows The enzymatic reaction is assumed to be
irreversible, and the product does not bind to
the enzyme.                               
Kf
Kp
ES ES? EP
Kr
EnzSub?Enz-Subs-complex ?EnzProd
Now our aim is to analyze this mechanism. With
Vcell we can find the reaction rate of production
of the product P and the complex ES and also
study the impacts of several rate constants
Kf,Kr,Kp.
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Now, consider the rate of effective production of
P
The Michaelis-Menten equation relates the
reaction rate V to the substrate
concentration S. The corresponding graph is a
hyperbolic function the maximum rate is
described as Vmax.
,Vmax KP Ein
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Start with a new Biomodel

• Name the compartment
• Add Specieses S, E, ES, P
• Set the Reactions
• Set Reaction kinetic Editor
• for two reactions.
• Set General as the kinetic Type
• Now we have to set the Reaction Rates.

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Here We have two reactions
1.Substrate binding, where E and S react to
produce the complex ES Reaction rate
J_reaction0 KfES - KrES -
KPES 2.Catalytic Step, where ES dissociates
to produce P and E Raction rate J_reaction1
KPES
Now go to FilegtSave as... to save the model.
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Remember two assumptions

• A lot of substrate molecules, very few
  expensive enzymes
• ( SgtgtE), so S does not change much for a
  long time.
• 2. The system is in steady-state, i.e. that the
  ES complex is
• being formed and broken down at the same rate, so
  that
• overall ES is constant .

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Steps are same as Mass-Action

• Go to Application?New?Deterministic
• Name the Application and OK.
• Put volume1 in Structure Mapping Text.
• Click Initial Condition Text and assign
• Value of E and S.(Remember Eltlt S)
• Save the Model once again to View Math
• and to start Simulation.
• Math Model will be generated Automatically.

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Clicking View Math we can see the Math Model
generated by the software
With the radio button we can see the value or
name of the parameter eqn.
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Run the Simulation
Clicking Edit we can change different parameters
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• Analyze formation rate of ES, P with time
• or with other parameter.
• We can choose Graphical results or
• data values by clicking

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Exercise
Consider the parameter values as follows

• Run simulation for t 1, 5 and 10 seconds.
• Keep all parameters the same as given on this
  slide. Solve the chemical reaction equations.
  Discuss the results. Compute V, check if the
  formula for V in the previous slide is correct.
• Make and solve the
  chemical reaction equations again. Discuss the
  results. Does Michaelis-Menten approximation
  still work?

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,Vmax KP Ein
See math description for J_reaction1 J_reaction1
V, calculate V. Check how V changes with Sin
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For small value of S, say Sin 1.0 uM