breed [ enzymes enzyme]      
breed [ substrates substrate]   
breed [ products product]     

turtles-own [complexing?]

to setup
  ca
  set-current-plot "Amounts"
  clear-plot
  create-substrates 100 [ set shape "substrate"
  set color red]
  create-enzymes 20 [set shape "enzyme"]
  ask turtles [setxy random-xcor random-ycor
  set complexing? false]            
end

to setup_system
  set-current-plot "SystemModel"
  clear-plot
  system-dynamics-setup
end

to go_system
  system-dynamics-go
  system-dynamics-do-plot
end

to go
  tick
  ask turtles  [move ]              
  ask enzymes [ if not complexing?
    [form-complex ] ]        
  ask enzymes [ if complexing?
  [dissociate] ]
  ask enzymes [if complexing? 
  [form-product] ]       
  plot-amounts                
end

to move  
    fd 1
    rt random-float 360 
end

to form-complex
  let partner 0
  if any? substrates-here and random-float 100 < Kfwd1  
    [ set complexing? true  
      set partner one-of substrates-here
      if not [complexing?] of partner
        [ask partner [die]
        set shape "complex"
      ] ]
end

to form-product
  if random-float 100 < Kfwd2
  [set complexing? false
  set shape "enzyme"
  hatch-products 1 [set shape "product"]
  ]
end


to dissociate
  if random-float 100 < Krev1
  [set complexing? false
  set shape "enzyme"
  hatch-substrates 1 [set shape "substrate"]
  ]
end


to plot-amounts
  set-current-plot "Amounts"
  set-current-plot-pen "Substrate"
  plot count substrates
  set-current-plot-pen "Enzyme"
  plot count enzymes with [not complexing?]
  set-current-plot-pen "Complex"
  plot count enzymes with [complexing?]
  set-current-plot-pen "Product"
  plot count products
end


@#$#@#$#@
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BUTTON
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watch an enzyme
watch one-of enzymes
NIL
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OBSERVER
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BUTTON
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reset
rp
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OBSERVER
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@#$#@#$#@
WHAT IS IT?
-----------
This model demonstrates the kinetics of single-substrate enzyme-catalysis. This model allows the user to compare an agent model and a system model.

The standard equation for this reaction is shown below.

|                Kfwd1          Kfwd2
|        E + S <=======>   E-S ------> E + P
|                Krev1

Here E represents Enzyme, S Substrate, E-S Enzyme-Substrate complex, and P product.  The rate constants are Kfwd1 for complex formation, Krev1 for complex dissociation, Kfwd2 for catalysis and product formation.  The first step in catalysis is the formation of the E-S complex.  The rates of complex formation and dissociation are very fast because they are determined by collision and separation of the molecules.  The next step is for the enzyme to catalyze the conversion of substrate to product.  This rate is much slower because the energy required for catalysis is much higher than that required for collision or separation.


HOW TO USE IT
--------------
Choose the values of Kfwd1, Krev1, and Kfwd2 with appropriate sliders:
- Kfwd1 controls the rate at which substrates (red) and enzymes (yellow) stick together so that catalysis can occur
- Krev1 controls the rate at which they come unstuck
- Kfwd2 controls the rate of the forward reaction by which an enzyme converts a substrate to a product (blue)

Having chosen appropriate values of the constants, press SETUP to clear the world and create a constant initial number of enzyme molecules. Play with several different values to observe variable effects on complex formation and catalysis.

Press GO to start the simulation.  The concentrations of enzyme, substrate, complex, and product are plotted in the AMOUNTS window.

On the systems side, choose values for each of the rate constants and run the model.

Finally, compare the two models and attempt to find the appropriate combination of rate constants which give comparable behavior.


THINGS TO NOTICE
----------------
Watch the rate at which the enzyme and substrate stick together. How does this affect the conversion of substrate into product? What would happen if Krev1 is very high and Kfwd1 is very low? If Kfwd2 is of the same order of magnitude as Kfwd1 and Krev1?



THINGS TO TRY
-------------

If Kfwd2 is MUCH greater than Krev1, what affect does this have on the reaction?  How important does complex formation become in this situation?

If Kfwd1 is MUCH less than Krev2, what does this mean in the real-world? How are the enzyme and substrate related under these conditions?



EXTENDING THE MODEL
------------------

Include a slider that allows you to change the concentration of substrate and/or enzyme.  What affect does this have on the plot?   


NETLOGO FEATURES
------------------
This model features the "docking" of an agent model and a systems model.


CREDITS AND REFERENCES
----------------------

NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.


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