breed [ enzymes enzyme] ;; red turtles that bind with and catalyze substrate breed [ substrates substrate ] ;; green turtles that bind with enzyme breed [ inhibitors inhibitor ] ;; yellow turtle that binds to enzyme, but does not react breed [ products product ] ;; blue turtle generated from enzyme catalysis turtles-own [ partner ;; holds the turtle this turtle is complexed with, ;; or nobody if not complexed ] globals [ substrate-added ;; keeps track of how much substrate has been added v ;; rate of complex formation at each time step+ x ;; driving force of periodic substrate addition Sub Enz Prod ds de dp ] to startup end ;; observer procedure to set up model to setup clear-all ;; clears view set substrate-added 0 set v 0 add enzymes 150 ;; starts with constant number of enzymes add substrates volume ;; add substrate based on slider add inhibitors volume2 ;; add inhibitor based on slider set Sub (list count substrates count substrates count substrates count substrates count substrates count substrates) set Enz (list count enzymes count enzymes count enzymes count enzymes count enzymes count enzymes) set Prod (list count products count products count products count products count products count products) set ds (list 0 0 0 0 0 0) ;; successive rates of substrate change, 0 entry is average of other 5 set de (list 0 0 0 0 0 0) ;; successive rates of enzyme change, 0 entry is average of other 5 set dp (list 0 0 0 0 0 0) ;; successive rates of product change, 0 entry is average of other 5 reset-ticks end ;; observer procedure to add molecules to reaction to add [kind amount] crt amount [ set breed kind setxy random-xcor random-ycor set partner nobody setshape ] if kind = substrates [ set substrate-added substrate-added + amount ] end ;; procedure that assigns a specific shape to a turtle, and shows ;; or hides it, depending on its state to setshape ifelse breed = enzymes [ set color red ifelse partner = nobody [ set shape "enzyme" ] [ ifelse ([breed] of (partner) = substrates) [ set shape "complex" ] [ set shape "inhib complex" ] ] ] [ ifelse breed = substrates [ set color green set shape "substrate" set hidden? (partner != nobody) ] [ ifelse breed = inhibitors [ set color yellow set shape "inhibitor" set hidden? (partner != nobody) ] [ if breed = products [ set color blue set shape "substrate" set hidden? false ] ] ] ] end ;; main procedure to go ask turtles [ move ] ;; only non-complexed turtles will move ask enzymes [ form-complex ] ;; enzyme may form complexes with substrate or inhibitor ask substrates [ react-forward ] ;; complexed substrate may turn into product ask enzymes [ dissociate ] ;; or complexes may just split apart ask enzymes [ reversereact ] ;; reverse reaction of product and enzyme calculate-velocity ;; calculate V for use in the Michaelis-Menten curve set Sub replace-item 5 Sub count substrates set Enz replace-item 5 Enz count enzymes set Prod replace-item 5 Prod count products set ds replace-item 5 ds ((item 5 Sub - item 0 Sub) / 5) set de replace-item 5 de ((item 5 Enz - item 0 Enz) / 5) set dp replace-item 5 dp ((item 5 Prod - item 0 Prod) / 5) set ds replace-item 4 ds item 5 ds set de replace-item 4 de item 5 de set dp replace-item 4 dp item 5 dp set ds replace-item 3 ds item 4 ds set de replace-item 3 de item 4 de set dp replace-item 3 dp item 4 dp set ds replace-item 2 ds item 3 ds set de replace-item 2 de item 3 de set dp replace-item 2 dp item 3 dp set ds replace-item 1 ds item 2 ds set de replace-item 1 de item 2 de set dp replace-item 1 dp item 2 dp set ds replace-item 0 ds ((item 1 ds + item 2 ds + item 3 ds + item 4 ds + item 5 ds) / 5) set de replace-item 0 de ((item 1 de + item 2 de + item 3 de + item 4 de + item 5 de) / 5) set dp replace-item 0 dp ((item 1 dp + item 2 dp + item 3 dp + item 4 dp + item 5 dp) / 5) ;set ds (item 5 Sub - item 2 Sub + item 3 Sub - item 0 Sub) / 4 ;set de (item 5 Enz - item 2 Enz + item 3 Enz - item 0 Enz) / 4 ;set dp (item 5 Prod - item 2 Prod + item 3 Prod - item 0 Prod) / 4 tick set Sub replace-item 0 Sub item 1 Sub set Sub replace-item 1 Sub item 2 Sub set Sub replace-item 2 Sub item 3 Sub set Sub replace-item 3 Sub item 4 Sub set Sub replace-item 4 Sub item 5 Sub set Enz replace-item 0 Enz item 1 Enz set Enz replace-item 1 Enz item 2 Enz set Enz replace-item 2 Enz item 3 Enz set Enz replace-item 3 Enz item 4 Enz set Enz replace-item 4 Enz item 5 Enz set Prod replace-item 0 Prod item 1 Prod set Prod replace-item 1 Prod item 2 Prod set Prod replace-item 2 Prod item 3 Prod set Prod replace-item 3 Prod item 4 Prod set Prod replace-item 4 Prod item 5 Prod if (drive) [driven ] end to move ;; turtle procedure if partner = nobody [ fd 1 rt random-float 360 ] end ;; An enzyme forms a complex by colliding on a patch with a substrate ;; or inhibitor. If it collides with an inhibitor, it always forms ;; a complex. If it collides with a substrate, Kc is its percent chance ;; of forming a complex. to form-complex ;; enzyme procedure if partner != nobody [ stop ] set partner one-of (other turtles-here with [partner = nobody]) if partner = nobody [ stop ] if [partner] of partner != nobody [ set partner nobody stop ] ;; just in case two enzymes grab the same partner ifelse ((([breed] of partner) = substrates) and ((random-float 100) < Kc)) or (([breed] of partner) = inhibitors) [ ask partner [ set partner myself ] setshape ask partner [ setshape ] ] [ set partner nobody ] end ;; substrate procedure that controls the rate at which complexed substrates ;; are converted into products and released from the complex to react-forward if (partner != nobody) and (random-float 1000 < Kr) [ set breed products ask partner [ set partner nobody ] let old-partner partner set partner nobody setshape ask old-partner [ setshape ] ] end ;; enzyme procedure that controls the rate at which complexed turtles break apart to dissociate if partner != nobody [ if ([breed] of partner = substrates) and (random-float 1000 < Kd) [ ask partner [ set partner nobody ] let old-partner partner set partner nobody setshape ask old-partner [ setshape ] ] ] end ;; If the last step is reversible, K-r is is percent chance ;; of forming an enzyme-substrate complex from enzyme and product. to reversereact if partner != nobody [ stop ] set partner one-of (other turtles-here with [partner = nobody]) if partner = nobody [ stop ] if [partner] of partner != nobody [ set partner nobody stop ] ;; just in case two enzymes grab the same partner ifelse ((([breed] of partner) = products) and ((random-float 100) < K-r)) or (([breed] of partner) = inhibitors) [ ask partner [ set partner myself ] setshape ask partner [ setshape ] ] [ set partner nobody ] end to calculate-velocity let initial-conc substrate-added let current-conc count substrates with [partner = nobody] if ticks > 0 [ set v (initial-conc - current-conc) / ticks ] end ; this is for a driven system . . . the substrate ; is added in a simple oscillation to driven ifelse (drive) [set x drive-amplitude + drive-amplitude * cos (ticks * drive-rate / ( 2 * pi))] [set x 0] add substrates round x end ; Copyright 2001 Uri Wilensky. ; See Info tab for full copyright and license. @#$#@#$#@ GRAPHICS-WINDOW 289 10 649 391 12 12 14.0 1 10 1 1 1 0 1 1 1 -12 12 -12 12 1 1 1 ticks 30.0 BUTTON 4 41 68 74 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 69 41 130 74 go go T 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 133 146 287 179 Kr Kr 0.0 100.0 100 1.0 1 NIL HORIZONTAL SLIDER 133 76 287 109 Kc Kc 0.0 100.0 100 1.0 1 NIL HORIZONTAL SLIDER 133 111 287 144 Kd Kd 0.0 100.0 100 1.0 1 NIL HORIZONTAL BUTTON 20 111 120 144 add substrate add substrates volume NIL 1 T OBSERVER NIL NIL NIL NIL 1 PLOT 3 181 287 359 Concentrations time C 0.0 50.0 0.0 50.0 true true "" "" PENS "Substrate" 1.0 0 -10899396 true "" "plot count substrates with [partner = nobody]" "Complex" 1.0 0 -2674135 true "" "plot count enzymes with [partner != nobody]" "Product" 1.0 0 -13345367 true "" "plot count products" SLIDER 133 41 287 74 volume volume 0.0 1000.0 500 25.0 1 molecules HORIZONTAL SWITCH 835 295 938 328 drive drive 0 1 -1000 SLIDER 111 361 283 394 k-r k-r 0 10 0.5 .1 1 NIL HORIZONTAL SLIDER 808 68 980 101 volume2 volume2 0 1000 25 1 1 NIL HORIZONTAL BUTTON 835 334 898 367 step go NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 808 28 908 61 add inhibitor add inhibitors volume2 NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 658 296 830 329 drive-amplitude drive-amplitude 0 2 2 .1 1 NIL HORIZONTAL SLIDER 658 333 830 366 drive-rate drive-rate 0 10 10 1 1 NIL HORIZONTAL PLOT 658 110 1100 288 Rates time rate 0.0 10.0 0.0 4.0 true true "" "" PENS "SubstrateR" 1.0 0 -13840069 true "" "plot item 0 ds" " EnzymeR" 1.0 0 -955883 true "" "plot item 0 de" "ProductR" 1.0 0 -13345367 true "" "plot item 0 dp" @#$#@#$#@ ## WHAT IS IT? This model demonstrates the kinetics of single-substrate enzyme-catalysis. The model allows users to visualize the reaction. The standard equation for this reaction is shown below. Kc Kr E + S <=======> E-S <==----> E + P Kd k-r Here E represents Enzyme, S Substrate, E-S Enzyme-Substrate complex, and P product. The rate constants are Kc for complex formation, Kd for complex dissociation, Kr for catalysis, k-r for a reversible last step (K-r is typically much smaller than Kr). 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 slower because the energy required for catalysis is much higher than that required for collision or separation. To be generically applicable, this model gives the option to set a reverse reaction rate k-r that is much lower than Kr. In Michaelis-Menten kinetics, there is typically a fixed initial substrate concentration. This is a limited model of biology. Enzymes in situ often work under rhythmic substrate input. Therefore, this model has the option to activate and modify a sigmoidal input of substrate. Enzyme catalysis can also be controlled using inhibitors. Inhibitors are molecules that are structurally similar to substrate molecules that can complex with the enzyme and interfere with the E-S complex formation. Subsequently, the kinetics of the reaction will be altered. The model demonstrates the effects of inhibitors on catalysis. ## HOW TO USE IT Choose the values of Kc, Kd, kr, and K-r with appropriate sliders: - Kc controls the rate at which substrates (green) and enzymes (red) stick together so that catalysis can occur - Kd controls the rate at which they come unstuck - Kr controls the rate of the forward reaction by which an enzyme (red) converts a substrate (green) to a product (blue) -k-r controls the rate of the reverse reaction by which a product (blue) turns into a complex of enzyme (red) and substrate (green) If you desire to model enzyme catalysis under the driving force of rhythmic substrate input set the driver switch to "on" and choose the values for drive-amplitude and drive-rate. Having chosen appropriate values of the constants, press SETUP to clear the world and create a constant initial number of enzyme (red) molecules. Play with several different values to observe variable effects on complex formation and catalysis. Press GO to start the simulation. A constant amount of enzyme (red) will be generated. The concentrations of substrate, complex, and product are plotted in the CONCENTRATIONS window. The rates of change per time unit in substrate, enzyme, and product are plotted in the RATES window. Experiment with using the ADD-SUBSTRATE and ADD-INHIBITOR buttons to observe the effects of adding more molecules to the system manually as it runs. The default setting for Kr is 0, which means that no product (blue) will be generated unless you change Kr to a non-zero value. Note that when complexes form they stop moving. This isn't intended to be physically realistic; it just makes the formation of complexes easier to see. (This shouldn't affect the overall behavior of the model.) Inhibitors can be irreversible or reversible. That is, they can bind to an enzyme and never let go, or they can stick and fall off. Currently, the model simulates irreversible inhibitors. ## NETLOGO FEATURES It is a little difficult to ensure that a reactant never participates in two reactions simultaneously. In the future, a primitive called GRAB may be added to NetLogo; then the code in the FORM-COMPLEX procedure wouldn't need to be quite so tricky. ## CREDITS AND REFERENCES This model was developed by Georg F. Weber and Tom Carter from the NetLogo library model "Enzyme kinetics" written by Mike Stieff. ## HOW TO CITE If you mention this model in a publication, the citations for the original model and for the NetLogo software are: - Stieff, M. and Wilensky, U. (2001). NetLogo Enzyme Kinetics model. http://ccl.northwestern.edu/netlogo/models/EnzymeKinetics. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. - Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## COPYRIGHT AND LICENSE Copyright 2001 Uri Wilensky. ![CC BY-NC-SA 3.0](http://i.creativecommons.org/l/by-nc-sa/3.0/88x31.png) This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu. This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 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