globals [ how-many-substrates? time-cycles RCA ;; rate constant for acylation phase RCD ;; rate constant for deacylation phase ;; these are global variable, set up if the substrate is changed and copied to the enzymes-own ;; variables of Ka and Kd. Actually RCD/Kd are currently identical for both substrates but added ;; as variables to make it easier to add other substrates at any potential additions to the model burst-time ;; time cycle at which enzyme is added ] breeds [ enzyme ;; chymotrypsin substrate ;; p-nitrophenyl acetate in the original burst expt. product-1 ;; the first product released (p-nitrophenol in the case of pNPA as the substrate). ;; This is the product that's detected by the spectrophotometer and recorded in the plot product-2 ] turtles-own [ partner ] enzyme-own [ Ka ;; rate constant of acylation of enzyme (cleavage and release of product-1 Kd ;; rate constant of deacylation of enzyme (release of product-2 ;; N.B. these constants are associated with the enzyme rather than the substrate as ;; after acylation the substrate will have died but the Kd value will still be needed ] to startup set how-many-enzymes? 50 set which-substrate? "pNPA" ;; start with pNPA as the substrate change-substrate ;; and put appropriate info in the output box end to setup ca set time-cycles 0 set how-many-substrates? 500 change-substrate ;; check to see if different substrate required and do it if so add-substrate how-many-substrates? end to go ifelse ( hide-substrate? = true ) [ ask substrate with [ partner = nobody ] [ set hidden? true ] ask substrate with [ partner != nobody ] [ set hidden? false ] ] [ ask substrate with [ partner = nobody ] [ set hidden? false ] ] ask turtles [ move ] ask enzyme [ catalyse ] do-plot if ( ( count substrate ) = 0 ) [ stop ] ;; no point continuing if substrate finished set time-cycles time-cycles + 1 if ( ( ( count enzyme ) > 1 ) and ( time-cycles = ( burst-time + 10 ) ) ) [ ;; the burst is the absorbance change which occurs immediately after the ;; enzyme is added. This is measured 10 time cycles after enzyme addition ;; to give the enzyme a chance to do something. 10 cycles is rather arbitray ;; but gives reasonable results. If the model runs at anything near full speed ;; the burst looks more or less instantaneous, as it would in a laboratory ;; experiment using a standard spectrophotometer output-print "" output-print "" output-type "Burst size: " + ( count product-1 ) ;; print burst size to output box ] if ( ( count product-1 ) > 299 ) [ stop ] ;; stop the model if product-1 is about to overflow the y-axis to keep the graph pretty end to add-substrate [ amount ] cct amount [ set partner nobody ;; not bound to anyone set breed substrate set shape "substrate" set xcor -17 + random 34 set ycor -17 + random 34 ] end to move if ( partner = nobody ) [ ;; enzymes with substrate bound are kept static for ease of study. ;; A similar idea is used in the enzyme kinetics model in the library set heading random 360 fd 1 ] end to add-enzyme set-current-plot "absorbance" set-plot-x-range ( time-cycles - 100 ) ( time-cycles + 1000 ) ;; reset x-axis renge depending on time of enzyme addition - keeps it pretty! cct how-many-enzymes? [ set partner nobody ;; no substrate bound set breed enzyme set shape "enzyme" set xcor -17 + random 34 set ycor -17 + random 34 set Ka RCA ;; set up rate constants based on the values depending on the chosen substrate set Kd RCD ] set burst-time time-cycles ;; note time of enzyme addition end to catalyse ifelse ( partner = nobody ) ;; no substrate bound ... [ set partner random-one-of ( substrate-here ) ;; ... so try to find one if ( partner = nobody ) [ stop ] ;; no luck! if ( ( partner-of partner ) != nobody ) [ ;; found one - bind it set partner nobody stop ] set partner-of partner self ] [ ifelse ( breed-of partner = substrate ) [ if ( random-float 1000 < Ka ) [ ;; susbtrate is bound so acylate enzyme at a speed dependent on Ka ask partner [ die ] ;; substrate gone let this-enzyme who ;; note which turtle this enzyme is ask patch-here [ sprout 1 [ ;; produce product-1 ... set partner nobody ;; ... which is released from enzyme ... set breed product-1 set shape "product-1" ] sprout 1 [ ;; ... and product-2 ... set partner ( turtle this-enzyme ) ;; ... which is still bound to the enzyme set ( partner-of partner ) self set breed product-2 set shape "product-2" ] ] ] ] [ if ( random-float 1000 < Kd ) [ ;; bound ligand wasn't substrate so it must be product-2 so set ( partner-of partner ) nobody ;; release at a rate dependent on Kd set partner nobody ] ] ] end to do-plot set-current-plot "absorbance" set-current-plot-pen "product-1" plot count product-1 set-current-plot-pen "enzyme" plot count enzyme end to change-substrate ifelse ( which-substrate? = "pNPA" ) [ set RCA 800 set RCD 5 ] [ set RCA 3 set RCD 5 ] ifelse ( which-substrate? = "pNPA" ) [ output-type "Chosen substrate: " output-print "" output-type "p-nitrophenyl acetate" output-print "" output-print "" output-type "Low stability means that" output-print "" output-type "acylation phase is easy" output-print "" output-type "and fast" output-print "" ] [ output-type "Chosen substrate: " output-print "" output-type "generic peptide" output-print "" output-print "" output-type "High stability means that" output-print "" output-type "acylation phase is relatively" output-print "" output-type "difficult and slow" output-print "" ] output-print "" output-type "Ka: " + RCA output-print "" output-type "Kd: " + RCD output-print "" output-print "" output-type "The Kd value is assumed to be" output-print "" output-type "the same for both substrates" end @#$#@#$#@ GRAPHICS-WINDOW 303 10 733 461 17 17 12.0 1 10 1 1 1 0 CC-WINDOW 5 475 1000 570 Command Center BUTTON 36 46 100 79 Setup setup NIL 1 T OBSERVER T NIL BUTTON 128 47 191 80 Go go T 1 T OBSERVER T NIL PLOT 17 96 217 246 Absorbance Time Absorbance 0.0 1000.0 0.0 300.0 true true PENS "Product-1" 1.0 0 -11352576 true "enzyme" 1.0 0 -65536 true SLIDER 32 259 204 292 how-many-enzymes? how-many-enzymes? 0 100 50 1 1 NIL BUTTON 75 303 177 336 Add enzyme add-enzyme NIL 1 T OBSERVER T NIL CHOOSER 794 74 932 119 Which-substrate? Which-substrate? "pNPA" "Peptide" 0 SWITCH 47 397 190 430 hide-substrate? hide-substrate? 1 1 -1000 OUTPUT 751 133 991 438 @#$#@#$#@ WHAT IS IT? ----------- This is a simulation of Hartley's "burst" experiment which provided evidence for the biphasic (ping-pong) nature of the catalytic reaction of chymotrypsin and the other serine proteases. Chymotrypsin catalyses the hydrolysis of peptide bonds in proteins using the following biphasic mechanism: E-OH + R-CO-NH-R' --> E-CO-R + R'-NH2 (Acylation phase) E-CO-R + H2O --> E-OH + R-COOH (Deacylation phase) Using a normal substrate the first phase is slower than the second phase as it involves the cleavage of a very stable peptide (amide) bond. Hartley's experiment made use of an artificial substrate, p-nitrophenyl acetate (pNPA). The bond broken by the enzyme with this substrate is the very unstable phenolic ester bond and this reverses the rate balance between the two phases so that the acylation phase is faster than the deacylation phase. On adding enzyme to a solution of pNPA every enzyme would very rapidly undergo the acylation phase, releasing one molecule of the product of that reaction (product 1) which is a yellow-coloured paranitrophenol, whose absorbance can be measured on a spectrophotometer. This produces a burst of colour whose absorbance is directly proportional to the enzyme concentration. The enzymes can only react with further substrates by releasing the second product which will take place at the much slower rate of the deacylation phase. The result of this is that on first addition of the reaction product 1 is generated, and absorbance due to it is observed, at the rate of the acylation phase. This occurs until all enzyme molecules have been acylated. Further generation of product 1 is dependent on the regeneration of free enzyme which occurs at the rate of the deacylation phase. There is an effective "separation" of the two phases showing a biphasic graph. If a "normal" substrate is used, in which the acylation phase is slower than the deacylation phase, this biphasic effect will not be seen. The initial release of product 1 would be at the rate of the slow acylation phase. The acylated enzyme would then be relatively rapidly regenerated by deacyltion but this would not be observed directly as it is absorbance due to product 1 which is being observed. The regenerated enzyme can react with another substrate and generated another product at the rate of the acylation phase. The graph would show a single phase at the rate of the acylation phase. HOW IT WORKS ------------ Uses some of the basic ideas of the enzyme kinetics module in the library. More details are commented in the procedures page. HOW TO USE IT ------------- By default the model starts with p-nitrophenyl acetate (pNPA) as the substrate and the number of enzyme molecules to be added set to fifty. These can be changed by using the chooser button and the slider. I suggest that you leave at the default setting to start with. The output box, to the right of the screen lists some basic information about the chosen substrate, which will be changed, if you alter the substrate, after you press the Setup button. Press the setup button. This will add 500 substrate molecules to the model. They'll appear as cyan coloured double blobs. You can hide them using the hide-substrate? switch, but this will not come into effect until you press the Go button. Press Go. Nothing much will happen as there is no enzyme present. If you look carefully at the graph window you'll see the line moving along the bottom of the graph. Press the Add enzyme button. This immediately adds the requested number of enzyme molecules to the reaction mixture. Look at the graph. The red line, which represents the amount of enzyme mixture, rises immediately at the point of addition and then stays unchanged. The green line, the amount of product 1, almost immediately rises to the same level as the enzyme graph (the initial burst) and then continues rising more slowly ( the rate of deacylation. The size of the burst will be printed at the bottom of the output window. Compare this to the amount of enzyme used. If you look at the graphics window you'll be able to see the enzyme's (red squares), product 1 molecules (small yellow circles) and product 2 molecules (small blue squares). You can slow the reaction down using the slider at the top left of the graphics window, and hide the substrate, if it's too obtrusive, using the hide button. Change to the other substrate (a generic peptide), press Setup and repeat the above excersize. Compare the results with the different substrates. THINGS TO NOTICE ---------------- THINGS TO TRY ------------- Try varying the amount of enzyme added and look at the size of the burst. Try using only one enzyme molecule so that you can concentrate on it. Run the graphic fairly slowly, using the slider, and hide the substrates. You'll be able to see the speed of binding to and release from, the enzyme of the substrate and the two products. Substrate bound to the enzyme is visible even when the hide-substrate button is on. Compare these binding/release activities using the different substrates. EXTENDING THE MODEL ------------------- It would be easy to add more substrate variations with differing Ka/Kd values or perhaps introduce slider to let the user vary Ka/Kd values themselves. You could set up a calculation of the rate of product 1 generation and compare these with Ka/Kd values. NETLOGO FEATURES ---------------- RELATED MODELS -------------- Enzyme Kinetics in the modules library CREDITS AND REFERENCES ---------------------- Copyright: Dr. P. L. Birch - University of Paisley Permission is granted to copy, distribute and adapt this model for any non-comercial use as long as this copyright notice is maintained. 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