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 boxendto 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?endto 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 prettyendto 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     ]endto 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  ]endto 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 additionendto 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      ]    ]  ]endto do-plot    set-current-plot "absorbance"  set-current-plot-pen "product-1"  plot count product-1  set-current-plot-pen "enzyme"  plot count enzyme  endto 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-WINDOW30310733461171712.01101110CC-WINDOW54751000570Command CenterBUTTON364610079SetupsetupNIL1TOBSERVERTNILBUTTON1284719180GogoT1TOBSERVERTNILPLOT1796217246AbsorbanceTimeAbsorbance0.01000.00.0300.0truetruePENS"Product-1" 1.0 0 -11352576 true"enzyme" 1.0 0 -65536 trueSLIDER32259204292how-many-enzymes?how-many-enzymes?01005011NILBUTTON75303177336Add enzymeadd-enzymeNIL1TOBSERVERTNILCHOOSER79474932119Which-substrate?Which-substrate?"pNPA" "Peptide"0SWITCH47397190430hide-substrate?hide-substrate?11-1000OUTPUT751133991438@#$#@#$#@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.