breeds [molecule1 molecule2 molecule1-pump molecule2-pump ] globals [osmolality-above osmolality-below dropper container-wall membrane compartment-above compartment-below ] patches-own [permeability1 permeability2 H2O edge membrane-wall ;;This is a patch holder variable to allow visualization of the membrane ;;when pcolor is being scaled to another variable (i.e. osmolality) ] to setup ;;This sets up the initial agentsets and the walls of the container ca ask patches [set H2O 1 ] set dropper patches with ;;This is the entry point of addition of molecules [pycor = -39 ] set container-wall patches with [pycor = -40 or pycor = 40 or pxcor = 20 or pxcor = -20 ] ask container-wall [set pcolor white set edge 1 ] set membrane patches with [pycor = 0 ] set compartment-above patches with [pycor > 0 ] set compartment-below patches with [pycor < 0 ] end to add-molecule1 ask dropper [sprout molecule1-amount [set breed molecule1 set color yellow set shape "circle" set heading 0 ] ] end to add-molecule2 ask dropper [sprout molecule2-amount [set breed molecule2 set color blue set shape "circle" set heading 0 ] ] end to go ask molecule1 [wiggle ;; This makes the molecule bounce off the container wall if edge-of (patch-ahead 1) = 1 [set heading heading - 180 ] ;; This determines whether molecule goes through membrane if pcolor-of (patch-ahead 1) = red [;; This determines whether there is a molecule pump present if any? molecule1-pump-on (patch-ahead 1) [;;This is the effect of having a pump present: ;;If the molecule is on the "right side" of the pump ;;then the molecule is passed through/past the membrane if ycor > 0 [jump 2 ] ] if random 101 >= set-permeability1 [set heading heading - 180 ] ] fd 1 ] ask molecule2 [wiggle ;; This makes the molecule bounce off the container wall if edge-of (patch-ahead 1) = 1 [set heading heading - 180 ] ;; This determines whether molecule goes through membrane if pcolor-of (patch-ahead 1) = red [if random 101 >= set-permeability2 [set heading heading - 180 ] ] fd 1 ] set osmolality-above count turtles with [ycor > 0] ;;Since the sizes of the chambers are set osmolality-below count turtles with [ycor < 0] ;;unchanging osmolality is just expressed ;;as a count of the turtles ifelse mode > 0 ;;Mode determines what variable the patches scale-to. Additional modes ;;can be added by interested individuals. [set-scale-pc ] [ask patches [set pcolor black ] ask container-wall [set pcolor white ] ask membrane [if membrane-wall = 1 [set pcolor red ] ] ] draw-graph end to move end to wiggle rt random 45 lt random 45 end to set-membrane ;;This sets the presence of the membrane. Sliders change the % permeability ask membrane [set membrane-wall 1 set pcolor red set permeability1 set-permeability1 set permeability2 set-permeability2 ] end to make-molecule1-pump ;;This produces the unidirectional molecule pump. Its effect is found ;;in procedure "to go => ask molecule1" ask membrane [if pxcor mod 2 = 0 [sprout 1 [set breed molecule1-pump set shape "triangle" set heading 0 set color yellow ] ] ] end to set-scale-pc ;;This procedure allows the scaling of pcolor of the background to ;;various variables to add in visulization ask compartment-above [if mode = 1 [set pcolor scale-color green osmolality-above 0 500 ] ] ask compartment-below [if mode = 1 [set pcolor scale-color green osmolality-below 0 500 ] ] end to draw-graph ;;Note that the graphs divide the chamber at the ycor = 0 ;;where a membrane would be created (even if one is not made). set-current-plot "Molecule1 Distribution" set-current-plot-pen "molecule1-below" plot count molecule1 with [ycor < 0] set-current-plot-pen "molecule1-above" plot count molecule1 with [ycor > 0] set-current-plot "Total Molecule Distribution" set-current-plot-pen "molecules-below" plot count turtles with [ycor < 0] set-current-plot-pen "molecules-above" plot count turtles with [ycor > 0] end @#$#@#$#@ GRAPHICS-WINDOW 396 14 652 531 20 40 6.0 1 10 1 1 1 0 1 1 1 CC-WINDOW 5 556 661 651 Command Center 0 BUTTON 8 10 74 43 Setup setup NIL 1 T OBSERVER T NIL BUTTON 80 10 143 43 Go go T 1 T OBSERVER T NIL BUTTON 11 89 138 122 Add-molecule1 add-molecule1 NIL 1 T OBSERVER T NIL SLIDER 156 12 328 45 molecule1-amount molecule1-amount 1 5 5 1 1 NIL SLIDER 158 52 330 85 molecule2-amount molecule2-amount 1 5 3 1 1 NIL BUTTON 14 128 141 161 Add-molecule2 add-molecule2 NIL 1 T OBSERVER T NIL SLIDER 158 91 330 124 set-permeability1 set-permeability1 0 100 0 1 1 NIL BUTTON 13 49 136 82 Set-membrane set-membrane NIL 1 T OBSERVER T NIL SLIDER 156 128 328 161 set-permeability2 set-permeability2 0 100 0 1 1 NIL BUTTON 12 172 187 205 Make-molecule1-pump make-molecule1-pump NIL 1 T OBSERVER T NIL PLOT 11 217 384 371 Molecule1 distribution NIL NIL 0.0 10.0 0.0 10.0 true false PENS "molecule1-below" 1.0 0 -13345367 true "molecule1-above" 1.0 0 -2674135 true PLOT 10 377 383 542 Total Molecule Distribution NIL NIL 0.0 10.0 0.0 10.0 true false PENS "molecules-below" 1.0 0 -13345367 true "molecules-above" 1.0 0 -2674135 true SLIDER 199 173 371 206 mode mode 0 10 0 1 1 NIL @#$#@#$#@ WHAT IS IT? ----------- This is a simple model that looks at diffusion of molecules with and without the presence of a membrane with variable permeability. It also includes a very abstracted active transport pump that counteracts the permeability limitations of the membrane. Of note, this model is "intentionally" not refined, to allow for planned input/improvement via student interactions. HOW IT WORKS ------------ The "world" is a container that can be divided into two by adding a membrane. Molecules are represented by circular agents that are added at the bottom screen edge via a button "add-molecule1" or "-2". The molecules have a random movement pattern, and upon initial addition of molecules they will diffuse to fill the space. With the addition of the membrane there is a barrier to this initial diffusion, and dependent upon the set permeability for the membrane it will take longer or shorter to reach equilibrium. The permeability represents a percentage likelyhood that a molecule will pass. The additon of the "Molecule1-pump" allows uni-drectional (from "above" to "below") complete permeability to molecule1. On the plots the blue line represents the number of molecules (either molecule1 or total) below the membrane, the red line the number of molecules above. The varible "Osmolality" is a density function of the total number of molecules in each compartment. With the slider "mode" turned to 1 the different compartments will scale to a shade of green dependent upon their osmolality (lighter shade = higher osmolality, darker shade = lower osmolality). HOW TO USE IT ------------- To start, use the "molecule-amount" sliders to set the number of molecules created per patch. Then hit "setup," "add-molecules" to set initial conditions. You can add the membrane and molecule1-pump at the same time. You can set the "mode" to the right of the screen. Hit "go" to go. You can also add molecules during the run as well. You can also change the membrane permeability to either molecule during the run as well. THINGS TO NOTICE ---------------- Notice the diffusion pattern after initial addition of molecule. The movement of the front egde of the particle "wave" looks volitional, but it is a byproduct of the random movement of particles from a higher concentration to a lower one. Notice the effect of a membrane on the rate of this diffusion. However, also notice that irrespective of the degree of permeability (as long as it is > 0) the system will eventually go to equilibrium. The time to this point, however, is a function of the set permeabilty. Noice that in order to reinforce any gradient there must be active transport with the molecule1-pump. Notice that with permeabilty = 100 the molecule-pump has no significant effect. Switching the "mode" to 1 to scale the background to the osmolality allows you to see the differential gradient enforced by the membrane more clearly. THINGS TO TRY ------------- You can add different numbers of molecules to see if there is a change in the time to equilibrium (would you expect there to be any effect?) You can change the permeability for molecule1 during a run to simulate a membrane depolarization and then re-establishment of the gradient with molecule1-pump. EXTENDING THE MODEL ------------------- Note that in this model the calculations for "osmolality-above" and "osmolality-below" assume the fixed sizes of the two chambers. Similarly, in "mode" = 1 the areas scaled to osmolality are constant. However, you can adjust the placement of the membrane to see the effect of unequal chambers. You can try adjusting the code to dynamically change the relative size of the chambers to keep osmolality constant. This would simulate the "swelling" of a cell in whom its cell membrane becomes more permeable to water. You can add additional molecule pumps, perhaps requiring an "energy-consumption" function. You can add enzyme kinetics between the existing molecules to produce a third molecule species with different permeability/molecular transport pumps. You can link enzyme kinetics to allow for one of the species of molecules to be the "energy source" for an "energy-consumption" molecule transport pump. The membrane is currently a patch-based agentset. You can use turtles for this instead to make the membrane spatially dynamic (i.e. shifting to adjust the relative sizes of the chambers in cases with a constant osmolality). This model could be expanded to simulate virtually any membrane transport/cell surface receptor function. NETLOGO FEATURES ---------------- This model uses the classic "wiggle" code for random movement. This model uses the code sequence to bounce turtles off barriers (in "to go" => ask molecule1) This model uses the "mode" slider to scale pcolor to a different variable. I have used multiply expanded versions of "mode" and "set-scale-pc" to check patch variable distributions in models with multiple patch variables as a debugging tool. CREDITS AND REFERENCES ---------------------- This model was developed by Gary An, MD. At time of development he was in the Department of Trauma, Cook County Hospital, Chicago, IL, USA. Email any questions or comments to docgca@earthlink.net @#$#@#$#@ 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 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 3.0.2 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@