turtles-own [ in-or-out ; "in" = molecule is inside the cell, "out" = molecule is outside the cell ] globals [ gosteps ; Number of ticks to move before stopping. total-in total-out ] to setup ; Setup command ca ask patches [ set pcolor blue ; Sets the background color to blue. ] ask patch 0 0 [ ; Creates an image of a cell in the center of the window. sprout 1 [ ; The size of the cell is cell-radius, which can be set color gray ; controlled via a slider bar on the interface. The set shape "circle" ; color of the membrane is gray, and the color of the set size cell-radius * 2 ; inside of the cell is white. ;stamp ; ;die ; This image is created by sprouting 2 circular patches ] ; with one circle smaller than the other by a radius of 1. sprout 1 [ ; The larger circle is gray and the smaller one is white. set color white ; Then the patches are stamped onto the background, and set shape "circle" ; asked to die. set size (cell-radius - 1) * 2 ;stamp ;die ] ] crt ions-in-cell [ ; Creates an ion at a random location inside the cell. set shape "square" ; An ion is a turtle with color red, shape square, and size .5. set size .5 ; set in-or-out "in" ; To set the boundary of where the ion can appear set color red ; as only inside the cell, random polar coordinates let radius random-float cell-radius - 1.5 ; are created (radius and angle), with the radius let angle random 360 ; being a random number between 0 and 1.5 less than setxy radius * cos angle radius * sin angle ; the cell-radius. The 1.5 is necessary so that an ] ; ion does not get created inside the membrane. crt ions-out-of-cell [ ; Randomly creates an ion outside the cell. set shape "square" ; set size .5 ; To set the boundary of where the ion can appear set in-or-out "out" ; as only outside the cell, first both x and y set color red ; values are generated. If the radius of this let x random-xcor ; coordinate falls within the cell-radius, then let y random-ycor ; new x and y values are generated. This process while [sqrt (x ^ 2 + y ^ 2) < cell-radius + .5] [ ; is repeated until a random xy coordinate is set x random-xcor ; generated that does not fall within the set y random-ycor ; cell-radius. ] setxy x y ] crt water-in-cell [ ; Randomly creates a water molecule inside the cell. set shape "circle" ; A water molecule appears as a green circle of size set size .5 ; 0.5. The same method of generating an ion in a set in-or-out "in" ; random location inside the cell is used here for water. set color green let radius random-float cell-radius - 1.5 let angle random 360 setxy radius * cos angle radius * sin angle ] crt water-out-of-cell [ ; Random creates a water molecule outside the cell. set shape "circle" ; The same method of generating an ion in a random set size .5 ; location outside the cell is used here for water. set in-or-out "out" set color green let x random-xcor let y random-ycor while [sqrt (x ^ 2 + y ^ 2) < cell-radius + .5] [ set x random-xcor set y random-ycor ] setxy x y ] crt channels [ ; Creates a channel at a random location somewhere along the cell set shape "hex" ; membrane. A channel is a turtle with shape hex (imported from the set color brown ; shapes library) and color brown. Also, due to the nature of the hex facexy 0 0 ; shape, it is made to face the center of the cell so that its let angle random 360 ; effectiveness remains the same at all points along the membrane. setxy (cell-radius - .5) * cos angle (cell-radius - .5) * sin angle facexy 0 0 ] crt pumps [ ; A pump looks exactly like a channel, except its color is black. set shape "hex" ; It is also created the same way as a channel. set color black facexy 0 0 let angle random 360 setxy (cell-radius - .5) * cos angle (cell-radius - .5) * sin angle facexy 0 0 ] set total-in 0 set total-out 0 end to go ; The go command: since all molecules are turtles, both water and ions can ask turtles [ ; be given the same move command (likewise channels and pumps are also given move ; this move command, but they don't actually move). For each set of movements, ] ; the window ticks by 1 and the plot is updated. tick if ticks mod 50 = 0 and osmotic-pressure = true [ change-radius ] do-plot set total-in total-in + count turtles with [in-or-out = "in"] set total-out total-out + count turtles with [in-or-out = "out"] end to go10 ; Command for the button labeled "Go 10 steps." Sets gosteps to 10 and calls set gosteps 10 ; the command gostep. gostep end to go100 ; Command for the button labeled "Go 100 steps." Sets gosteps to 100 and calls set gosteps 100 ; the command gostep. gostep end to gostep ; Processes go and moves all molecules gosteps number of times. let steps 0 while [steps < gosteps] [ ask turtles [ move ] tick do-plot set steps steps + 1 ] stop end to move ; Moves a molecule randomly and in/out of the cell through the membrane. if color = green or color = red [ ; Pump and channels don't move. Ions and water rt random 360 ; molecules move 1 space in a random direction. fd 1 ] if color = red and any? turtles-here with [color = brown] [ ; An ion that moves on top of a channel passes ifelse in-or-out = "in" [ ; through the membrane to the other side. move-out ] [ move-in ] ] if color = red and any? turtles-here with [color = black] [ ; An ion that moves on top of a pump passes if in-or-out = "in" and pump-direction = "out" [ ; through the membrane to the other side, but only move-out ; in 1 direction determined by the variable ] ; pump-direction (controlled by chooser on the if in-or-out = "out" and pump-direction = "in" [ ; interface). move-in ] ] if distancexy 0 0 > cell-radius - 1 and in-or-out = "in" [ ; If an ion is inside the cell and moves into a membrane, if color = red [ ; a random number is created between 0 and 100. If the number ifelse random-float 100 > ion-permeability [ ; is less than the ion-permeability variable, then the ion fd -1 ; can cross the membrane. Otherwise, it moves backwards 1 space ] [ ; (effectively not moving at all for this time step). move-out ; ] ; Water molecules will move out of the cell no matter what upon ] ; entering the membrane. if color = green [ move-out ] ] if distancexy 0 0 < cell-radius and in-or-out = "out" [ ; Same as above, except for ions and water molecules moving into if color = red [ ; into the cell from outside the cell. ifelse random-float 100 > ion-permeability [ fd -1 ] [ move-in ] ] if color = green [ move-in ] ] end to move-out ; To cross the membrane and move out of a cell, the molecule facexy 0 0 ; faces the the direction opposite from the center of the cell, rt 180 ; and moves the remainder of the distance (cell-radius - molecule's fd cell-radius + .5 - distancexy 0 0 ; current distance from the center of the cell) + .5 (so that it set in-or-out "out" ; is completely out of the cell). The in-or-out variable is changed end ; accordingly. to move-in ; Same as above, except for moving into the cell. facexy 0 0 fd distancexy 0 0 - cell-radius + 1.5 set in-or-out "in" end to do-plot ; Updating the plot for the amounts of ions and water molecules set-current-plot "Concentrations" ; both inside and outside the cell. There is no 1 variable that set-current-plot-pen "ions in" ; keeps track of the number of ions inside or outside the cell, plot count turtles with [color = red and in-or-out = "in"] / count turtles with [color = red] * 100 ; since all ions and water molecules are both still turtles. ; Therefore they must be differentiated by their color and their set-current-plot-pen "ions out" ; in-or-out variable. plot count turtles with [color = red and in-or-out = "out"] / count turtles with [color = red] * 100 set-current-plot-pen "water in" plot count turtles with [color = green and in-or-out = "in"] / count turtles with [color = green] * 100 set-current-plot-pen "water out" plot count turtles with [color = green and in-or-out = "out"] / count turtles with [color = green] * 100 end to-report ions-in ; Monitors that simply report the exact report count turtles with [color = red and in-or-out = "in"] ; values of what is being plotted. end to-report ions-out report count turtles with [color = red and in-or-out = "out"] end to-report water-in report count turtles with [color = green and in-or-out = "in"] end to-report water-out report count turtles with [color = green and in-or-out = "out"] end to change-radius ifelse count turtles with [in-or-out = "in"] / (3.14 * (cell-radius - 1) ^ 2) > count turtles with [in-or-out = "out"] / (2 * max-pxcor * 2 * max-pycor - 3.14 * cell-radius ^ 2) [ set cell-radius cell-radius + .5 ask turtles [ if color = brown or color = black [ fd -.5 ] ] ] [ set cell-radius cell-radius - .5 ask turtles [ if color = brown or color = black [ fd .5 ] ] ] ask turtle 0 [ set size cell-radius * 2 ] ask turtle 1 [ set size (cell-radius - 1) * 2 ] end to-report avg-in report total-in / ticks / (water-in-cell + ions-in-cell + ions-out-of-cell + water-out-of-cell) * 100 end to-report avg-out report total-out / ticks / (water-out-of-cell + ions-out-of-cell + ions-in-cell + water-in-cell) * 100 end @#$#@#$#@ GRAPHICS-WINDOW 325 10 842 548 19 19 13.0 1 10 1 1 1 0 1 1 1 -19 19 -19 19 0 0 1 ticks CC-WINDOW 5 562 851 657 Command Center 0 BUTTON 47 27 113 60 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 135 27 198 60 NIL go T 1 T OBSERVER NIL NIL NIL NIL SLIDER 33 81 162 114 ions-in-cell ions-in-cell 0 100 100 1 1 NIL HORIZONTAL SLIDER 163 263 292 296 ion-permeability ion-permeability 0 5 0.05 .01 1 % HORIZONTAL SLIDER 33 115 162 148 water-in-cell water-in-cell 0 100 100 1 1 NIL HORIZONTAL SLIDER 33 149 162 182 channels channels 0 100 0 1 1 NIL HORIZONTAL PLOT 3 306 321 491 Concentrations Time Conc. In/Out % 0.0 10.0 0.0 100.0 true true PENS "ions in" 1.0 0 -2674135 true "ions out" 1.0 0 -955883 true "water in" 1.0 0 -10899396 true "water out" 1.0 0 -11221820 true SLIDER 163 81 292 114 ions-out-of-cell ions-out-of-cell 0 100 0 1 1 NIL HORIZONTAL SLIDER 163 115 292 148 water-out-of-cell water-out-of-cell 0 100 0 1 1 NIL HORIZONTAL SLIDER 163 149 292 182 pumps pumps 0 100 0 1 1 NIL HORIZONTAL SLIDER 32 263 162 296 cell-radius cell-radius 3 19 10 .5 1 NIL HORIZONTAL BUTTON 199 44 279 77 go 100 steps go100 NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 199 10 279 43 go 10 steps go10 NIL 1 T OBSERVER NIL NIL NIL NIL MONITOR 3 492 73 537 # ions in ions-in 0 1 11 MONITOR 86 492 158 537 # ions out ions-out 0 1 11 MONITOR 169 492 239 537 # water in water-in 0 1 11 MONITOR 251 492 321 537 # water out water-out 0 1 11 CHOOSER 108 183 217 228 pump-direction pump-direction "in" "out" 0 MONITOR 254 392 315 437 avg in % avg-in 0 1 11 MONITOR 254 439 315 484 avg out % avg-out 0 1 11 SWITCH 89 229 236 262 osmotic-pressure osmotic-pressure 1 1 -1000 @#$#@#$#@ WHAT IS IT? ----------- The cell membrane, or plasma membrane, physically separates the intracellular components of the cell from the extracellular environment. Its most notable characteristic is its selective permeability, which allows it to regulate what enters and exits the cell. This feature is essential for the movement and transport of molecules across the membrane. The model demonstrates many features of the cell membrane and membrane transport. Some molecules, such as water, are membrane-permeable and thus are free to move in and out of the cell via diffusion, the movement of substances from an area of higher concentration to an area of lower concentration. Other molecules, including most ions, are not membrane-permeable and thus cannot easily diffuse through the membrane. Ions are molecules with electronic charges on them (either positive or negative); examples are K+ and Cl-. To allow ions in and out of the cell, many places along the cell membrane contain channels which let ions across the membrane in a process known as facilitated diffusion. This passage of molecules is a type of passive transport, and no energy is required because molecules are still moving according to the concentration gradient. However, the cell may require a high concentration of certain molecules that are in low concentrations outside the cell. For example, a cell may need to maintain a high concentration of nutrients and energy inside a cell that may naturally exist in low concentrations in the external cell environment. To move molecules against the concentration gradient, a cell relies on the process of active transport. At the cost of some energy, a cell can use pumps to transport molecules from areas of low concentration to areas of high concentration. HOW IT WORKS ------------ The blue background represents the external environment of the cell, the gray ring represents the cell membrane, and the white circle represents the inside of the cell. Green circles, labeled as water, and red squares, labeled as ions, randomly move about the environment. Water can freely pass through the membrane while ions cannot. The slider bar labeled "ion-permeability" controls the probability of an ion passing through the membrane. Usually this probability is extremely small, and in this model it begins as a 0.01% chance. Channels, which are represented by brown pentagons, can be created along the cell membrane, and ions can pass through these channels in and out of the cell. Pumps, which are represented by black pentagons, allow the one-way movement of ions either in or out of the cell. The direction of the movement can be controlled by the switch labeled "pump-direction." HOW TO USE IT ------------- The six smaller slider bars control the number of ions and water created both inside the cell and outside the cell, and the number of channels and pumps in the cell membrane. The ion-permeability slider bar controls the probability of an ion passing through the cell membrane. The size of the cell can also be adjusted via the cell-radius slider bar. In the plot, the green line represents the number of water molecules inside the cell, the blue line represents the number of water molecules outside of the cell, the red line represents the number of ions inside the cell, and the orange line represents the number of ions outside of the cell. THINGS TO NOTICE ---------------- Diffusion - molecules move from areas of higher transportation to areas of lower transportation. Place 50 water molecules inside the cell, and many will diffuse out of the cell because the concentration of water molecules outside the cell is lower than the concentration of water molecules inside the cell. Selective permeability - the membrane allows the passage of water molecules but not ions. Place 50 water molecules and 50 ions inside the cell, and although water molecules will diffuse out the cell, ions cannot. Facilitated diffusion and passive transport - channels facilitate the diffusion of ions across the membrane. Placing channels in the membrane allows ions to bidirectionally diffuse across the membrane. With many channels in the membrane, the behavior of ions become similar to the behavior of water. Active transport - pumps move ions against the concentration gradient at the cost of energy. By placing pumps in the membrane, we can force all ions either into the cell or out of the cell. THINGS TO TRY ------------- Being with only 50 water molecules inside the cell, and nothing else. Start the simulation. What happens after awhile? Approximately how many ticks does it take for an equilibrium to be achieved? Now instead of 50 water molecules, place 50 ions inside the cell, and nothing else. Set the ion-permeability to 0. What happens to the ions? Change the ion-permeability to 1.00. Now what happens? How long does it take for an equilibrium to be reached now? Add in 5 channels. What do you notice about the time it takes for equilibrium to reached? 50 channels? Instead of channels, put in 50 pumps. Make sure the "pump-direction" switch is on the "on" position. What happens now? Finally, can you manipulate the settings in a certain way to achieve an equilibrium where there is an even amount of ions inside and outside the cell? What about a 75-25 equilibrium? 90-10? Hint: it might be easier to work with 100 as your total amount of ions. EXTENDING THE MODEL ------------------- This model can be extended in numerous ways. Cell membranes contain an assortment of channels, pumps, gates, pores, and other passageways. Each type has a different behavior. Particularly interesting may be cotransporters, which couple the movement of one molecule across the membrane with the movement of another. For example, the Na+/K+ ATPase transports 3 sodium ions out of the cell to pump 2 potassium ions into the cell. Coupled transport will introduce the concept of a second-order reaction or transport rate. NETLOGO FEATURES ---------------- To simulate the cell membrane as a barrier against ions, an ion actually moves backwards 1 step towards the center of the cell if it happens to move inside the cell membrane (or 1 step away from the center of the cell if it is outside the cell). This workaround is probably due to my lack of experience with NetLogo rather than its functionality. CREDITS AND REFERENCES ---------------------- This model was created by Julian Xu at Shodor, under the mentorship of Jeff Krause. www.shodor.org www.shodor.org/~jxu @#$#@#$#@ 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 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