Effect of quorum sensing inhibitors on P. aeruginosa biofilms

; extensions [ profiler ]
extensions [ vid ]

globals [
  film-output-prefix ; date and time of start of film for use in naming images for film
  total-mass ; total mass of bacteria at that timestep
  new-shuffle-step-size ; shuffle step size in terms of patches
  top-patches ; row of patches at the top of the system
]

patches-own [
  ahl ; AHL concentration
  antibiotic ; antibiotic concentration
  nutrient ; growth-limiting nutrient concentration
  old-ahl old-nutrient ; concentrations on previous tick
  biofilm? ; true if patch is covered by biofilm
  ahl-threshold-adj ; ahl threshold adjusted by local antibiotic concentration
]

breed [bacteria bacterium]

bacteria-own [
  attached? ; true if attached to surface/part of biofilm
  move-count ; counts steps taken for move procedure
  mass ; mass of cell
  resistant? ; true if bacterium is resistant to the antibiotic
]

; setup simulation - see individual procedures for comments on what they do

to setup
  clear-all
  setup-patches
  setup-bacteria
  update-patches
  set-globals
  format-patches
  setup-film
  reset-ticks
  if film? [ vid:start-recorder ]
end 

; run simulation - see individual procedures for comments on what they do

to go
  ; profiler:start
  while [ ticks <= 1441 ] [ ; stops simulation after 60 days
    if ticks > 25 [ disperse ] ; doesn't start dispersal immediately to avoid cases where all bacteria quickly disperse
    move
    grow-bacteria
    divide-bacteria
    die-bacteria
    mutate
    kill-antibiotic
    shuffle-bacteria
    update-patches
    synthesise-ahl
    diffuse-ahl
    degrade-ahl
    diffuse-nutrient
    format-patches
    format-bacteria
    plot-density
    if film? [ vid:record-view ]
    tick
  ]
end 

;;; --- Setup Procedures --- ;;;

; sets patch variables and colour at start of simulation

to setup-patches
  ask patches [
    set pcolor white
    set ahl 0
    set nutrient nutrient-dose
    set old-ahl 0
    set old-nutrient nutrient-dose
    set antibiotic antibiotic-dose
    set biofilm? FALSE
    set ahl-threshold-adj ahl-threshold
  ]
  ask patches with [ pycor < 0 ] [ set pcolor 8 ]
end 

; simulation starts with single bacterium in centre of surface

to setup-bacteria
 create-bacteria 1 [
    setxy (max-pxcor / 2) 0
    set attached? TRUE
    set resistant? FALSE
    set mass (division-mass / 2)
    format-bacteria
  ]
end 

; set global variables

to set-globals
  set new-shuffle-step-size shuffle-step-size / patch-length
  set top-patches patches with [pycor = max-pycor]
end 

; prepares to output film with name of the current date and time

to setup-film
  if film? [
    set film-output-prefix (word "output/film/" date-and-time "_")
  ]
end 

;;; --- Simulation Procedures --- ;;;

; dispersal of bacteria from the biofilm
; disperses with probability dispersal-rate if below (adjusted) ahl threshold. Dispersal rate increases if above threshold

to disperse
  ask bacteria with [attached?] [
    ifelse not resistant? or antibiotic-type != "effect-quorum-sensing" [
      ifelse ahl > ahl-threshold-adj [
        if dispersal-rate * dispersal-increase >= random-float 1 [set attached? FALSE]
        ]
      [
        if dispersal-rate >= random-float 1 [ set attached? FALSE ]
      ]
    ]
    [
      ifelse ahl > ahl-threshold [
        if dispersal-rate * dispersal-increase >= random-float 1 [set attached? FALSE]
        ]
      [
        if dispersal-rate >= random-float 1 [ set attached? FALSE ]
      ]
    ]
  ]
end 


; random movement of detached cells

to move
  set total-mass sum [mass] of bacteria
  ask bacteria with [not attached?] [ ; since movement happens much faster than cell division, assumes either cells will move out of frame of reference or they will attach every hour
    while [not attached?] [
      set heading random 360
      set move-count 0
      while [ move-count < speed * tumble-frequency / patch-length ] ; moves for at given speed, tumbles and changes direction according to tumble-frequency
      [ fd 1
        bounce
        set move-count move-count + 1
      ]
    ]
  ]
end 

; either diffuse out of system, bounce off surface or attach to biofilm

to bounce ; bacteria procedure

  ; die when hit outside walls - simulates diffusion out of system
  if abs pxcor = max-pxcor [ die ]
  if abs pxcor = 0 [ die ]
  if abs pycor = max-pycor [ die ]

  ; bounce off bottom surface
  if pycor = 0 [ set heading ( - heading ) ]

  ; attach or bounce off biofilm
  if  count bacteria-here with [attached?] > 0 [ ; if collide with an attached bacterium

    let mass-tot sum [mass] of bacteria-here - mass / total-mass ; mass of other bacteria at this patch as a fraction of total bacteria
    let probability-attachment (attachment-rate * mass-tot) / (attachment-k + mass-tot) ; MM-like attachment kinetics as in Emerinini 2015 model

    ifelse probability-attachment > random-float 1 ; attaches according to probability-attchment
    [ set attached? TRUE
      set move-count speed
      ]
    [ set heading ( - heading ) ]
    ]
end 

; grow bacteria

to grow-bacteria
  ask bacteria [
    let mass-increase (mass * nutrient * growth-rate) / (growth-k + nutrient) ; Monod growth kinetics as in Emerinini 2015 model
    set mass mass + mass-increase
    set nutrient nutrient - (mass-increase / yield) ; removes consumed nutrient
    if nutrient < 0 [set nutrient 0]
  ]
end 

; bacterial divide when they reach division-mass

to divide-bacteria
  ask bacteria [
    if mass >= division-mass [
      let new-mass (division-mass / 2) + random-normal 0 (division-mass / 20) ; mass of daughter cell is half mass of mother cell with some random variation
      set mass new-mass
      hatch 1 [ ; new cell
        set mass division-mass - new-mass ; mass of both daughters adds up to original cell
        set heading random 360 ; set random direction
        fd shuffle-step-size ; move away in random direction so not directly on top of parent
      ]
    ]
  ]
end 

; bacteria die with probability lysis-rate

to die-bacteria
  ask bacteria [
    if lysis-rate > random-float 1 [die]
  ]
end 

; some bacteria randomly mutate and become antibiotic resistant

to mutate
  if antibiotic-type != "none" [
    ask bacteria [
      if resistance-mutation-rate * 10 ^ -5 > random-float 1 [ set resistant? TRUE ]
    ]
  ]
end 

; if bacteria-killing antibiotic treatment used, bacteria die according to death rate and antibiotic concentration

to kill-antibiotic
  if antibiotic-type = "kill-bacteria" [
    ask bacteria [
      ifelse not resistant? [
        let probability-death (antibiotic-death-rate * antibiotic) / ( half-max-conc + antibiotic)
        if probability-death >= random-float 1 [ die ]
      ]
      [
        let probability-death (antibiotic-death-rate-resistant * antibiotic) / ( half-max-conc + antibiotic)
        if probability-death >= random-float 1 [ die ]
      ]
    ]
  ]
end 

; bacteria move slowly in random directions in the biofilm to reduce overlapping

to shuffle-bacteria
  ask bacteria [
    set heading random 360
    if [pycor] of patch-ahead new-shuffle-step-size >= 0 [ fd new-shuffle-step-size ]

    ; stops movement out of system
    if ycor < 0.5 [ set ycor -0.5 + random-float 1 ]
    if xcor < 0.5 [ set xcor 0.5 + random-float 1 ]
    if xcor > ( max-pxcor - 0.5 ) [ set xcor max-pxcor - 0.5 - random-float 1 ]
    if ycor > ( max-pycor - 0.5 ) [ set ycor max-pycor - 0.5 - random-float 1 ]
  ]
end 

; all living bacteria synthesise ahl according to ahl-synthesis-rate. This increases if over ahl-threshold

to synthesise-ahl
  ask bacteria [
    ifelse not resistant? or antibiotic-type != "effect-intracellular-quorum-sensing" [
      ask patch-here [
        ifelse ahl < ahl-threshold-adj [
          set ahl ahl + ahl-synthesis-rate
        ]
        [ set ahl ahl + (ahl-synthesis-rate * ahl-synthesis-increase) ] ; increase by additional amount if over ahl threshold
      ]
    ]
      [ ask patch-here [
        ifelse ahl < ahl-threshold [
          set ahl ahl + ahl-synthesis-rate
        ]
        [ set ahl ahl + (ahl-synthesis-rate * ahl-synthesis-increase) ] ; increase by additional amount if over ahl threshold
      ]
      ]
  ]
  ask patches [set old-ahl ahl]
end 

; diffusion of ahl - diffuses into neighbouring patches according to diffusion rate. Adapted from the model Heat Diffusion (Wilensky, 1998)

to diffuse-ahl
    ask patches [
      ifelse biofilm? [
        set ahl ( diffusion-rate * diffusion-decrease-biofilm * (sum [old-ahl] of neighbors4) / ( patch-length ^ 2 ) + ((1 - (4 * diffusion-decrease-biofilm * diffusion-rate / patch-length ^ 2))  * old-ahl ))
      ]
      [
        set ahl ( diffusion-rate *  (sum [old-ahl] of neighbors4) / patch-length ^ 2 ) + ((1 - ( 4 * diffusion-rate / patch-length ^ 2)) * old-ahl )
      ]
    if ahl < 0 [ set ahl 0 ]
    set old-ahl ahl
    ]
end 

; as above for nutrient

to diffuse-nutrient
  ; top patches have constant nutrient concentration
  ask top-patches [
    set nutrient nutrient-dose
    set old-nutrient nutrient-dose
  ]
    ask patches [
      ifelse biofilm? [
        set nutrient ( diffusion-rate * diffusion-decrease-biofilm * (sum [old-nutrient] of neighbors4) / patch-length ^ 2 ) + ((1 - ( 4 * diffusion-decrease-biofilm * diffusion-rate / patch-length ^ 2 )) * old-nutrient)
      ]
      [
        set nutrient (diffusion-rate *  (sum [old-nutrient] of neighbors4) / patch-length ^ 2 ) + ((1 - ( 4 * diffusion-rate / patch-length ^ 2 )) * old-nutrient)
      ]
    if nutrient < 0 [ set nutrient 0 ]
    if nutrient > nutrient-dose [ set nutrient nutrient-dose ]
    set old-nutrient nutrient
    ]
end 

; constant rate of degradation of AHL, increased by an ahl-degrading antibiotic

to degrade-ahl
  ask patches [
    set ahl ahl - (ahl * ahl-degradation-rate)
    if antibiotic-type = "degrade-ahl" [
      let degradation (antibiotic * aiia-reaction-rate * ahl) / (aiia-km + ahl)
      set ahl ahl - degradation
    ]
    if ahl < 0 [set ahl 0]
    set old-ahl ahl
  ]
end 

; set patch variables

to update-patches
  ask patches with [ count bacteria-here with [attached?] > 0 ] [ set biofilm? TRUE ]
  ask patches with [ count bacteria-here with [attached?] = 0 ] [ set biofilm? FALSE ]

  ; drugs affecting QS adjust the effective ahl threshold concentration
  if antibiotic-type = "effect-intracellular-quorum-sensing" [
    ask patches [ set ahl-threshold-adj ahl-threshold - ( antibiotic-qs-effect * ahl-threshold * antibiotic / antibiotic-dose ) ]
  ]
end 

; sets antibiotic dose according to antibiotic type. Run by button in interface

to set-antibiotic-dose
  ifelse antibiotic-type = "none" [ set antibiotic-dose 0 ] [ set antibiotic-dose 50 ]
end 

;;; --- Plots etc --- ;;;

to export-bacteria-plot
  export-plot "Bacteria" (word "output/bacteria_plots/" date-and-time ".csv")
end 

to export-biofilm-mass-plot
  export-plot "Biofilm Mass" (word "output/biofilm_mass_plots/" date-and-time ".csv")
end 

to export-ahl-plot
  export-plot "Patches with AHL concentration greater than threshold" (word "output/ahl_plots/" date-and-time ".csv")
end 

;;; --- Visualisation Procedures --- ;;;

to format-patches
  ask patches with [ pycor >= 0 ] [ set pcolor scale-color blue ahl (2 * ahl-threshold) 0 ]; darker blue corresponds to higher AHL concentration
end 

to format-bacteria
  ask bacteria [
    set shape "circle"
    set color green
    if resistant? [ set color 72 ]
    set size (((3 * mass) / (cell-density * pi * 4)) ^ (1 / 3)) / patch-length ; calculate diameter from mass and density
  ]
end 

; Plots bacterial density rather than standard visualisation

to plot-density
  if plot-density? [
    ask bacteria [set color [0 0 0 0]]
    ask patches [set pcolor scale-color red (sum [mass] of bacteria-here) (10000) 0]
  ]
end