# MIHS VirusCompetition

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## WHAT IS IT?

A model of different virus strains infecting a host organism. There are two strains (Virus-1 and Virus-2) competing to become the dominant strain without killing the host.

## HOW IT WORKS

Cells of the host are modeled by patches. Virus particles are modeled with turtles.

Free virus particles diffuse randomly and can enter an uninfected host cell when they encounter it. The particles only survive for a short time outside of a host cell.

Once inside the host cell, the virus may enter a lytic (i.e. reproductive) cycle or a lysogenic cycle where it copies its DNA into the host cell's DNA and becomes dormant for a time. The lytic cycle produces new virus copies and eventually kills the host cell, releasing free virus particles to infect other host cells. The lysogenic cycle allows the host cell to survive and reproduce, making copies of the viral DNA in the process. Eventually the dormant viral genes will "awaken" and enter a lytic cycle, reproducing and killing the host cell.

Different strains of the virus have different probabilities of entering the lytic or lysogenic cycle, and will remain dormant in the lysogenic cycle for various amounts of time. Healthy, uninfected cells are Gray. Cells with active (lytic cycle) infections of either strain are Red. Cells with dormant (lysogenoc cycle) infections are Green or Blue (depending onwhether they are infected by Virus-1 or Virus-2 strains, respectively).

If too many host cells die, the virus will be unable to reproduce and will also die off. The model attempts to capture the dynamic behavior of virus strains which are competing to reproduce as fast as possible without killing off the host (and each other) in the process.

## HOW TO USE IT

Click Setup, then Go, to see the model run. You can change several variables using the sliders, including the starting number of host cells, starting number of virus particles, relative amounts of the two strains (Virus-1 vs Virus-2), and the probability that each strain will enter the lysogenic (dormant) life-cycle.

The model will automatically end if either of these conditions are met:

- There are no virus particles of either strain remaining and the cells have reached their maximum value.
- There are no cells and no virus particles of either strain remaining.

Various Monitors allow the user to see important values in the model, as explained below:

Total Cells: Total # of host cells Infected: Total # of host cells with infected by either strain of the virus Virus-1, Virus-2 & arbtrm: Total # of particles of each strain or # of arbitrium molecules

# -Infected-1, #-Infected-2: Total # of host cells with an infection by each strain of the virus (this # includes both lytic and lysogenic infections)

# -Lyso-1, #-Lyso-2: Total # of cells with lysogenic infections by each strain (this # excludes lytic infections)

## THINGS TO NOTICE

Changing the probability that a virus strain enters the lysogenic (dormant) cycle will have the biggest effect on viral behavior: decreasing the probability will produce more active infections and tend to kill off the host cells more quickly, while increasing the probability will produce fewer active infections and allow host cells to survive and reproduce (perhaps with viral DNA stowing away inside them!).

Changing the starting number of host cells, number of virus particles or ratio of the two strains will primarily alter the chance that the host cells die off or survive.

Can you figure out what is happening with the mysterious *arbitrium*?

## THINGS TO TRY

Which settings will tend to kill off the host most rapidly? Which ones will allow the host cells and virus to survive in a sort of equilibrium? What advantage does the virus gain by entering the lysogenic cycle? What happens when the two viral strains have very different probabilities of entering the lysogenic phase? Is this outcome affected by the starting numbers of cells and/or virus particles? The relative amounts of the two strains at the start?

Try stopping the model at various times to see how the levels of arbitrium are related to the number of virus particles. How are the level of arbitrium and the number of cells with lysogenic infections related?

Read the following article from Nature which is the basis for this model: https://www.nature.com/articles/d41586-019-01880-6

It will help you to understand the role of arbitrium in viral behavior. Is there a way to set up the two strains of the virus to simulate how a strain could "cheat" by ignoring the arbitrium signal, thereby gaining a competitive advantage over theo other strain? Over what range of settings is it possible for this "strategy" to be successful? Over what range is it doomed to failure?

## EXTENDING THE MODEL

The model could be altered to allow multiple virus strains to infect the same host cell. Additional strains of the virus could be introduced.

The host cells currently have no defenses against viral infection; the behavior of the model would be dramatically altered if host cells could fight off infection by virus particles.

It could be interesting to explore an evolutionary model by giving the viruses genes which can mutate as the host cells produce new virus particles during lytic cycles. Thus, new strains of the virus would tend to emerge spntaneousy and begin competing with each other. Some interesting "genes" might control the lysogenic probability, replication speed, arbitrium sensitivity, etc.

## NETLOGO FEATURES

One interesting feature of this model is the use of patches to represent cells and turtles to represent molecules/virus particle which are diffusing.

## RELATED MODELS

This model is based upon an earlier model called "Cells in a Petri Dish".

## CREDITS AND REFERENCES

Larry Bencivengo - Mercer Island High School (2022).

Dolgin, Elie (2019). "The Secret Social Lives of Viruses" in Nature, 18 June 2019. https://www.nature.com/articles/d41586-019-01880-6

## Comments and Questions

;; ********************************************************************************* ;; ************* Virus Competition Model *********************** ;; ************* By Larry Bencivengo *********************** ;; ************* May, 2022 - Mercer Island High School *********************** ;; ********************************************************************************* ;; This model simulates virus strains competing to reproduce without killing the host globals [ #-cells #-infected-cells #-virus-1 #-virus-2 #-Infected-1 #-Infected-2 #-Lyso-1 #-Lyso-2 virus-1-decay-rate virus-2-decay-rate arbitrium-decay-rate #-new-virus-1 #-new-virus-2 #-new-arbitrium ] patches-own [cell? infected-1? infected-2? lytic? arbitrium-absorbed] breed [viruses virus] breed [arbitria arbitrium] turtles-own [decay-rate] viruses-own [virus-strain] to setup clear-all ask patches [set pcolor white] ;; create a white background setup-cells ;; randomly identify start-#-cells patches as cells set #-infected-cells 0 set #-Infected-1 0 set #-Lyso-1 0 set #-Infected-2 0 set #-Lyso-2 0 ;; set up virus shapes, starting numbers, decay-rate, etc. set #-virus-1 0 set #-virus-2 0 set virus-1-decay-rate 20 set virus-2-decay-rate 20 ;; generate starting viruses set-default-shape viruses "pentagon" setup-viruses ;; set up arbitrium shape, decay-rate, etc. set-default-shape arbitria "dot" set arbitrium-decay-rate 30 reset-ticks end ;; ****** coded to here ****** ;; *************************** to setup-cells ;; generate cells by selecting random patches and setting cell? to true ;; repeat until the correct number of cells has been generated set #-cells 0 while [#-cells < start-#-cells] [ ;; select a random patch - if it is not already a cell, make it a cell ask patch random-pxcor random-pycor [if cell? = 0 [ become-cell set #-cells #-cells + 1 ] ] ] end to become-cell ;; this routine only called for starting cells set cell? 1 set infected-1? 0 ;; change when infected virus set infected-2? 0 ;; change when infected set lytic? 0 ;; change when infected by virus in lytic cycle set pcolor gray end to setup-viruses ;; use Virus-1_to_Virus-2_Ratio slider to create the initial virus population ;; create virus-1 particles set #-new-virus-1 start-#-viruses * (Virus-1_to_Virus-2_Ratio / 100) create-viruses #-new-virus-1 [ set color green set size 0.5 set virus-strain 1 set decay-rate virus-1-decay-rate setxy random-xcor random-ycor ] ;; update #-virus-1 set #-virus-1 #-new-virus-1 ;; create virus-2 particles set #-new-virus-2 start-#-viruses - #-new-virus-1 create-viruses #-new-virus-2 [ set color blue set size 0.5 set virus-strain 2 set decay-rate virus-2-decay-rate setxy random-xcor random-ycor ] ;; update #-virus-2 set #-virus-2 #-new-virus-2 ;; update #-all-viruses and reset #-new-virus values to 0 set #-new-virus-1 0 set #-new-virus-2 0 end ;; to go ;; arbitria molecules and virus particles move randomly ;; arbitria and viruses are "absorbed" by cells as they pass through patches ;; when viruses enter a cell, they will transition to a lytic or lysogenic cycle ;; depending on their lysogenic-probabilty and the level of arbitrium-absorbed ;; when cells accumulate enough viruses [lytic? = # of virus particles], they die ... ;; ... producing a number of new virus particles of the infecting strain equal to lytic? ;; if #-cells is less than 500, all cells with lytic? = 0 have a chance to reproduce ;; free viruses and arbitrium in cells will decay/die at a set rate ;; if #-cells with lytic? = 0 ever falls to zero, the host dies and the simulation ends to go ;; stop when all uninfected cells and viruses dead if count patches with [cell? = 1] <= 0 and count viruses <= 0 [stop] ;; stop when viruses eradicated and cells take over if count viruses <= 0 and #-infected-cells = 0 and count patches with [cell? = 1] >= 500 [stop] ask turtles [move] ask patches [metabolize] add-viruses add-arbitrium ask patches [reproduce] ask patches [update-status] tick end to move ;; molecules and virus particles decay at random intervals if random 100 <= decay-rate [ ifelse is-arbitrium? self [die] [ if virus-strain = 1 [set #-virus-1 #-virus-1 - 1] if virus-strain = 2 [set #-virus-2 #-virus-2 - 1] die ] ] ;; arbitrium molecules and viruses diffuse randomly right random 30 left random 30 forward 1 end to metabolize ;; absorb viruses and arbitrium, metabolize arbitrium, generate new viruses, etc. ;; only cells metabolize if cell? = 1 [ ;; absorb arbitrium from surroundings - arbitrium builds up and decays over time absorb-arbitrium if arbitrium-absorbed > 2 [set arbitrium-absorbed arbitrium-absorbed / 2] ;; absorb free viruses and become infected if infected-1? = 0 and infected-2? = 0 [become-infected] ;; if in lytic cycle of infection, produce new virus particles if lytic? != 0 [lytic-cycle] ] end to absorb-arbitrium ; cell procedure let available-arbitrium one-of arbitria-here ; grab a random arbitrium molecule if available-arbitrium != nobody [ ask available-arbitrium [die] set arbitrium-absorbed arbitrium-absorbed + 1 ] while [count arbitria-here > 1] [ set available-arbitrium one-of arbitria-here ; keep absorbing arbitrium if available-arbitrium != nobody [ ask available-arbitrium [die] set arbitrium-absorbed arbitrium-absorbed + 1 ] ] end to become-infected ; cell procedure ; grab a random virus molecule let available-virus one-of viruses-here if available-virus != nobody [ ; if viruses present ... if [virus-strain] of available-virus = 1 [ ; ... become infected set infected-1? 1 set #-Infected-1 #-Infected-1 + 1 set #-Lyso-1 #-Lyso-1 + 1 set #-virus-1 #-virus-1 - 1] if [virus-strain] of available-virus = 2 [ set infected-2? 1 set #-Infected-2 #-Infected-2 + 1 set #-Lyso-2 #-Lyso-2 + 1 set #-virus-2 #-virus-2 - 1] ask available-virus [die] ; original virus dies set #-infected-cells #-infected-cells + 1 update-infection-status ] end to lytic-cycle ;; if viruses in cell too high, cell dies ... ifelse lytic? >= 5 [ ;; ... and releases free viruses of correct strain ;; if infected with strain-1, add new viruses of strain-1 if infected-1? = 1 [set #-new-virus-1 #-new-virus-1 + lytic?] ;; else add new viruses of strain-2 if infected-2? = 1 [set #-new-virus-2 #-new-virus-2 + lytic?] cell-death ] [ ;; keep producing viruses and arbitrium. ;; Rate of virus production inversely proportional to Lysogenic-Probability if infected-1? = 1 [ (ifelse Virus-1-%-Lysogenic <= 25 [set lytic? lytic? + 3] Virus-1-%-Lysogenic <= 50 [set lytic? lytic? + 2] [set lytic? lytic? + 1])] if infected-2? = 1 [ (ifelse Virus-2-%-Lysogenic <= 25 [set lytic? lytic? + 3] Virus-2-%-Lysogenic <= 50 [set lytic? lytic? + 2] [set lytic? lytic? + 1])] set #-new-arbitrium #-new-arbitrium + lytic? ] end to update-infection-status let chance-lytic 0 if lytic? = 0 [ if infected-1? = 1 [ ifelse arbitrium-absorbed > 1 [ set chance-lytic (Virus-1-%-Lysogenic * arbitrium-absorbed)] [set chance-lytic Virus-1-%-Lysogenic] if random 101 > chance-lytic [ set lytic? 1 set #-Lyso-1 #-Lyso-1 - 1 ] ] if infected-2? = 1 [ ifelse arbitrium-absorbed > 1 [ set chance-lytic (Virus-2-%-Lysogenic * arbitrium-absorbed)] [set chance-lytic Virus-2-%-Lysogenic] if random 101 > chance-lytic [ set lytic? 1 set #-Lyso-2 #-Lyso-2 - 1 ] ] ] end to cell-death set cell? 0 set pcolor white if infected-1? = 1 [ set infected-1? 0 set #-Infected-1 #-Infected-1 - 1 ] if infected-2? = 1 [ set infected-2? 0 set #-Infected-2 #-Infected-2 - 1 ] set lytic? 0 set arbitrium-absorbed 0 set #-cells #-cells - 1 set #-infected-cells #-infected-cells - 1 end to add-viruses ;; create new viruses of strain-1 based on #-new-virus-1 if #-new-virus-1 > 0 [ create-viruses #-new-virus-1 [ set virus-strain 1 set decay-rate virus-1-decay-rate set color green set size 0.5 setxy random-xcor random-ycor ] set #-virus-1 #-virus-1 + #-new-virus-1 ] ;; create new viruses of strain-2 based on #-new-virus-2 if #-new-virus-2 > 0 [ create-viruses #-new-virus-2 [ set virus-strain 2 set decay-rate virus-2-decay-rate set color blue set size 0.5 setxy random-xcor random-ycor ] set #-virus-2 #-virus-2 + #-new-virus-2 ] ;; reset values of #-new-virus-1 and #-new-virus-2 for next tick set #-new-virus-1 0 set #-new-virus-2 0 end to add-arbitrium ;; produce new arbitrium molecules based on #-new-arbitrium if #-new-arbitrium > 0 [ create-arbitria #-new-arbitrium [ set decay-rate arbitrium-decay-rate set color black set size 0.5 setxy random-xcor random-ycor ] ] ;; reset value of #-new-arbitrium for next tick set #-new-arbitrium 0 end to reproduce ;; only cells reproduce if cell? = 1 and lytic? = 0 [ ;; if not in lytic phase, chance to divide ;; check for empty adjacent patch if any? neighbors with [cell? = 0] [ ;; probability of dividing decreases as #-cells approaches 500 if random 500 < ((1 - #-cells / 500) * 100) [ ;; create a new cell in an adjacent patch ;; new cell inherits infection status of original and one half of arbitrium-absorbed let virus-1-status infected-1? let virus-2-status infected-2? set arbitrium-absorbed arbitrium-absorbed / 2 let amount-arbitrium arbitrium-absorbed ;; turn a neighboring patch into a cell ask one-of neighbors with [cell? = 0] [ set cell? 1 set lytic? 0 set infected-1? virus-1-status set infected-2? virus-2-status set arbitrium-absorbed amount-arbitrium ] ;; update global variables set #-cells #-cells + 1 if infected-1? = 1 or infected-2? = 1 [set #-infected-cells #-infected-cells + 1] if infected-1? = 1 [ set #-Infected-1 #-Infected-1 + 1 set #-Lyso-1 #-Lyso-1 + 1] if infected-2? = 1 [ set #-Infected-2 #-Infected-2 + 1 set #-Lyso-2 #-Lyso-2 + 1] ] ] ] end to update-status ;; update each cell's pcolor to indicate its status: ;; healthy = gray, lytic = red, lysogenic = green (virus-1) or blue (virus-2) if cell? = 1 [ update-infection-status ifelse lytic? > 0 [ set pcolor red ] [(ifelse infected-1? = 1 [ set pcolor green] infected-2? = 1 [ set pcolor blue] [set pcolor gray]) ] ] end

There are 5 versions of this model.

## Attached files

File | Type | Description | Last updated | |
---|---|---|---|---|

MIHS VirusCompetition.png | preview | Preview for 'MIHS VirusCompetition' | almost 2 years ago, by Larry Bencivengo | Download |

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