NetLogo 4 auto stress strategies
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NOTE
Note from Feb 14, 2014: This is an early version of the host-versus-pathogen (infection) model, but it has 4 types of automatic-systemic stressor (fast, slow, cycle, and hi-cycle) which were tested at a setting of 60 (set within the code). The subsequent version omitted all of the auto-systemic-stressors except the fast version, which subsequently became known as auto-systemic-stressor-hostcell# (to be distinguished from a later auto-systemic-stressor-pathogen#).
The text of this Info section and the code has not been cleaned up in this version.
-Edmund K. LeGrand
HOST-VERSUS-PATHOGENS MODEL: USE OF STRESSORS FOR DEFENSE
WHAT IS IT?
This is a host-versus-pathogens model that explores how the host can use stressors (harmful conditions) to fight pathogens. The struggle, from the host's viewpoint, is built around harming the pathogens relatively more than the host. In this program energy is used as the currency for survival and replication by the host cells and pathogens.
The program models life-threatening infections, where the host uses stressors to fight an infection but may be killed by being overwhelmed by the pathogens or by its own vigorous defense (sepsis). The host has a number of potential defenses, from invoking: 1) direct toxicity to the pathogen, 2) localized stressful conditions for all nearby cells, 3) regional stressful conditions, to 4) systemic stressors which harm the entire host including the pathogen cells contained within. In the program the pathogen phenotype can be varied according to 1) the amount of harm pathogen cells can do to adjacent host cells, 2) the amount of energy they can obtain when adjacent to host cells, 3) the amount of energy they need to survive, and 4) whether or not they can wander to adjacent vacant spaces. The pathogens can be thought of as a large extracellular pathogens (comparable in size and energy requirements as a host cell) or as infected cells taken over by pathogens. Similarly, the pathogens can be viewed as tumor cells.
Levels of Host Defense
1) The "local-host-directed" defense mechanism models the standard view of immune defenses where defense is directed specifically at the pathogen with little, if any, host damage (e.g., phagocytosis with killing within the phagolysosome, and direct pathogen killing via complement, antimicrobial peptides, antibodies, etc.). The only cost to the host is the energy involved in creating this defense. In this program there is no additional cost for "local-host-directed" defense since these costs are already incorporated into the routine functioning of the host cells. Note that in this program there are no specialized immune cells; rather, any host cell has the ability to respond to the pathogens.
2) The "local-host-stressor" defense component is typically ignored in discussions of host defense. However, this program was developed to show how even non-specific self-harm can be utilized in host defense. In inflammatory sites all local cells, including pathogens, can be harmed by a variety of non-specific stressors such as: lactic acidosis, hypoxia, reduced energy-providing nutrients such as glucose and glutamine, reduced iron and zinc, and even slightly increased local heat (beyond that caused by vasodilation and fever) (Refs). Inflammatory cells utilize both glucose and glutamine, key sources of nutrition for pathogens and host cells, in what appears to be a deliberately wasteful manner (Refs). The waste of glucose contributes to the local lactic acidosis. In the program, "local-host-stressors" reduces energy from all cells adjacent to any host cell which is in contact with a pathogen.
3) Regional stressors are modeled by two mechanisms. The first is similar to "local-host-stressor" in that it reduces energy from all cells within 5 spaces of the contact between a host cell and a pathogen. This roughly models the reduced blood flow in zones of inflammation due to thrombosis (a feature co-induced by inflammatory mediators), extracellular fibrin formation, and edema (vascular leakage leading to tissue compression) (Alcock J, Brainard AH. Hemostatic containment - an evolutionary hypothesis of injury by innate immune cells. Med. Hypotheses 2008, 71:960-8). An additional regional stressor, "regional-amputation", reduces energy to a 6 x 16 space region in the lower right corner of the screen/host. This is comparable to the host's abandonment of a region of tissue through amputation. In plants the hypersensitive response involves programmed cell death of host cells in a zone around an infection to deprive the pathogen of nutrients.
4) "Systemic-host-stressor" models endogenous stressors of the acute-phase response, such as fever, nutrient restriction, anemia/hypoxia, etc. which affect all cells within the host. By analogy, it models exogenous systemic therapies which have substantial host toxicity.
It is important to note that in this program, except for "local-host-directed", the defense offered by every host-induced stressor harms host cells as much as pathogens. Any efficacy is due to the pathogens being relatively more vulnerable to the stressor than the host cells or the host as a whole. The primary vulnerability of the pathogens is that upon replication, they must split their energy between the mother and daughter cells, such that both cells have less energy reserves to weather stressful events. There are 3 outcomes (besides stalemate) in this program: 1) the host wins by eliminating all pathogens, 2) the pathogen wins by overrunning and killing the host, or 3) both lose when the host dies because of too vigorous a defense (sepsis).
HOW IT WORKS
The screen starts with 1081 host cells (1056 cyan circles and 25 orange flags) and with 8 pathogens (red triangles) along the surface (though the number and location of the pathogens can be modified with sliders). These cells (turtles) represent an organism with a small infection at its surface. Each cell sits on one of the 1089 green spaces (patches), representing extracellular space. The cells derive approximately 14 units of energy per time interval (tick) and expend approximately 10 units of energy per tick. The randomness of the model is based on slight randomness in the amount of energy received and spent by each cell at each tick.
The central 25 orange flags represent "key host cells" which are unable to replicate, but which can store more energy than the cyan circles ("host cells", which are able to replicate if they have enough energy and are adjacent to a vacant space). The key host cells represent a critical organ such as the heart or brain. In this program the key host cells have no function, but enough of them must survive for the host to survive (here more than 20 key host cells must survive). They are centrally located so as to be less vulnerable to pathogen attack from the surface of the organism.
Vulnerability of the cells depends on energy, related to differences in their parameters.
Parameters of host cells (cyan circles):
start-energy = 120 units (energy the program starts with) birth-energy = 90 units (energy that daughter cells start with in adjacent vacant space) max-energy = 300 units (energy above this value can't be stored) energy-to-survive = 40 units Replication can occur if there is a vacant space in one of the 4 neighboring spaces and if they have at least twice the birth-energy (i.e., 180 units). Replication splits the energy between the mother and daughter cells. At least 700 of the original 1056 host cells must be present for the host to survive. There is an on-off switch which allows host cells to move to vacant adjacent spaces without replicating.
Parameters of key host cells (orange flags):
start-energy = 120 units (energy the program starts with) max-energy = 500 units (energy above this value can't be stored) energy-to-survive = 30 units No replication is possible. At least 21 of the original 25 key host cells must be present for the host to survive.
Parameters of pathogens (red triangles):
start-energy = 120 units (energy the program starts with) birth-energy = 60 units (energy that daughter cells start with in adjacent vacant space) max-energy = 200 units (energy above this value can't be stored) energy-to-survive = 40 units. To enhance virulence this can be lowered with a slider down to 10 units, with the maximum energy stored being 160 more units. Replication can occur if there is a vacant space in one of the 4 neighboring spaces and if they have at least twice the birth-energy (i.e., 120 units). Replication splits the energy between the mother and daughter cells.
Depending on the pathogen attributes (see below), pathogens can reduce energy of adjacent host cells and/or can gain energy when adjacent to host cells. A switch allows pathogen cells to wander in vacant spaces without replicating.
Rationale for selected parameters
The energy-to-survive for the key host cells is set lower than for the host cells since they are irreplaceable. This is consistent with the resistance to apoptosis of cardiomyocytes and neurons. Also to compensate for their irreplaceability, they are allowed to store more energy.
The energy-to-survive and start-energy of the pathogens is set the same as for host cells (though the pathogens' energy-to-survive can be lowered to enhance their virulence). This permits demonstration that other differences in susceptibility to stressors can be used for host defense. Additionally, the pathogens could be modeled as infected host cells or host-derived tumor cells having similar basic physiology as host cells.
Pathogens are adapted for rapid replication, hence they require less energy to replicate and have less need for energy storage than host cells. This rapid replication is their main vulnerability in this program.
Starting with 8 pathogens along the edge is the recommended starting point. It is harder to get an infection started with smaller numbers of pathogens, especially since chance plays a larger role. Additionally, with smaller numbers of pathogens there is more contact with host cells and exposure to their pathogen-harming defenses.
The host wins when the pathogen is eliminated and it has sufficient host cells and key host cells to survive. It is possible to adjust the stressor levels such that the pathogen numbers can be kept under control indefinitely, but the host will never have its full number of host cells and thus will remain impaired and vulnerable to other threats, besides the threat of pathogen re-emergence.
Pathogen Phenotypes and Host Defenses
Pathogen Phenotypes
pathogen-harm-hostcell This slider harms host cells and key host cells that are in contact with the pathogen by reducing energy to those cells. A setting of 10 or 20 is recommended for starters.
pathogen-take-up-energy This slider adds energy to pathogens that are in contact with a host cell, but does not harm the host cells. it is recommended that the setting of this slider be kept the same as that for "pathogen-harm-hostcell" since in real-life a pathogen would tend to harm the adjacent host cells and gain energy in the process. If this slider is used while "pathogen-harm-hostcell" is set to 0, the number of pathogens will be unchanged, with all cells getting to their maximum (or temporarily more, based on the how the program is coded). "pathogen-harm-hostcell" must be set to at least 2 for these high-energy pathogens to be able to break out and spread.
pathogen-survive-low-energy With this slider, the lower value of 10 provides a little more pathogenicity by letting the pathogens survive down to 10 units of energy, rather than the default of 40 units (same as the host cells). This can be demonstrated at settings of "pathogen-harm-hostcell" = 20, "pathogen-take-up-energy" = 20, "pathogen-wander?" = on, "local-host-directed" = 10, and "local-host-stressor" = 10. At the default setting of 40, the host typically wins (pathogens destroyed), while at 10, the pathogen typically wins (pathogens overrun the host).
pathogen-wander? This switch allows pathogens to randomly move to vacant adjacent spaces. Without it being on, only the pathogen daughter cells can to an adjacent vacant space upon replication. The ability to wander lets virulent pathogens become more aggressive, while less virulent pathogens become more vulnerable because of their more frequent contact with more aggressive host cells.
When unopposed (all host defenses set at 0) the full extent of pathogenicity leads to the pathogens winning (overrunning the host to the point of the host dying) in 65-70 ticks.
Host Defenses
The host defenses are ordered from most specific to least specific.
local-host-directed This slider removes energy units from adjacent pathogens. A recommended setting is half of the "pathogen-harm-hostcell" setting.
local-host-stressor This slider removes energy units from all cells within a radius of 1 from the host cell in contact with a pathogen. A recommended setting is that it be the same as "local-host-directed". Interestingly, this defense is comparable to or slightly more effective than "local-host-directed".
regional-host-stressor When a host cell is within 2 spaces of a pathogen, this slider reduces energy by a percentage for all cells in a radius of 5 spaces from the host cell. This creates fairly wide zones of destruction. It is especially effective at the start of the infection.
regional-amputation This slider reduces energy by a percentage for all cells in the lower right region of the host. While it is highly effective early on, once pathogens have spread from this region, it has little value.
systemic-host-stressor This slider reduces energy by a percentage for all cells in the host. This slider allows modeling of sepsis, the condition where the host defense, rather than the pathogen, has killed the host. In this program a failure of the other defenses simply allows overgrowth of the pathogens leading to host death. However, this slider has the ability to kill the host while only a few pathogens are present. This slider can reverse a losing battle, but it is difficult to use effectively, and it is suggested that the action be slowed down with the slider at the top of the screen.
auto-systemic-stressor This switch was developed from a generally winning strategy of using the "systemic-host-stressor" slider. The host is prevented from killing itself (sepsis) while trying to maximize the harm that is done to the pathogens. Once there is a significant threat (when the number of host cells drops from 1056 to 1040 AND the mean energy of the host cells is at least 180) the "systemic-host-stressor" slider moves to 60. This quickly drains the cells of energy, with the pathogens being relatively more affected since they've spent their spare energy on replication. When the number of host cells drops to 975, the slider moves back to 0, allowing all cells to recover. This will cycle again and again. Sometimes the pathogens can be eliminated with one bout of "fever", and other times it may take several cycles. However, if the pathogen is so aggressive that the host never gets more than 975 cells (or if the mean energy never reaches 180), the auto-stressor will not turn on. Then the host will die because of pathogen overgrowth.
Because of the cell-by-cell calculations involved in running the program and creating a tick of time, there can be considerable lag and overshooting in the auto-stressor. Setting the lower safe zone closer to the required 700 surviving host cells (thus killing more pathogens as well as host cells) would lead to frequent overshooting and host death (sepsis).
In the course of playing with the "systemic-host-stressor" slider, it became clear that it is best to rapidly apply the systemic stress. It is anxiety-producing to slowly increase the systemic stress while watching the pathogens continue to spread, thus making success that much more difficult. Likewise, a rapid reprieve from systemic stress is useful when one watches more and more host cells dying. Even with the instantaneoous stress and relief from stress in this program, there is still a lag time for the effects to be apparent. This was not apparent to me before using the program.
hostcell-wander? When on, this switch allows host cells to wander to a vacant adjacent cell. It has limited utility. If host cells are set to be aggressive relative to the pathogens, then it will have some efficacy.
THINGS TO NOTICE
The primary vulnerability of the pathogens in this program is that they replicate rapidly. In doing so, they convert one well-energized cell into two cells with low energy levels. This reflects real-life since replication requires acquiring the material and energy resources to duplicate oneself. Additionally, DNA is vulnerable during replication, as are newly forming and folding proteins. The reasonable strategy during stressful conditions is to inhibit growth and reproduction.
The only movement of cells in this program is reproduction into vacant spaces (only one cell is permitted in a space). Key host cells, in not replicating, never move. One of the pathogen strategy choices allows pathogen cells to move to empty adjacent spaces even when not replicating. Under most situations movement of pathogens can enhance pathogenicity by increasing the spread of the infection. However, if the pathogens are less toxic than the host cells, the increased contact with host cells will tend to be harmful to the motile pathogens. Likewise for movement of host cells when that option is turned on.
None of the host strategies directly monitor the pathogen number. The auto-host-stressor strategy monitors mean energy of host cells and host cell number before applying a fixed systemic-stressor-level (60 or 0). It is not clear how host strategies could be improved by monitoring pathogen number (except to know that all pathogens were killed). Mean pathogen energy would be useful in deciding whether or not systemic stressors would be effective. In this program it would be useful to automatically decide on the strategy of applying regional-amputation. Obviously, this drastic strategy is only effective before the pathogen has spread beyond the affected region.
THINGS TO TRY
For a given pathogen phenotype, one can be an active participant by adjusting the sliders for the various host defenses. Most notably one can play with the systemic-host-stressor switch to try to use the stressors of the acute-phase response (fever, etc.). The auto-systemic-stressor switch was developed to simplify host defense without killing the host from excessive stress. The settings were developed through trial-and-error and have not been optimized, so it should be possible to improve upon it.
The effect of dual infections could be modeled by programming in an additional pathogen with a differing phenotype. For a mouse model of concomitant infection see Lundqvist J, et al. Concomitant infection decreases the malaria burden but escalates relapsing fever borreliosis. Infect. Immun. 2010, 78:1924-30.
NETLOGO FEATURES
CREDITS AND REFERENCES
COPYRIGHT AND LICENSE
Feb 14, 2014 to Edmund K. LeGrand and Judy Day
EXTENDING THE MODEL
Comments and Questions
breed [ circles circle ] ;; Host cells breed [ flags flag ] ;; Key host cells breed [ triangles triangle ] ;; Pathogens A breed [ stars star ] ;; Pathogens B turtles-own [energy max-energy start-energy birth-energy] ;; All turtles have energy and a maximum amount of energy they can take on. patches-own [countdown patch-energy] ;; Countdown makes it run. Patch-energy is new to the program. circles-own [circle-energy-to-survive] flags-own [flag-energy-to-survive] triangles-own [triangle-energy-to-survive] stars-own [star-energy-to-survive] globals [pathB cumulative-energy-deficit] to setup clear-all set pathB 1 ;; Turns the pathB switch in the code to "on" in the setup. The user must still physically turn on the switch at the interface screen. ask patches [ set pcolor green set patch-energy 100] ;; New code here with patch-energy. set-default-shape circles "circle" ;; Host cells ask patches [ sprout-circles 1 [ set color blue set start-energy 300 set birth-energy 90 set max-energy 300 set circle-energy-to-survive 40] ] ;; START-ENERGY HAD BEEN 120 FOR ALL CELLS set-default-shape flags "flag" ;; key host cells such as heart cells ask patches with [(pycor < 3) and (pycor > -3 ) and (pxcor < 3) and (pxcor > -3)] [sprout-flags 1 [ set color orange set start-energy 300 set max-energy 300 set flag-energy-to-survive 30] ] ;; Can store lots of energy; not prone to apoptosis since irreplaceable. ask circles with [ (pycor < 3) and (pycor > -3 ) and (pxcor < 3) and (pxcor > -3)] [ die ] ;; This clears out the circles underneath the flags. ;; FLAG MAX-ENERGY HAD BEEN 500 set-default-shape triangles "triangle" ;; Pathogens A (these are like large extracellular pathogens) ask circles with [ (pycor <= start-upper-pathogen-pycor) and (pycor > start-lower-pathogen-pycor) and (pxcor <= start-upper-pathogen-pxcor) and (pxcor > start-lower-pathogen-pxcor) ] [ die ] ;; This clears out the circles underneath where the triangles will be. ask patches with [ (pycor <= start-upper-pathogen-pycor) and (pycor > start-lower-pathogen-pycor) and (pxcor <= start-upper-pathogen-pxcor) and (pxcor > start-lower-pathogen-pxcor)] [sprout-triangles 1 [ set color red set start-energy 300 set birth-energy 60 set max-energy 300 set triangle-energy-to-survive 40] ] ;; Low energy storage compared to host cells is a vulnerability; same energy to survive as host cells. ;; The pathogens' energy to survive can be modified by the slider (see below). ask turtles [ set energy start-energy ] ;; Even though start-energy is mentioned above for each breed, this code is needed to actually impart the energy. reset-ticks end to go set cumulative-energy-deficit 326700 - ((sum [energy] of circles) + (sum [energy] of flags)) + cumulative-energy-deficit ;; There are 1089 potential host cells and key host cell x 300 max energy units per cell. ;; Note that the host starts with a deficit of 3000 because the of the initial infection (e.g. a bite wound). ;; The host must recover to its full 1089 cells. ;; Also changed the formula from 323700 to 326700 in the instantaneous-energy-deficit monitor on the interface. stop-adding-energy keep-turtles-still invoke-pathogen-harm invoke-pathogen-take-energy invoke-pathogen-low-energy invoke-pathogen-wander if auto-infect-with-pathogenB? and pathB = 1 ;; This is a switch in the code that permits turning off the secondary infection (pathogen B) after one tick. [if count circles <= 1000 ;;and mean [energy] of circles <= 90 ;; I added the mean energy statement, but this could have been instantaneoud-energy-deficit. [invoke-auto-infection-pathogenB] ] ;; This code for pathogenB, the secondary infection, is farther down. invoke-pathogenB-harm invoke-pathogenB-take-energy invoke-pathogenB-low-energy invoke-pathogenB-wander invoke-local-directed invoke-local-stressor invoke-regional-stressor invoke-amputation invoke-amputationB invoke-hostcell-wander invoke-auto-systemic-stressor invoke-auto-systemic-stressor-slow invoke-auto-systemic-stressor-cycle invoke-auto-systemic-stressor-hi-cycle replicate check-death tick end to stop-adding-energy ;; Limits the amount of energy each cell can store, but there can be temporary overshooting of the amount. ask turtles [ if energy >= max-energy [set energy max-energy ]] end to keep-turtles-still ;; This sets the action. The switches on the interface screen allow movement to adjacent vacant spacesfor either pathogens or host cells. ask turtles [ right random 360 forward 0 ;; This gets the turtles, especially the flags, to move in place; therefore no visible movement but it lets time occur (ticks go). ;; All turtles derive energy from the patches as patch-energy at each tick and lose a little less energy (metabolic energy) with each tick. set energy (random-normal 1 0.02) * (energy + ((patch-energy * 0.14) * ((100 - systemic-host-stressor) / 100))) ;; The systemic host stressor is here. ;; set energy (random-normal 1 0.02) * (energy + (14 * (100 - systemic-host-stressor) / 100)) ;; This was old code where the turtles were simply given energy at each tick. set energy (random-normal 1 0.02) * (energy - 10) ;; Every tick costs the turtles about 10 units of energy. ;; This is the energy gain and loss per tick; the random-normal (mean of 1 and SD of 0.02) gives a bit of randomness to the whole program. ;; I don't want too much randomness since all turtles are bathed in the same fluid of patch-energy and are superficially identical ;; There's additional randomness in the pathogen damage routine and in the host defense routines. ;; The systemic host stressor represents the acute-phase response: fever, iron & zinc sequestration, anorexia/nutrient restriction, anemia/hypoxia, systemic acidosis, etc. ifelse show-energy? ;; This is for the switch on the interface screen. Best to have it on. [ set label round energy ] ;; "round" rounds the energy value on the screen to a readable integer. [ set label ""] ;; If set to "No", no energy values show on the screen ] end ;; PATHOGEN PHENOTYPE SLIDERS & SWITCH to invoke-pathogen-harm ;; This acts like a toxin to harm adjacent host cells. ask triangles [ ask circles in-radius 1 [ set energy (random-normal 1 0.02) * (energy - pathogen-harm-hostcells) ]] ask triangles [ ask flags in-radius 1 [ set energy (random-normal 1 0.02) * (energy - pathogen-harm-hostcells) ]] end to invoke-pathogen-take-energy ;; This gives the pathogen energy when it's adjacent to a host cell. ask triangles [ if any? circles in-radius 1 [ set energy (random-normal 1 0.02) * (energy + pathogen-take-up-energy) ]] ask triangles [ if any? flags in-radius 1 [ set energy (random-normal 1 0.02) * (energy + pathogen-take-up-energy) ]] end to invoke-pathogen-low-energy ;; Lowering the "pathogen-survive-low-energy" number lets them survive better. They still need 120 energy units to reproduce (2 * birth-energy). ask triangles [ set triangle-energy-to-survive pathogen-survive-low-energy ] ask triangles [ set max-energy pathogen-survive-low-energy + 260 ] ;; As a minor handicap for enhanced survival, I've also reduced the max-energy they can store. end to invoke-pathogen-wander ;; In this model, letting the pathogens move to free spaces helps them only if they are more lethal than host cells; otherwise they're more vulnerable. ifelse pathogen-wander? [ ask triangles [ let empty-patches neighbors4 with [ not any? turtles-here ] if any? empty-patches [ let target one-of empty-patches face target move-to target ]] ] [ ] end ;; PATHOGEN B PHENOTYPE SLIDERS & SWITCH to invoke-auto-infection-pathogenB ;; The parameters needed to start this secondary infection are coded earlier in the program. ask circles with [ (pycor <= start-upper-pathogenB-pycor) and (pycor > start-lower-pathogenB-pycor) and (pxcor <= start-upper-pathogenB-pxcor) and (pxcor > start-lower-pathogenB-pxcor)] [die] ;; This clears out the host cells at the site before pathogen B comes along (otherwise the pathogens and the host cells are on the same patch and most pathogens die). ask patches with [ (pycor <= start-upper-pathogenB-pycor) and (pycor > start-lower-pathogenB-pycor) and (pxcor <= start-upper-pathogenB-pxcor) and (pxcor > start-lower-pathogenB-pxcor)] [sprout-stars 1 [ set color red set start-energy 300 set birth-energy 60 set max-energy 300 set star-energy-to-survive 40] ] ask stars [ set energy start-energy ] set pathB 0 ;; This turns off the infection with pathogen B after a single round. end to invoke-pathogenB-harm ;; This acts like a toxin to harm adjacent host cells ask stars [ ask circles in-radius 1 [ set energy (random-normal 1 0.02) * (energy - pathogenB-harm-hostcells) ]] ask stars [ ask flags in-radius 1 [ set energy (random-normal 1 0.02) * (energy - pathogenB-harm-hostcells) ]] end to invoke-pathogenB-take-energy ;; This gives pathogen B energy when adjacent to host cell ask stars [ if any? circles in-radius 1 [ set energy (random-normal 1 0.02) * (energy + pathogenB-take-up-energy) ]] ask stars [ if any? flags in-radius 1 [ set energy (random-normal 1 0.02) * (energy + pathogenB-take-up-energy) ]] end to invoke-pathogenB-low-energy ;; Lowering the "pathogenB-survive-low-energy" number lets them survive better ask stars [ set star-energy-to-survive pathogenB-survive-low-energy ] ask stars [set max-energy pathogenB-survive-low-energy + 160 ] ;; I've linked the max-energy they can use to the survival energy threshold as a minor handicap end to invoke-pathogenB-wander ;; In this model, letting the pathogens move to free spaces helps them only if they are more lethal than host cells; otherwise they're more vulnerable. ifelse pathogenB-wander? [ask stars [ let empty-patches neighbors4 with [ not any? turtles-here ] if any? empty-patches [ let target one-of empty-patches face target move-to target ]] ] [ ] end ;; HOST DEFENSES: SLIDERS & SWITCHES (Systemic stressor slider is already incorporated above) to invoke-local-directed ;; Host cells directly harm adjacent pathogens (as if injecting a toxin). ask circles [ ask triangles in-radius 1 [ set energy (random-normal 1 0.02) * (energy - local-host-directed) ]] ask circles [ ask stars in-radius 1 [ set energy (random-normal 1 0.02) * (energy - local-host-directed) ]] end to invoke-local-stressor ;; Harms all adjacent cells if the host cell is in contact with a pathogen as if depriving the area of nutrients or causing acidosis. ask triangles [ ask circles in-radius 1 [ ask turtles in-radius 1 [ set energy (random-normal 1 0.02) * (energy - local-host-stressor) ]]] ask stars [ ask circles in-radius 1 [ ask turtles in-radius 1 [ set energy (random-normal 1 0.02) * (energy - local-host-stressor) ]]] end to invoke-regional-stressor ;; Harms all cells within 5 patches from conflict interface as if depriving the region of blood supply due to clotting & edema. ask triangles [ ask circles in-radius 2 [ ask turtles in-radius 5 [ set energy (random-normal 1 0.02) * (energy * ((100 - regional-host-stressor) / 100)) ]]] ask stars [ ask circles in-radius 2 [ ask turtles in-radius 5 [ set energy (random-normal 1 0.02) * (energy * ((100 - regional-host-stressor) / 100)) ]]] ;; Not sure why the effect is so dramatic with a "regional-host-stressor" setting of 1 or 2 end to invoke-amputation ;; This code harms all cells in the lower right region as if using a tourniquet (or hypersensitive reaction in plants). ask turtles with [ (pycor < 0) and (pxcor > 10)] [ set energy (random-normal 1 0.02) * (energy * ((100 - regional-amputation) / 100)) ] end to invoke-amputationB ;; This code harms all cells in the lower left region as if using a tourniquet (or hypersensitive reaction in plants). ask turtles with [ (pycor < 0) and (pxcor < -10)] [ set energy (random-normal 1 0.02) * (energy * ((100 - regional-amputationB) / 100)) ] end to invoke-hostcell-wander ;; Lets the host cells move to free spaces. ifelse hostcell-wander? ;; This slightly helps the host IF the host cells can harm the pathogens either directly or by local stressing. [ask circles [ let empty-patches neighbors4 with [ not any? turtles-here ] if any? empty-patches [ let target one-of empty-patches face target move-to target ]] ] [ ] end to invoke-auto-systemic-stressor ;; An automatic device that quickly turns the systemic stressor on and then off, etc. Lots of overshooting with this strategy. ifelse auto-systemic-stressor? ;; However, once the pathogen invades enough that there are less than 925 host cells, it won't turn on anymore. [ if count circles <= 1030 ;;and count circles > 950 ;; This "and" allows one to get bigger cycles instead of just hovering around and overshooting 925. [ set systemic-host-stressor 60 ] if count circles <= 925 [ set systemic-host-stressor 0 ]] [ ] if (count triangles + count stars) = 0 ;; These 2 lines allow the host to recover after eliminating the pathogens (otherwise the stressor stays at 60). [set systemic-host-stressor 0] end to invoke-auto-systemic-stressor-slow ;; An automatic device that slowly turns the systemic stressor on and finally has strong 60 to 0 cycling at the end. ifelse auto-systemic-stressor-slow? [ if count circles <= 1030 [ set systemic-host-stressor 10 ] if count circles <= 1020 [ set systemic-host-stressor 20 ] if count circles <= 1010 [ set systemic-host-stressor 30 ] if count circles <= 1000 [ set systemic-host-stressor 40 ] if count circles <= 990 [ set systemic-host-stressor 50 ] if count circles <= 980 [ set systemic-host-stressor 60 ] if count circles <= 925 [ set systemic-host-stressor 0 ]] [ ] if (count triangles + count stars) = 0 ;; These 2 lines allow the host to recover after eliminating the pathogens (otherwise the stressor stays at the final level). [set systemic-host-stressor 0] end to invoke-auto-systemic-stressor-cycle ;; An automatic device that cycles stress slowly ifelse auto-systemic-stressor-cycle? [ if count circles <= 1030 [ set systemic-host-stressor 30 ] if count circles <= 1010 [ set systemic-host-stressor 60 ] if count circles <= 990 [ set systemic-host-stressor 30 ] if count circles <= 970 [ set systemic-host-stressor 0 ] if count circles <= 950 [ set systemic-host-stressor 30 ] if count circles <= 930 [ set systemic-host-stressor 60 ] if count circles <= 910 [ set systemic-host-stressor 30 ] if count circles <= 890 [ set systemic-host-stressor 0 ] if count circles <= 870 [ set systemic-host-stressor 30 ] if count circles <= 850 [ set systemic-host-stressor 60 ] if count circles <= 830 [ set systemic-host-stressor 30 ] if count circles <= 810 [ set systemic-host-stressor 0 ]] [ ] if (count triangles + count stars) = 0 ;; These 2 lines allow the host to recover after eliminating the pathogens (otherwise the stressor stays at the final level). [set systemic-host-stressor 0] end to invoke-auto-systemic-stressor-hi-cycle ;; An automatic device that quickly cycles from 60 to 0. This minimizes overshooting. ifelse auto-systemic-stressor-hi-cycle? [ if count circles <= 1030 [ set systemic-host-stressor 60 ] if count circles <= 1015 [ set systemic-host-stressor 0 ] if count circles <= 1000 [ set systemic-host-stressor 60 ] if count circles <= 985 [ set systemic-host-stressor 0 ] if count circles <= 970 [ set systemic-host-stressor 60 ] if count circles <= 955 [ set systemic-host-stressor 0 ] if count circles <= 940 [ set systemic-host-stressor 60 ] if count circles <= 925 [ set systemic-host-stressor 0 ]] [ ] if (count triangles + count stars) = 0 ;; These 2 lines allow the host to recover after eliminating the pathogens (otherwise the stressor stays at the final level). [set systemic-host-stressor 0] end to replicate ask triangles ;; Pathogens replicate if they have 2x birth-energy (60 units) and a vacant patch for the hatchling to move to. [ if energy > 2 * birth-energy and any? neighbors4 with [not any? turtles-here] [ set energy energy / 2 ;; This cuts the energy in half before hatching. hatch 1 [set energy birth-energy ;; There's a little lost energy since mother may have more than 2x birth-energy, let target one-of neighbors4 with [not any? turtles-here] ;; but daughter cell (hatchling) only gets the birth-energy. face target move-to target ] ] ] ask stars [ ;; Pathogen B replicate if they have 2x birth-energy (60 units) and a vacant patch for the hatchling to move to. if energy > 2 * birth-energy and any? neighbors4 with [not any? turtles-here] [ set energy energy / 2 ;; This cuts the energy in half before hatching. hatch 1 [set energy birth-energy ;; There's a little lost energy since mother may have more than 2x birth-energy, let target one-of neighbors4 with [not any? turtles-here] ;; but daughter cell (hatchling) only gets the birth-energy. face target move-to target ] ] ] ask circles [ if energy > 2 * birth-energy and any? neighbors4 with [not any? turtles-here] ;; Host cells replicate if they have 2x birth-energy (90 units) and a vacant patch for the hatchling to move to. [ set energy energy / 2 ;; This cuts the energy before hatching. hatch 1 [set energy birth-energy ;; There's a little lost energy since mother may have more than 2x birth-energy, let target one-of neighbors4 with [not any? turtles-here] ;; but daughter cell (hatchling) only gets the birth-energy. face target face target move-to target ] ] ] ;; Flags (key host cells) don't replicate end to check-death ask circles [ if energy <= circle-energy-to-survive [ die ]] ask flags [ if energy <= flag-energy-to-survive [ die ]] ask triangles [ if energy <= triangle-energy-to-survive [ die ]] ask stars [ if energy <= star-energy-to-survive [ die ]] end
There is only one version of this model, created over 11 years ago by Edmund LeGrand.
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