globals [ numAbs ;; the number of antibodies secreted by plasma cells at each time step numCyto ;; the number of cytokines produced by effector T helper cells at each time step dom-epitope ;; the dominant viral epitope entities ;; the number of all non-viral entities in the simulation life_B ;; half-life of a B cell life_Plasma ;; half-life of a plasma cell life_MemB ;; the half-life of a memory B cell life_Th ;; the half-life of a naive T helper cell life_MemTh ;; the half-life of a memory T helper cell life_EffTh ;; the half-life of an effector T helper cell life_Tc ;; the half-life of a naive T cytotoxic (Tc) cell life_MemTc ;; the half-life of a memory Tc cell life_EffTc ;; the half-life of an effector Tc cell life_Ab ;; the half-life of an antibody life_Cyto ;; the half-life of a cytokine life_Apc ;; the half-life of an antigen-presenting cell (apc) life_Virion ;; the half-life of a virion - an extracellular viral particle antibodies cytokines plasmacells epcells infected ;; keeps track of the number of infected cells at any given time during the simulation steps neutralized ;; keeps track of the total number of virions neutralized by antibodies killed ;; keeps track of the total number of infected cells killed by effector Tc cells pdissociation ;; the probability that an APC or, in this case, a follicular denritic cell bound to hiv will dissociate at a given time step p_nonspec ;; probability of successful binding in a nonspecific interaction, e.g., APC/Ag bystander_thr max_sti ;; the number of stimulations needed to render a B cell anergic life_anergy ;; the half-life of the anergic state mutB ;; the B cell hypermutation rate mutV ;; the viral mutation rate maxspec ;; the upper bound of the numerical values for the receptors, epitoptes, paratopes, etc, used in the simulation. ] breeds [ bCell ;; A B cell - they are a major component of the humoral immune response to hiv. Upon activation, B cells divide and give rise to memory and effector (or plasma) B cells. memB ;; memory B cells - these cells become activated upon successful interaction with a previously encountered virion and divide, producing plasma cells and new memory B cells plasma ;; plasma cells - these are short-lived cells that continuously secrete antibodies thCell ;; t helper (Th) cells - the orchestrators of the immune response to hiv. Upon activation, they divide and give rise to memory and effector Th cells memTh ;; memory Th cells - they assist in conferring long-term protection against previously encountered virions. Following successful interaction with such virions, memory Th cells divide and give rise to both effector and memory Th cells effTh ;; effector Th cells - they continuously secrete cytokines that activate other components of the immune response, including B cells and Tc cells tcCell ;; naive Tc cells - very important in controlling hiv infection. Divide upon activation, by cytokines, to produce effector and memory Tc cells. memTc ;; memory Tc cells - divide upon activation to produce effector and memory Tc cells effTc ;; effector Tc cells - they recognize viral peptides complexed to HLA1 molecules of infected cells and secrete substances (e.g., perforin) that can kill these cells ab ;; antibodies - recognize and neutralize cell-free virions, preventing these from infecting target cells in the body apc ;; antigen-presenting cells - bind, nonsepecifically, to cell-free virions and aid in the activation of Th cells hiv cyto ;; cytokines epCell ;; epithelial cells ara ;; anti-retroviral agents - substances that can bind to and render cell-free virions incapable of replication. The virions can infect target cells but cannot cause these cells to produce new virions. ] turtles-own [ stimulated? state infected? halfL ;; half-life numDivs sinceInf ;; the number of time steps since the given turtle has been infected. The value of this variable, ;; together with the viral replication rate, is used to calculate the number of viral particles present in a ;; productively infected cell at any given time, post infection partner ;; the virion with which this turtle is complexed, if any HLA1/pep HLA2/pep receptor ;; the numeric value of this cell's receptor inf_lethal_load ;; the viral load of the virion with which this cell is infected, if applicable inf_lethality ;; the infectivity/lethality of the virion with which this cell is infected, if applicable inf_rep_rate ;; the replication rate of the virion with which this cell is infected, if applicable vLoad ;; viral load ] patches-own [ cytos ;; the number of cytokines on a given patch - used to simulating chemotaxis inf ;; the number of infected cells on a given patch - used to simulate chemotaxis ] hiv-own [ neutralized? ;; determines if a virion has been neutralized by an antibody inactivated? ;; determines if the virion has been inactivated by an anti-retroviral agent - inactivated virions are incapable of replication of replication, following infection of a target cell lethality ;; the probability that a virion will infect a cell on contact lethal_load ;; the threshold of viral particles that elicits the lysis of an infected cell rep_rate ;; the replication rate of this virion (in an infected cell) peptide ;; the numerical value of the viral peptides that is presented on HLA1/peptide and HLA2/peptide complexes epitope ;; the numerical value of the epitope of a virion ] ab-own [ paratope ] ara-own [ effect ;; the effectiveness of an anti-retroviral agent ] apc-own [ vRNA ] to setup ca random-seed 250 initialize-globals initialize-turtle-shapes create-cells initialize-patch-vars update-monitors end to initialize-globals set life_B 15 set life_Plasma 5 set life_MemB 10 set life_Th 15 set life_MemTh 10 set life_EffTh 5 set life_Tc 15 set life_MemTc 10 set life_EffTc 5 set life_Ab 2 set life_Cyto 2 set life_Apc 15 set life_Virion 1000 set numAbs 2 set numCyto 2 set steps -1 set neutralized 0 set killed 0 set pdissociation 0.001 set p_nonspec .5 set bystander_thr 5 set life_anergy 10 set mutV 0 set mutB 0 set maxspec 3 end to initialize-patch-vars ask patches [ set pcolor red set inf (count turtles-here with [ infected? ]) ] end to start ask turtles with [ breed != hiv and breed != epCell ] [ without-interruption [ do-interact] ] ask turtles with [ infected? and state != "anergic" ] [ do-viral-production ] ask turtles [ do-apoptosis ] ask ab [ do-ab-neutralization ] ask plasma with [ state != "anergic" ] [ do-ab-secretion ] ask effTh with [ state != "anergic" ] [ do-cyto-production ] ask turtles with [ stimulated? and not infected? and (breed != apc) and state != "anergic"] [ do-cell-division ] ask effTc [ do-ctl ] ask hiv with [ not neutralized? ] [ do-infection ] ask apc with [ state = "stimulated" ] [ do-dissociation ] do-resupply ask turtles with [ state = "anergic" ] [ remove-anergy ] ask turtles with [ breed = hiv or breed = cyto ] [ do-diffuse ] update-patch-vars ask turtles with [ breed != hiv and breed != cyto and breed != epCell ] [ do-diffuse ] ask ara [ do-ART ] ask apc [ do-dissociation ] if plots [ do-plots ] if monitors [ update-monitors ] ;;if((count hiv > count turtles with [ breed != hiv ]) or (count epCell < .5 * numEp) or (((count hiv with [ not neutralized? ]) = 0) and (count turtles with [ infected? ]) = 0 and (count apc with [ vRNA != []]) = 0) ) [ show "Simulation has reached a pre-configured end point" stop ] end to remove-anergy locals [ diff ] set diff ((ln 2) * life_anergy) if(prob exp (0 - diff)) [ set state "resting" ] end ;; this procedure can be used to simulate antibody therapy; simply provide the specificity and number of ;; antibodies you wish to introduce into the simulation. Note that you can use the real-time information about the dominant epitope ;; to guide you in your choice of specificity and quantity of antobodies to introduce. to simulate-ABT [specificity number] create-custom-ab number [ initialize-turtle-vars set paratope specificity ] show number + " new antibodies added at time step " + steps end ;; this procedure can be used to simulate anti-retriviral therapy; simply provide the specificity, effectiveness, and number of ;; anti-retroviral agents you wish to introduce into the simulation to simulate-ART [efficacy number] create-custom-ara number [ initialize-turtle-vars set effect efficacy ] show number + " new anti-retroviral agents added at time step " + steps end ;; this procedure can be used to introduce into the simulation new virions of a particular specificity to infect [ specificity leth bsize repRate number ] create-custom-hiv number [ initialize-turtle-vars set receptor specificity set epitope specificity set lethality leth set lethal_load bsize set rep_rate repRate ] show number + " new virions added at time step " + steps end to update-patch-vars ask patches [ set inf (count turtles-here with [ infected? ]) set cytos (count cyto-here) ] end to do-ART locals [ other ] set other random-one-of hiv in-radius 0.2 with [ not neutralized? ] if((other != nobody) and (prob effect)) [ ask other [ die ] ] end to update-monitors ifelse(count hiv > 0) [ set dom-epitope get-dom-epitope ] [ set dom-epitope "------ NONE ------" ] set entities (count turtles with [ breed != hiv ]) set antibodies (count ab) set cytokines (count cyto) set plasmacells (count plasma) set infected get-infected set epcells (count epCell) set steps (steps + 1) end to-report get-infected locals [ diff ] set diff 0 if(not any? turtles with [ infected? ]) [ report "0 / 0" ] foreach values-from (turtles with [ infected? ]) [ vLoad ] [ set diff (diff + ?) ] report (count turtles with [ infected? ]) + " / " + int(diff) end to-report get-dom-epitope locals [maximum value mspec aspec] set aspec 0 set maximum 0 set value 0 while [ aspec < maxspec ] [ set value count (hiv with [ epitope = aspec ]) if(value > maximum) [ set maximum value set mspec aspec ] set aspec (aspec + 1) ] report mspec + " | " + maximum + " | " + int((maximum / (max (list 1 count hiv))) * 100) + "%" + " | " + count (ab with [ exp(0 - abs(receptor - mspec)) >= .7 ]) end to initialize-turtle-shapes set-default-shape turtles "cell" end to initialize-turtle-vars set infected? false set stimulated? false set state "resting" set numDivs 0 set receptor random maxspec set sinceInf 0 set partner nobody set halfL 1000 if(breed = hiv) [ set neutralized? false set inactivated? false set color black set peptide random maxspec set epitope peptide set lethality infectivity set lethal_load 24 set rep_rate 0.05 ] if(breed = bCell) [ set halfL life_B set color white ] if(breed = plasma) [ set halfL life_Plasma set color green ] if(breed = memB) [ set halfL life_MemB set color white ] if(breed = thCell) [ set halfL life_Th set color blue ] if(breed = memTh) [ set halfL life_MemTh set color blue ] if(breed = effTh) [ set halfL life_EffTh set color green ] if(breed = epCell) [ set halfL 1000 set color green ] if(breed = tcCell) [ set halfL life_Tc set color blue ] if(breed = memTc) [ set halfL life_MemTc set color blue ] if(breed = effTc) [ set halfL life_EffTc set color green ] if(breed = ab) [ set halfL life_Ab set color yellow ] if(breed = cyto) [ set halfL life_Cyto set color brown ] if(breed = apc) [ set halfL life_Apc set vRNA [] set color grey ] end to create-cells create-custom-bCell numB [ initialize-turtle-vars disperse ] create-custom-epCell numEp [ initialize-turtle-vars disperse ] create-custom-hiv numHiv [ initialize-turtle-vars disperse ] create-custom-thCell numTh [ initialize-turtle-vars disperse ] create-custom-apc numApc [ initialize-turtle-vars disperse ] create-custom-tcCell numTc [ initialize-turtle-vars disperse ] end ;; the interactions of entities, as described in the supplemental materials to do-interact locals [this other ] set this self if ((breed = bCell or breed = memB) and (state = "resting")) [ set other random-one-of hiv in-radius .2 with [ not neutralized? ] if((other != nobody) and (success receptor (epitope-of other))) [ set state "activated" ;; the B cell is still in resting state but is presenting an HLA2/peptide complex. ;; Subsequent binding with a Th cell will result in its activation set HLA2/pep (peptide-of other) ask other [ die ] ] ] if((breed = bCell or breed = memB) and not stimulated?) [ if((count cyto-here) >= bystander_thr) ;; bystander activation of B cells and memory B cells [ set state "activated" set stimulated? true ] ] if((breed = bCell or breed = memB) and not stimulated? and (state = "activated")) [ set other random-one-of turtles in-radius .2 with [ ((breed = thCell) or (breed = memTh)) ] if(other != nobody and (success HLA2/pep (receptor-of other))) [ set stimulated? true set stimulated?-of other true ;; B cells are also APCs and can thus stimulate Th cells ] ] if(((breed = thCell) or (breed = memTh)) and not stimulated?) [ set other random-one-of turtles in-radius .2 with [ ((breed = apc)) and (state = "activated") ] if((other != nobody) and (success receptor (HLA2/pep-of other))) [ set state "activated" set stimulated? true set stimulated?-of other true ;; this has no effect on apcs. However, stimulated B cells are able to divide ] ] if(((breed = tcCell) or (breed = memTc)) and not stimulated?) [ set other random-one-of apc in-radius .2 with [ stimulated? ] if((other != nobody) and (success receptor (HLA1/pep-of other))) [ set state "activated" set stimulated? true ] ] if(((breed = tcCell) or (breed = memTc)) and not stimulated?) [ if((count cyto-here) >= bystander_thr) [ set state "activated" set stimulated? true ] ] if(breed = apc) ;; apcs (particularly folicular dendritic cells) may serve as viral reservoirs [ set other random-one-of hiv in-radius .2 with [ not neutralized? ] if((other != nobody) and prob p_nonspec) [ set state "activated" set HLA1/pep (peptide-of other) ;; an activated apc presents viral peptides on both HLA1 and HLA2 set HLA2/pep (peptide-of other) set vRNA lput (peptide-of other) vRNA ask other [ die ] ] ] end ;; the half-life of each entity is used to determine the probability that it will die during a given time step. Because the gradual ;; depletion of Th cells, a hallmark of hiv pathogenesis, is thought to arise not only from direct hiv-mediated killing of infected ;; Th cells but also from indirect killing (or bystander effect) of Th cells. We assume ;; that this indirect killing of Th cells is a function of the number of both activated and infected cells in the vicinity of a ;; Th cell and on the value of the AICD parameter. to do-apoptosis locals [ diff tau ] if((breed = thCell) or (breed = memTh) or (breed = effTh)) [ set halfL max (list 0 (halfL - (aicd * ((count turtles-here with [ infected? ]) + (count hiv-here))))) ] set tau halfL set diff ((ln 2) * tau) if(prob exp (0 - diff)) [ die ] end ;; the dissociation of an apc from a bound virion. This is thought to contribute to the pepertuation of viremia in chronically ;; infected patients. to do-dissociation locals [ this ] set this self if(prob pdissociation and not empty? vRNA) [ foreach vRNA [ hatch 1 [ set breed hiv initialize-turtle-vars set epitope ? set peptide ? ] ] set vRNA [ ] set state "resting" set stimulated? false ] end ;; the neutralization of a virion by an antibody. Note that to keep the number of turtles relatively low and, consequently, improve the ;; speed of the simulation, all neutralized virions and the antibodies involved are immediately removed from the simulation. to do-ab-neutralization locals [ other this ] set this self set other random-one-of hiv in-radius .2 with [ not neutralized? and (success epitope (paratope-of this)) ] if((other != nobody) and (prob neutRate)) [ set neutralized (neutralized + 1) ask other [ die ] die ] end ;; viral infection of target cells. The probability of infection is determined by the infectivity parameter or the lethality variable to do-infection locals [ this other ] set this self set other random-one-of turtles in-radius .2 with [ (breed = thCell) or (breed = memth) or (breed = effTh) ] ;; hiv preferentially infect th cells if(other = nobody) [ set other random-one-of turtles in-radius .2 with [ (breed != hiv) and (breed != cyto) and (breed != ab) and (breed != ara)] ] if(other != nobody) [ if(prob lethality) [ set infected?-of other true set HLA1/pep-of other peptide set inf_rep_rate-of other rep_rate ;; the replication rate for inactivated virions, in vivo, is set to 0 set inf_lethality-of other lethality set inf_lethal_load-of other lethal_load die ] ] end ;; plasma cells secrete numAbs antibodies during each time step to do-ab-secretion locals [ this ] set this self hatch numAbs [ set breed ab initialize-turtle-vars set paratope (receptor-of this) ] end ;; effector Th cells secrete numCyto cytokines during each time step to do-cyto-production locals [ this ] set this self hatch numCyto [ set breed cyto initialize-turtle-vars ] end ;; the killing of infected cells by Tc cells. The probability that a Tc cell will kill an infected cell on initial contact is given ;; by the ctlRate parameter to do-ctl locals [ other ] set other random-one-of turtles in-radius .2 with [ infected? ] if((other != nobody) and (success receptor (HLA1/pep-of other)) and (prob ctlRate)) [ ask other [ die ] set killed (killed + 1)] end ;; activated B, memory B, Th, memory Th, Tc, and memory Tc cells divide over two time steps to produce 4 cells - 2 effectors cells and ;; 2 memory cells to do-cell-division locals [ this ] set this self ifelse(numDivs >= 2) [ if((breed = bCell) or (breed = memB)) [ hatch 2 [ set breed memB initialize-turtle-vars ifelse(prob mutB) [ set receptor random maxspec ] [ set receptor (receptor-of self) ] ] hatch 2 [ set breed plasma initialize-turtle-vars set receptor (receptor-of this) ] die ] if((breed = thCell) or (breed = memTh)) [ hatch 2 [ set breed memTh initialize-turtle-vars set receptor (receptor-of this) ] hatch 2 [ set breed effTh initialize-turtle-vars set receptor (receptor-of this) ] die ] if((breed = tcCell) or (breed = memTc)) [ hatch 2 [ set breed memTc initialize-turtle-vars set receptor (receptor-of this) ] hatch 2 [ set breed effTc initialize-turtle-vars set receptor (receptor-of this) ] die ] ] [ set numDivs (numDivs + 1) ] end ;; productively infected cells (as opposed to infected but dormant/anergic cells) continue to produce new virions until ;; either a) they are killed during CTL or (b) their viral load exceeds the lethal load of the infecting virus. In the latter ;; case, the infected cells undergo lysis, releasing new virions into the simulation. to do-viral-production locals [ this ] set this self set vLoad floor(exp(inf_rep_rate * sinceInf)) ifelse( vLoad > inf_lethal_load) [ hatch vLoad [ set breed hiv initialize-turtle-vars ifelse(prob mutV) [ set peptide random maxspec set epitope random maxspec ] [ set peptide HLA1/pep set epitope HLA1/pep ] set lethal_load inf_lethal_load set rep_rate inf_rep_rate set lethality inf_lethality ] die ] [ set sinceInf (sinceInf + 1) ] end ;; to maintain a relatively constant supply of naive lymphocytes, these cells are replenished by the bone marrow and thymus at the same rate ;; as they undergo apoptotic death to do-resupply locals [ diff tau ] set diff 0 while [ diff < numTh ] [ if(prob exp (- ((ln 2) * life_Th))) [ create-custom-thCell 1 [ initialize-turtle-vars ] ] set diff (diff + 1) ] set diff 0 while [ diff < numTc ] [ if(prob exp (- ((ln 2) * life_Tc))) [ create-custom-tcCell 1 [ initialize-turtle-vars ] ] set diff (diff + 1) ] set diff 0 while [ diff < numB ] [ if(prob exp (- ((ln 2) * life_B))) [ create-custom-bCell 1 [ initialize-turtle-vars ] ] set diff (diff + 1) ] set diff 0 while [ diff < numApc ] [ if(prob exp (- ((ln 2) * life_Apc))) [ create-custom-apc 1 [ initialize-turtle-vars ] ] set diff (diff + 1) ] end ;; an alternate implementation of the resupply process to do-resupply2 locals [ tauB tauTc tauTh ] set tauB ((ln 2) * numB / life_B) set tauTh ((ln 2) * numTh / life_Th) set tauTc ((ln 2) * numTc / life_Tc) create-custom-bCell ceiling(tauB) [ initialize-turtle-vars disperse ] create-custom-thCell ceiling(tauTh) [ initialize-turtle-vars disperse ] create-custom-tcCell ceiling(tauTc) [ initialize-turtle-vars disperse ] end to disperse setxy random screen-size-x random screen-size-y end ;; the dissufion of entities is assumed to be driven by a chemotactic gradient. For example, naive Tc cells diffuse in the ;; direction of greatest cytokine concentration, while effector Tc cells seek out sites with high numbers of infected cells. to do-diffuse repeat 2 [ ifelse(breed = tcCell or breed = memTc or breed = bCell or breed = memB) [ set heading uphill cytos ] [ ifelse(breed = effTc) [ set heading uphill inf ] [ set heading random 360 ] ] fd 1 if (partner != nobody) [ set heading-of partner heading ask partner [ fd 1 ] ] ] end ;; this procedure determines the probability of successful interaction (e.g., bond formation) between two entities to-report success [ receptor1 receptor2 ] locals [ var ] ifelse((not is-number? receptor1) or (not is-number? receptor2)) [ report false ] [ set var abs(receptor1 - receptor2) ifelse(prob exp (0 - var)) [ report true ] [ report false ] ] end ;; this procedure determines the outcome of events (i.e. true or false) based on the probabilities of the events to-report prob [ probability ] locals [ var ] if(probability = 0) [ report false ] set var (1 / probability) ifelse(random-float var < 1.0) [ report true ] [ report false ] end to do-plots set-current-plot "hiv/th/tc dynamics" set-current-plot-pen "hiv" plot count hiv with [ not neutralized? ] set-current-plot-pen "th" plot (count thCell + count memTh + count effTh) set-current-plot-pen "tc" plot (count tcCell + count memTc + count effTc) set-current-plot "Antibodies" plot (count ab) set-current-plot "Cytokines" plot (count cyto) set-current-plot "Bcells" plot (count bCell + count memB + count plasma) end @#$#@#$#@ GRAPHICS-WINDOW 379 13 717 372 20 20 8.0 1 10 1 1 1 CC-WINDOW 14 467 414 603 Command Center PLOT 440 387 733 598 HIV/Th/Tc Dynamics Time Step NIL 0.0 100.0 0.0 100.0 true false PENS "th" 1.0 0 -16777216 true "hiv" 1.0 0 -65536 false "tc" 1.0 0 -16776961 true BUTTON 11 13 80 75 Setup setup NIL 1 T OBSERVER T BUTTON 93 15 166 76 Run start T 1 T OBSERVER T SLIDER 10 112 170 145 numB numB 0 100 50 1 1 NIL SLIDER 183 112 337 145 numTh numTh 0 100 50 1 1 NIL SLIDER 11 153 170 186 numTc numTc 0 100 50 1 1 NIL SLIDER 183 153 337 186 numApc numApc 0 100 50 1 1 NIL SLIDER 183 195 337 228 numHiv numHiv 0 300 50 1 1 NIL SLIDER 13 195 170 228 numEp numEp 0 1000 500 1 1 NIL SLIDER 13 235 168 268 ctlRate ctlRate 0 1 0.85 0.0010 1 NIL SLIDER 14 279 169 312 infectivity infectivity 0 1 0.0070 0.0010 1 NIL SLIDER 183 278 336 311 AICD AICD 0 5 0.11 0.01 1 NIL MONITOR 18 400 213 449 Epitope | No. | Prop. | Abs dom-epitope 3 1 SLIDER 183 236 336 269 neutRate neutRate 0 1 0.109 0.0010 1 NIL MONITOR 114 336 205 385 Non-Viral Entities entities 3 1 MONITOR 214 336 346 385 Infected Cells/ Viral Load infected 3 1 MONITOR 18 336 104 385 Steps steps 3 1 SWITCH 204 19 317 52 plots plots 0 1 -1000 SWITCH 204 64 316 97 monitors monitors 0 1 -1000 MONITOR 322 400 415 449 Neutralized HIV neutralized 3 1 MONITOR 226 400 309 449 Killed killed 3 1 PLOT 766 16 990 187 Antibodies Time Step NIL 0.0 100.0 0.0 100.0 true false PLOT 767 401 992 592 Bcells Time Step NIL 0.0 100.0 0.0 100.0 true false PLOT 768 205 992 383 cytokines Time Step NIL 0.0 100.0 0.0 100.0 true false @#$#@#$#@ WHAT IS IT? ----------- HIVSIM is an agent-based simulation of HIV immunodynamics that is currently being developped in NetLogo. It allows users to investigate dependencies between various components of the cellular and humoral immune responses to HIV. Users can interactively manipulate simulation parameters (e.g., the number of Th, Tc, and B cells, and the infectivity of viral particles) and, in real-time, observe graphical plots of the results. Additionally, users can simulate antibody and anti-retroviral therapies at various stages of infection (e.g., the user can introduce into the simulation antibodies with affinity for the dominant HIV epitope). HIVSIM is still a work in progress. As time permits, the underlying model will be further calibrated against experimental data to make it robust and applicable to the qualitative evaluation of hypotheses on HIV immunodynamics. HOW IT WORKS ------------ The simulation HIVSIM simulates the interactions of five major cell types - B, T helper, T cytotoxic, epithelial, and antigen-presenting cells - and four non-cellular entities - antibodies, cytokines, HIV, and anti-retroviral agents. The interactions occur in a cellular matrix consisting of 1681 (41 * 41) sites. During each time step, all entities at a given site are allowed to interact. After the interactions, other processes such as cell division, apoptosis or decay, antibody and cytokine production, necrosis, and HIV infection of target cells are allowed to proceed. The completion of these processes marks the end of a time step, after which all entities, except epithelial cells, are allowed to diffuse into neighboring sites. HIV particles, antibodies and anti-retroviral agents can be introduced from the outside at any time. The simulation ends when one of the following occurs (1) the number of healthy epithelial cells drops to below 50% of its original value, (2) the viral load exceeds the combined total of all non-viral entities, or (3) the viral load falls to 0. Described below are some of the entities, interactions, and biological processes implemented in HIVSIM. Except where otherwise noted, information regarding the various interactions and processes came from [1]. Also, some of the parameters used in the simulation were adapted from [2]. For detailed information about the simulation, please see comments within the code. Let us first of all discuss the prerequisites for a "successul interaction" between two entities. Note that except for nonspecifc interactions such as those involving APCs and cell-free HIV, the outcome (e.g., successful formation of a bond) of most interactions depends on the receptors (or epitopes and paratopes) of the entities involved. Each cellular entity possesses a receptor, represented by a randomly chosen integer belonging to the closed-open interval [0, maxspec), where the upper bound maxspec is determined by the user. Cellular entities also possess HLA1 (human leukocyte antigen type 1) with similar numeric values as their receptors. In additon to HLA1, APCs and B cells also have HLA2. Among the non-cellular entities, viruses have epitopes while antibodies have paratopes. When two entities A and B, say, with receptors x and y, respectively, interact, the probability that their interaction will be successful is given by exp(|x-y|). The closer the numeric values of the interacting entities' receptors, the higher their affinities for each other and, hence, the higher the probability of a successful interaction. Entities and interactions B cells: B cells are components of the humoral immune response to HIV. When a naive B cell encounters an HIV particle, it attempts to bind to it. Successful binding of a B cell to HIV results in the former ingesting the latter. After ingestion, the B cell digests the HIV into small peptides, 11 to 20 amino acids long, and inserts these into molecules called human leukocyte antigen type II (HLA2), forming HLA2-peptide complexes. It then transports these HLA2-peptide complexes to its surface. Th cells, which will be described later, can recognize and bind to the HLA2-peptide complexes. Such binding activates B and Th cells and induces these cells to divide (see "Cell Division" below). The division of B cells yields memory and effector (or plasma) cells. The long-lived memory B cells confer long-term protection against previously encountered HIV particles. When a memory B cell becomes activated (e.g. via a successful interaction with an APC-activated Th cell or by-stander, cytokine-induced activation), it undergoes cell division, increasing the population of plasma and memory B cells with affinity for the HIV. The short-lived and terminally differentiated plasma cells continuously produce antibodies which can recognize and bind to cell-free HIV. Such binding can neutralize the HIV, rendering it incapable of infecting target cells in the body. T helper (Th) cells: Also known as CD4+ T cells, these cells are the orchestrators of the adaptive immune response to HIV. When a naive Th cell binds to HIV peptides presented on HLA2 surface molecules of antigen presenting cells (APCs) they become activated. Activated Th cells divide to produce memory and effector Th cells (see "Cell Division" below). The short-lived effector Th cells continuously secrete cytokines which participate in the activation of other immune system components including B cells and Tc cells (see below). Upon activation, the long-lived memory Th cells divide, as described below, producing more memory and effector Th cells. Th cells also facilitate the lysis of infected cells by natural killer (NK) cells in a process called antibody dependent cell-mediated cytotoxicity. The gradual depletion of Th cells, a hallmark of HIV pathogenesis, is thought to arise not only from direct hiv-mediated killing of infected Th cells but also from indirect killing of Th cells or activation-induced cell death (AICD) [3]. It is assumed here that this indirect killing of Th cells is a function of the number of infected cells and virions in the vicinity of a Th cell. The parameter AICD is used to simulate this increased susceptibility of Th cells to HIV. T cytotoxic (Tc) cells: Tc cells are very important in the control of HIV infection. They are activated either by direct contact with APC-activated Th cells or by cytokines. Once activated, they divide and produce memory and effector Tc cells. Effector Tc cells recognize HIV peptides, 9 to 11 nucleotides in length, bound to molecules called human leukocyte antigens type 1 (HLA1) found on most human cell types. Effector Tc cells bind to and kill infected cells displaying such HLA1-peptide complexes on their surfaces, at a rate that is determined by the ctl-rate parameter.Memory Tc cells, on the other hand, afford long-term protection against infection. Upon activation (see naive Tc cell activation) the memory cells divide, as described below. Antigen-presenting cells (APCs): These include macrophages, dendrites and lymphocytes. All APCs possess HLA2 molecules. Note that if Th cell activation was exclusively dependent on B cell activation, the primary response to HIV would be very slow due to the initial low numbers of B and T cells with affinity for the HIV pathogens. Fortunately, that is not the case; APCs other than B cells can bind non-specifically to HIV. After binding, the APCs ingest, digest and present HLA2-peptide complexes on their surfaces. The binding of Th cells to these complexes activates the Th cells and causes them to divide. Biological processes Apoptosis/decay: Each entity has a half-life, halfL. During each time step, this half-life is used to determine the probability, exp(-ln2/halfL), that a cellular entity undergoes apoptosis [2]. The probability of decay of non-cellular entities such as antibodies and cytokines is computed in a similar manner. Once an entity (cellular or non-cellular) undergoes apoptotic death, it is immediately removed from the simulation. Resupply: To maintain a relatively constant population of all lymphocytes, these cells are continuously produced by the bone marrow and thymus to make up for those lost through apoptosis. During each time step, the half-life and original population size of each class of lymphocytes are used to determine the number of new cells of the given class to be added to the simulation. Necrosis: During each time step, an infected cell undergoes necrosis or lysis if the number of intracellular viral particles it contains exceeds the viral burst size (i.e., the threshold of viral particles needed to elicit the lysis of an infected cell). Following necrosis, the cell releases new viral particles and is immediately removed from the simulation. Cell Division: Only stimulated B, Th and Tc cells undergo cell division. A stimulated B cell divides over two time steps producing 4 new cells with the same receptors/specificity as the parent B cell. Fifty percent of the new cells become memory cells while the remaining 50% become plasma cells. The division of a stimulated Th (or Tc) cell follows similar rules with the difference being that 50% of the new cells become long-lived memory Th (or Tc) cells while the remaining 50% become effector Th (or Tc) cells. Note that dividing B cells may undergo hypermutation at a rate determined by the bMut parameter. HIV infection: During a time step, each un-bound HIV particle is allowed to infect a randomly chosen neighboring cell. The probability of infection is determined by the infectivity of the HIV epitope. If infection occurs, the HIV disappears into the cytoplasm of the infected cell where it integrates its RNA into the cell's DNA. Infected cells present viral peptides on their surface, complexed with HLA1 molecules. Viral replication: During each time step, HIV particles, found in infected cells, are allowed to replicate - each HIV divides once, producing two new viruses. Each new virus may mutate (i.e., it can be assigned a new randomly chosen (numerical) epitope and peptide). The probability of such mutation is determined by the vMut parameter. CTL: This denotes the killing of infected cells by Tc cells. During each time step, a Tc cell is allowed to randomly kill one infected cell in its neighborhood/vicinity. The probability that a Tc cell will kill an infected cell on contact is determined by the parameter ctl-rate. HOW TO USE IT ------------- The interface contains 10 sliders, two switches, six monitors, three plots, and the buttons "Setup" and "Run". Click the "Setup" button to initialize a new simulation and click "Run" to run the simulation. The following information is reported during a simulation: The number of (1) non-viral entities (2) infected cells (3) viruses in the cytoplasms of productively infected cells, (5) neutralized HIV, and (6) infected cells killed by CTL. Also, the population size of the dominant HIV epitope and number of antibodies with high affinity (>70%) for this epitope is reported. This information can be used to determine what kind of therapeutic strategy (antibody or anti-retroviral) to simulate. In addition, the dynamics of antibodies, cytokines, B cells (naive, memory and plasma cells), Th cells (naive, memory and effector cells), Tc cells (naive, memory and effector cells), and HIV is plotted in real-time. While running a simulation, you can use the Command Center to perform the following: 1) Simulate infection Simple type "infect specificity leth bsize repRate number," where "specificity" is the numerical value of each new virion's receptor and peptide, "leth" is the infectivity of each virion, "bsize" is the viral burst size, "repRate" is the viral replication rate, and "number" is the number of new virions you want to introduce into the simulation. 2) Simulate antibody therapy Simply type "Simulate-ABT specificity number" to introduce "number" new antibodies into the simulation. The value of "specificity" will be assigned to each antibody's paratope. 3) Simulate anti-retroviral therapy Simply type "Simulate-ART efficacy number" to introduce "number" new anti-retroviral agents (ara's) into the simulation. During each time step, the ara's thus introduced will be allowed to interact with a randomly chosen, neighboring virion and, if successful, inactivate the virion. The probability that an ara will inactivate a virion on contact is determined by the "efficacy" parameter. The Sliders: 1) numTh - the initial number of Th cells 2) numB - the initial number of B cells 3) numTc - the initial number of Tc cells 4) numHIV - the initial number of HIV 5) numApc - the initial number of APCs 6) numEp - the initial number of epithelial cells 7) infectivity - the represents the default infectivity of HIV - the probability that a virion will infect an cell on contact. Virions introduced after the simulation has begun can be assigned different infectivity. 8) AICD - the rate of indirect killing of Th cells by HIV 9) ctlRate - the probability that a Tc cell will kill an infected cell on contact. CTL rate is crucial to the control of HIV infection. However, it has been hypothesized that some Tc cells may be defective, suggesting that CTL rate is less that 1.0 (or 100%). 10) neutRate - the rate at which an antibody neutralizes a virion, on contact. Also, the values of about 30 global variables can be manipulated from the Procedures Tab. The Switches: 1) plots - use this to turn on/off real-time plots 2) monitors - use this to turn/off updates to the monitors The Plots: 1) Antibodies - shows changes in the number of antibodies 2) Cytokines - show changes in the number of cytokines 3) Bcells - depicts the dynamics of B cells (includes naive, memory and effector or plasma cells) 4) HIV/Th/Tc - depicts the dynamics of cell-free HIV, Th cells (includes naive, memory and effector cells), and Tc cells (includes naive, memory and effector cells). KEY: Red - HIV, Green - Tc, and Black - Th. THINGS TO TRY ------------- Try to determine an optimal choice of parameter values for which each of the following occurs: 1) Rapid (resp. slow) viral clearance. 2) Rapid Th and Tc cell turnover. 3) High/low antibody production. 4) viral blips (periodic bursts of viraemia). (Hints: Decrease the value of pdissociation - follicular dendrytic cells, APCs in this case, may serve as viral reservoirs that help perpetuate chronic viraemia via occasional dissociation and the concomitant release of new virions [4]. Also, advanced users may want to implement anergic states for B, Th, and Tc cells) 5) Depletion of Th cells (Hint: Manipulate the value of the AICD parameter) Based on your observations, suggest putative critical parameters (e.g., viral infectivity) for the immune response to HIV. EXTENDING THE MODEL ------------------- HIVSIM is still far from being a comprehensive simulation of HIV immunodynamics. A number of other components of the immune response to HIV are yet to be implemented. Listed below are a few of them: 1) B, Th, and Tc anergy 2) Antibody-dependent cell-mediated cytotoxicity 3) A better implementation of activation-induced cell death 4) A better implementation of by-stander (cytokine-mediated) stimulation of B and Tc cells In addition, further calibration with experimental data is necessary in order to make the simulation more robust and less sensitive to small changes in the values of some parameters. CREDITS AND REFERENCES ---------------------- References 1. McMichael A. J. and S. L. Rowland-Jones, 2001. "Cellular immune responses to HIV," Nature, 410:980-987. 2. Kleinstein, S. H. and P. E. Seiden, 2000. "Simulating the immune system," Computing in Science and Engineering, pp.69-77. 3. Silvestri, G. and M. B. Feinberg, 2003. "Turnover of lymphocytes and conceptual paradigms in HIV infection," J. Clin. Invest., 112:821–824. 4. Hlavacek, W. S., N. I. Stilianakis, D. W. Notermansi, S. A. Danner, and A. S. Perelson, 2000. "Influence of follicular dendritic cells on decay of HIV during antiretroviral therapy," PNAS, 97(20):10966-10971. 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