We present preliminary work on modelling aspects of the immune system using process algebra. The problem addressed is how T-helper cell populations respond to co-infections with parasites making conflicting immunological demands. Our goal is to build PEPA models of alternative hypotheses around T-helper cell behaviour and to evaluate those with respect to experimental data

Allen, Judith E

Brand-Spencer, Timothy

Graham, Andrea L

Mahajan, Simmi M

Norman, Rachel

Scott, Erin

Shankland, Carron

English

Stirling Online Research Repository

Submitted to:PASTA 2010c© E. Scott, S.M. Mahajan, T. Brand-Spencer, J.E. Allen, R. Norman, A.L. Graham and C. ShanklandThis work is licensed under theCreative Commons Attribution License.Modelling Immunological Systems using PEPA: apreliminary reportErin Scott∗ Simmi M. Mahajan† Timothy Brand-Spencer∗ Judith E. Allen†Rachel Norman∗ Andrea L. Graham† Carron Shankland∗We present preliminary work on modelling aspects of the immune system using process algebra. Theproblem addressed is how T-helper cell populations respond to co-infections with parasites makingconflicting immunological demands. Our goal is to build PEPA models of alternative hypothesesaround T-helper cell behaviour and to evaluate those with respect to experimental data.1 IntroductionComputer Science techniques are increasingly being used to describe biological systems. There arethree advantages: the process of formalising the system can lead to deeper understanding through havingto make assumptions explicit; formal analysis can be carried out, leading to discovery of previouslyunknown system properties; and experiments can be carried out in silico, usually much more quicklyand cheaply than in the laboratory, allowing in vivo experiments to be guided towards the most focussedhypothesis tests [7]. Process algebra is one of the modelling methodologies achieving some success inthis arena [1, 2, 9, 11] because of its ability to represent systems in an abstract and modular fashion.Immunological systems are ideally suited to modelling using process algebra. In many ways the im-mune system is a black box; although many of its inputs and outputs are known, exactly how the systemachieves its function is the subject of much investigation. Laboratory experiments have provided largequantities of data, allowing components within the black box to be identified, but there remain manydetails to be uncovered about the exact details of how components carry out their functions, or on thenature of interaction between components. There are so many potential variables in such systems that ex-haustive testing to establish these details is not feasible. Process algebras are ideally suited to describingimmunological systems at this level: they may be viewed as networks of (many) interacting components,where the components themselves may have complex, nondeterministic, individual behaviour. In addi-tion, use of process algebra gives access to a range of investigatory techniques, including simulation,verification via logical properties, and transformation from an individual-based discrete state space toa population-based continuous state space via derivation of Ordinary Differential Equations. Throughmodelling, different hypotheses about the biology of the systems may be investigated, providing focusfor future laboratory experiments.The goal of the current work is the novel application of process algebra to immunological systems.The particular process algebra adopted here is PEPA (Performance Evaluation Process Algebra) [6].1.1 The Biological ProblemThe focus of this work is a particular aspect of how particular components of the immune system,the T-helper cell populations, respond to co-infections with parasites making conflicting immunologi-∗Department of Computing Science and Mathematics, University of Stirling, UK. {tsp,egs,ces}@cs.stir.ac.uk†Institutes of Evolution, Immunology and Infection Research, University of Edinburgh, UK. XXX@XXXFigure 1: Experimental timeline and groups (from Mahajan et al [8])cal demands. A full presentation of immunological details is beyond the scope of this paper: see, e.g.Janeway’s Immunobiology textbook [10] for a very detailed introduction.T-helper cells, also known as CD4+ T cells, are central to the modulation of the adaptive immuneresponse. Adaptive immunity is the ability to recognise a pathogen, generate an antigenically tailoredresponse, and remember that pathogen (for a better response next time). There are known to be many dif-ferent CD4+ cells [13]; here the focus is on T-helper (Th)1 and Th2 cell types. It is now well recognisedthat the control of helminth infections depends on the presence of CD4+ T cells with a Th2 cytokineprofile [3, 4], while most microbial infection as controlled by Th1 CD4+ cells [13]. These contrastingimmune responses can interact in helminth-microparasite co-infection and can affect severity and theoutcome of disease as Th1 and Th2 responses are mutually inhibitory [5].Laboratory experiments were carried out [8] to explore the relationship between Th2 responses in-duced by immunisation with filarial (helminth) antigen and Th1 responses induced by infection withmalaria in rodents. One of the questions addressed is the effect of malaria on pre-existing responsesto filarial antigens. Essentially, cells were “primed” by exposure to worm antigen and transferred to acongenic mouse, which was exposed to malarial infection, and then given an injection of worm antigen.Figure 1.1 shows this experimental design, with timeline, and with variants to expose the behaviour ofthe Th1 and Th2 populations.Experimental results show there is a switch from Th2 to Th1 cytokine profiles. Figure 1.1 gives anindication of Th1 population sizes (defined by production of the cytokine interferon (IFN)-γ) on the left,with Th2 population sizes (defined by production of the cytokine interleukin (IL)-4), on the right. Thegraph shows multiple results for different filarial antigen. Points indicate particular results, and the linesare the average results. Notice that in mice exposed to malaria infections the level of Th2 falls while theTh1 population increases compared to mice injected with worm antigen only.It is not known how this change occurs, but there are two alternate hypotheses:Hypothesis 1: a sub-population of Th1 cells grow out of the Th2 cells.Hypothesis 2: there is phenotypic switching of individual Th2 cells to Th1 cellsFigure 2: Th1 population (left) and Th2 population (right)These alternatives can be investigated further using process algebra.2 PEPA ModelsTo facilitate description of the event-driven nature of the experiments, models were constructed to repre-sent a single stage of the experiment, e.g. the period between the start of the experiment and exposure tomalaria, or the period between malarial infection and the worm boost. The different stages may introducenew behaviour (e.g. switching) or simply change rates to inhibition or promotion of different T-helpercell populations by cytokines such as IL-4 and IFN-γ . Cytokines are not explicitly modelled.Each experiment is represented by a set of models, run consecutively. In this preliminary work thereare four sets of models representing each experimental timeline and group in Figure 1.1. In addition,to investigate the hypothesis above, replicated in silico experiments (simulations) were carried out withmodels incorporating switching behaviour.The details of the models are not shown here due to space constraints. They may be downloadedfrom www.cs.stir.ac.uk/SystemDynamics.2.1 AgentsThe models are made up of agents which represent cells and the behaviour of the immune system.There are T-helper cell agents which are either Th1 or Th2. In this model, the functions of Th1 andTh2 are not implemented: the label simply distinguishes the populations. The agents representing Th1and Th2 have the same range of behaviour. They can recruit naive T cells to become their specific type.This behaviour is controlled by a recruitment rate which will change throughout the timeline dependingon the introduction of malarial infection or filarial antigen. T-helper cell agents can divide, producingnew T-helper cells with the same type. The division rate is constant and set at one division per week, assuggested by Zhu and Paul [13]. The Th2 cells have a further behaviour of switching which occurs in theWorm-primed + Malaria + Switching experiment only. This is when the Th2 cell switches to become aTh1 cell. This behaviour is controlled by a switching rate (not available from biological data). Zhu andPaul [13] suggest that switching may occur in either direction (Th1 to Th2 and Th2 to Th1), multipletimes. In these preliminary experiments we have restricted our attention to switching from Th2 to Th1only, with no multiple switching.Additionally there are naive T cell agents with two recruitment behaviours: they either become Th1or Th2 cells. This behaviour requires co-operation with the T-helper cell agents of that type. The naivepopulations throughout the models are set at a level to ensure no resource issues are introduced, i.e. thenaive population should never become zero.2.2 Experiments: initial conditions and model setsThe initial populations of T-helper cells are not available experimentally: instead we are measuring thepercentage uplift in the final populations. Two different proportions of initial T-helper cell populationsare used (noted in the experimental details below). These distinguish the worm-primed case (20:80 ratioof Th1:Th2) from the unprimed case (50:50 ratio of Th1:Th2).1. Worm-primed The T-helper cell population is only exposed to the worm antigen.The initial population of T-helper cells consists of 80% Th2 and 20% Th1. This population takesinto account of the first introduction of the worm antigen. The duration of the first stage model is 16days (384 hours), representing the period in which the populations of Th1 and Th2 grow and recruit at abackground level. There is no exposure to Malaria in this model. The resulting population becomes theinitial population of the second stage model. The second stage model corresponds to second introductionof worm antigen. The duration of the second stage model is 3 days (72 hours).The worm-primed experiment population results are used as a base against which we measure theincrease/decrease in population of Th cells in the other experiment models.2. Worm-primed +Malaria This represents when the T-helper cell population is exposed to the wormantigen and malaria infection.The initial population of T-helper cells consists of 80% Th2 and 20% Th1, as in experiment 1. Theduration of the first stage model is 3 days (72 hours), representing background growth and recruitmentin Th populations. The second stage model introduces malaria. Practically this is done by increasing therecruit rate for Th1. The duration of the second model is 13 days (312 hours). The third stage modelcorresponds to the second exposure to worm antigen. The duration of the third model is 3 days (72hours).The population results are compared with the worm-primed population results and rates adjusted tobe consistent with biological experimental results as seen in Figure 1.1 :-1. the Th1 population should increase by approximately 55.2% - 57.6%. We are using the two setsof experiments (with different filarial antigen) to provide a range of acceptable results.2. the Th2 population should either increase by approximately 14.8% or a slightly decrease by 3.2%3. Worm-primed + Malaria + Switching This repeats experiment (2) and introduces the switchingbehaviour of the Th2 agent in the second stage model only. The population results are compared withthe worm-primed population results as above.In experiments (2) and (3) the results assist in assessing the two suggested hypotheses (see Section 3).4. Unprimed + Malaria This represents when the T-helper cell population is only exposed to Malariaand thereafter exposed to the worm antigen.The initial population of T-helper cells consists of 50% Th2 and 50% Th1. This population takesinto account no exposure to the worm antigen or malaria. The duration of the first stage model is 3days (72 hours), representing background growth and recruitment in Th populations. The second stagemodel introduces malaria. The duration of the second model is 13 days (312 hours). The third modelis introduced due to the first introduction of the worm antigen, therefore different levels of response areencoded in the recruitment rates here (primary exposure rather than secondary exposure). The duration ofthe third model is 3 days (72 hours). The population results are compared with the worm-primed+malariapopulation results.Expected results with comparison to experiment (1) and to mirror biological experimental results :-1. the Th1 population should increase by approximately 5.6% - 30%2. the Th2 population should show a significant decrease approximately by 76% to 78%.3 Analysis and DiscussionThe PEPA-Eclipse plugin has been used to simulate the models. The goal of the simulations was todetermine the rate of cell growth required under Hypothesis 1, or the rate of Th2-Th1 switching requiredunder Hypothesis 2, that was consistent with empirical data. Note that the sample size of the experimentaldata is quite small (as seen on Figure 1.1) while we are able to reduce stochastic effects by runningrepeated simulations and using average population sizes. The output of the PEPA models was handcalibrated initially against the Worm-primed results. The experimental data we have is proportions ofTh1 versus Th2 cells in samples taken from mice on day nineteen of a nineteen day experiment (seeFigure 1.1).This produces rates as follows for the worm-primed plus malaria case:rate description Hypothesis 1 Hypothesis 2Th1 recruitment 0.021 0.014Th2 recruitment 0.021 0.014malaria contact 0.87 1worm Ag contact 1 1switching (Th2→ Th1) 0 0.001It must be noted that many more simulations over a range of possible parameters are still to be ex-plored. Our biological collaborators have indicated that the rates above are not ridiculous; however, thereare no confirmatory experimental data available for this congenic system. Further laboratory experimentsare required to try to verify the rates suggested above, and relevant laboratory techniques are increasinglyavailable [13].Our main conclusion at this stage is that much further work is required from this initial starting point.There are many interesting further avenues to explore. The first is to enhance the biological realism ofthe models. For example, would it be beneficial to include cytokine details explicitly in the model, sothat the mutually inhibitory effects of Th1 and Th2 are included directly? Might we want to includespatial aspects in the model, to reflect that recruitment is based on proximity?We also have experimental data for a slightly different set of experiments, including an additionalexposure to worm antigen. Models should be constructed to match this.There are other investigatory techniques which can be explored. Currently we have only used sim-ulation to produce time series data for the models. For example, it would be instructive to compare theODEs derived from our models to those proposed by Yates et al [12]. Currently our models are toosimplistic to make such a comparison feasible.Lastly, and most excitingly, the use of process algebra models allows the possibility that we can con-struct models following completely different experimental design. For example, modelling the situationwith an initial malarial infection (or antigen) followed by worm infection. This could then be followedup by wet lab experiments. Our hope would be that these would confirm the in silico results, supportingour aim that models are a true representation of the behaviour and function of the immune system.AcknowledgementThis work was supported by the Wellcome Trust through a BioMedical Vacation Scholarship (TB, Sum-mer 2009), by the Carnegie Trust for the Universities of Scotland (ES, Summer 2010), and by the EPSRCthrough System Dynamics from Individual Interactions: A process algebra approach to epidemiology(EP/E006280/1, CS and RN, 2007-2010). The in vivo work was funded by the BBSRC (BB/C508734/1to ALG and JEA).References[1] A. Bracciali, M. Brunelli, E. Cataldo & P. Degano (2008): Synapses as stochastic concurrent systems. The-oretical Computer Science 408, pp. 66–82.[2] M. Calder & J. Hillston (2009): Process algebra modelling styles for biomolecular processes. In: Transac-tions on Computational Systems Biology XI, Lecture Notes in Computer Science 5750, pp. 1–25.[3] F.D. Finkelman, T. Shea-Donohue, J. Goldhill, C. A. Sullivan, S. C. Morris, K. B. Madden, W.C. Gause& J.F. Urban Jr. (1997): Cytokine regulation of host defense against parasitic gastrointestinal nematodes:lessons from studies with rodent models. Annual Review of Immunology 15, pp. 505–533.[4] L.T. Le Goff, J. Lamb, A.L. Graham, Y. Harcus & J. E. Allen (2002): IL-4 is required to prevent filarialnematode development in resistant but not susceptible strains of mice. International Journal for Parasitology32, pp. 1277–1284.[5] F.C. Hartgers &M. Yazdanbakhsh (2006): Co-infection of helminths and malaria: modulation of the immuneresponses to malaria. Parasite Immunology 28, pp. 497–506.[6] J. Hillston (1996): A Compositional Approach to Performance Modelling. Cambridge University Press.[7] H. Kitano (2002): Systems Biology: A Brief Overview. Science 295, pp. 1662–1664.[8] S. Mahajan, D. Gray, W. Harnett, A.L. Graham & J.E. Allen (2010): Helminth-induced unmodified Th2 cellsaffect malaria-induced immune responses but alter disease little. Unpublished draft.[9] C. McCaig, R. Norman & C. Shankland (2009): From Individuals to Populations: A Symbolic ProcessAlgebra Approach to Epidemiology. Mathematics in Computer Science 2(3), pp. 139–155.[10] K. Murphy, P. Travers & M. Walport (2008): Janeway’s Immunobiology. Garland Science. 7th edition.[11] C. Priami (2006): Process Calculi and Life Science. Electronic Notes in Theoretical Computer Science 162,pp. 301–304.[12] A. Yates, C. Bergmann, J.L. van Hemmen, J. Stark & R. Callard (2000): Cytokine-modulated Regulation ofHelper T Cell Populations. Journal of Theoretical Biology 206, pp. 539–560.[13] J. Zhu & W.E. Paul (2010): Heterogeneity and plasticity of T helper cells. Cell Research 20, pp. 4–12.

Modelling Immunological Systems using PEPA: a preliminary report

Stirling Online Research Repository (RIOXX)

Submitted to:PASTA 2010c© E. Scott, S.M. Mahajan, T. Brand-Spencer, J.E. Allen, R. Norman, A.L. Graham and C. ShanklandThis work is licensed under theCreative Commons Attribution License.Modelling Immunological Systems using PEPA: apreliminary reportErin Scott∗ Simmi M. Mahajan† Timothy Brand-Spencer∗ Judith E. Allen†Rachel Norman∗ Andrea L. Graham† Carron Shankland∗We present preliminary work on modelling aspects of the immune system using process algebra. Theproblem addressed is how T-helper cell populations respond to co-infections with parasites makingconflicting immunological demands. Our goal is to build PEPA models of alternative hypothesesaround T-helper cell behaviour and to evaluate those with respect to experimental data.1 IntroductionComputer Science techniques are increasingly being used to describe biological systems. There arethree advantages: the process of formalising the system can lead to deeper understanding through havingto make assumptions explicit; formal analysis can be carried out, leading to discovery of previouslyunknown system properties; and experiments can be carried out in silico, usually much more quicklyand cheaply than in the laboratory, allowing in vivo experiments to be guided towards the most focussedhypothesis tests [7]. Process algebra is one of the modelling methodologies achieving some success inthis arena [1, 2, 9, 11] because of its ability to represent systems in an abstract and modular fashion.Immunological systems are ideally suited to modelling using process algebra. In many ways the im-mune system is a black box; although many of its inputs and outputs are known, exactly how the systemachieves its function is the subject of much investigation. Laboratory experiments have provided largequantities of data, allowing components within the black box to be identified, but there remain manydetails to be uncovered about the exact details of how components carry out their functions, or on thenature of interaction between components. There are so many potential variables in such systems that ex-haustive testing to establish these details is not feasible. Process algebras are ideally suited to describingimmunological systems at this level: they may be viewed as networks of (many) interacting components,where the components themselves may have complex, nondeterministic, individual behaviour. In addi-tion, use of process algebra gives access to a range of investigatory techniques, including simulation,verification via logical properties, and transformation from an individual-based discrete state space toa population-based continuous state space via derivation of Ordinary Differential Equations. Throughmodelling, different hypotheses about the biology of the systems may be investigated, providing focusfor future laboratory experiments.The goal of the current work is the novel application of process algebra to immunological systems.The particular process algebra adopted here is PEPA (Performance Evaluation Process Algebra) [6].1.1 The Biological ProblemThe focus of this work is a particular aspect of how particular components of the immune system,the T-helper cell populations, respond to co-infections with parasites making conflicting immunologi-∗Department of Computing Science and Mathematics, University of Stirling, UK. {tsp,egs,ces}@cs.stir.ac.uk†Institutes of Evolution, Immunology and Infection Research, University of Edinburgh, UK. XXX@XXXFigure 1: Experimental timeline and groups (from Mahajan et al [8])cal demands. A full presentation of immunological details is beyond the scope of this paper: see, e.g.Janeway’s Immunobiology textbook [10] for a very detailed introduction.T-helper cells, also known as CD4+ T cells, are central to the modulation of the adaptive immuneresponse. Adaptive immunity is the ability to recognise a pathogen, generate an antigenically tailoredresponse, and remember that pathogen (for a better response next time). There are known to be many dif-ferent CD4+ cells [13]; here the focus is on T-helper (Th)1 and Th2 cell types. It is now well recognisedthat the control of helminth infections depends on the presence of CD4+ T cells with a Th2 cytokineprofile [3, 4], while most microbial infection as controlled by Th1 CD4+ cells [13]. These contrastingimmune responses can interact in helminth-microparasite co-infection and can affect severity and theoutcome of disease as Th1 and Th2 responses are mutually inhibitory [5].Laboratory experiments were carried out [8] to explore the relationship between Th2 responses in-duced by immunisation with filarial (helminth) antigen and Th1 responses induced by infection withmalaria in rodents. One of the questions addressed is the effect of malaria on pre-existing responsesto filarial antigens. Essentially, cells were “primed” by exposure to worm antigen and transferred to acongenic mouse, which was exposed to malarial infection, and then given an injection of worm antigen.Figure 1.1 shows this experimental design, with timeline, and with variants to expose the behaviour ofthe Th1 and Th2 populations.Experimental results show there is a switch from Th2 to Th1 cytokine profiles. Figure 1.1 gives anindication of Th1 population sizes (defined by production of the cytokine interferon (IFN)-γ) on the left,with Th2 population sizes (defined by production of the cytokine interleukin (IL)-4), on the right. Thegraph shows multiple results for different filarial antigen. Points indicate particular results, and the linesare the average results. Notice that in mice exposed to malaria infections the level of Th2 falls while theTh1 population increases compared to mice injected with worm antigen only.It is not known how this change occurs, but there are two alternate hypotheses:Hypothesis 1: a sub-population of Th1 cells grow out of the Th2 cells.Hypothesis 2: there is phenotypic switching of individual Th2 cells to Th1 cellsFigure 2: Th1 population (left) and Th2 population (right)These alternatives can be investigated further using process algebra.2 PEPA ModelsTo facilitate description of the event-driven nature of the experiments, models were constructed to repre-sent a single stage of the experiment, e.g. the period between the start of the experiment and exposure tomalaria, or the period between malarial infection and the worm boost. The different stages may introducenew behaviour (e.g. switching) or simply change rates to inhibition or promotion of different T-helpercell populations by cytokines such as IL-4 and IFN-γ . Cytokines are not explicitly modelled.Each experiment is represented by a set of models, run consecutively. In this preliminary work thereare four sets of models representing each experimental timeline and group in Figure 1.1. In addition,to investigate the hypothesis above, replicated in silico experiments (simulations) were carried out withmodels incorporating switching behaviour.The details of the models are not shown here due to space constraints. They may be downloadedfrom www.cs.stir.ac.uk/SystemDynamics.2.1 AgentsThe models are made up of agents which represent cells and the behaviour of the immune system.There are T-helper cell agents which are either Th1 or Th2. In this model, the functions of Th1 andTh2 are not implemented: the label simply distinguishes the populations. The agents representing Th1and Th2 have the same range of behaviour. They can recruit naive T cells to become their specific type.This behaviour is controlled by a recruitment rate which will change throughout the timeline dependingon the introduction of malarial infection or filarial antigen. T-helper cell agents can divide, producingnew T-helper cells with the same type. The division rate is constant and set at one division per week, assuggested by Zhu and Paul [13]. The Th2 cells have a further behaviour of switching which occurs in theWorm-primed + Malaria + Switching experiment only. This is when the Th2 cell switches to become aTh1 cell. This behaviour is controlled by a switching rate (not available from biological data). Zhu andPaul [13] suggest that switching may occur in either direction (Th1 to Th2 and Th2 to Th1), multipletimes. In these preliminary experiments we have restricted our attention to switching from Th2 to Th1only, with no multiple switching.Additionally there are naive T cell agents with two recruitment behaviours: they either become Th1or Th2 cells. This behaviour requires co-operation with the T-helper cell agents of that type. The naivepopulations throughout the models are set at a level to ensure no resource issues are introduced, i.e. thenaive population should never become zero.2.2 Experiments: initial conditions and model setsThe initial populations of T-helper cells are not available experimentally: instead we are measuring thepercentage uplift in the final populations. Two different proportions of initial T-helper cell populationsare used (noted in the experimental details below). These distinguish the worm-primed case (20:80 ratioof Th1:Th2) from the unprimed case (50:50 ratio of Th1:Th2).1. Worm-primed The T-helper cell population is only exposed to the worm antigen.The initial population of T-helper cells consists of 80% Th2 and 20% Th1. This population takesinto account of the first introduction of the worm antigen. The duration of the first stage model is 16days (384 hours), representing the period in which the populations of Th1 and Th2 grow and recruit at abackground level. There is no exposure to Malaria in this model. The resulting population becomes theinitial population of the second stage model. The second stage model corresponds to second introductionof worm antigen. The duration of the second stage model is 3 days (72 hours).The worm-primed experiment population results are used as a base against which we measure theincrease/decrease in population of Th cells in the other experiment models.2. Worm-primed + Malaria This represents when the T-helper cell population is exposed to the wormantigen and malaria infection.The initial population of T-helper cells consists of 80% Th2 and 20% Th1, as in experiment 1. Theduration of the first stage model is 3 days (72 hours), representing background growth and recruitmentin Th populations. The second stage model introduces malaria. Practically this is done by increasing therecruit rate for Th1. The duration of the second model is 13 days (312 hours). The third stage modelcorresponds to the second exposure to worm antigen. The duration of the third model is 3 days (72hours).The population results are compared with the worm-primed population results and rates adjusted tobe consistent with biological experimental results as seen in Figure 1.1 :-1. the Th1 population should increase by approximately 55.2% - 57.6%. We are using the two setsof experiments (with different filarial antigen) to provide a range of acceptable results.2. the Th2 population should either increase by approximately 14.8% or a slightly decrease by 3.2%3. Worm-primed + Malaria + Switching This repeats experiment (2) and introduces the switchingbehaviour of the Th2 agent in the second stage model only. The population results are compared withthe worm-primed population results as above.In experiments (2) and (3) the results assist in assessing the two suggested hypotheses (see Section 3).4. Unprimed + Malaria This represents when the T-helper cell population is only exposed to Malariaand thereafter exposed to the worm antigen.The initial population of T-helper cells consists of 50% Th2 and 50% Th1. This population takesinto account no exposure to the worm antigen or malaria. The duration of the first stage model is 3days (72 hours), representing background growth and recruitment in Th populations. The second stagemodel introduces malaria. The duration of the second model is 13 days (312 hours). The third modelis introduced due to the first introduction of the worm antigen, therefore different levels of response areencoded in the recruitment rates here (primary exposure rather than secondary exposure). The duration ofthe third model is 3 days (72 hours). The population results are compared with the worm-primed+malariapopulation results.Expected results with comparison to experiment (1) and to mirror biological experimental results :-1. the Th1 population should increase by approximately 5.6% - 30%2. the Th2 population should show a significant decrease approximately by 76% to 78%.3 Analysis and DiscussionThe PEPA-Eclipse plugin has been used to simulate the models. The goal of the simulations was todetermine the rate of cell growth required under Hypothesis 1, or the rate of Th2-Th1 switching requiredunder Hypothesis 2, that was consistent with empirical data. Note that the sample size of the experimentaldata is quite small (as seen on Figure 1.1) while we are able to reduce stochastic effects by runningrepeated simulations and using average population sizes. The output of the PEPA models was handcalibrated initially against the Worm-primed results. The experimental data we have is proportions ofTh1 versus Th2 cells in samples taken from mice on day nineteen of a nineteen day experiment (seeFigure 1.1).This produces rates as follows for the worm-primed plus malaria case:rate description Hypothesis 1 Hypothesis 2Th1 recruitment 0.021 0.014Th2 recruitment 0.021 0.014malaria contact 0.87 1worm Ag contact 1 1switching (Th2→ Th1) 0 0.001It must be noted that many more simulations over a range of possible parameters are still to be ex-plored. Our biological collaborators have indicated that the rates above are not ridiculous; however, thereare no confirmatory experimental data available for this congenic system. Further laboratory experimentsare required to try to verify the rates suggested above, and relevant laboratory techniques are increasinglyavailable [13].Our main conclusion at this stage is that much further work is required from this initial starting point.There are many interesting further avenues to explore. The first is to enhance the biological realism ofthe models. For example, would it be beneficial to include cytokine details explicitly in the model, sothat the mutually inhibitory effects of Th1 and Th2 are included directly? Might we want to includespatial aspects in the model, to reflect that recruitment is based on proximity?We also have experimental data for a slightly different set of experiments, including an additionalexposure to worm antigen. Models should be constructed to match this.There are other investigatory techniques which can be explored. Currently we have only used sim-ulation to produce time series data for the models. For example, it would be instructive to compare theODEs derived from our models to those proposed by Yates et al [12]. Currently our models are toosimplistic to make such a comparison feasible.Lastly, and most excitingly, the use of process algebra models allows the possibility that we can con-struct models following completely different experimental design. For example, modelling the situationwith an initial malarial infection (or antigen) followed by worm infection. This could then be followedup by wet lab experiments. Our hope would be that these would confirm the in silico results, supportingour aim that models are a true representation of the behaviour and function of the immune system.AcknowledgementThis work was supported by the Wellcome Trust through a BioMedical Vacation Scholarship (TB, Sum-mer 2009), by the Carnegie Trust for the Universities of Scotland (ES, Summer 2010), and by the EPSRCthrough System Dynamics from Individual Interactions: A process algebra approach to epidemiology(EP/E006280/1, CS and RN, 2007-2010). The in vivo work was funded by the BBSRC (BB/C508734/1to ALG and JEA).References[1] A. Bracciali, M. Brunelli, E. Cataldo & P. Degano (2008): Synapses as stochastic concurrent systems. The-oretical Computer Science 408, pp. 66–82.[2] M. Calder & J. Hillston (2009): Process algebra modelling styles for biomolecular processes. In: Transac-tions on Computational Systems Biology XI, Lecture Notes in Computer Science 5750, pp. 1–25.[3] F.D. Finkelman, T. Shea-Donohue, J. Goldhill, C. A. Sullivan, S. C. Morris, K. B. Madden, W.C. Gause& J.F. Urban Jr. (1997): Cytokine regulation of host defense against parasitic gastrointestinal nematodes:lessons from studies with rodent models. Annual Review of Immunology 15, pp. 505–533.[4] L.T. Le Goff, J. Lamb, A.L. Graham, Y. Harcus & J. E. Allen (2002): IL-4 is required to prevent filarialnematode development in resistant but not susceptible strains of mice. International Journal for Parasitology32, pp. 1277–1284.[5] F.C. Hartgers & M. Yazdanbakhsh (2006): Co-infection of helminths and malaria: modulation of the immuneresponses to malaria. Parasite Immunology 28, pp. 497–506.[6] J. Hillston (1996): A Compositional Approach to Performance Modelling. Cambridge University Press.[7] H. Kitano (2002): Systems Biology: A Brief Overview. Science 295, pp. 1662–1664.[8] S. Mahajan, D. Gray, W. Harnett, A.L. Graham & J.E. Allen (2010): Helminth-induced unmodified Th2 cellsaffect malaria-induced immune responses but alter disease little. Unpublished draft.[9] C. McCaig, R. Norman & C. Shankland (2009): From Individuals to Populations: A Symbolic ProcessAlgebra Approach to Epidemiology. Mathematics in Computer Science 2(3), pp. 139–155.[10] K. Murphy, P. Travers & M. Walport (2008): Janeway’s Immunobiology. Garland Science. 7th edition.[11] C. Priami (2006): Process Calculi and Life Science. Electronic Notes in Theoretical Computer Science 162,pp. 301–304.[12] A. Yates, C. Bergmann, J.L. van Hemmen, J. Stark & R. Callard (2000): Cytokine-modulated Regulation ofHelper T Cell Populations. Journal of Theoretical Biology 206, pp. 539–560.[13] J. Zhu & W.E. Paul (2010): Heterogeneity and plasticity of T helper cells. Cell Research 20, pp. 4–12.

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Modelling Immunological Systems using PEPA: a preliminary report

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