Immune System

1. Immune System • Skin • Complement • Immune cells • Macrophages • T cells • B cells Cytokines Intro-cellular events

2. Complement System • 25 Proteins that complement the activity of antibodies in destroying bacteria • Phagocytosis • Puncturing cell membrane • Proteases cleave proteins • Rids body of antigen-antibody complexes • Circulate in blood in in-active form • Creates complement cascade

3. Phagocytes • Macrophages • Antigen Presentation • All over • Dendritic cells • Tenticles used to present antigen • Located in Spleen • Neutrophils • Contain granules that have potent chemicals

4. T cells • Mature in Thymus • Regulatory • Helper T cells • Present antigen to B cells • CD4 • Cytotoxic • CD8 • Both secrete necessary cytokines • Orchestrate elaborate response • Memory T cells

5. MHC Complexes Two types Bound or Free Type 1 Most cells Type 2 APC

6. B cells • Programmed to make one antibody • Needs APC/Cytokines • Creates Plasma cell • Factories for antibody • Done by Geometry

7. Where do they come from

8. Cytokines

9. Cytokine network

10. Disease of Immune System • Allergy • Auto Immune Diseases • Rheumatoid Arthritis • Lupus • Diabetes • Leukemia • HIV

11. Memory T cells Angela Mclean

12. Memory T Cells • They are antigen-specific T cells that persist long-term after an infection • If there is a second encounter with an infection, the memory T cells are reactivated and can reproduce to provide a faster and stronger immune response

13. The Model and Goals • Uses 5 populations: resting Th cells (W), activated Th cells (X) memory T cells (M), interleukin 2 (IL-2) (I), and antigen (A). • Using the model, the population dynamics are illustrated both in vitro and in vivo. In previous models, in vivo and in vitro had the same results, but in experiments it was shown that the two were quite different. This model aims to correct this error. • The model is created to have no numerical estimates of parameters, so the model’s behavior has all possible types of population behavior.

14. A Antigen Antigen driven activation W X M Immigration from the bone marrow Antigen driven activation Background activation Interleukin-2 driven proliferation Native Activated Memory IL-2

15. Equation 1 Assume that naïve Th cells migrate from thymus at a constant rate and naïve cells are activated at a rate proportional to the amount of activated Th cells. • W = Naïve Th cells • Λ = constant rate of migration • 1/μ = half life of the naïve cells • A = Specific antigen • α = rate of activation of naïve cells dW/dt = Λ–αAW –μW

16. Equation 2 Assume that: • Proliferation of an activated cell creates two memory cells • Occurs at a constant rate with high concentration of activated cells • The half-life of all Th cells are equal • Memory cells can be reactivated by either reintroduction of the antigen or from background influences, such as a sequestered antigen • Memory cells are activated at a faster rate than naïve cells

17. Equation 2 • X = Activated helper T cells • M = Memory cells • δ= Difference in the rate of activation of memory cells and the rate of activation of naïve cells • ε = background activation rate (accounts for random chances that a cell was activated for a different reason) Rate of activation dX/dt = αAW - ρIX/1+ξX + (δαA+ε)M - μX

18. Equation 2 dX/dt = αAW - ρIX/1+ξX + (δαA+ε)M - μX • The rate of change of the activated Th cells is equal to the rate of activation of the naïve cell multiplied by the probability of an antigen and cell binding minus the proliferation rate of the activated Th cells changing to memory cells plus the rate of memory cells reactivating minus the death rate of activated cells.

19. Equation 3 dM/dt = 2ρIX/1+ξX - (δαA+ε)M - μM • The rate of change of memory cells is equal to double the rate of proliferation of activated cells (because 2 memory cells are produced) minus the rate of reactivation of memory cells minus the death rate of memory cells.

20. Equation 4 Assume that: • IL-2 is produced and absorbed by only activated Th cells • The half-life of IL-2 is constant

21. Equation 4 1/ψ = half-life of IL-2 I = amount of IL-2 dI/dt = φX - βIX - ψI • The rate of change of the amount of IL-2 is equal to the amount of IL-2 made by activated cells minus the amount absorbed by activated Th cells minus the death rate of IL-2.

22. Equation 5 Assume that: • Activated cells have a constant growth rate when they are not in the presence of specific immunity

23. Equation 5 r = growth rate of antigen dA/dt = rA - γAX • The rate of change of the specific antigen is equal to the growth rate of the antigen in the absence of specific immunity minus the rate of interaction of activated cells and the antigen that causes removal of the antigen.

24. Finding a Steady State • In order to find when the change of the different populations would be steady, the derivatives are set equal to zero. • After doing this, it is found that the rates are constant only when A (the amount of antigen) equals zero and when X (the amount of activated Th cells) equals a constant. • A quadratic equation is derived to find what this constant is. Because it is quadratic, we know two roots will be found or X will be equal to zero.

25. Finding a Steady State cont • For a replicating antigen, the only X that can be stable is the positive root of the equation. • For a non-replicating antigen, X can be the positive root or X can be zero. • The only time that memory cells will be formed is if X is positive, so we are only interested in the replicating antigen. • The root will not be a real number unless the background activation rate (ε) is greater than the death rate of the Th cells. This is represented by the fact that when e (e = ε/μ) is less than one, there are no real solutions to the equation.

26. In Vivo Simulation • This models the changes in the amounts of memory, naïve, and activated cells in the presence of antigen in vivo (in the body) • All parameters are the same for each trial, the only difference is the growth rate of the antigen • At time 0 there was a small amount of replicating antigen was added to the system • At time 10 there was a large challenging dose of antigen introduced

28. In Vivo Simulation contd. • With an intermediate growth rate the T cells are able to clear out the antigen relatively quickly, and can clear out the infection again much more quickly • With a fast growth rate, the T cells can’t clear it out completely, and there always is a small amount of the antigen present even after reintroduction of the antigen

29. In Vivo Simulation contd. • With a slow growth rate a persistent infection is also established, and the T cells do not clear out the infection because they are only slightly stimulated by the slow-growing antigens. The T cells take a long time to proliferate but when a larger dose of the antigen is reintroduced it is able to completely clear it. • At the reintroduction, where the amount was equal to the initial amounts in the first two trials, the memory and activated cells are pushed past their threshold, clearing the antigen and returning to a stable state.

30. In Vitro Simulation • This model is much different because of three major factors: • There is no chance of random activation • No extra naïve cells come from the bone marrow • The antigen cannot grow • The model no longer displays immune memory and a single exposure to antigen leads to a short-lived activation and proliferation. • All cells convert from naïve to memory

32. In Vitro Simulation contd. • This shows that the amount of activated cells increases because it is in the presence of an antigen, but decreases with IL-2 exposure because the activated cells become memory cells. • When exogenous IL-2 is added to the system the amount of activated cells decreases at a faster rate. • The cells convert from being mostly naïve to mostly memory

33. Conclusions • In vitro cultures of Th cells must be re-exposed to antigens if they want to maintain proliferation. • In vivo this achieved through background stimulation (random chance of reactivation)

34. Our Conclusions • This new model has achieved its goal, the distinction between in vivo and in vitro situations. There may be some problems with it, but is so far the best representation of the population dynamics of T helper cells and antigens in the human body and in a culture. • Possible problems: • In this model, rates including death and growth rates were assumed to be constant. If the rates were varying, even slightly, there may be a great difference in results. • In has not been shown that memory cells can hold their memory for as long as the model shows. • There are many things going on in the body that are unpredictable and impossible to model perfectly.

35. Basic modelEquation for the dynamics of activated Th cells

36. Result of modeling T-cell • A reduced version of the model with just two variables is considered so that isoclines can be inspected.

37. Result of modeling T-cell-model-

38. Result of modeling T-cell-in vivo simulation- • First, a small amount of replicating antigen is introduced at time zero, when all cells are present are naïve cells. • When there is not response of immune system, antigen grow initially. • Antigen drives naïve cells to become activated and activated cell is divided into two memory cells.

39. Result of modeling T-cell-in vivo simulation- • Antigen causes a rise in the number of activated and memory cells. • The size of the activated and memory population maintained in the absence of the replicating antigen depends only on interactions among immune system.

40. Result of modeling T-cell-in vitro simulation- • All is same as earier model in 1990. • There is no cross-reactive stimulation or antigens. • There is no influx of naive cells.

41. Conclusion • T-helper cells need to be re-exposed to antigens every few weeks. • Immune memory, persistent infection, slow growing persistent infection.

42. Conclusion • Memory cell have some special properties but not long-lived. • Their ability maintain immune system. • This model displays memory without invoking long time.