Jianwei Shuai ( 帅建伟 ), Hai Lin ( 林海 ) Physics Department Xiamen University A Stochastic HIV Dynamics

 Immune system  HIV infection  Modeling HIV dynamics - previous works  Modeling HIV dynamics - Our work Contents

 Immune system  HIV infection  Modeling HIV dynamics - previous works  Modeling HIV dynamics - Our work (A)

Specific immune system B cell T cell Innate immune system antibody antigen Clear the antigen virus Three defense lines of immune system  The first line of defense against viral invasion of our body is skin and mucosa.  The second line of defense is the innate immune system: macrophage, natural killer cell and complement system.  If the viral invades beyond the innate immune system, the third defense line, specific immune system, will be activated to fight the viruses. Skin Mucosa (1) (2) (3)

B cell and antibody B cell virus Receptor epitope virus antibody  B cells express the receptor (BCR) on their surface, some receptors are released from the surface. The free receptor called antibody.  BCR and antibody recognize the protein on the viral surface (epitope) and bind to the epitope.

virus antibody epitope virus Function of B cell virus macrophag e B cell

T Cells: CD4 and CD8  CD4+ T cell offers the necessary help to B cell and CD8+ T Cell.  CD8+ T cells express the receptors (TCR) and recognize the viral proteins presented on the surface of infected cells.  CD8+ T Cell can kill the virus-infected cell. T

virus Host cell CD8 T CD4 T Function of T cells

 Different viruses have different epitopes.  Each B cell or T cell can only express one specific type of receptor and recognize one specific epitope on the virus. Why is it called “specific” immune system? Virus B/T Cell

Clonal selection When the viruses invade the host, the B cells or T cells will competitively bind to the viruses. The cells with the highest binding affinity will be chosen to self-reproduce and generate many clonal cells to fight the viruses.

 Effector immune cells Fight the viruses and die in a few days.  Memory immune cells Retain in body for a long time as a memory Clonal selection produces two types of immune cells EffectorMemory

Viruses can escape the immune memory by genetic mutation. Viral escapes the immune memory Genetic mutation Antigen change Recognition failure

 Immune system  HIV infection  Modeling HIV dynamics - previous works  Modeling HIV dynamics - Our work (B)

HIV infection  HIV (Human Immunodeficiency Virus) was found in 1983 and was confirmed to be the cause of AIDS (Acquired ImmunoDeficiency Syndrome) in Two finders won 2009 Nobel prize. Luc Montagnier and Francoise Barre-Sinoussi

HIV Structure 0.1 um Epitope RND-based virus Glycoprotein

HIV infects CD4 T-cell 1. Free virus 2. Bind to CD4 T-cell 3. Inject RNA into the cell 4. Reverse transcript RNA to DNA 5. Integrate DNA into cell’s genome. 6. Transcription 7. Assembly 8. Budding 9. Maturation CD4 T-cell HIV Glycoprotein

Three-phase dynamics of the HIV infection  Acute phase: virus number increases rapidly followed by a sharp decline.  Asymptomatic phase: virus number remains low, CD4 T-cell population continues to decline slowly.  AIDS phase: virus number climbs up again, leading the onset of AIDS.

The proportion developing AIDS from infection Lancet 355 (2000) 1131

What makes the HIV different from other viruses?  HIV mainly infects and kills CD4 T-cell. The progressive decline of the CD4 T-cell eventually results in the loss of many immune functions.  HIV has a high mutation rate. So the viruses can create highly diverse population to escape from the recognition of immune memory cells.  The reason of the transition from the asymptomatic phase to the onset of AIDS still remains unknown. Several models have been developed to explained the three-phase dynamics of HIV.

 Immune system  HIV infection  Modeling HIV dynamics - previous works  Modeling HIV dynamics - Our work (C)

Phillips, Science 271 (1996) 497 T-cell Health T cells Latently Infected T cells Virus  Actively infected T-cells Act T* Lat T*

Latent Health Active

Nowak, May, Anderson. AIDS 4 (1990) 1095 Specific immune response Common immune response Virus Virus mutation T1T1 TiTi ViVi V1V1 ViVi V1V1 T1T1 TiTi TCTC

Simulation Results Immune cell Virus mutation rate 1.75 Virus mutation rate 2

 Each cell has four states: (a) health cell; (b) infected cell; (c) AIDS cell; (d) dead cell.  Evolution rules: Rule 1: For health cell (a) If it has at least one infected neighbor, it becomes infected. (b) If it has no infected neighbor but does have at least R (2<R<8) AIDS neighbors, it becomes infected. (c) Otherwise it stays healthy. Rule 2: An infected cell becomes AIDS after 4 time steps. Rule 3: AIDS cell becomes dead cell at next step. Rule 4: (a) Dead cells can be replaced by healthy cells with probability P in the next step, otherwise remain dead. (b) Each new health cell introduced may be replaced by an infected cell with probability k. Cellular automata HIV model Santos and Coutinho, Phys. Rev. Lett. 87 (2001)

Simulation results of CA model Three phase of HIV infection Spatial structure of HIV evolution

Comments by Strain and Levine

Wang and Deem, Phys. Rev. Lett. 97 (2006) HIV Antigen HIV ViVi V0V0  A string with length 9 is used to represent the viral epitope and immune cell gene type.  When mutation occurs, a random site is selected and the number is changed.

， HIV Dynamics Virus Mutation Cross killing of virus by T-cells T0T0 TiTi ViVi V0V0 Virus recognization Cross inhibition among different types of T-cells.

The three-phase pattern of HIV infection in the model (c)

 Immune system  HIV infection  Modeling HIV dynamics - previous works  Modeling HIV dynamics - Our work New Journal of Physics 12 (2010) (D)

A stochastic spatial model of HIV dynamics New Journal of Physics 12 (2010) CD4 CD8 HIV  Viruses, CD8 T-cells, and CD4 T- cells are arranged on the lattices.  One lattice can only locate one individual of the same type.  Different types of individuals can occupy the same site at the same time.

HIV infecting and immune responding networks Antibody Virus (V) Uninfected CD4 T-cell Infected CD4 T-cell B cell CD8 T-cell Help Stimulate Proliferate Release Kill

CD CD HIV Binary string T-cells and virus  A binary string: To represent T cell’s receptor or viral epitope.  Hamming distance: The number of different sites between two strings.  The strength of cell-virus interaction depends on their Hamming distance.  Asymmetric battle between the virus and the immune system.

Three-phase dynamics Example 1 Example 2 Example 3 Averaged result

Acute Phase The functions of three immune mechanisms (a) No immune response (b) Only B cell response, without CD8 T-cell. (c) Only CD8 T-cell response, without B cell. (d) Fully responses

Asymptomatic Phase Effects of Diversity of virus mutation

AIDS phase  Our simulation result is in good agreement with the clinical data from literature CASCADE Collaboration, Lancet 355 (2000) 1131

Conclusions 1.We show that the different durations (from a few years to more than 15 years) of the asymptomatic phase among different patients can be simply due to the stochastic evolution of immune system, not due to the different intrinsic immune abilities among patients. 2.We assess the relative importances of various immune system components (CD4+, CD8+ T cells, and B cells) in acute phase and have found that the CD8+ T cells play a decisive role to suppress the viral load. 3.This observation implies that CD8+T cell response might be an important goal in the development of an effective vaccine against AIDS.

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