jianwei shuai ( 帅建伟 ), hai lin ( 林海 ) physics department xiamen university a stochastic...

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.

SkinMucosa

(1)

(2)

(3)

B cell and antibody

B cell

viru

s

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

viru

s

Function of B cell

virus

macrophage

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

Effector Memory

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 1984. Two finders won 2009 Nobel prize.

Luc MontagnierandFrancoise Barre-Sinoussi

HIV Structure

0.1 umEpitope

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

0 3 6 9 12 15

0

20

40

60

Pro

port

ion

deve

lopi

ng A

IDS

(%) Clinical data

Years

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

Virus

RVRdt

dR

LLRVpdt

dL

ELRVpdt

dE )1(

VEdt

dV

Actively infected T-cells

Act T*

p1

pLat T*

Latent

Health

Active

Nowak, May, Anderson. AIDS 4 (1990) 1095

ii i

dxkv uvx

dt Specific immune

response

Common immune response

Virus ( )ii i i i

dvrv px v szv M v

dt

dzk v uvz

dt

Virus mutation

ii

v v

( )M v bQ v t

T1

TiVi

V1

Vi

V1 T1

Ti

TC

Simulation Results

0 2 4 60.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

viru

s /

de

nsi

t o

f ly

mp

ho

cute

s

time in years

Immune cell

Virus

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

1.2

Virus

Lymphocytes specific to HIV

time in yearsvi

rus

/ d

en

sity

of

lym

ph

ocy

tes

Immune cell

Virus mutation rate 1.75Virus 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) 168102

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) 188106

HIV

Antigen

HIV

000000000

000001000

0 1id Vi

V0

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.

，( , , , ) ( , , , ) ( , ,..., )( )N 1 1 N 1 N N 1

A

i j a a a j a a a j ij 0v v v Nv

1

3

(x) , (1)

( ) (x) , (2)

ii i i i i i

i ii i i

dvrv mNAv m c f v

dtdx v

x c g xdt v

( ) ( ) / [ ( )]i i 2 if y c y x x x

( ) ( )i j ji i ii jg x k y x

x x

( ) exp( )I 1 I 1

i j ji j jij 0 j 0y x k x d

x

HIV Dynamics

Virus Mutation Cross killing of virus by T-cells

T0

Ti

Vi

V0

Virus recognization Cross inhibition among different types of T-cells.

0 2 4 6 8 10 120

100

200

300

400

500

600

700

Plasm

a HIV-1

titer

w e e k s

v ( t )

1 2 3 4 5 6 7 8 9 10

years

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) 043051 1-18

(D)

A stochastic spatial model of HIV dynamics

New Journal of Physics 12 (2010) 043051 1-18

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

HelpStimulate Stimulate

Proliferate

Release

Release

Kill

Kill

CD4 1000111000

CD8 0100100011

HIV 1100100011

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

0.00.20.40.60.81.00.00.20.40.60.81.0

(d)

YearsWeeks0 5 10 15 4 8 12 16 20

Den

sitie

s

(c)

0.00.20.40.60.81.0

(b)

0.00.20.40.60.81.0

(a)

HIV CD4 CD8

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

0 50 1000.0

0.2

0.4

0.6

0.8

CD8

CD4

Den

sitie

s HIV

(a)

0 50 100

(b)

CD8

CD4

HIV

Days

0 50 100

CD8

CD4

HIV

(c)

0 50 100

(d)

HIV

CD8

CD4

Asymptomatic

Phase

0 1000 2000 3000 4000 5000 6000 7000

0.0

0.2

0.4

0.6

0.8

HIV

CD8

CD4

M=16 (e)

Days

0.0

0.2

0.4

0.6

0.8 M=8 (d)

0.0

0.2

0.4

0.6

0.8

HIV

CD8

CD4M=4 (c)

Densi

ties

0.0

0.2

0.4

0.6

0.8 (b)M=2

0.0

0.2

0.4

0.6

0.8

HIV

CD8

M=1 (a)

CD4

Effects of Diversity

of virus mutation

16

8

4

2

0

0 3 6 9 12 15

0

20

40

60

80P

ropo

rtio

n de

velo

ping

AID

S(%

)

Clinical data

mv=4.5*10-5

mv=5.5*10-5

mv=6.5*10-5

Years

AIDS phase

Our simulation result is in good agreement with the clinical data from

literature CASCADE Collaboration, Lancet 355 (2000) 1131

Conclusions1. 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.

Thank you