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