Download HIV infection

A Stochastic HIV Dynamics
Jianwei Shuai (帅建伟), Hai Lin (林海)
Physics Department
Xiamen University
Contents

Immune system

HIV infection

Modeling HIV dynamics - previous works

Modeling HIV dynamics - Our work
(A)

Immune system

HIV infection

Modeling HIV dynamics - previous works

Modeling HIV dynamics - Our work
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.
virus
(2) Innate immune
system
(1)
Skin
Mucosa
(3) Specific immune
antigen
Clear the antigen
antibody
system
B cell
T cell
B cell and 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.
Receptor
B cell
epitope
antibody
Function of B cell
antibody
epitope
crophag
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
Function of T cells
CD4 T
virus
Host cell
CD8 T
Why is it called “specific” immune system?
Virus
B/T Cell
 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 .
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.
Clonal selection produces two types of immune cells
 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
Effector
Memory
Viral escapes the immune memory
Viruses can escape the
immune memory by
genetic mutation.
Genetic mutation
Antigen change
Recognition failure
(B)

Immune system

HIV infection

Modeling HIV dynamics - previous works

Modeling HIV dynamics - Our work
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 Montagnier
and
Francoise Barre-Sinoussi
HIV Structure
Glycoprotein
Epitope
0.1 um
RND-based virus
HIV infects CD4 T-cell
Glycoprotein
1.
2.
HIV
3.
4.
5.
6.
CD4 T-cell
7.
8.
9.
Free virus
Bind to CD4 T-cell
Inject RNA into the cell
Reverse transcript RNA to
DNA
Integrate DNA into cell’s
genome.
Transcription
Assembly
Budding
Maturation
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.
Proportion developing AIDS(%)
The proportion developing AIDS from infection
Clinical data
60
40
20
0
0
3
6
9
Years
Lancet 355 (2000) 1131
12
15
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.
(C)

Immune system

HIV infection

Modeling HIV dynamics - previous works

Modeling HIV dynamics - Our work
Phillips, Science 271 (1996) 497

T-cell

b

p
Lat T*
1 p


Act T*
Health T cells
Latently Infected T cells
Actively infected T-cells
Virus


Virus

dR
   R  b RV
dt
dL
 pbRV  L  L
dt
dE
 (1  p) bRV  L  E
dt
dV
 E  V
dt
Latent
Active
Health
Nowak, May, Anderson. AIDS 4 (1990) 1095
Virus
Specific immune
response
Common immune
response
Virus mutation
dvi
 rvi  pxi vi  szvi  M (v )
dt
dxi
 kvi  uvxi
v   vi
dt
i
dz
 k v  uvz
dt
M (v)  bQvt
TC
T1
V1
Ti
Vi
V1
T1
Vi
Ti
1.4
1.2
1.2
1.0
virus / density of lymphocytes
virus / densit of lymphocutes
Simulation Results
Immune cell
1.0
0.8
0.6
0.4
Virus
0.2
0.0
0
2
4
6
time in years
Virus mutation rate 2
Immune cell
Lymphocytes specific to HIV
0.8
0.6
0.4
0.2
Virus
0.0
0
2
4
6
8
time in years
Virus mutation rate 1.75
10
Santos and Coutinho, Phys. Rev. Lett. 87 (2001) 168102
Cellular automata HIV model
Each cell has four states: (a) health cell;
(c) AIDS cell;
(b) infected 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.
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
 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.
Antigen
HIV
0
0
0
0
V0
0
0
0
di 0  1
HIV
0
0
0
1
0
0
0
Vi
0
0
0
0
HIV Dynamics
Virus Mutation
Cross killing of virus by T-cells
dvi
 ri vi  mNAvi  mi  c1 f i (x)vi ,(1)
dt
dxi
v
  ( i  xi )  c3 gi (x) xi ,
(2)
dt
v
Virus recognization Cross inhibition among different types of T-cells.
i   j 0 (v( j ,aN 1 ,
A
, a1 )
v( aN ，, j ,
, a1 )

 v( aN ,aN 1 ,..., j ) )  Nvi
fi (x)  yi (x) / [c2  yi (x)]
V0
T0
gi (x)   i  j x j k ji  yi (x)  xi
yi (x)   j 0 x j k ji   j 0 x j exp(b d ji )
I 1
I 1
Ti
Vi
The three-phase pattern of HIV infection in the model
700
Plasma HIV-1 titer
600
v(t)
500
400
300
200
100
0
0
2
4
6
weeks
8
10
12 1
2
3
4
5
6
years
7
8
9
10
(c)
(D)

Immune system

HIV infection

Modeling HIV dynamics - previous works

Modeling HIV dynamics - Our work
New Journal of Physics 12 (2010) 043051 1-18
A stochastic spatial model of HIV dynamics
New Journal of Physics 12 (2010) 043051 1-18

Viruses, CD8 T-cells, and CD4 Tcells are arranged on the lattices.

CD4
One lattice can only locate one
individual of the same type.

HIV
Different types of individuals can
occupy the same site at the same
CD8
time.
HIV infecting and immune responding networks
Release
Uninfected
CD4 T-cell
Virus (V)
Infected CD4
T-cell
Kill
Help
Stimulate
Stimulate
Antibody
Kill
Proliferate
Release
B cell
CD8 T-cell
Binary string T-cells and virus
CD4 1000111000
CD8 0100100011
HIV 1100100011

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.
Densities
Three-phase dynamics
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
(a)
Example 1
HIV
CD4
CD8
(b)
Example 2
(c)
Example 3
(d)
Averaged result
0
5 10 15
Weeks
4
8
12
Years
16
20
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
(a)
(b)
0.8
(c)
(d)
CD4
CD4
CD4
Densities
0.6
HIV
0.4
HIV
CD4
CD8
CD8
0.2
HIV
CD8
0.0
0
50
HIV
CD8
100
0
50
100
0
Days
50
100
0
50
100
(a)
M=1
0.8
CD4
0.6
Asymptomatic
0
CD8
0.4
0.2
HIV
0.0
Phase
(b)
M=2
0.8
0.6
2
0.4
0.2
0.0
(c)
M=4
0.8
CD4
Effects of Diversity
of virus mutation
Densities
0.6
4
0.4
0.2
CD8
0.0
HIV
(d)
M=8
0.8
0.6
8
0.4
0.2
0.0
(e)
M=16
0.8
HIV
0.6
16
0.4
CD4
0.2
CD8
0.0
0
1000
2000
3000
4000
Days
5000
6000
7000
Proportion developing AIDS(%)
AIDS phase
80
Clinical data
-5
mv=4.5*10
60
mv=5.5*10
-5
mv=6.5*10
-5
40
20
0
0
3
6
9
12
15
Years

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.
Thank you