Download Conformon-P systems

Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Conformon-P systems
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Image downloaded on the 24/7/2007 from
http://www.enchantedlearning.com/subjects/animals/cell/anatomy.GIF
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Conformon-P systems
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Image downloaded on the 24/7/2007 from
http://www.enchantedlearning.com/subjects/animals/cell/anatomy.GIF
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Conformon-P systems: conformons
[ G, 5 ]
[ R, 9 ]
[ G, 9 ]
Conformon-P systems: interaction
3
r: G  R
interaction rule:
[ G, 5 ]
[ G, 2 ]
r
[ R, 9 ]
[ R, 12 ]
Conformon-P systems: example
Conformon-P systems: module
Module: A group of membranes with conformons and
interaction rules in a conformon-P system able
to perform a specific task.
1
[G, 3]
[R, 0]
[R, 2]
2
Conformon-P systems: modules
1
[A, ]
A()

 B()
2
only conformon [A, ],   N
can pass from membrane 1
to membrane 2.
a conformon with name A can
interact with B passing  only if the
value of A and B before the
interaction is  and  respectively,
, ,   N.
Conformon-P systems: modules



A(5)
3
 B(4)
[A, 5]
[B, 7]
[A, 3]
[B, 4]
[A, 5]
[B, 4]
a conformon with name A can
interact with B passing 3 only if the
value of A and B before the
interaction is 5 and 4 respectively.
Conformon-P systems: probabilities
When a simulation of a conformon-P system is performed,
then probabilities are associated to
interaction and passage rules.
Grid of conformon-P systems
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Cellular automata
Rule
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Dynamics of HIV infection
1. the amount of virus in the host grows in exponential way;
2. the viral load drops to a “set point”;
3. the amount of virus in the host increases slowly,
accelerating near the onset of AIDS.
H
I
H
I
Healthy
Infected
Dead
D
I
D
1
2
first weeks
3
later years
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Dynamics of HIV infection studied with
cellular automata and conformon-P systems
David Corne
Pierluigi Frisco
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh
Workshop on Membrane Computing 25-28 June 2007, Thessaloniki (Greece)
Studied with
R. M. Z. Dos Santos and S. Coutinho. Dynamics of HIV infection: a cellular
automata approach. Physical review letters, 87(16): 168102, 2001.
If an healthy cell has at least one
A-infected neighbour, then it
becomes infected.
Healthy cell;
A-infected cell: infected cell free
to spread the infection;
AA-infected cell: final stage of an
infected cell before it dies due to
action of the immune system;
Dead cell: killed by the immune
response.
If an healthy cell has no A-infected
neighbours but at least 2 < R
< 8 AA-infected neighbours,
then it become A-infected.
An A-infected cell becomes
AA-infected after  time
steps.
AA-infected cells become dead cells.
Dead cells can become healthy with
probability prepl.
Each newly introduced healthy may
be replaced by an A-infected
cell with probability pinfec.
Studied with conformon-P systems
Healthy:
[H, 1]
[A, 0]
[AA, 0]
[PD, 0]
[D, 0]
A-infected:
[H, 0]
[A, 1]
[AA, 0]
[PD, 0]
[D, 0]
AA-infected:
[H, 0]
[A, 0]
[AA, 1]
[PD, 0]
[D, 0]
Pre-dead:
[H, 0]
[A, 0]
[AA, 0]
[PD, 1]
[D, 0]
Dead:
[H, 0]
[A, 0]
[AA, 0]
[PD, 0]
[D, 1]
[R, 1]
[V, 10]
[E, 0]
 copies
[W, 0]
Studied with conformon-P systems
if a cell is A-infected, then it can generate [V, 11]
<if a cell is A-infected, then it can generate a virus>
[H, 0]
[A, 1]
[R, 1]
[AA, 0]
[V, 10]
[PD, 0]
[E, 0]
[D, 0]
[W, 0]
 copies
1
R(1)  A(1)
1
A(2)  V(10)
[A, 2] [R, 0]
[A, 1] [V, 11]
Studied with conformon-P systems
an healthy cell can become A-infected if it contains a virus
[H, 1]
[A, 0]
[R, 1]
[AA, 0]
[V, 10]
[PD, 0]
[E, 0]
[D, 0]
[W, 0]
 copies
[V, 11]
V(11)
11
 H(1)
[V, 0] [H, 12]
H(12)
12
 A(0)
[H, 0] [A, 12]
A(12)
11
 W(0)
[A, 1] [W, 11]
Studied with conformon-P systems and cellular automata
If a cell is A-infected, then it can
generate a virus.
An healthy cell can become A-infected
if it contains a virus.
An AA-infected cell can generate [E, 1].
[E, 1] conformons can generate [E, 4].
An healthy cell can become A-infected
if it contains [E, 4].
An A-infected cell can become AAinfected.
An AA-infected cell can become predead.
A pre-dead cell removes viruses and E
conformons present in it.
A pre-dead cell can become a dead
cell.
If an healthy cell has at least one
A-infected neighbour, then it
becomes infected.
If an healthy cell has no A1-infected
neighbours but at least 2 < R
< 8 AA-infected neighbours,
then it become A-infected.
An A-infected cell becomes
AA-infected after  time
steps.
AA-infected cells become dead cells.
Dead cells can become healthy with
probability prepl.
Each newly introduced healthy may
be replaced by an A-infected
cell with probability pinfec.
Studied with: rules
If a cell is A-infected, then it can
generate a virus.
An healthy cell can become A-infected
if it contains a virus.
An AA-infected cell can generate [E, 1].
[E, 1] conformons can generate [E, 4].
An healthy cell can become A-infected
if it contains [E, 4].
An A-infected cell can become AAinfected.
An AA-infected cell can become predead.
A pre-dead cell removes viruses and E
conformons present in it.
A pre-dead cell can become a dead
cell.
Studied with: rules
If a cell is A-infected, then it can
generate a virus.
An healthy cell can become A-infected
if it contains a virus.
An AA-infected cell can generate [E, 1].
[E, 1] conformons can generate [E, 4].
An healthy cell can become A-infected
if it contains [E, 4].
An A-infected cell can become AAinfected.
An AA-infected cell can become predead.
A pre-dead cell removes viruses and E
conformons present in it.
A pre-dead cell can become a dead
cell.
Studied with: neighbourhood
[V, 11]
[E, 1]
[E, 2]
[E, 4]
Tests
cellular automata
grid
neighbourhoods
pHIV
pinfec
conformon-P systems
400x400 torus
50x50 torus
3 kinds
3 kinds
0.05,
0.00005
0.00001, 0.00005
0.05,
0.2,
0.0004
1
Results: qualitative agreement
cellular
automata
first weeks
conformon-P
systems
later years
Tests
cellular automata
grid
neighbourhoods
pHIV
pinfec
conformon-P systems
400x400 torus
50x50 torus
3 kinds
3 kinds
0.05,
0.00005
0.00001, 0.00005
0.05,
0.2,
0.0004
1
M. C. Strain and H. Levine. Comment on “Dynamics of HIV infection: a cellular
automata approach”. Physical review letters, 89(21):219805, 2002.
Results: overall

The conformon-P system model proved to be more robust to a
wide range of conditions and parameters, with more reproducible
qualitative agreement to the overall dynamics and to the
densities of healthy and infected cells observed in vivo.

The number of infected, healthy, and dead cells at the end of
the third phase is not in accordance with the observed
values.
About the rules
• rules are divided in two sets: part 1
and part 2;
• state-change rules and filling rules;
• the probabilities of the filling rules
are equal in the two sets;
• the probabilities of the statechange rules are smaller in part 2
Future work
• obtain a better fit of the curve;
• study the simulation on bigger grids;
• simulate the best cure the infection;
• ...