Conformon-P systems
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Transcript 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
X
Z
1
Y
2
W
3
Z
Image downloaded on the 24/7/2007 from
http://www.enchantedlearning.com/subjects/animals/cell/anatomy.GIF
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Conformon-P systems
X
Z
1
Y
2
W
3
Z
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;
• ...