David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

Conformon-P systems X Y Z Z W Image downloaded on the 24/7/2007 from

Conformon-P systems X Y Z Z W Image downloaded on the 24/7/2007 from

[ G, 9 ] [ R, 9 ][ G, 5 ] Conformon-P systems: conformons

[ G, 2 ]  r [ R, 12 ] interaction rule: r : G  R 3 [ G, 5 ] [ R, 9 ] Conformon-P systems: interaction

Conformon-P systems: example

Conformon-P systems: module A group of membranes with conformons and interaction rules in a conformon-P system able to perform a specific task. Module: [R, 2] [G, 3] [R, 0] 1 2

Conformon-P systems: modules [A,  ] only conformon [A,  ],   N can pass from membrane 1 to membrane A (  )  B (  )  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)  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. 3    [A, 5] [B, 7] [A, 3] [B, 4] [A, 5] [B, 4]

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

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

Cellular automata Rule

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

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. first weekslater years 12 3 H H I I I D D Healthy Infected Dead

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

David CornePierluigi Frisco School of Mathematical and Computer Sciences Heriot-Watt University Edinburgh Workshop on Membrane Computing June 2007, Thessaloniki (Greece) Dynamics of HIV infection studied with cellular automata and conformon-P systems

Studied with R. M. Z. Dos Santos and S. Coutinho. Dynamics of HIV infection: a cellular automata approach. Physical review letters, 87(16): , 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 at least one A-infected neighbour, then it becomes infected. 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 p repl. Each newly introduced healthy may be replaced by an A-infected cell with probability p infec.

Studied with conformon-P systems Healthy: A-infected: AA-infected: Pre-dead: Dead: [R, 1] [V, 10] [E, 0] [W, 0]  copies [H, 1] [A, 0] [AA, 0] [PD, 0] [D, 0] [H, 0] [A, 1] [AA, 0] [PD, 0] [D, 0] [H, 0] [A, 0] [AA, 1] [PD, 0] [D, 0] [H, 0] [A, 0] [AA, 0] [PD, 1] [D, 0] [H, 0] [A, 0] [AA, 0] [PD, 0] [D, 1]

Studied with conformon-P systems [H, 0] [A, 1] [AA, 0] [PD, 0] [D, 0] [R, 1] [V, 10] [E, 0] [W, 0]  copies if a cell is A-infected, then it can generate [V, 11] R (1)  A (1) 1 A (2)  V (10) 1 [A, 2] [R, 0] [A, 1] [V, 11]

Studied with conformon-P systems [H, 1] [A, 0] [AA, 0] [PD, 0] [D, 0] [R, 1] [V, 10] [E, 0] [W, 0]  copies an healthy cell can become A-infected if it contains a virus [V, 11] V (11)  H (1) H (12)  A (0) A (12)  W (0) [V, 0] [H, 12][H, 0] [A, 12][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 AA- infected. An AA-infected cell can become pre- dead. 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 p repl. Each newly introduced healthy may be replaced by an A-infected cell with probability p infec.

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 AA- infected. An AA-infected cell can become pre- dead. 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 AA- infected. An AA-infected cell can become pre- dead. 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 conformon-P systems grid neighbourhoods p HIV p infec 400x400 torus50x50 torus 3 kinds 0.05, , , , 1

Results: qualitative agreement cellular automata conformon-P systems first weeks later years

Tests cellular automata conformon-P systems grid neighbourhoods p HIV p infec 400x400 torus50x50 torus 3 kinds 0.05, , , , 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 state- change 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;...

Thank you