HIV dynamics in sequence space

1
HIV dynamics in sequence space

• Shiwu Zhang
• Based on Kamp2002from, Kamp2002co-evolution

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Issues on HIV dynamics

• HIV infection in patient
• HIV development stages. Santos2001,
  Hershberg2000, AAMAS-HIVreport
• Factors influence (mutation rate, antigenic
  diversity)
• Distribution of HIV latency period Kamp2002from,
  Kamp2002co-evolution
• HIV epidemic
• Spreading on social network Dezso2002,
  Satorras2001

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Background Percolation theory

• Occupation probability (Susceptibility)
• Clusters
• Spanning probability (transmissibility)
• Percolation threshold (Pc)

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Background Sequence space

• Viral genome immune receptor length l
• Viral mutation change one bit (1,2, ?)
• Constructing a sequence space, size ? l
• Viral mutation means random walk in space
• Dimension l

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Model

• Site status
• Susceptible S(t)
• Site can harbor a virus
• Infected ?v(t)
• Site is infected by virus
• Recovered R(t)
• After immune response (immune memory)
• Viral genome is not arbitrary (D0)
• Immunological presence (?0)

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Model (2)

• Rules
• Random select site
• If the site harbor immune receptor
• Mutate with certain probability
• If mutate and the mutant match an infected site
  then set the infected site to recovered
• If the site is infected
• Mutate with certain probability
• If a new strain is generated and corresponds to a
  susceptible site, the site become infected
• For HIV, another rule
• Viral strain has probability ?is(t) to meet an
  receptor infect it with probability p

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Result

• Simulation result could capture HIV population
  dynamics from clinical latency stage to onset on
  AIDS, but fail to reflect initial immune response
• Initial distribution ?0 is important factor to
  affect result
• Increasing probability p will shorten waiting
  time
• Distribution of HIV incubation period
  distribution from simulation fits in well with
  that from real data

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Summary

• Characteristics
• Sequence space
• Percolation theory
• Accounting for important interactions
• HIV mutation
• Immune cells stimulation
• Immune systems global abilitymemory
• Shortage
• Omitting physical space
• Using strain denote population (without strain
  size distribution)
• Dont account for initial response

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Related Papers

• C. Kamp, S. Bornholdt (2002). From HIV infection
  to AIDS A dynamically induced percolation
  transition?, Proc. R. Soc. London B (2002),
  accepted for publication. http//arxiv.org/abs/con
  d-mat/0201482
• C. Kamp, S. Bornholdt (2002). Co-evolution of
  quasispecies B-cell mutation rates maximize
  viral error catastrophes, Phys. Rev. Lett. 88,
  068104. http//www.tp.umu.se/kim/Network/Marek/se
  m.pdf
• D. Stauffer, A. Aharony (1992). Introduction to
  Percolation Theory, (Taylor and Francis, London).
  
• H. Mannion et al. (2000). A Monte Carlo Approach
  to Population Dynamics of Cell in an HIV Immune
  Response Model. Theory in Bioscience 119(94)
• U. Hershberg et al.(2001). HIV time hierarchy
  Winning the war while losing all the battles.
  Physica A289 (1-2). http//arxiv.org/abs/nlin.AO/
  0006023