Does immunodominance maintain the diversity of the common cold?

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Does immunodominance maintain the diversity of
the common cold?

• William Koppelman
• University of Utah
• Masters Oral Examination

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Outline

• Biological background
• Mathematical model
• Analysis/Simulations
• Results
• Conclusions

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Biological Background

• Rhinovirus characteristics
• Mutation
• Cross-reactivity
• Immunodominance

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Human Rhinovirus (HRV)

• Co-circulation of over 100 strains
• Cause 50 of common colds
• Limited to high level primates
• Adults average 2-3 colds per year
• Able to survive outside host for up to 3 days

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HRV cont.

• Sufficient dose is 1-30 particles of the virus
• Attaches to ICAM-1 receptor of nasal cells
• Replication of the virus and rupture of the host
  cell leads to infection of other nasal cells
• Incubation period of 8-12 hours

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HRV Mutation

• RNA virus (typically have high mutation rates
• Predicted to have 0.67 mutations per genome per
  replication
• 21 replications/infection 14 mutations per
  infection
• Suggested that new serotype created in 2 to 4
  years from mutation (Stott Walker, 1969)

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HRV Cross-Reactivity

• Cross-reactivity is the ability of B and T cells
  to react with an epitope on the antigen that they
  are not designated for.
• A single HRV serotype is, on average, related to
  3.75 other serotypes (Cooney et al., 1975).
• Therefore, related serotypes may elicit similar
  immune responses.

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HRV Immunodominance

• A process in which the immune response focuses on
  only a few of the many potential epitopes.
• Original antigenic sin is a process in which the
  sequence a host encounters antigenic variants
  influences the specificity of the immune response.

Antigens Immune Response
Primary Exposure A a
Secondary Exposure A a
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Mathematical Model

• Discrete
• Stochastic
• Multiple Strain
• SIRS dynamics

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Model Components

• HRV strains exist in a 2-D genetic space.
• Domain is a 10 x 10 grid with periodic boundaries
• Each 1 x 1 square represents a strain (i.e. 100
  strains)

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Model Components cont.

• Mutation is a distance in the genetic domain.
• Strains differ by 10 or 800 sites
• From derived mutation rate gt 50 infections to
  produce new serotype
• Therefore, a mutation distance of 1/50 per
  infection is reasonable for the domain.

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Model Components cont.

• Serotypes will cross-react with related serotypes
• This corresponds to an area around a particular
  strain in the genetic domain
• Equivalent to a circle (radius Xim) not including
  the original serotype

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Model Components cont.

• Immunodominance will affect the transmission of
  HRV
• The function of transmission will be related to
  the amount of variance from strains previously
  seen by the immune system
• Step function is simplest, realistic form

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Model components cont.

• Sub-population of environmental surfaces obey SIS
  dynamics
• Stochastic elements
• Random contact (uniform)
• Random mutation (normal)
• Random recovery time (log-normal)
• Random birth death (uniform)
• Transmitting antigen compared against hosts
  immunity history

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Analysis of continuous equivalent

• Continuous time, single strain, SIR model with
  births/deaths (constant pop.)
• Assuming the birth rate is much smaller than the
  recovery rate then i is the equilibrium
  prevalence

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Endemic analysis

• Strain remains endemic if R0gt1
• Using estimated parameters from discrete model
• Human birth rate is O(10-4)

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Sub-population analysis

• Model with hosts following SIR dynamics and
  surfaces following SIS dynamics
• System has two equilibria with the trivial
  solution never being unstable

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Simulations (Infection)
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Simulations (Immunity)
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Simulations (Prev. Div.)
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Results

• In order to consider mechanisms influencing
  serotype diversity, the virus must be endemic in
  hosts
• Different functions of transmission should lead
  to endemic by increasing virus dynamics within
  cross-reactivity distance.

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Conclusions

• Virus must be endemic to analyze diversity
• Serotype interactions are crucial to virus
  remaining endemic
• Once endemic, the diversity of serotypes will
  evolve through serotype interactions
• Serotype interactions are governed by
  immunodominance

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Thanks

• Dr. Adler
• Drs. Keener Coley
• Dr. Guy
• Brynja Kohler
• John Zobitz
• Dr. Sherry