1. Does immunodominance maintain the diversity of the common cold? William Koppelman University of Utah Master’s Oral Examination

2. Outline  Biological background  Mathematical model  Analysis/Simulations  Results  Conclusions

3. Biological Background  Rhinovirus characteristics  Mutation  Cross-reactivity  Immunodominance

4. 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

5. 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

6. 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)

7. 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.

8. 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. AntigensImmune Response Primary ExposureAa Secondary ExposureA’a

9. Mathematical Model  Discrete  Stochastic  Multiple Strain  SIRS dynamics

10. 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)

11. Model Components cont.  Mutation is a distance in the genetic domain.  Strains differ by ~10% or 800 sites  From derived mutation rate => ~50 infections to produce new serotype  Therefore, a mutation distance of 1/50 per infection is reasonable for the domain.

12. 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

13. 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

14. 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 host’s immunity history

15. 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

16. Endemic analysis  Strain remains endemic if R 0 >1  Using estimated parameters from discrete model  Human birth rate is O(10 -4 )

17. 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

18. Simulations (Infection)

19. Simulations (Immunity)

20. Simulations (Prev. & Div.)

21. 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.

22. 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

23. Thanks  Dr. Adler  Drs. Keener & Coley  Dr. Guy  Brynja Kohler  John Zobitz  Dr. Sherry