Does immunodominance maintain the diversity of the common cold?

William KoppelmanUniversity of UtahMaster’s Oral Examination

Outline

Biological background Mathematical model Analysis/Simulations Results Conclusions

Biological Background

Rhinovirus characteristics Mutation Cross-reactivity Immunodominance

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

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

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)

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.

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

Mathematical Model

Discrete Stochastic Multiple Strain SIRS dynamics

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)

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.

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

23.175.4

75.31)( 2

Xim

Xim

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

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

Analysis of continuous equivalent

RIdt

dR

N

SI

dt

dI

SNN

IS

dt

dS

)(

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

1*i

Endemic analysis Strain remains endemic if R0>1 Using estimated parameters from discrete

model Human birth rate is O(10-4)

0R

12.0

10.0

210 O

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

*****2

5,4,3,2

1

1

,,,,

0

0

0,,0,0,

ddhhh

dh

ISRISE

NNE

Simulations (Infection)

Simulations (Immunity)

Simulations (Prev. & Div.)

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.

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

Thanks

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