Download Does immunodominance maintain the diversity of the common cold?

Does immunodominance
maintain the diversity of the
common cold?
William Koppelman
University of Utah
Master’s Oral Examination
Outline
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Biological background
Mathematical model
Analysis/Simulations
Results
Conclusions
Biological Background
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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
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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
  ( Xim) 2  1  3.75
 Xim 
4.75

 1.23
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
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Random
Random
Random
Random
contact (uniform)
mutation (normal)
recovery time (log-normal)
birth death (uniform)
 Transmitting antigen compared
against host’s immunity history
Analysis of continuous equivalent
IS
 dS
 dt   N   ( N  S )

 dI
 S

   
  I
 N

 dt
 dR
 I  R

 dt
 
i  1  
  
*
 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
Endemic analysis
 Strain remains endemic if R0>1
 Using estimated parameters from discrete
model
 Human birth rate is O(10-4)
R0 

 
  0.10
2
   O10 
  0.12
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
E1  N h ,0,0, N d ,0
1  0
2,3, 4,5  0

E2  S h* , I h* , Rh* , S d* , I d*

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 crossreactivity 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
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Dr. Adler
Drs. Keener & Coley
Dr. Guy
Brynja Kohler
John Zobitz
Dr. Sherry