Optimisation of the
immune response
Graham Medley
Ecology & Epidemiology group
Warwick, UK
Age-dependant Intensity
Macroparasite Immunity Models
• Immune response is a function of history of
exposure
– Memory, M(a)
– Immunity is a non-linear, increasing function of
M(a)
• But why?
– If it takes hours to respond to a virus, why does
it take years to respond to macroparasites?
– Hosts should be more concerned with present &
future than past
a
M a  ~  Ps e  a  s ds
0
Also applies to other chronic
infections, e.g. malaria.
As intensity of transmission
(immigration rate)
increases:
>> the overall intensity of
infection increases
>> the age at peak intensity
decreases
>> there is a “change” at
sexual maturity
Lusingu et al. , Malaria Journal 2004, 3:26
What is the Immune System for?
• Hosts use their IS to maximise survival and
reproduction
– Possibly tautological, but true
– The IS does not have the sole aim of killing parasites
• IS is constrained by other physiology
• Persistence of infection does not immediately
imply parasite cunning or immunity failure
• Generate questions about the functions of
immunity
– and therefore the mechanisms that might be expected
Constraints to Immunity
• IS is expensive in terms of limited
resources (energy & protein)
– Other processes that enhance “fitness”
• E.g. growth & reproduction
– Many physiological processes
constrained by “minimum energy” or
“minimum protein”
• IS is dangerous
– Autoimmune disease
• Hosts may choose to devote
resources to things other than
immunity
– especially if infection is rarely
immediately lethal and continuous
(macroparasites)
– not if infection will be lethal if
uncontrolled (viruses)
Immunopathology
• For many infections, the immune response
“causes” the disease
– Respiratory syncytial virus
• Eosinophilia creates the clinical disease
• Ablate eosinophilia & mice die without symptoms
– Schistosomiasis
• Circulatory failure due to granuloma formation around
eggs embedded in liver
– Ascaris suum
• Single large dose leads to explusion
• Same dose trickled leads to establishment & little
pathology
Adaptive Immunity
• Adaptive to overcome pathogen adaptation
– Adaptive to host requirements: protein & energy
• Also adaptive to survival / reproduction context
– Nutrition (resources)
• Malnourished hosts experience more disease
– Gender & Social Status
• Males & females do not have same priorities
• Hormonal influence (effect of testosterone)
– Age
• Priorities change
• Immuno-modulation of parasite burden
Trickle Exposure:  Dose
30
25
20
15
10
5
30
0
0
6-
21-
41-
61-
10
30
50
70
>80
25
20
15
10
5
0
0
6-
21-
41-
61-
10
30
50
70
>80
Natural Exposure:  Duration
30
25
20
15
10
5
30
0
0
6-
21-
41-
61-
10
30
50
70
>80
25
20
15
10
5
0
0
6-
21-
41-
61-
10
30
50
70
>80
Maternal Exposure
14
12
10
8
6
4
14
2
12
0
0
-10
-20
-30
-40
-50
-60
10
8
6
4
2
0
0
-10
-20
-30
-40
-50
-60
Adaptive Immunity
• Exposure modulates infection so that
prevalence increases and maximum burdens
decrease
– Variability is decreased
• Immune system is the modulator
• Exposure results in “shuffling” of individual
burdens within a group of hosts
– No expulsion
Model of Resource Allocation
• How should hosts devote resources
between immunity and other
functions as they age?
• Simple model of infection, immunity
and fitness
• Single host over age
• Constrained optimisation problem
Macroparasites
• Within-host
parasite population,
p
p    p
– Immigration-death
process
• Parasites do not
reproduce within the
host
– Immigration &
death rates of
parasite depend on
level of immunity
p  e
3 I
 e p
3I
Simple Model : Immunity
• Resource input is constant: R
• Partitioned into immunity (I), growth &
reproduction
• Resources devoted to immunity are
dependent on
– parasite population
– individual host dependent parameter, (a)
p
I  R
1 p
Simple Model : Host
• Fixed age at maturity, w
• Investment in growth during immaturity to increase
size, g
• Survival to any age is dependent on relative size and
current parasite burden determine survival, s
• Reproduction is dependent on size and resources
available
g  R  I g (1  g )
aw


g
s   0  1  1 
 g max

m  R  I g a  w


  p  s


Reproductive Value, RV
• Maximum age, L
• Expected future reproductive success
– survival is related to size and parasite burden
– reproductive effort is related to size and resources (not
used for parasite resistance)
• Maximise fitness as a trade-off between
– reducing parasites now
• less likely to die
– and growing to be bigger
• less likely to die in the future & reproduce more
L
V   s (a)m(a)da
0
Model Structure
• Differential equations
– Three equations ( g, p, s )
– Solved & maximised numerically
• IBM stochastic simulations
• Unscaled
– Redundancy: pathogenicity ~ immigration
– Quantitatively meaningless
Optimisation Problem
• Aim is to optimise the host fitness by
varying proportion of resources
devoted to immunity, (a)
• Initially assume  constant
throughout life
– RV at birth maximised
Effect of control parameter, 
50
40
4
Parasites, p
Repro. Value
5
3
2
20
10
1
0
0.5
0
0
1

1
1
0.8
0.8
0.6
0.4
0.2
0
0
10
20
30
20
30
Age
Survival, s
Size, g
30
0.6
0.4
0.2
10
20
Age
30
0
0
10
Age
Immunity is always “sub-optimal”
• Reproductive value is optimised at when
resources devoted to immunity are
intermediate
– There is an “optimal” parasite burden
• Given continuous (constant) immigration and constant
resources
• Optimised values change with conditions
– Changing immigration & resource level…
Dependence on 
0.35
12
0.3
10
0.25
8
opt
p
 opt
0.2
6
0.15
4
0.1
2
0.05
0
0
50
Immigration, 
100
0
0
50
Immigration, 
100
Dependence on resources
0.35
50
45
0.3
40
0.25
35
30
opt
p
 opt
0.2
0.15
25
20
15
0.1
10
0.05
5
0
0
1
2
Resource, R
3
Medley, G.F. (2002) Parasitology 125 (7), S61-S70
0
0
1
2
Resource, R
3
Age-related immunity
• Allow (a)
– Linear segments
– RV calculated throughout life
• Amounts to maximising at each age
• “Dynamic programming” approach: each (a)
depends on the others
• All other parameters (R, ) constant
with age
Effect of Resources R
50
45
40
Parasite Burden
35
30
25
20
15
10
5
0
0
R=0.5,1,1.5,2
5
10
15
Age
20
25
30
Effect of Resources R
0.5
0.45
0.4
0.35
 (a)opt
0.3
0.25
0.2
0.15
0.1
0.05
0
0
R=0.5,1,1.5,2
5
10
15
Age
20
25
30
Effect of Immigration 
0.4
0.35
0.3

0.25
0.2
0.15
0.1
0.05
0
0
=5,25,50,100
5
10
15
Age
20
25
30
Age-Related RV
Effect of Immigration 
12
10
Repro. Val.
8
6
4
2
0
0
=5,25,50,100
5
10
15
Age
20
25
30
Effect of Immigration 
80
70
Parasite Burden, p
60
50
40
30
20
10
0
0
=5,25,50,100
5
10
15
Age
20
25
30
Effect of Immigration 
14
12
Parasite Burden, p
10
8
6
4
2
0
0
5
10
Age
=5,25,50,100
15
Age-dependant Intensity
Results
• Maximum age span (30)
– Immunity reduced as death approaches
– No value in compromising reproduction for
survival
• Reproductive maturity
– Big change in immunity
• Emphasise growth during immaturity
• Emphasise survival in maturity
– Optimal strategy is to increase risk of death in
order to be “fitter” when older
Mutapi et al. – S.haematobium
BMC Infectious Diseases 2006, 6:96
Peak Shift
14
13
Maximum p ( a<15 )
12
14
11
10
13
9
7
20
30
40
50
60
70
Immigration, 
80
90
100
110
5.5
Maximum p ( a<15 )
12
8
11
10
9
5
Age at Maximum ( a<15 )
4.5
8
4
3.5
7
1
3
2.5
2
1.5
1
20
30
40
50
60
70
Immigration, 
80
90
100
110
1.5
2
2.5
3
3.5
4
Age at Maximum p
4.5
5
5.5
1.4
1.2
100
k
Frequency
150
50
0
0
1
0.8
200
400
Parasite burden, p
0.6
0
600
20
40
60
Mean Parasite Burden
80
0.5
g
1
3
1
10
0.8
2
10
g
p
0.6
0.4
1
10
0.2
0
0 0
10
2
10
p
10
0
500 hosts with uniform random R,  and β; (constant )
Conclusions
• IR in host context
– Reproduces observed phenomena:
•
•
•
•
Age-related intensity
Peak shift
Heterogeneity
Predisposition
Speculations
• What we can expect the IS to do
– Dynamic
• Mechanisms for continual monitoring of damage,
changes in parasite population size, physiological state
• Effectiveness (e.g. B-cell affinity maturation)
– Defined by host context (age, nutrition etc)
• Mechanisms for interaction with remainder of
physiology
• Molecules that operate in both, e.g. leptin
– Learning
• Adaptive immunity is a sensory system
– Controls innate immunity
– Determines immune response in context, e.g.
effects of age vs HLA in HIV
Proportion surviving
Survival against age at HIV seroconversion
1.0
0.8
2.5
0.6
10
0.4
20
0.2
40
30
70
0.0
0
5
60
10
Years since infection
50
15
Time from HIV-1 seroconversion to AIDS and death before widespread use of highly-active antiretroviral therapy A collaborative re-analysis. Cascade Collaboration. Lancet 2001:355 11311137
Is Death a Failure?
• Death does not immediately imply immune system
failure
– Risking death to be bigger
• Apoptosis
– Cell death to kill intracellular parasites
– Do eusocial insects die to kill their parasites & protect
their sisters?
• Since infection transmits least some immunomodulation is not optimal for individual
– Hand-waving arguments involving inclusive fitness
Individuals  Populations
• Infection rate depends on sum of individual
parasite burdens
• Resources are limiting
– Competition for resources: dependent on size?
• Dynamic game
– Individual strategies determine others (and
own) conditions
• Real time optimisation of individual IR
– High “discount rate” (e.g. random death) will
emphasise current immunity
• Immuno-ecology