Optimisation of the immune response

Graham MedleyEcology & Epidemiology

groupWarwick, 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

dsesPaM saa

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

0

5

10

15

20

25

30

0 6-

10

21-

30

41-

50

61-

70

>80

0

5

10

15

20

25

30

0 6-

10

21-

30

41-

50

61-

70

>80

Natural Exposure: Duration

0

5

10

15

20

25

30

0 6-

10

21-

30

41-

50

61-

70

>80

0

5

10

15

20

25

30

0 6-

10

21-

30

41-

50

61-

70

>80

Maternal Exposure

0

2

4

6

8

10

12

14

0 - 10 - 20 - 30 - 40 - 50 - 60

0

2

4

6

8

10

12

14

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– Immigration-death

process• Parasites do not

reproduce within the host

– Immigration & death rates of parasite depend on level of immunity

pp

peep II 33

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

pRI

1

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

wagIRm

spg

gs

waggIRg

max

10 1

)1(

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

daamasV0

)()(

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,

0 0.5 11

2

3

4

5

Rep

ro. V

alu

e

0 10 20 300

10

20

30

40

50

Age

Par

asit

es, p

0 10 20 300

0.2

0.4

0.6

0.8

1

Age

Siz

e, g

0 10 20 300

0.2

0.4

0.6

0.8

1

Age

Su

rviv

al, s

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 50 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Immigration,

o

pt

0 50 1000

2

4

6

8

10

12

Immigration,

po

pt

Dependence on resources

0 1 2 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Resource, R

o

pt

0 1 2 30

5

10

15

20

25

30

35

40

45

50

Resource, R

po

pt

Medley, G.F. (2002) Parasitology 125 (7), S61-S70

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

0 5 10 15 20 25 300

5

10

15

20

25

30

35

40

45

50Effect of Resources R

Age

Par

asit

e B

urd

en

R=0.5,1,1.5,2

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5Effect of Resources R

Age

(a

) op

t

R=0.5,1,1.5,2

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4Effect of Immigration

Age

=5,25,50,100

Age-Related RV

0 5 10 15 20 25 300

2

4

6

8

10

12Effect of Immigration

Age

Rep

ro. V

al.

=5,25,50,100

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80Effect of Immigration

Age

Par

asit

e B

urd

en, p

=5,25,50,100

0 5 10 150

2

4

6

8

10

12

14Effect of Immigration

Age

Par

asit

e B

urd

en, p

=5,25,50,100

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.haematobiumBMC Infectious Diseases 2006, 6:96

Peak Shift

20 30 40 50 60 70 80 90 100 1101

1.5

2

2.5

3

3.5

4

4.5

5

5.5

Immigration,

Ag

e at

Max

imu

m (

a<

15 )

20 30 40 50 60 70 80 90 100 1107

8

9

10

11

12

13

14

Immigration,

Max

imu

m p

( a

<15

)

1 1.5 2 2.5 3 3.5 4 4.5 5 5.57

8

9

10

11

12

13

14

Age at Maximum p

Max

imum

p (

a<15

)

0 200 400 6000

50

100

150

Parasite burden, p

Fre

qu

en

cy

0 20 40 60 800.6

0.8

1

1.2

1.4

Mean Parasite Burden

k

100

102

0

0.2

0.4

0.6

0.8

1

p

g

0 0.5 110

0

101

102

103

g

p

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

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15

2.5

10

20

30

40

5070 60

Years since infection

Proportion surviving

Survival against age at HIV seroconversion

Time from HIV-1 seroconversion to AIDS and death before widespread use of highly-active anti-retroviral therapy A collaborative re-analysis. Cascade Collaboration. Lancet 2001:355 11311137

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 immuno-modulation 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