QUANTITATIVE LAWS June 13 -June 24

1. Emergence of elevated levels of
multiple infection in spatial host-
virus dynamics
Bradford Taylor1, Catherine Penington2, Joshua Weitz3,1
1School of Physics and 3School of Biology, Georgia Institute of Technology
2School of Mathematical Sciences, Queensland University of Technology
http://ecotheory.biology.gatech.edu
Quantitative Laws II

2. Multiple infection allows
intracellular interactions between
viruses
La Scola et al,
Nature (2008)
Coinfection alters ecological parameters

3. Multiple infections alter
evolutionary rates due to shared
resources
Recombination vs. Complementation

4. Multiple infection rates are
unknown in vivo

5. How does space affect:
 the distribution of multiplicity of
infection (MOI)?
RM Donlan,
Emerg infect dis, 2002

6. Adsorption mediates clustering
Low adsorption
High adsorption

7. Well-mixed model dynamics
Host
Infected
hosts
Viruses

8. Well-mixed model yields geometric
MOI distribution
Host
Infected
hosts
Viruses
Geometric distribution for MOI

9. MOI distribution follows geometric
distribution for low adsorption
Viruses
0
[1 5]
[6 10]
[11 15]
[16 20]
>20
Hosts
E
H
I1
C

10. Clustered MOI distributions feature
fat tails
Hosts
E
H
I1
C
Viruses
0
[1 5]
[6 10]
[11 15]
[16 20]
>20

11. How many viruses are colocated
with a host of a specific MOI?
MOI Layer (internal viruses) Viral Layer (external viruses)
11

12. How many viruses are colocated
with a host of a specific MOI?
MOI Layer (internal viruses) Viral Layer (external viruses)
12

13. How many viruses are colocated
with a host of a specific MOI?
MOI Layer (internal viruses) Viral Layer (external viruses)
1
13

14. How many viruses are colocated
with a host of a specific MOI?
MOI Layer (internal viruses) Viral Layer (external viruses)
1 2
14

15. Random dispersal gives Poisson
distribution of viruses
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
15
No clustering clustering

16. 0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
Clustered Viral distribution skew
right with increasing MOI16
No clustering clustering

17. 0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
Clustered Viral distribution skew
right with increasing MOI17
No clustering clustering

18. 0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
MOI =2
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
MOI =2
Clustered Viral distribution skew
right with increasing MOI18
No clustering clustering

19. 0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
MOI =2
MOI =3
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
MOI =2
MOI =3
Clustered Viral distribution skew
right with increasing MOI19
No clustering clustering

20. 0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
MOI =2
MOI =3
MOI =4
MOI =5
MOI =6
0 5 10
Local Viruses
0
0.2
0.4
0.6
0.8
1
ProbabilityDensity
MOI =0
MOI =1
MOI =2
MOI =3
MOI =4
MOI =5
MOI =6
Clustered Viral distribution skew
right with increasing MOI20
No clustering clustering

21. Well-mixed model yields geometric
MOI distribution
Host
Infected
hosts
Viruses
Deviates from geometric distribution

22. Clustered MOI distributions feature
fat tails
Hosts
E
H
I1
C
Viruses
0
[1 5]
[6 10]
[11 15]
[16 20]
>20

23. Multiple infection dynamics driven
by invasions of clusters

24. Invasions of larger clusters skews
viral distributions
Viruses
0 5 10
Probabilitydensity
0
0.2
0.4
0.6
0.8
1
<Viral Distribution> MOI =1
R=3
R=4
R=5
R=7
R=10
24

25. Invasions of larger clusters skews
viral distributions
Viruses
0 5 10
Probabilitydensity
0
0.2
0.4
0.6
0.8
1
<Viral Distribution> MOI =2
R=3
R=4
R=5
R=7
R=10
Viruses
0 5 10
Probabilitydensity
0
0.2
0.4
0.6
0.8
1
<Viral Distribution> MOI =3
R=3
R=4
R=5
R=7
R=10
Viruses
0 5 10
Probabilitydensity
0
0.2
0.4
0.6
0.8
1
<Viral Distribution> MOI =1
R=3
R=4
R=5
R=7
R=10
25

26. Conclusions
 High adsorption leads to clustering
 Clustering leads to fat tails in MOI distribution
 Cluster invasions drive the dynamics to skew
MOI distributions

27. Future work: spatial models of
Virophage—viruses of viruses
Taylor et al,
JTB (2014)
Paired Entry Mode (PEM)
Independent Entry Mode (IEM)
Desnues et al. PNAS
(2012)
Fischer and Suttle
Science (2011)

28. Acknowledgements
 Weitz Lab (GaTech)
 Funding:
 Quantitative Laws II
 NSF Physics of Living Systems
 James S Mcdonnell Foundation
 Nerem Fellowship
 Burroughs Wellcome Fund

29. Acknowledgements
Questions?
Hosts
E
H
I1
C
Viruses
0
[1 5]
[6 10]
[11 15]
[16 20]
>20
BP Taylor, CJ Penington, JS W
bioRxiv: 048876
 Weitz Lab (GaTech)
 Funding:
 Quantitative Laws II
 NSF Physics of Living Systems
 James S Mcdonnell Foundation
 Nerem Fellowship
 Burroughs Wellcome Fund

31. Analogous PDE model
31

32. Parametrize based on
prochlorococcus
single
time step
System size: 500 x 500 lattice pts=¼ ml
32
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