Transcript Dynamics of Transposable Elements in Genetically Modified

Successful conditions for
the early spread of a TE in a
disease vector population
John Marshall, Department of Biomathematics, UCLA
IR
effector
gene
transposase
gene
IR
Requirements for a successful
control strategy:
1.
2.
Element loss probability: < 1%
Rate of element spread: reach 10% prevalence in < 1 year
Question: What conditions satisfy
these requirements?
•
•
•
•
Replicative transposition rate
Reduction of transposition rate
with additional TE copies
Fitness cost of TE copies
Rate of population growth/decline
•
•
•
Release size
Time of release
TE copy number of
released mosquitoes
Transposition and deletion (i = 2)
TE
Diploid cell:
TE
Element deletion
Replicative transposition
 2  2v
 2  2u2
TE
TE
No transposition
or deletion

1
TE
(1   2   2 )
TE
TE
TE
Repression of
transposition
Transposition rate
Host fitness
costs
Host death rate
i
ui
i  1  di
TE copy number
TE copy number
i
ui  a(1  b(i 1))
Sources:
• Self repression
• Host repression
i
i  1  di
Sources:
• Insertional mutagenesis
• Ectopic recombination
• Act of transposition
Production of gametes (i = 2)
Diploid cell:
TE
TE
1  2
 
2  
2  2
1  2
 
2  
Gametes: 2  0 
1  2
 
2  
2 1 
TE
TE
0.5 0.25 -
1 TE
2 TEs
0-
TE
Population size changes of An.
gambiae in Mali, West Africa
What this means mathematically
1  i  1 
1
  i  i
f ij  i 1 
2  j  i
2
i  
  (1   i   i )
 j  i
1  i  1 

  i  1{i  j}
 i 1 
2  j  i
i
Use to calculate:
• TE extinction probabilities
• Mean and variance of host counts over time
Optimal release time is end of dry
season/beginning of rainy season
• Optimal release
at beginning of
population
growth phase
• Bias towards
release later
rather than
earlier
TE loss probabilities
vs. transposition rate
vs. release size
vs. release copy no.
• Release size has the greatest
influence on TE loss probability
• Loss probability is < 1%
for release size > 25
No. transgenic hosts vs. time
• Almost all An.
gambiae only
have a single TE
copy in the early
stages of spread
1
2
3
• Transposition rate has the
greatest influence on rate of
TE spread
• TE reaches 10% prevalence
in < 1 year for transposition
rate > 0.087
Model conclusions
Transposition rate:
• Most efficient way to increase rate of element spread
• Recommend transposition rate > 0.1 per element per generation
Release size:
• Most efficient way to reduce loss probability
• Recommend release size > 50
Fall off of transposition rate with increasing copy number:
• Recommend focus on transposition rate and fitness cost when there
is only a single element in the genome