Dynamics of Transposable Elements in Genetically Modified Mosquitoes - PowerPoint PPT Presentation

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Dynamics of Transposable Elements in Genetically Modified Mosquitoes

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Selection for hosts with fewer deleterious mutations. Mechanisms: ... Results in deleterious chromosomal rearrangements. Fitness cost proportional to n2 ... – PowerPoint PPT presentation

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Title: Dynamics of Transposable Elements in Genetically Modified Mosquitoes


1
Dynamics of Transposable Elements in Genetically
Modified Mosquitoes
  • John Marshall
  • Department of Biomathematics
  • UCLA

2
Malaria control using genetically modified
mosquitoes
3
The transgene construct
4
Meiotic drive and HWE
  • P ww 2Q wt R tt

wt x tt -gt 4QR
ww x ww -gt P2 ww
½ ½ t t ½(1-i) w wt wt ½(1i) t
tt tt
tt x tt -gt R2 tt
ww x tt -gt 2PR wt
wt x wt -gt 4Q2
wt x ww -gt 4PQ
½(1-i) ½(1-i) w t ½(1-i) w ww
wt ½(1i) t wt tt
½ ½ w w ½(1-i) w ww ww ½(1i) t
wt wt
5
Repression of replicative transposition
  • Mechanisms have evolved to achieve a balance
    between
  • Selection for high element copy number
  • Selection for hosts with fewer deleterious
    mutations
  • Mechanisms
  • Host factors involved in (transposase) gene
    silencing
  • Post-transcriptional regulation of the
    transposable element by itself
  • Models

6
Kinetic model of self-repression of transposition
in Mariner
7
Costs to mosquito fitness with increasing element
copy number
  • Insertional mutagenesis
  • Each element copy can disrupt a functioning gene
  • Fitness cost proportional to n
  • Ectopic recombination
  • Recombination can occur between elements at
    different sites
  • Results in deleterious chromosomal rearrangements
  • Fitness cost proportional to n2
  • Act of transposition
  • Transposition can create nicks in chromosomes
  • Fitness cost proportional to un
  • Models

8
Proposed Markov chain model
n
n1
n-1
9
Solving the system of ODEs
  • From probability theory
  • Define the generating function,
  • Manipulate to obtain mean element copy number at
    time t

10
Proposed branching process model
Continuous time haploid branching process
i
i1
i-1
  • Continuous time diploid branching process
  • Consider the early stages of the spread of a
    transposable element
  • Imagine a reservoir of uninfected hosts
  • Assume matings involving infected hosts will be
    with uninfected hosts
  • For a gamete derived from a cell with i copies of
    the element it is possible to generate offspring
    with jE0, 1, 2,, i copies
  • Assume each offspring genotype occurs with equal
    probability,

11
Diploid branching process model
i-1
i
i-2
i1

12
Left boundary transitions
0
1
2
13
Solving the proposed branching process model
Populating the branching process matrix
The solution to the branching process is
  • The branching process is supercritical if its
    dominant eigenvalue is positive
  • Check for positive eigenvalue using
    Person-Frobenius Theorem
  • Or look for positive roots of the characteristic
    equaiton,
  • Problems
  • Only considers initial dynamics
  • Recombination are frequently of medium copy
    number
  • Ignores tendency for local transposition,
    recombination, etc.

14
Site-specific model
  • Motivation
  • Preferential transposition to nearby sites
  • Site-varying fitness costs
  • Recombination in diploid hosts
  • Label states according to their occupancy
  • T sites available for TE to insert into
  • 2T possible states numbered from 0 to 2T-1

0 0 1 0
2
TE
0 1 0 1
9
TE
TE
1 1 0 0
12
TE
TE
15
Local preference for transposition
Replicative transposition
TE
TE
TE
TE
TE
TE
TE
(autoregulation)
(preference for local transposition)
Non-replicative transposition
TE
TE
TE
TE
(preference for local transposition)
16
Enumerating the transitions
17
Analysis of equilibrium distributions
18
First and second order perturbation approximations
First order perturbation approximation
Second order perturbation approximation
19
Dissociation of the transposable element and
transgene
20
Markov chain model of dissociation
n,m1
n-1,m1
n,m
n1,m
n-1,m
n1,m-1
n,m-1
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