unravelling the nuclear pore complexucapijf/presentations/leeds talk.pdf · •the nuclear pore...
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![Page 1: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/1.jpg)
Unravelling the nuclear
pore complex
Ian Ford +
Department of Physics and Astronomy and
London Centre for Nanotechnology
University College London, UK
also the Thomas Young Centre!
Osmanović et al PRE 85 (2012) 061917
Dino Osmanović, Tony Harker, Aizhan
Bestembayeva, Bart Hoogenboom
(UCL P&A/LCN)
Ariberto Fassati (UCL Virology)
Armin Kramer, Ivan Leshkovich
(Univ Münster)
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Summary
• The nuclear pore complex
• Some statistical physics of tethered polymers
– Monte Carlo
– Free energy density functional theory
• Bimodal behaviour: an open and shut case!
• How nuclear transport receptors (importins)
might unlock the pore
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The nuclear pore complex (NPC)
![Page 4: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/4.jpg)
A can (or better, a pipe) of worms
~100 polymers
(nucleoporins, nups) of
length ~100 nm
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Nuclear transport receptors import proteins
through the NPC
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Electron
micrograph of
baculovirus
entering the
cytoplasm
Some viruses have learnt to perform this trick too
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Probing the NPC with an AFM
Kramer et al,
in preparation
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How does it work?
• Certain proteins as big as the
channel can get through
• Others are excluded
• Do proteins squeeze through gaps?
• Or is the portcullis raised?
• Can we exploit this for other purposes?
![Page 9: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/9.jpg)
Do proteins dissolve into the nup nanospaghetti?
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Or is the nanospaghetti naturally clumpy?
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Monte Carlo simulations of tethered freely
jointed chains
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Monte Carlo snapshots
Repulsive (2-d) polymers fill the pore
Attractive (3-d) polymers clump at the wall
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One clump or two?
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Let’s do mean field free energy density
functional theory of tethered polymers!
• Monte Carlo too slow
• Gives little idea about relative stability of clumpy
structures
• DFT provides equilibrium average profiles and
free energies
• We develop a perturbative free energy functional,
using a freely jointed chain reference model
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Density Functional Theory of tethered polymers
• Represent the system not as polymer configurations,
but through a mean monomer density
• Construct a free energy functional of the monomer
(bead) density.
r
z
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The detail:
constrains the length of bonds
d
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Introduce a mean field )()( rr kTwV
In DFT we seek a representation of in terms of the bead density )(r
10 HHH
010 HFFF m
mF
Bogoliubov approximation
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• Green’s function of a related diffusion equation
• s is the polymer length; acts like a time. Edwards (1965).
: Freely jointed chain in a mean field
• Polymer configuration is a
realisation of a random
walk in 3-d.
b
0rr
w0H
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The reference model free energy
• is a functional of the mean field potential
• requires a numerical solution for Green’s function
• gives a bead density:
)/exp( 0 kTF
0F
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Bead density profile:
for an external mean field that favours the wall
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Add the effect of self-interactions:
and we have ourselves a free energy functional
m
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How to choose the mean field?
• Optimise the Bogoliubov approximation
by minimising the DFT free energy over the mean
field
Euler-Lagrange equation for optimal mean field
• Iterate mean field and density to convergence
![Page 23: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/23.jpg)
Bimodality of profiles
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To clump or not to clump
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Compatibility between MC and DFT profiles
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Peleg et al (2011) Monte Carlo study
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[n
m]
![Page 28: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/28.jpg)
Open or shut case?
Strength of
attraction
Range of
attraction
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Longer polymers condense centrally at a
lower stickiness
constant
central
wall
![Page 30: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/30.jpg)
Stiffness
![Page 31: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/31.jpg)
Indentation stiffness map:
evidence for central condensation
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Bathe in nuclear transport receptors:
What does this mean?
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Represent nuclear transport
receptors as large beads:
Importin-
Monte Carlo DFT using polymer functional plus
the free energy of attractive hard
spheres
![Page 35: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/35.jpg)
Importin fluid modelled by Fundamental
Measure Theory
8 nm diameter
spheres in a 50 nm
diameter cylinder
MC FMT
MC red
DFT black
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Str
en
gth
of im
po
rtin
-nu
p a
ttra
ctio
nchemical potential of importin
Mean number of
importins in the
NPC
kTpp 05.0
![Page 37: Unravelling the nuclear pore complexucapijf/presentations/Leeds talk.pdf · •The nuclear pore complex •Some statistical physics of tethered polymers –Monte Carlo –Free energy](https://reader036.vdocuments.net/reader036/viewer/2022063016/5fd63df901e02f4fb22ebad2/html5/thumbnails/37.jpg)
kTpp 1.0
Str
en
gth
of im
po
rtin
-nu
p a
ttra
ctio
n
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semi-grand
potential
Strength of importin-nup
attraction
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Cargo penetration: free energy surface
axial position
free energy
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Summary
• Polymers in tubes can be finely tuned to allow the
opening and closing of the channel
• Complex thermodynamic phase behaviour
• Maybe we can learn from Nature to design pores
that differentiate between species?
• Thanks for listening!