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)

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

The nuclear pore complex (NPC)

A can (or better, a pipe) of worms

~100 polymers

(nucleoporins, nups) of

length ~100 nm

Nuclear transport receptors import proteins

through the NPC

Electron

micrograph of

baculovirus

entering the

cytoplasm

Some viruses have learnt to perform this trick too

Probing the NPC with an AFM

Kramer et al,

in preparation

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?

Do proteins dissolve into the nup nanospaghetti?

Or is the nanospaghetti naturally clumpy?

Monte Carlo simulations of tethered freely

jointed chains

Monte Carlo snapshots

Repulsive (2-d) polymers fill the pore

Attractive (3-d) polymers clump at the wall

One clump or two?

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

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

The detail:

constrains the length of bonds

d

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

• 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

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

Bead density profile:

for an external mean field that favours the wall

Add the effect of self-interactions:

and we have ourselves a free energy functional

m

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

Bimodality of profiles

To clump or not to clump

Compatibility between MC and DFT profiles

Peleg et al (2011) Monte Carlo study

[n

m]

Open or shut case?

Strength of

attraction

Range of

attraction

Longer polymers condense centrally at a

lower stickiness

constant

central

wall

Stiffness

Indentation stiffness map:

evidence for central condensation

Bathe in nuclear transport receptors:

What does this mean?

Represent nuclear transport

receptors as large beads:

Importin-

Monte Carlo DFT using polymer functional plus

the free energy of attractive hard

spheres

Importin fluid modelled by Fundamental

Measure Theory

8 nm diameter

spheres in a 50 nm

diameter cylinder

MC FMT

MC red

DFT black

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

kTpp 1.0

Str

en

gth

of im

po

rtin

-nu

p a

ttra

ctio

n

semi-grand

potential

Strength of importin-nup

attraction

Cargo penetration: free energy surface

axial position

free energy

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!