Unravelling the nuclear pore complex

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Pearl Wright
5 years ago
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Ivan Leshkovich (Univ Münster) Department of Physics and Astronomy and London Centre for

1 Unravelling the nuclear pore complex Ian Ford + Dino Osmanović, Tony Harker, Aizhan Bestembayeva, Bart Hoogenboom (UCL P&A/LCN) Ariberto Fassati (UCL Virology) Armin Kramer, Ivan Leshkovich (Univ Münster) 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)

functional theory Bimodal behaviour: an open and shut case!

2 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

3 The nuclear pore complex (NPC)

4 A can (or better, a pipe) of worms ~100 polymers (nucleoporins, nups) of length ~100 nm

5 Nuclear transport receptors import proteins through the NPC

6 Some viruses have learnt to perform this trick too Electron micrograph of baculovirus entering the cytoplasm

7 Probing the NPC with an AFM Kramer et al, in preparation

8 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?

9 Do proteins dissolve into the nup nanospaghetti?

10 Or is the nanospaghetti naturally clumpy?

11 Monte Carlo simulations of tethered freely jointed chains

12 Monte Carlo snapshots Repulsive (2-d) polymers fill the pore Attractive (3-d) polymers clump at the wall

13 One clump or two?

14 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

15 Density Functional Theory of tethered polymers Represent the system not as polymer configurations, but through a mean monomer density z r Construct a free energy functional of the monomer (bead) density.

16 The detail: constrains the length of bonds d

17 Introduce a mean field V( r) ktw( r) H H 0 H 1 F Fm F 0 H 1 0 Bogoliubov approximation In DFT we seek a representation of in terms of the bead density (r) F m

18 H 0 : Freely jointed chain in a mean field Polymer configuration is a realisation of a random walk in 3-d. Green s function of a related diffusion equation r 0 b w r s is the polymer length; acts like a time. Edwards (1965).

19 The reference model free energy F 0 exp( F0 / kt) is a functional of the mean field potential requires a numerical solution for Green s function gives a bead density:

20 Bead density profile: for an external mean field that favours the wall

21 Add the effect of self-interactions: m and we have ourselves a free energy functional

22 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

23 Bimodality of profiles

24 To clump or not to clump

25 Compatibility between MC and DFT profiles

26 Peleg et al (2011) Monte Carlo study

27 [nm]

28 Open or shut case? Strength of attraction Range of attraction

29 Longer polymers condense centrally at a lower stickiness constant central wall

30 Stiffness

31 Indentation stiffness map: evidence for central condensation

33 Bathe in nuclear transport receptors: What does this mean?

34 Represent nuclear transport receptors as large beads: Importin- Monte Carlo DFT using polymer functional plus the free energy of attractive hard spheres

35 Importin fluid modelled by Fundamental Measure Theory MC FMT 8 nm diameter spheres in a 50 nm diameter cylinder MC red DFT black

36 Strength of importin-nup attraction chemical potential of importin 0. 05kT pp Mean number of importins in the NPC

37 Strength of importin-nup attraction 0. 1kT pp

38 semi-grand potential Strength of importin-nup attraction

39 Cargo penetration: free energy surface free energy axial position

40 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!

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