IPLS Retreat Bath, Oct 17, 2017 Novel Physics arising from phase transitions in biology

Transcription

1 IPLS Retreat Bath, Oct 17, 2017 Novel Physics arising from phase transitions in biology Chiu Fan Lee Department of Bioengineering, Imperial College London, UK

2 Biology inspires new physics Biology Physics Physics leads to quantitative biology

3 Phase transitions in biology Amyloid fibrils RNA granules Active matter 200nm Brangwynne [Hyman Lab] mbzusmak8

4 Plan 1. Physics of polymer self-assembly 2. Non-equilibrium phase separation 3. Universality in active matter 4. Summary & Outlook

5 Slyngborg & Fojan (2015) Phys. Chem. Chem. Phys. 1. Physics of polymer self-assembly

6 Toy model Liu, Lee & Huang, in Biophysics and biochemistry of protein aggregation (World Scientific, 2017)

7 Wang et al. (2012) Nature 491, 51 A colloidal example

8 Statistical mechanics Energy of a s-mer: Monomer number conservation: Partition function (dilute limit): Factorial because of indistinguishability by our choice (nothing to do with quantum mechanics!) Liu, Lee & Huang, in Biophysics and biochemistry of protein aggregation (World Scientific, 2017)

9 Mass density Static configuration NOT a thermodynamic phase transition Monomer Critical fibrillar concentraion (CFC) Solute concentration P(l) Length distribution Monomer concentration ~ CFC Cates & Candau (1990) J. Phys.: Condens. Matter Lee (2009) Phys. Rev. E; Lee (2012) J. Phys.: Condens. Matter l

10 Steady-State Kinetics B i j,j A i j,j Thermal equilibrium: ρ k : Concentration of k-mers A ij and B ij are not independent!

11 Breakage rate B ij Over-damped EOM: Breakage rate = (First-passage time) -1

12 Energy U (θ) Asymptotic results 1D Kramers escape problem Quasi-static approximation: P(θ) e Bθ2 Exit rate: Mulitdimensional Kramers escape problem Breakage rate of a s-mer by thermal bending: Lee (2009) Phys. Rev. E; Lee (2015) J. Phys.: Condens. Matter

13 Revisiting the kinetic equation Uniform breakage profile -> B ij = B Steady state configuration -> A ij = A Namely, all joining rates of any pair of polymers are identical, irrespective of the sizes How does this square with the Smoluchowski picture?

14 Smoluchowski reaction kinetics Diffusion-controlled binary association rate: where Considering the rod-like nature as well: What s wrong with this picture? Hill (1983) Biophys. J.

15 Breakage-controlled, NOT diffusion-controlled We can compute the breakage rate from the Smoluchowski picture and compare it to the true breakage rate Therefore, a polymer interacts predominately with its own fragments! Lee (2017) Eprint: arxiv:

16 Spatial correlation Distribution of dimer s center of mass Lee (2017) Eprint: arxiv:

17 2. Non-equilibrium phase separations

18 Formation by phase separation No membrane Rapid turnover Coalescence

19 Phase diagram T Vapour Liquid ε : supersaturation Phase separation region ρ

20

21 Drop growth x ρ x

22 Drop growth x ρ Vapour conc. outside small drop is higher than vapour conc. outside large drop Gibbs-Thomson relation: ρ R = ρ 1 + ν R x

23 Universality of surface-tension driven droplet growth Ostwald coarsening Lifshitz-Slyozov universal growth law: R(t) ~t 1/3 Universal droplet size distribution

24 Chemical reaction-controlled phase separation Wurtz & Lee (2017) E-print: arxiv:

25 Concentration Chemical reactions create R r gradients S SG Cytoplasm P SG R Cytoplasm

26 Wurtz & Lee (2017) E-print: arxiv:

27 3. Universality in active matter

28 Incompressible fluids t v = P + f λ v v a + bv 2 v μ 2 v + cv 4 v + ξ 2 2 v + Symmetries + coarse-graining via renormalisation group transformation t v = P + f v v μ 2 v Parameter-free prediction: v(t) v(0) t d/2 (Long-time tail) Physical systems Translational invariance Rotational invariance c Galilean invariance Fluctuation-dissipation

29 Incompressible active fluids t v = P + f λ v v a + bv 2 v μ 2 v + cv 4 v + ξ 2 2 v + Symmetries + coarse-grain via renormalisation group transformation t v = P + f λ v v a + bv 2 v μ 2 v Biological systems Translational invariance Rotational invariance c Galilean invariance Fluctuation-dissipation

30 Energy The bottom has become very flat x y Adapted from QuantumDiaries.org Critical order-disorder transition

31 Phase diagram of incompressible active fluids v Critical region

32 Critical incompressible active fluids EOM: t v + P f = λ v v a + bv 2 v μ 2 v + cv 4 v + ξ( 2 ) 2 v + RG transformation t v + P + f l = λ l v v a l + b l v 2 v μ l 2 v Exact hydrodynamic EOM with TWO coefficients governing the model s scale-invariance properties: Level of coarse-graining g 1 (l) ~ D lλ l 2 μ l 3, g 2 l ~ D lb l μ l 2

33 Advective term: g 1 v v Incompressible active matter (Today) g 1 l ~ D 2 lλ l μ ; g 3 2 l ~ D lb l l μ 2 l Chen, Toner, Lee (2015) New J. Phys. 17, Ferromagnets with dipolar interactions Aharony and Fisher (1973) Phys. Rev. Lett.

34 Randomly stirred fluids (Model B) Forster, Nelson & Stephen (1977) Phys. Rev. A Incompressible active matter (Today) g 1 l ~ D 2 lλ l μ ; g 3 2 l ~ D lb l l μ 2 l Chen, Toner, Lee (2015) New J. Phys. 17, Ferromagnets with dipolar interactions Aharony and Fisher (1973) Phys. Rev. Lett.

35 Randomly stirred fluids (Model B) Forster, Nelson & Stephen (1977) Phys. Rev. A g 1 l ~ D 2 lλ l μ ; g 3 2 l ~ D lb l l μ 2 l Chen, Toner, Lee (2015) New J. Phys. 17, Ferromagnets with dipolar interactions Aharony and Fisher (1973) Phys. Rev. Lett.

36 Randomly stirred fluids (Model B) Forster, Nelson & Stephen (1977) Phys. Rev. A Incompressible active fluids In 3D: v( r) v( r ) ~ r r (1.35±0.08) g 1 l ~ D 2 lλ l μ ; g 3 2 l ~ D lb l l μ 2 l Chen, Toner, Lee (2015) New J. Phys. 17, Ferromagnets with dipolar interactions Aharony and Fisher (1973) Phys. Rev. Lett.

37 Energy y x Adapted from QuantumDiaries.org Ordered phase (2D)

38 Ordered incompressible active fluids v Ordered phase Critical region Universality is more than criticality! Universal behaviour expected in the symmetry-broken phase of a continuous symmetry Belitz, Kirkpatrick, Vojta (2005) Rev. Mod. Phys.

39 Ordered phase of 2D incompressible active fluids EOM: t v + P f = λ v v a + bv 2 v μ 2 v + cv 4 v + ξ( 2 ) 2 v + Ordered phase: RG transformation Level of coarse-graining

40 Active fluids in 2D Chen, Lee, Toner (2016) Nature Comm.

41 M.C. Escher (1938) Day and Night

42 Summary 1. Biopolymer self-assembly Breakage-controlled thermalisation kinetics 2. Chemically active phase separations Coarsening arrested by chemical reactions 3. Universality in active matter Symmetry-based categorisation of nonequilibrium systems

43 Outlook 1 In physics, we (try to) teach principles and derive the predictions for particular examples. In biology, teaching proceeds (mostly) from example to example. Although physics has subfields, to a remarkable extent the physics community clings to the romantic notion that Physics is one subject. [Biophysics: Searching for Principles (2012)] William Bialek

44 Outlook 2 Anthony Zee, Quantum Field Theory in a Nutshell (Princeton University Press, 2003)

45 The Team Amyloids Vaux Group (Dunn School of Pathology, Oxford) Liu Hong (Tsinghua University) Active Matter Leiming Chen (China University of Mining and Technology John Toner (Oregon) Ben Jean David Partridge Wurtz David Nesbitt Andrea Cairoli Alice Spenlauhauer Thank you for your attention!