Theoretical Perspectives on Biomolecular Condensates

Transcription

1 JBB 2026H Lecture 7 (2nd half) Hue Sun Chan Department of Biochemistry October 26, 2018 University of Toronto Theoretical Perspectives on Biomolecular Condensates

2 Intracellular Biomolecular Condensates or Membraneless Organelles are organizers of biochemistry Image from: Banani, Lee, Hyman & Rosen, Nat Rev Mol Cell Biol 2017

3 Theory and Computational Simulation of Multiple-Chain Systems Rubber elasticity: An application of the Gaussian chain theory Figure Credit: Pomès Group, The Hospital for Sick Children & University of Toronto

4 Note: R = k B (Avogadro #) where

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6 Figure from: Rauscher & Pomès, Structural disorder and protein elasticity. In: Fuzziness: Structural Disorder in Protein Complexes. Edited by Fuxreiter & Tompa. Springer (2012).

7 Mean-field Flory-Huggins Theory addresses sequence composition of intrinsically disordered proteins (IDPs) such as overall hydrophobicity but not other encoded information such as hydrophobic & charge patterns, etc. in the sequence. Mean-field refers to approximations in which some fluctuations/variations in IDP concentrations and/or sequence-dependent interactions, etc., are averaged/smeared over.

8 Flory-Huggins uses a conceptual (non-explicit) lattice argument z = lattice coordination number # of ways of placing the first bead of the first chain = V # of ways of placing the second bead = (z 1) (probability that the site is not occupied). This probability is given by (V 1)/V in the mean-field approximation B Therefore, the # of ways of placing the entire first chain in this approximation is [(z 1)(V 1)/V][(z 1)(V 2)/V] [(z 1) (V m+1)] = [V!/(V m)!][(z 1)/V] m-1 The N chains are identical = total solvent volume Then repeat the argument for the other N 1 chains.

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10 When b solvent (s), m b = 1, a p (polymer/protein), ϕ s = 1 ϕ p, the contact free energy per unit volume in the mixed state E/V=z [ε pp ϕ p 2 /2 + ε ss (1 ϕ p ) 2 /2 + ε ps ϕ p (1 ϕ p )], whereas the contact free energy per unit volume in the unmixed state =z [ε pp ϕ p /2 + ε ss (1 ϕ p ) /2]. E/V=z ( ) B Hence the contact free energy per unit volume = (former) (latter) = Δ H mix /V = k B T χ ϕ p (1 ϕ p )

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12 Depending on the IDP sequence, phase separation can be induced by an increase or a decrease in temperature Dill, Hutchinson & Alonso 1989 LCST example: tropoelastin = χ -1 (T) Lin, Forman-Kay & Chan, Biochemistry 57: (2018) Image Credit: Muiznieks & Keeley 2013 Study.com

13 Binodal and Spinodal Phase Separations Binodal (Local) Phase Separation, Droplets Spinodal region lies inside the coexistence region Single-phase globally unstable Spinodal (Global) Phase Separation, Spinodal Decomposition

14 Theoretical Formulations Available at Various Levels of Structural and Energetic Details IDP phase separation is sequence dependent : not only depends on composition Flory-Huggins Overbeek-Voorn RPA Advanced Theory Explicit-Chain Random Phase Approximation (RPA) is an analytical theory of sequence-dependent polyampholyte (polymer chains with both + and charges) phase separation Lin, Forman-Kay & Chan, Biochemistry 57: (2018)

15 RNA helicase Ddx4: Wildtype forms condensates in cell or in vitro, but a charge-scrambled mutant does not Sequence-dependent RPA theory captures this trend: (theoretical units) Temperature T* binodal spinodal Nott et al., Forman-Kay & Baldwin, Mol Cell (2015) Protein volume fraction ϕ m Spinodal decomposition in Ddx4 N1 drying experiment Lin, Forman-Kay & Chan, Phys Rev Lett (2016); Lin, Song, Forman-Kay & Chan, J Mol Liquids (2017)

16 Sequence charge pattern parameters align well with RPA-predicted phase separation propensity Sawle & Ghosh, J Chem Phys (2015) Das & Pappu, PNAS (2013) beyond simple blockiness? same number of + and charges Das & Pappu, PNAS, 2013 Y.-H. Lin & H.S. Chan, Biophys J (2017)

17 Single-chain conformational compactness and multiple-chain phase separation are favored by similar block-like charge patterns that promote sequence-nonlocal attraction Y.-H. Lin & H.S. Chan, Biophys J (2017)

18 Phase Separation as a Mechanism for Homeostasis Compositions of the phase-separated states are less varied than the underlying bulk concentrations Lin, Forman-Kay & Chan, Biochemistry 57: (2018)

19 How do different IDPs find one another to from the many separate intracellular compartments and subcompartments? Why don t they all condense together into a large gemisch? FIB1 NPM1 A multivalent, stochastic, fuzzy mode of molecular recognition? nucleoli Image credit: Marina Feric & Cliff Brangwynne, Princeton University. From: New J Phys Focus on Phase Transitions in Cells: From Metastable Droplets to Cytoplasmic Assemblies

20 The Binary Phase Diagram (Pattern of Coexistence) for a Pair of Polyampholytes Varies Significantly with the Charge Patterns Along their Sequences SCD 1 SCD 2 = 1.01 SCD 1 SCD 2 = 8.62 SCD 1 SCD 2 = The two IDP components co-mix when their charge patterns are similar (as measured by κ or SCD); de-mix when their charge patterns are dissimilar. Lin, Brady, Forman-Kay & Chan, New J Phys (2017)

21 Assessing analytical theories and rationalizing experiments by explicit-chain simulations 500 Cα-chains Below T cr : Above T cr : Marginal? : Das, Amin, Lin & Chan, q-bio-arxiv: (2018) See also: Das, Eisen, Lin & Chan, J Phys Chem B 2018, Dignon, Zheng, Kim, Best & Mittal, PLoS Comput Biol 2018; Silmore, Howard & Panagiotopoulos, Mol Phys 2017

22 Current sequence charge pattern parameters are predictive of simulated phase behaviors to a certain degree for some polyampholyte sequences Fully charged sequences with more blocky charge patterns have higher UCSTs (upper critical solution temperatures), i.e., higher propensities to phase separate. Simulated results from: Das, Amin, Lin & Chan, q-bio-arxiv: (2018)

23 Applications of the residue-based model Correlation between single-chain collapse and multiple-chain phase separation propensities (cf. Lin & Chan) Lower phase separation propensities of FUS variants with phosphomimetic mutations (as in experiment). Dignon et al., PLoS Comput Biol 14:e (2018) Dignon et al., PNAS (2018) doi.org/ /pnas

24 Lattice Models in which each lattice site (bead) represents a multiple-residue group/domain, beads are connected by disordered linkers Example ( experimental system studied in the Mike Rosen lab): i.e., poly-(proline-rich module) Results and figures from: Harmon, Holehouse & Pappu, New J Phys 20: (2018); see also Feric et al., Cell 165:1686 (2016) and Harmon et al., elife 6:e30294 (2017).

25 More complex scenarios with liquid-liquid, liquid-gel, and gel-gel phase separations Illustrative example using the extended FH theory of Semenov & Rubinstein [Macromolecules 31:1373 (1998)], with N = 100, # of stickers/chain = f = 5. [cf. lattice model of Harmon, Holehouse, Rosen & Pappu, elife 6:e30294 (2017)] Figure from: Lin, Forman-Kay & Chan, Biochemistry 57: (2018)