theoretical perspectives on biomolecular...

JBB 2026H • Lecture 7 (2nd half) Hue Sun Chan

Department of Biochemistry October 26, 2018

University of Toronto

Theoretical Perspectives on Biomolecular Condensates

Image from: Banani, Lee, Hyman & Rosen, Nat Rev Mol Cell Biol 2017

Intracellular Biomolecular Condensates or “Membraneless Organelles” are organizers of biochemistry

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

where

Note: R = kB (Avogadro #)

Figure from: Rauscher & Pomès, “Structural disorder and protein elasticity”. In: Fuzziness: Structural

Disorder in Protein Complexes. Edited by Fuxreiter & Tompa. Springer (2012).

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.

= total solvent volume

B

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

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

• Then repeat the argument for

the other N ‒ 1 chains. The N chains are identical

When b → solvent (s), mb = 1,

a → p (polymer/protein),

ϕs = 1 ‒ ϕp ,

the contact free energy per unit

volume in the mixed state

E/V=z [εpp ϕp2/2 +

εss (1 ‒ ϕp )2/2 +

εps ϕp (1 ‒ ϕp)],

whereas the contact free energy per

unit volume in the unmixed state

=z [εpp ϕp/2 + εss (1 ‒ ϕp) /2].

Hence the contact free energy per

unit volume = (former) – (latter) =

Δ“H”mix/V = kBT χ ϕp(1 ‒ ϕp)

E/V=z ( )

B

Lin, Forman-Kay & Chan, Biochemistry 57:2499-2508 (2018)

Depending on the IDP sequence, phase separation can be induced

by an increase or a decrease in temperature

= χ-1(T)

Image Credit:

Muiznieks & Keeley 2013

Study.com

LCST example:

tropoelastin

Dill, Hutchinson & Alonso 1989

Binodal and Spinodal Phase Separations

Single-phase globally unstable ⤍ Spinodal (Global) Phase Separation, Spinodal Decomposition

Binodal (Local) Phase Separation, Droplets

Spinodal region lies inside

the coexistence region

Theoretical Formulations Available at Various Levels of Structural and Energetic Details

Flory-Huggins Overbeek-Voorn RPA Advanced Theory Explicit-Chain

IDP phase separation is sequence dependent : not only depends on composition

Random Phase Approximation (RPA) is an analytical theory of sequence-dependent

polyampholyte (polymer chains with both + and ‒ charges) phase separation


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:

Nott et al., Forman-Kay & Baldwin, Mol Cell (2015)

Protein volume fraction ϕm

binodal

spinodal Tem

pera

ture

T*

(th

eo

retica

l u

nits)

Lin, Forman-Kay & Chan, Phys Rev Lett (2016); Lin, Song, Forman-Kay & Chan, J Mol Liquids (2017)

Spinodal decomposition in Ddx4N1 drying experiment

Sawle & Ghosh, J Chem Phys (2015)

Das & Pappu, PNAS (2013)

Sequence charge pattern parameters align well with

RPA-predicted phase separation propensity

Y.-H. Lin & H.S. Chan, Biophys J (2017)

beyond simple “blockiness”?

same number of + and ‒ charges

Das & Pappu, PNAS , 2013

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)

Phase Separation as a Mechanism for Homeostasis

Compositions of the phase-separated states are less varied than the underlying bulk concentrations


FIB1

NPM1

Image credit: Marina Feric & Cliff Brangwynne,

Princeton University.

From: New J Phys Focus on “Phase Transitions in Cells:

From Metastable Droplets to Cytoplasmic

Assemblies”

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? A multivalent, stochastic, “fuzzy” mode of molecular recognition?

nucleoli

The Binary Phase Diagram (Pattern of Coexistence) for a Pair of Polyampholytes

Varies Significantly with the Charge Patterns Along their Sequences

Lin, Brady, Forman-Kay & Chan, New J Phys (2017)

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.

SCD1‒ SCD2

= ‒1.01 SCD1‒ SCD2

= 8.62

SCD1‒ SCD2

= 15.58

Assessing analytical theories and rationalizing experiments by explicit-chain simulations

Das, Amin, Lin & Chan, q-bio-arXiv:1808.10023 (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

Below Tcr : Above Tcr : Marginal? :

500 Cα-chains

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:1808.10023 (2018)

Dignon et al., PNAS (2018) doi.org/10.1073/pnas.1804177115 Dignon et al., PLoS Comput Biol 14:e1005941 (2018)

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).

Results and figures from: Harmon, Holehouse & Pappu, New J Phys 20: 045002 (2018); see also Feric et al., Cell 165:1686 (2016) and Harmon et al., eLife 6:e30294 (2017).

Lattice Models in which each lattice site (bead)

represents a multiple-residue group/domain,

beads are connected by disordered linkers

i.e., poly-(proline-rich module)

Example (∼experimental system studied in the

Mike Rosen lab):

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 57:2499-2508 (2018)

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