physics of protein function and evolution: from sequence...

Hue Sun Chan Departments of Biochemistry and Molecular Genetics

University of Toronto, Ontario M5S 1A8 Canada

http://biochemistry.utoronto.ca/person/hue-sun-chan/

UofT Physics November 30, 2017

Physics of Protein Function and Evolution: From Sequence-Structure to

Sequence-Ensemble Relationships

Figure from: L. Stryler, Biochemistry. W.H. Freeman & Co., NY (1981)

Proteins are polymer chains of specific sequences of amino acids.

bovine

ribonuclease

● As a polymer, a protein

molecule with n amino

acids can adopt many

(~μn) different shapes

(conformations), many of

which are open and

disordered, others are

more compact and

ordered.

● All conformational

states can be utilized

by Nature to perform

biological functions.

Figure from: Radisky & Koshland,

PNAS 99:10316 (2002)

CI2

subtilisin

chymotrypsin inhibitor 2 (CI2)

The “classical” Sequence-(Folded) Structure-Function Paradigm

Example of a protein functioning in its folded form:

Figure Credit: Pomès Group, The Hospital for Sick

Children & University of Toronto

Example:

The spring/rubber-like

elasticity of skin, lungs, blood

vessels, and uterine tissue is

imparted by the protein elastin.

Entropy-driven rubber

elasticity:

The functional

conformations of some

proteins are disordered

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

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

Figure from: Chan, Zhang, Wallin & Liu, Annu Rev Phys Chem (2011)

Intrinsically Disordered Proteins (IDPs) ● IDPs do not fold spontaneously

● IDPs perform prominent functions in cellular signaling and regulation

● IDPs are made up of “low complexity” amino acid sequences

● Compared with sequences for globular proteins, IDP sequences have more

polar, charged, and aromatic residues and fewer hydrophobic/nonpolar residues

Some IDPs fold (become ordered) upon binding:

phosphorylated kinase-

inducible domain (pKID)

kinase-inducible domain

interacting domain (KIX)

Mittag, Orlicky, Choy, Tang, Lin, Sicheri, Kay, Tyers & Forman-Kay, PNAS 105:17772-17777 (2008)

NMR experiments show that multiple phosphorylated

sites of Sic1 engage Cdc4 without global ordering

a dynamic,

“fuzzy”

complex

Cdc4

7pSic1 dynamic complex

Some IDPs remain largely disordered even upon binding, forming “fuzzy complexes”:

Borg, Mittag, Pawson, Tyers, Forman-Kay & Chan, PNAS 104:9650-9655 (2007)

Some IDPs function not only as individual molecules but also collectively by undergoing phase separation on a mesoscopic

length scale to form condensed liquid-phase IDP-rich droplets that may encompass RNA and other biomolecules.

■ A phase-separated “assemblage” is formed reversibly when a critical

concentration is reached. The formation of the assemblage provides spatial

organization that can be regulated. Its liquid-phase properties allow exchange

of constituent molecules with the surrounding solution to facilitate localization

of and biochemical interactions with other protein and/or RNA species.

Figure: Toretsky & Wright, J Cell Biol (2014)

Zeng et al. & Zhang, Cell 166:1163–1175 (2016) http://www.ust.hk/

Protein Phase Transition in Synaptic Function

Organelles: Substructures - “little organs” - of the Cell Organelles can be membrane-bound or membrane-less

Plant cell Animal cell

Figures from: Encyclopædia Britannica (2010)

Membraneless Organelles underpinned by IDP phase separation

A form of cellular compartmentalization

P granules

as liquid droplets.

◄Fluorescence recovery after

photobleaching.

▼Two P granules fuse.

Figure: Hyman, Weber & Jülicher, Annu Rev Cell Dev Biol (2014)

One-cell stage of

C. elegans embryo

Figure:

Wang &

Seydoux,

Curr Biol

(2014) Adult hermaphrodite

gonad

Figure: Biology Reference http://www.biologyreference.com/Mo-Nu/Nucleolus.html

Nucleolus (“ribosome factory”)

as coexisting liquid phases

[see Feric et al., Cell (2016)]

Nucleoli in C. elegan

Image credit: Stephanie Weber, Department of Biology, McGill University

Weber & Brangwynne, Curr Biol 25:64106 (2015)

How do the basic physical forces

encoded by protein amino acid

sequences give rise to these

remarkable biological phenomena?

● Conformational Switches Between Folded Globular Structures

● Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

Hydrophobic Interaction is a Major Driving Force for Protein Folding

Chan & Dill, Physics Today (1993)

Kauzmann (1959), Dill (1990), etc.

Lau & Dill, Macromolecules (1989); Chan & Dill, J Chem Phys (1991) ▪ Figure from: Chan & Dill, Physics Today (1993)

A Simple Exact Biophysical Model: The Hydrophobic-Polar (HP) Model

Superfunnels: Correlation between Thermodynamic and Mutational Stabilities

Neutral net of sequences encoding for a given

structure tends to organized around a “prototype

sequence” with maximum thermodynamic stability and

mutational stability (robustness).

prototype sequence

Bornberg-Bauer & Chan, PNAS (1999);

Wroe, Bornberg-Bauer & Chan, Biophys J (2005)

● Sequences with higher mutational robustness tend to have

higher steady-state populations under evolutionary dynamics cf. van Nimwegen et al,

PNAS 96, 9716 (1999)

Evolutionary Paths and Conformational Switches in

Sequence Space

Lipman & Wilbur, Proc R Soc London B (1991)

Neutral net Neutral net

str

uctu

ral/seq

uen

ce

sim

ilari

ty t

o t

arg

et

Latent Evolutionary Potentials: Selection of excited-state (promiscuous) functions can speed up evolution dramatically

Wroe, Chan & Bornberg-Bauer, HFSP J (2007)

with excited-state

selection

without excited-state

selection

cf. Amitai, Gupta & Tawfik, HFSP J 1, 67 (2007); Tokuriki & Tawfik, Science 324, 203 (2009) for a review.

Role of excited-state selection in Escape from Adaptive Conflict

The “Escape from Adaptive Conflict” Perspective focuses on

adaptation before gene duplication [Hittinger & Carrol, Nature

449, 677 (2007); Des Marais & Rausher, Nature 454, 762 (2008)]

Neofunctionalization Subfunctionalization

specialist generalist

gene

duplication

Sikosek, Chan & Bornberg-Bauer, PNAS (2012)

Escape from Adaptive Conflict Follows from Weak Functional Trade-Offs and Mutational Robustness.

● Biophysics-based network connections.

● Evolutionary dynamics under mutations

and gene duplications computed using

both an analytical master equation and

stochastic Monte Carlo simulations.

● Fitness is proportional to the stability

(concentration) of the functional

structures up to a certain optimum

concentration above which fitness does

not increase further with concentration.

● The optimal concentration corresponds

to a measure of selection pressure.

Sikosek et al., PNAS (2012); Sikosek et al., PLoS Comput Biol (2012); Sikosek & Chan, J R Soc Interface (2014)

Evolving a

new folded

structure:

traversing two superfunnels

Sikosek & Chan, J R Soc Interface (2014)

Subfunctionalization can be driven solely by Mutational Robustness

mu

tati

onal

rob

ust

nes

s

generalists less robust than specialists

Figure from: Ugalde, Chang & Matz, Science 305, 1433 (2004)

Escape from Adaptive Conflict (EAC) in the real world

Experiments showing that a reconstructed common ancestor of the fluorescent proteins in corals that emit either red or green

light can emit light of both colors are indicative of EAC.

Sikosek & Chan (2014)

Experimentally designed bi-stable proteins and mutation-induced conformational switches

Bouvignies et al.,

Nature (2011)

Cordes et al., Nature

Struct Biol (2000)

Meier et al.,

Curr Biol (2007)

Alexander et al.,

PNAS (2009)

Anderson et al.,

Protein Eng Des Sel

(2011) Figure from:

Sikosek & Chan, J R Soc Interface (2014)

The GA/GB System: An Experimentally Designed Conformational Switch

Fig

ure

fro

m:

Ale

xan

der

et

al

(2009)

GA: 3α GB: 4β+α

● One-mutation switch between the human

serum albumin-binding domain (GA) and

the IgG-binding domain (GB) of

Streptococcus protein G [Alexander, He,

Chen, Orban & Bryan, PNAS 106, 21149

(2009)]. NMR structures were determined for GA98 & GB98 (the 56aa sequences are 98% identical,

differ only by one single L45Y substitution ).

Can theory capture the

biophysics of this

switching behavior?

Explicit-water molecular dynamics

simulations using current force

fields cannot account for this

behavior to date [van Gunsteren

and coworkers, Biochemistry

50:10965 (2011); 52:4962 (2013)]

Shea et al., PNAS (1999); Micheletti et al., Phys Rev Lett (1999); Clementi et al., JMB (2000); Koga & Takada, JMB (2001); Kaya & Chan, JMB (2003)

Gō (Native-Centric, Structure-Based) Protein Chain Models

CI2

Taketomi, Ueda & Gō, Int J Peptide Res (1975)

“Hybrid Models”

Augmenting the native-centric (SBM) potential with

sequence-dependent (transferrable) physical nonnative

effects such as hydrophobic interactions

total native-centric sequence-dependent

[cf. Shea et al., J Chem Phys (1998); Clementi & Plotkin, Protein Sci (2004); Pogorelov & Luthey-Schulten, Biophys J (2004)]

Zarrine-Afsar, Wallin, Neculai, Neudecker, Howell, Davidson & Chan, PNAS (2008)

Sikosek, Krobath & Chan, PLoS Comput Biol (2016)

Explicit-chain model for the GA/GB system:

A bi-stable, multiple-structure structure-based (native-centric)

potential (SBM)

Sikosek, Krobath & Chan, PLoS Comput Biol (2016)

*Irbäck & Mohanty, J Comput Chem 27:1548-55 (2006)

‡Chen, Song & Chan, Curr Opin Struct Biol (2015)

The experimental GA/GB trend is captured by an explicit-chain hybrid‡ atomic model

bi-stable Gō (native-centric SBM) + PROFASI* (simple, physical & transferrable)

−T

ln(p

op

ulatio

n)

QB

QA

0 1

1 L45Y

■ Biophysical sequence-to-structure

mappings based upon simple explicit-

chain protein models are versatile

conceptual tools for addressing general

principles of evolution.

■ Subfunctionalization after duplication

of a bi-stable gene with dual functions

can be driven by sequence-space

topology (i.e., mutational robustness) in

an essentially nonadaptive manner.

■ The hybrid approach to modeling

protein folding can be applied in the

context of a simple atomic potential to

Summary

Mutational effects on the GA/GB

energy landscape (Sikosek et al., 2016)

rationalize the GA/GB conformational switch. Our physics-based analysis

suggests a significant role of nonpolar and aromatic interactions in the striking

behavior of this system. But probably much remains to be learn before we can

provide an account based entirely on a transferrable interaction potential.

Experimental study by: Nott, Petsalaki, Farber, Jervis, Fussner, Plochowietz, Craggs,

Bazett-Jones, Pawson, Forman-Kay & Baldwin, Mol Cell (2015)

Intrinsically Disordered N Terminus of RNA Helicase Ddx4 Forms Organelles in Cells and in vitro

● Ddx4 proteins are

essential for the assembly

and maintenance

of the related nuage in

mammals, P-granules in

worms, and

pole plasm and polar

granules in flies.

Modeling Liquid-Liquid Phase Separation of Intrinsically Disordered Proteins

Results & Figure from: Nott et al., Mol Cell (2015)

HeLa cells

Ddx4 Spontaneously Self-Assembles to Form Organelles in Live Cells

150 mM → ~150 μM ionic strength

in live

cell:

in

vitro:

Fluorescence recovery

after photobleaching

in v

itro

in c

ell

Ddx4 Reversibly Forms Organelles In Live Cell and In Vitro


Charge-Scrambled and F→A Mutants of Ddx4 Do Not Form

Organelles in Cell or in vitro under Physiological Conditions


Sequence dependence of IDP liquid-liquid phase separation:

An Approximate Analytical Theory for Electrostatics-Driven Sequence-Dependent Heteropolymer Phase Separation

■ The approximate partition function

depends only on the 0th-order and 2-body

correlation of density (ρ) fluctuation:

■ This approach is known as “random phase

approximation” (RPA)*.

■ RPA accounts for pairwise electrostatic

interactions but neglected higher order

density correlation arising from chain

connectivity.

■ RPA provides an approximate account of

chain connectivity and hence sequence-

dependent interactions (beyond mean-field).

density ρ(r) ~ concentration c(r)

biphasic region

Figures from:

Doi & Edwards,

The Theory of

Polymer

Dynamics

(Oxford 1986). *see, e.g., Mahdi & Olvera de la Cruz, Macromolecules 33:7649 (2000)

■ Free energy per

unit volume:

■ Flory-Huggins (FH)

mixing and excluded

volume entropy:

■ Electrostatic free

energy in RPA:

where Ĝk, Ûk, and ρ ̂ are (N + 2) × (N + 2) matrices; N = chain length. The formulation is set up to account for the charge pattern of the N amino acids along the sequence.

■ The other 2 components are for the +/‒ ions (salt and/or counterions) in solution. A dielectric constant is used but electrostatic screening is treated directly (not via Debye length).

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

Theory of Sequence-Dependent Polyampholyte Phase Separation


positive

negative

aromatic

salt-free and

salt-dependent

co-existence

curves

Consistent with experiment, RPA predicts a significantly higher propensity for

wildtype Ddx4N1 than the charge-scrambled mutant Ddx4N1CS to phase separate

wildtype charges exhibit

block-like properties


Figure from: Meyer, Castellano & Diederich,

Angew Chem Int Ed (2003)

π-π stacking

cation-π

π-π stacking O-H/π fe → fe + fFH

Augmented RPA+FH Theory that accounts also for π-interactions and possibly other effects

where fFH is a mean-field term for π-interactions

agrees well

with

experiments

π-interactions

Figures from: R. K. Das & R. V. Pappu, Proc Natl Acad Sci USA 110:13392–13397 (2013)

same number of + and ‒ charges

Average

radius of

gyration

κ: a charge pattern parameter that quantifies local deviations from global charge asymmetry

Single-chain IDP conformational dimensions are highly sensitive to not

only total positive and negative charges but also the exact charge pattern

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

Multiple-chain phase separation and single-chain conformational compactness of charged disordered proteins are strongly correlated

critical temperature radius of gyration

γ ≈ 5.8

Single-chain conformational compactness and multiple-chain

phase separation are favored by similar block-like charge

patterns that promote sequence-nonlocal attraction


Sawle & Ghosh, J Chem Phys (2015)

Das & Pappu, PNAS (2013)

Sequence charge pattern parameters are predictive of

conformational dimensions and phase separation tendency


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

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

Binary Coexistence of Two Charged Sequences: A step toward understanding the mechanisms of molecular recognition in IDP phase separation

generalization:

generalization:


Coexistence Conditions are determined numerically by

identifying phase-separated volume fractions that are consistent

with the bulk volume fractions but yield a lower free energy


T* = 4

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

Varies Significantly with the Charge Patterns Along their Sequences



Asymmetry in the concentration ratios of two polyampholytes 1, 2 in the two phase-separated states α, β correlates with the difference in the sequences’ charge patterns

Some membraneless organelles are essentially condensed liquids

underpinned by IDP liquid-liquid phase separation. It is a fundamental

form of cellular compartmentalization enabling spatial and temporal

organization of biomolecular processes.

Some IDP phase separation are associated with pathologies.

The phase behaviors of IDPs – involving a single or multiple IDP

species – are based on sequence-dependent multivalent interactions.

RPA provides a reasonable account of the effect of charge pattern on

phase separation, as exemplified by the comparison with experimental

data on Ddx4.

Charge pattern matching can be a “fuzzy” mode of molecular

recognition for partitioning different IDPs into different membraneless

organelles and their subcompartments.

Future efforts should be extended to treat the sequence dependence of

other forms of interactions and to assess the accuracy of the analytical

theory by explicit-chain simulations.

Summary

Suman DAS • Yi-Hsuan LIN Alan AMIN

Former group members:

Artem Badasyan

Mikael Borg

Tao Chen

Cristiano Dias

Allison Ferguson

Loan Huynh

Hüseyin Kaya

Michael Knott

Heinrich Krobath

Zhirong Liu

Maria Sabaye Moghaddam

Seishi Shimizu

Tobias Sikosek

Jianhui Song

Stefan Wallin

Zhuqing Zhang

Coworkers University of Toronto University of Toronto

Prof. Julie D. Forman-Kay Dr. Patrick Farber Dr. Veronika Csizmok

Prof. Claudiu C. Gradinaru Gregory-Neal Gomes

Prof. Régis Pomès

University of Münster Prof. Erich Bornberg-Bauer

Supported by the Canadian Institutes of Health Research, Natural Sciences and Engineering Research Council of Canada

Baylor College of

Medicine Prof. E. Lynn Zechiedrich Jennifer K. Mann

Current group members:

Peking University Prof. Zhirong Liu

physics of protein function and evolution: from sequence...

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