-
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
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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.
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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:
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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).
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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)
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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)
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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)
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Zeng et al. & Zhang, Cell 166:1163–1175 (2016)
http://www.ust.hk/
Protein Phase Transition in Synaptic Function
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Organelles: Substructures - “little organs” - of the Cell
Organelles can be membrane-bound or membrane-less
Plant cell Animal cell
Figures from: Encyclopædia Britannica (2010)
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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)]
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Nucleoli in C. elegan
Image credit: Stephanie Weber, Department of Biology, McGill
University
Weber & Brangwynne, Curr Biol 25:64106 (2015)
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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
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Hydrophobic Interaction is a Major Driving Force for Protein
Folding
Chan & Dill, Physics Today (1993)
Kauzmann (1959), Dill (1990), etc.
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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
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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)
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Evolutionary Paths and Conformational Switches in
Sequence Space
Lipman & Wilbur, Proc R Soc London B (1991)
Neutral net Neutral net
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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.
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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
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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.
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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
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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
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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.
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Sikosek & Chan (2014)
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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)
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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)]
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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)
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“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)
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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)
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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
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■ 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.
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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
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Results & Figure from: Nott et al., Mol Cell (2015)
HeLa cells
Ddx4 Spontaneously Self-Assembles to Form Organelles in Live
Cells
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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
Results & Figure from: Nott et al., Mol Cell (2015)
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Charge-Scrambled and F→A Mutants of Ddx4 Do Not Form
Organelles in Cell or in vitro under Physiological
Conditions
Results & Figure from: Nott et al., Mol Cell (2015)
Sequence dependence of IDP liquid-liquid phase separation:
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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)
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■ 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
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Lin, Forman-Kay & Chan, Phys Rev Lett (2016); Lin, Song,
Forman-Kay & Chan, J Mol Liquids (2017)
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
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Lin, Forman-Kay & Chan, Phys Rev Lett (2016); Lin, Song,
Forman-Kay & Chan, J Mol Liquids (2017)
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
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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
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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
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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)
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Sawle & Ghosh, J Chem Phys (2015)
Das & Pappu, PNAS (2013)
Sequence charge pattern parameters are predictive of
conformational dimensions and phase separation tendency
Y.-H. Lin & H.S. Chan, Biophys J (2017)
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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
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Lin, Brady, Forman-Kay & Chan, New J Phys (2017)
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Binary Coexistence of Two Charged Sequences: A step toward
understanding the mechanisms of molecular recognition in IDP phase
separation
generalization:
generalization:
Lin, Brady, Forman-Kay & Chan, New J Phys (2017)
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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
Lin, Brady, Forman-Kay & Chan, New J Phys (2017)
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T* = 4
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)
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Lin, Brady, Forman-Kay & Chan, New J Phys (2017)
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
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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
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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