Liquid–liquid phase separation (LLPS) in macromolecular solutions (e.g., coacervation) is relevant both to technology and to the process of mesoscale structure formation in cells. The LLPS process is characterized by a phase diagram, i.e., binodal lines in the temperature/concentration plane, which must be quantified to predict the system’s behavior. Experimentally, this can be difficult due to complications in handling the dense macromolecular phase. Here, we develop a method for accurately quantifying the phase diagram without direct handling: We confine the sample within micron-scale, water-in-oil emulsion droplets and then use precision fluorescent imaging to measure the volume fraction of the condensate within the droplet. We find that this volume fraction grows linearly with macromolecule concentration; thus, by applying the lever rule, we can directly extract the dense and dilute binodal concentrations. We use this approach to study a model LLPS system of self-assembled, fixed-valence DNA particles termed nanostars (NSs). We find that temperature/concentration phase diagrams of NSs display, with certain exceptions, a larger co-existence regime upon increasing salt or valence, in line with expectations. Aspects of the measured phase behavior validate recent predictions that account for the role of valence in modulating the connectivity of the condensed phase. Generally, our results on NS phase diagrams give fundamental insight into limited-valence phase separation, while the method we have developed will likely be useful in the study of other LLPS systems.

1.
H. R.
Kruyt
and
H. G.
Bungenberg de Jong
, “
Zur kenntnis der lyophilen kolloide
,”
Kolloidchem. Beih.
28
,
1
54
(
1928
).
2.
R. J.
Stewart
,
J. C.
Weaver
,
D. E.
Morse
, and
J. H.
Waite
, “
The tube cement of Phragmatopoma californica: A solid foam
,”
J. Exp. Biol.
207
,
4727
4734
(
2004
).
3.
J. H.
Waite
,
N. H.
Andersen
,
S.
Jewhurst
, and
C.
Sun
, “
Mussel adhesion: Finding the tricks worth mimicking
,”
J. Adhes.
81
,
297
317
(
2005
).
4.
C. P.
Brangwynne
,
T. J.
Mitchison
, and
A. A.
Hyman
, “
Active liquid-like behavior of nucleoli determines their size and shape in Xenopus laevis oocytes
,”
Proc. Natl. Acad. Sci. U. S. A.
108
,
4334
4339
(
2010
).
5.
D.
Bracha
,
M. T.
Walls
,
M.-T.
Wei
,
L.
Zhu
,
M.
Kurian
,
J. L.
Avalos
,
J. E.
Toettcher
, and
C. P.
Brangwynne
, “
Mapping local and global liquid phase behavior in living cells using photo-oligomerizable seeds
,”
Cell
175
,
1467
1480
(
2018
).
6.
K.
Rippe
, “
Liquid–liquid phase separation in chromatin
,” in
Cold Spring Harbor Perspectives in Biology
(
Cold Spring Harbor Laboratory Press
,
2021
).
7.
J.-K.
Ryu
,
D.-E.
Hwang
, and
J.-M.
Choi
, “
Current understanding of molecular phase separation in chromosomes
,”
Int. J. Mol. Sci.
22
,
10736
(
2021
).
8.
R. A.
Jain
, “
The manufacturing techniques of various drug loaded biodegradable poly(lactide-co-glycolide) (PLGA) devices
,”
Biomaterials
21
,
2475
2490
(
2000
).
9.
C.
Luebbert
,
F.
Huxoll
, and
G.
Sadowski
, “
Amorphous-amorphous phase separation in API/polymer formulations
,”
Molecules
22
,
1
17
(
2017
).
10.
C.
Luebbert
,
E.
Stoyanov
, and
G.
Sadowski
, “
Phase behavior of ASDs based on hydroxypropyl cellulose
,”
Int. J. Pharm.: X
3
,
100070
(
2021
).
11.
D.
Eratte
,
B.
Wang
,
K.
Dowling
,
C. J.
Barrow
, and
B. P.
Adhikari
, “
Complex coacervation with whey protein isolate and gum Arabic for the microencapsulation of omega-3 rich tuna oil
,”
Food Funct.
5
,
2743
2750
(
2014
).
12.
Z.
Xiao
,
W.
Liu
,
G.
Zhu
,
R.
Zhou
, and
Y.
Niu
, “
A review of the preparation and application of flavour and essential oils microcapsules based on complex coacervation technology
,”
J. Sci. Food Agric.
94
,
1482
1494
(
2014
).
13.
S.
Alberti
,
A.
Gladfelter
, and
T.
Mittag
, “
Considerations and challenges in studying liquid-liquid phase separation and biomolecular condensates
,”
Cell
176
,
419
434
(
2019
).
14.
Y.
Luo
,
M.
Gu
,
C. E. R.
Edwards
,
M. T.
Valentine
, and
M. E.
Helgeson
, “
High-throughput microscopy to determine morphology, microrheology, and phase boundaries applied to phase separating coacervates
,”
Soft Matter
18
,
3063
3075
(
2022
).
15.
S.
Biffi
,
R.
Cerbino
,
F.
Bomboi
,
E. M.
Paraboschi
,
R.
Asselta
,
F.
Sciortino
, and
T.
Bellini
, “
Phase behavior and critical activated dynamics of limited-valence DNA nanostars
,”
Proc. Natl. Acad. Sci. U. S. A.
110
,
15633
15637
(
2013
).
16.
K. A.
Black
,
D.
Priftis
,
S. L.
Perry
,
J.
Yip
,
W. Y.
Byun
, and
M.
Tirrell
, “
Protein encapsulation via polypeptide complex coacervation
,”
ACS Macro Lett.
3
,
1088
1091
(
2014
).
17.
S.
Deshpande
and
C.
Dekker
, “
Studying phase separation in confinement
,”
Curr. Opin. Colloid Interface Sci.
52
,
101419
(
2021
).
18.
A.
Hensley
,
W. M.
Jacobs
, and
W. B.
Rogers
, “
Self-assembly of photonic crystals by controlling the nucleation and growth of dna-coated colloids
,”
Proc. Natl. Acad. Sci. U. S. A.
119
,
e2114050118
(
2022
).
19.
A.
Villois
,
U.
Capasso Palmiero
,
P.
Mathur
,
G.
Perone
,
T.
Schneider
,
L.
Li
,
M.
Salvalaglio
,
A.
deMello
,
S.
Stavrakis
, and
P.
Arosio
, “
Droplet microfluidics for the label-free extraction of complete phase diagrams and kinetics of liquid–liquid phase separation in finite volumes
,”
Small
18
,
2202606
(
2022
).
20.
D. C.
Johnston
,
Advances in Thermodynamics of the van der Waals Fluid
(
Institute of Physics Publishing
,
2014
).
21.
B.-j.
Jeon
,
D. T.
Nguyen
,
G. R.
Abraham
,
N.
Conrad
,
D. K.
Fygenson
, and
O. A.
Saleh
, “
Salt-dependent properties of a coacervate-like, self-assembled DNA liquid
,”
Soft Matter
14
,
7009
7015
(
2018
).
22.
N.
Conrad
,
T.
Kennedy
,
D. K.
Fygenson
, and
O. A.
Saleh
, “
Increasing valence pushes DNA nanostar networks to the isostatic point
,”
Proc. Natl. Acad. Sci. U. S. A.
116
,
7238
7243
(
2019
).
23.
F.
Bomboi
,
S.
Biffi
,
R.
Cerbino
,
T.
Bellini
,
F.
Bordi
, and
F.
Sciortino
, “
Equilibrium gels of trivalent DNA-nanostars: Effect of the ionic strength on the dynamics
,”
Eur. Phys. J. E
38
,
64
(
2015
).
24.
S.
Biffi
,
R.
Cerbino
,
G.
Nava
,
F.
Bomboi
,
F.
Sciortino
, and
T.
Bellini
, “
Equilibrium gels of low-valence DNA nanostars: A colloidal model for strong glass former
,”
Soft Matter
11
,
3132
3138
(
2015
).
25.
G.
Nava
,
M.
Rossi
,
S.
Biffi
,
F.
Sciortino
, and
T.
Bellini
, “
Fluctuating elasticity mode in transient molecular networks
,”
Phys. Rev. Lett.
119
,
078002
(
2017
).
26.
L.
Rovigatti
and
F.
Sciortino
, “
An accurate estimate of the free energy and phase diagram of all-DNA bulk fluids
,”
Polymers
10
,
447
(
2018
).
27.
E.
Lattuada
,
D.
Caprara
,
R.
Piazza
, and
F.
Sciortino
, “
Spatially uniform dynamics in equilibrium colloidal gels
,”
Sci. Adv.
7
,
eabk2360
(
2021
).
28.
T.
Lee
,
S.
Do
,
J. G.
Lee
,
D.-N.
Kim
, and
Y.
Shin
, “
The flexibility-based modulation of DNA nanostar phase separation
,”
Nanoscale
13
,
17638
17647
(
2021
).
29.
L.
Rovigatti
,
F.
Smallenburg
,
F.
Romano
, and
F.
Sciortino
, “
Gels of DNA nanostars never crystallize
,”
ACS Nano
8
,
3567
3574
(
2014
).
30.
E.
Locatelli
,
P. H.
Handle
,
C. N.
Likos
,
F.
Sciortino
, and
L.
Rovigatti
, “
Condensation and demixing in solutions of DNA nanostars and their mixtures
,”
ACS Nano
11
,
2094
2102
(
2017
).
31.
J.
SantaLucia
and
D.
Hicks
, “
The thermodynamics of DNA structural motifs
,”
Annu. Rev. Biophys. Biomol. Struct.
33
,
415
440
(
2004
).
32.
L.
Di Michele
,
B. M.
Mognetti
,
T.
Yanagishima
,
P.
Varilly
,
Z.
Ruff
,
D.
Frenkel
, and
E.
Eiser
, “
Effect of inert tails on the thermodynamics of DNA hybridization
,”
J. Am. Chem. Soc.
136
,
6538
6541
(
2014
).
33.
L.
Rovigatti
,
F.
Bomboi
, and
F.
Sciortino
, “
Accurate phase diagram of tetravalent DNA nanostars
,”
J. Chem. Phys.
140
,
154903
(
2014
).
34.
M. S.
Wertheim
, “
Fluids with highly directional attractive forces. I. Statistical thermodynamics
,”
J. Stat. Phys.
35
,
19
34
(
1984
).
35.
M. S.
Wertheim
, “
Fluids with highly directional attractive forces. II. Thermodynamic perturbation theory and integral equations
,”
J. Stat. Phys.
35
,
35
47
(
1984
).
36.
M. S.
Wertheim
, “
Fluids with highly directional attractive forces. III. Multiple attraction sites
,”
J. Stat. Phys.
42
,
459
476
(
1986
).
37.
W. G.
Chapman
,
G.
Jackson
, and
K. E.
Gubbins
, “
Phase equilibria of associating fluids
,”
Mol. Phys.
65
,
1057
1079
(
1988
).
38.
W. G.
Chapman
,
K. E.
Gubbins
,
G.
Jackson
, and
M.
Radosz
, “
New reference equation of state for associating liquids
,”
Ind. Eng. Chem. Res.
29
,
1709
1721
(
1990
).
39.
W.
Zmpitas
and
J.
Gross
, “
Detailed pedagogical review and analysis of Wertheim’s thermodynamic perturbation theory
,”
Fluid Phase Equilib.
428
,
121
152
(
2016
).
40.
S.
Alberti
,
S.
Saha
,
J. B.
Woodruff
,
T. M.
Franzmann
,
J.
Wang
, and
A. A.
Hyman
, “
A user’s guide for phase separation assays with purified proteins
,”
J. Mol. Biol.
430
,
4806
4820
(
2018
).
41.
S.
Choi
,
M. O.
Meyer
,
P. C.
Bevilacqua
, and
C. D.
Keating
, “
Phase-specific RNA accumulation and duplex thermodynamics in multiphase coacervate models for membraneless organelles
,”
Nat. Chem.
14
,
1110
1117
(
2022
).
42.
Y.
Hong
,
K. P.
Dao
,
T.
Kim
,
S.
Lee
,
Y.
Shin
,
Y.
Park
, and
D. S.
Hwang
, “
Label-free quantitative analysis of coacervates via 3D phase imaging
,”
Adv. Opt. Mater.
9
,
2100697
(
2021
).
43.
V. C.
Coffman
and
J.-Q.
Wu
, “
Counting protein molecules using quantitative fluorescence microscopy
,”
Trends Biochem. Sci.
37
,
499
506
(
2012
).
44.
T.
Kekic
and
J.
Lietard
, “
Sequence-dependence of Cy3 and Cy5 dyes in 3′ terminally-labeled single-stranded DNA
,”
Sci. Rep.
12
,
14803
(
2022
).
45.
P. M.
McCall
,
K.
Kim
,
A. W.
Fritsch
,
J.
Iglesias-Artola
,
L.
Jawerth
,
J.
Wang
,
M.
Ruer
,
J.
Peychl
,
A.
Poznyakovskiy
,
J.
Guck
,
S.
Alberti
,
A. A.
Hyman
, and
J.
Brugués
, “
Quantitative phase microscopy enables precise and efficient determination of biomolecular condensate composition
,” bioRxiv 2020.10.25.352823 (
2020
).
46.
D. R.
Jacobson
and
O. A.
Saleh
, “
Counting the ions surrounding nucleic acids
,”
Nucleic Acids Res.
45
,
1596
1605
(
2016
).
47.
M. J.
Cavaluzzi
and
P. N.
Borer
, “
Revised UV extinction coefficients for nucleoside-5′-monophosphates and unpaired DNA and RNA
,”
Nucleic Acids Res.
32
,
e13
(
2004
).
48.
J.
Schindelin
,
I.
Arganda-Carreras
,
E.
Frise
,
V.
Kaynig
,
M.
Longair
,
T.
Pietzsch
et al., “
Fiji: An open-source platform for biological-image analysis
,”
Nat. Methods
9
(
7
),
676
682
(
2012
).

Supplementary Material

You do not currently have access to this content.