*For correspondence:
icisse@mit.edu
Competing interests: The
authors declare that no
competing interests exist.
Funding: See page 23
Received: 29 June 2018
Accepted: 17 December 2018
Published: 04 February 2019
Reviewing editor: Antoine M
van Oijen, University of
Wollongong, Australia
Copyright Narayanan et al.
This article is distributed under
the terms of the Creative
Commons Attribution License,
which permits unrestricted use
and redistribution provided that
the original author and source are
credited.
A first order phase transition mechanism
underlies protein aggregation in
mammalian cells
Arjun Narayanan1, Anatoli Meriin2, J Owen Andrews1, Jan-Hendrik Spille1,
Michael Y Sherman3, Ibrahim I Cisse1*
1Department of Physics, Massachusetts Institute of Technology, Cambridge, United
States; 2Department of Biochemistry, Boston University School of Medicine, Boston,
United States; 3Department of Molecular Biology, Ariel University, Ariel, Israel
Abstract The formation of misfolded protein aggregates is a hallmark of neurodegenerative
diseases. The aggregate formation process exhibits an initial lag phase when precursor clusters
spontaneously assemble. However, most experimental assays are blind to this lag phase. We
develop a quantitative assay based on super-resolution imaging in fixed cells and light sheet
imaging of living cells to study the early steps of aggregation in mammalian cells. We find that even
under normal growth conditions mammalian cells have precursor clusters. The cluster size
distribution is precisely that expected for a so-called super-saturated system in first order phase
transition. This means there exists a nucleation barrier, and a critical size above which clusters grow
and mature. Homeostasis is maintained through a Szilard model entailing the preferential clearance
of super-critical clusters. We uncover a role for a putative chaperone (RuvBL) in this disassembly of
large clusters. The results indicate early aggregates behave like condensates.
Editorial note: This article has been through an editorial process in which the authors decide how
to respond to the issues raised during peer review. The Reviewing Editor’s assessment is that all
the issues have been addressed (see decision letter).
DOI: https://doi.org/10.7554/eLife.39695.001
Introduction
Neurodegenerative diseases, such as Parkinson’s disease, Amyotrophic Lateral Sclerosis, and Alz-
heimer’s disease, are characterized by the appearance of large protein aggregates in cells and in the
extracellular space (Selkoe, 2004). But the presence of aggregates does not always directly corre-
late with disease progression (Ross and Poirier, 2004). Intermediate species of aggregates, created
early in the aggregation process, could be more toxic to cells than large aggregates, plaques and
fibres (Cookson, 2005; Gosavi et al., 2002; Karpinar et al., 2009; Lashuel et al., 2002a;
Lashuel et al., 2002b; Pountney et al., 2004; Ross and Poirier, 2004; Xu et al., 2002). However,
the early steps of aggregate formation have been difficult to study, and may be critical to untangling
the relationship between aggregation and disease
Experimentally, late stages of aggregation can be measured both in vitro and in living cells, but
the very early steps of aggregate formation remain elusive due to methodological limitations. In pre-
vious studies, the dynamics of nucleation and growth (Fink, 1998; Morris et al., 2009) of protein
aggregates were most commonly measured experimentally in vitro (Buell et al., 2014; Jarrett and
Lansbury, 1993; Krishnan and Lindquist, 2005; Lomakin et al., 1996; Serio et al., 2000). Nucle-
ation in vitro typically requires a high concentration of purified monomers, which may not represent
physiological conditions in living cells. Alternatively, aggregate growth dynamics have been studied
in living cells, typically by seeding preformed ‘nuclei’ inside the living cells (Kaminski and Kaminski
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 1 of 26
RESEARCH COMMUNICATION
Schierle, 2016; Nonaka et al., 2010). These live cell experiments bypass the nucleation step alto-
gether by externally seeding the aggregation. Thus, neither of these approaches has captured the
early stages of protein aggregation that are likely to occur in unperturbed cells.
A direct experimental readout of the very early nucleation steps, ideally directly inside an unper-
turbed cell, is a challenge. The initial nuclei may be sub-diffractive in size (and indeed they are for
this study), which makes them difficult to capture by conventional imaging techniques. In vitro imag-
ing of de novo assembly must rely on high resolution techniques like scanning transmission electron
microscopy (STEM), atomic force microscopy (AFM), or super-resolution fluorescence microscopy to
observe early aggregates (Gaczynska and Osmulski, 2008; Kaminski and Kaminski Schierle, 2016;
Sunde and Blake, 1997). Although super-resolution imaging has been performed in living cells after
seeding the cells with preformed small fibers, these studies have focused primarily on capturing sta-
bly growing fibers (Kaminski and Kaminski Schierle, 2016) rather than the transient early precur-
sors. To our knowledge the size distribution, cluster dynamics, and physical nature of early pre-
nucleation stage protein aggregates have not been previously determined.
Here, we elucidate the early formation mechanism of misfolded protein aggregates directly in
mammalian cells. We use super-resolution microscopy in fixed cells and light sheet microscopy in liv-
ing cells to capture the nucleation stage of aggregate formation (Figure 1A). We find that precursor
clusters exist in cells even under normal growth conditions. Moreover, the size distribution of these
precursor clusters is robustly consistent with a textbook example of classical nucleation theory. Clas-
sical nucleation theory considers a simple question: Given a collection of molecules, if a subset of
the molecules cluster together, would this raise or lower the energy of the system. It makes a spe-
cific prediction about the distribution of cluster sizes. An alternative mechanism, such as a vectorial
active transport that locally clusters monomers, is unlikely to result in the same cluster size
distribution.
The details of classical nucleation theory are revealing about how cells maintain homeostasis. The
so-called homogenous nucleation is a prototypical mechanism by which first order phase transitions
proceed (Kalikmanov, 2013; Sear, 2007; Slezov, 2009). A first-order phase transition describes the
discontinuous changes needed for a system to go from a dispersed phase to a condensed phase (or
vice versa). This may correspond to the concentration of a single component from its dispersed
phase (for example condensation) or the demixing of some components from a multicomponent
mixture (for example liquid-liquid phase separation). In these cases, there exists a saturation concen-
tration above which the system transitions from dispersed to clustered phase – or from the mixed to
the de-mixed phase. The saturation point then categorizes systems in two possible regimes, either
sub-saturated or super-saturated. In the sub-saturated regime, the concentration of monomers is
lower than the saturation concentration. The system can form clusters, but the clusters spontane-
ously lose molecules and dissolve. The sub-saturated state is a stable state in that the system
remains in the dispersed or mixed phase. In contrast, in a super-saturated state – when the ambient
concentration is above the saturation concentration - there exists a critical cluster size, below which
clusters spontaneously dissolve, and above which clusters will spontaneously grow. The super-satu-
rated state is metastable because clusters reaching a size above the critical size will grow at the
expense of the dispersed phase. The condensed phase is favoured, and the concentration of mono-
mers in the disperse phase –that is the super-saturation level of the system– gradually decreases as
larger clusters absorb monomers from the ambient environment. The theory of first order phase
transitions makes a distinct prediction for the distribution of the dissolving clusters which can be
used to distinguish sub-saturated from super-saturated states.
Because cells under normal growth conditions do not show large growing clusters traced by Syn-
philin1, the naive hypothesis is that the cell is in a sub-saturated state, which is normally a steady
state. However, we find that even under normal growth conditions, the distribution of clusters sug-
gest the cells are in a super-saturated state, which is normally not a steady state. Rather, our results
suggest that cells maintain homeostasis through a so-called Szilard model of non-equilibrium steady-
state super-saturation (Farkas, 1927; Slezov, 2009). The Szilard model describes how a system can
be maintained in steady state super-saturation if there is a mechanism to constantly clear the largest
clusters. This size-dependent clearance of large aggregates appears to be mediated by the putative
chaperone RuvbL.
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 2 of 26
Research Communication Physics of Living Systems
ED F
100 1000
3
7
20

G
=
-L
o
g
(P
(n
))
n
1=2/3
x103
0 1000 2000 3000
-8
-4
0
n

G
-n
2
/3
 f
it
x103
Data
Fit
0 1500 3000
4
8
-L
o
g
(P
(n
))
n
x103
5m Localizations/m
2
20000
B C Fixed
A Nucleation 
phase
(Lag Phase)
 
Growth
phase
Stationary
phase
 
Time from supersaturation
A
g
g
re
g
a
ti
o
n
 r
e
a
d
o
u
t
?
Rapid
growth  
Coarsening
Rc=nc
1/3
= 162 nm + 4 nm

Gbarrier=7.2 + 0.5 kBT
G
Aggregate size, n

G
(k
B
T
)
nc

Gbarrier
-
-
Figure 1. Super resolution imaging of fixed cells suggests that a condensation transition underlies aggregate formation. (A) Schematic of traditional
experimental readouts of protein aggregation. Such measurements are blind to the nucleation phase but begin to show signal during the growth phase
and stationary phase. (B) Conventional fluorescence image of Synphilin1-Dendra2 in mammalian cell. (C) Super resolved reconstruction of the same cell
reveals multiple sub-diffractive aggregates (see Figure 1—figure supplement 1 for representative DBSCAN images). (D) log-log plot of the free
energy from the distribution of aggregate sizes (see Box 1) reveal a low-n asymptote of slope 2/3, reminiscent of a surface energy limited system (an
2
3)
(See Figure 1—figure supplement 3 for evidence for homogenous decoration of clusters by Synphilin1). (E) Plot of the resultant after correction of
surface energy: by fitting an n2/3 surface energy term from the asymptote of (D) and subtracting it from the data,the resultant data is strikingly linear,
and has a negative slope, suggesting the second term (bn). (F) Fit of the distribution of aggregate sizes to the full function an
2
3  bn to obtain the a
and b parameters. The parameters define the nucleation barrier height and critical aggregate size (see Figure 1—figure supplement 2 for expression
level control and alternative tracer control, see Figure 1—figure supplement 5 for application to in neuronal precursor cells). (G) Schematic of the
energy function, as predicted for a super-saturated system undergoing first order phase transition. The line is dashed after the critical size to highlight
that the functional form is experimentally valid only below this size. The barrier height and critical radius from the fit in F are represented (see
Figure 1—figure supplement 4 for larger schematic and definition of terms in text). Data is from 25,000 aggregates from 28 fixed cells. Errors
represent s.e.m. All cells imaged in this figure were fixed cells. Log refers to the natural logarithm (base ‘e’) (see Figure 1—figure supplement 5 for
control in neuronal precursor cell line).
DOI: https://doi.org/10.7554/eLife.39695.002
The following figure supplements are available for figure 1:
Figure supplement 1. Super-resolution imaging and cluster identification using DBSCAN.
DOI: https://doi.org/10.7554/eLife.39695.003
Figure supplement 2. The effect of expression level, alternative protein markers.
DOI: https://doi.org/10.7554/eLife.39695.004
Figure supplement 3. The clusters have a well defined density.
DOI: https://doi.org/10.7554/eLife.39695.005
Figure supplement 4. Definition of terms in condensation theory.
DOI: https://doi.org/10.7554/eLife.39695.006
Figure supplement 5. Comparison between cluster size distributions in MCF10A and Neuro2A cell lines.
DOI: https://doi.org/10.7554/eLife.39695.007
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 3 of 26
Research Communication Physics of Living Systems
Results
Super-resolution imaging of fixed cells suggests classical nucleation
theory underlies aggregate formation
We engineered mammalian cell lines expressing Synphilin1 - a tracer of aggregates in Parkinson’s
disease (Chung et al., 2001; Tanaka et al., 2004; Wakabayashi et al., 2000) - fused to a fluorescent
protein Dendra2 (Chudakov et al., 2007). Dendra2 is a green to red photo-convertible protein that
enables photo-activation localization microscopy (PALM) (Betzig et al., 2006), a single-molecule
based super-resolution (Betzig et al., 2006; Hess et al., 2006; Rust et al., 2006) approach we used
previously to study protein clustering in mammalian cells (Cho et al., 2016; Cisse et al., 2013). How
Synphilin1 is recruited to aggregates is not fully understood. However, this protein is a commonly
used tracer for well-studied misfolded protein aggregates such as Lewy bodies (Tanaka et al., 2004;
Wakabayashi et al., 2000). Here, we concentrate on sub-diffractive Synphilin1 traced aggregates
whose size distribution we measure. We checked that neither the expression level of Synphilin1
tracer protein nor the identity of the tracer (alternative tracer alpha-Synuclein) have any detectable
effect on the size distribution of sub-diffractive clusters (Figure 1—figure supplement 2). This sug-
gests that Synphilin1 in our sub-diffractive clusters merely serves as a tracer and does not on its own
affect cluster formation at the expression levels tested.
Wide-field epi-illumination (conventional) imaging of Synphilin1 in a fixed cell showed a diffuse
cytoplasmic signal without any apparent aggregation (Figure 1B) as expected for a normal (i.e. with-
out drug treatments) cell. However, super-resolution imaging of the same cell clearly revealed a
large population of sub-diffractive clusters (Figure 1C).
We characterized the properties of these sub-diffractive clusters using density based spatial clus-
tering of applications with noise (DBSCAN) (Ester et al., 1996) (Figure 1—figure supplement 1).
We measured the radius and the number of localization events (corresponding to the fluorescent
photo-activation and detection events) (see Materials and methods and Figure 1—figure supple-
ment 3). We find that the number of localization events in a cluster, scales with the cube of the mea-
sured cluster radius This suggest that, at the relevant cluster sizes, the fluorescent detection events
of the Synphilin1 tracer protein may be spread throughout the cluster volume at uniform density
(Figure 1—figure supplement 3). Only clusters with a radius greater than our localization accuracy
[estimated to be ~20nm (Cho et al., 2016)] are interpreted in our analysis. For the analysis that fol-
lows, we defined the cluster size as a variable ‘n’, given by n ¼ R
1 nm
 
3
where R is the measured clus-
ter radius in nanometres (Figure 1—figure supplement 3). Here, the parameter n is proportional to,
but different from the actual number of molecules in a cluster; the proportionality constant is deter-
mined by the density of all monomers in the cluster which is not known.
Following our observation of sub-diffractive clusters in the cell, we searched for signs of a thermo-
dynamically driven first order phase transition in which spontaneous nucleation and growth mecha-
nisms arise (Slezov, 2009). In condensation, the free energy change accompanying the clustering of
n molecules into a single condensate is: G ¼ an2=3  bn [See Box 1]. The first term is the surface term
and accounts for the interfacial energy of the n2=3 / R2 molecules on the surface of the condensate;
the parameter ‘a’ serves as (positive) surface energy parameter. The second term is the bulk term
and depends on the total number of molecules in the volume (n1 / R3Þ of the cluster; ‘b’ serves as a
(positive) bulk energy parameter, and the positive or negative signs in front depends on whether the
system is sub-saturated or super-saturated respectively [See Box 1]. The theory of first order phase
transitions allows the determination of the free energy directly from the distribution of cluster sizes
(which will follow P nð Þ ¼ AeG=kBT but with corresponding positive or negative bulk energy term in
the free energy differentiating between sub- or super- saturation respectively) [See Box 1]
To test the applicability of this theory to our data, we examine the distribution of cluster sizes.
For either a sub-saturated or a super-saturated system the free energy as a function of cluster size is
DG nð Þ ¼ kBTLog P nð Þð Þ [for n<nc, in the super-saturated case (Slezov, 2009)] where kB is the Boltz-
mann constant, T the temperature (in Kelvin); P(n) represents the histogram (formally the normalized
distribution function) of cluster sizes, and nc the size of maximum DG [Figure 1—figure supplement
4 and (Slezov, 2009)]. That any of this is valid for the formation of endogenous aggregates inside
living cells – complex, highly regulated, multicomponent entities forming in an intrinsically non-equi-
librium environment in vivo – we could not a priori know. However, by investigating the features of
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 4 of 26
Research Communication Physics of Living Systems
Box 1. Determining the free energy from distribution of
cluster sizes.
Here we briefly describe how the free energy change in assembling a cluster of n molecules
from the disperse phase - introduced in the main text as consisting of a surface and a bulk term
– depends on system composition, how it describes behavior above and below the saturation
concentration and how we can directly compute this function from experimental measurements.
The equation DG ¼ an2=3  bn presented in the main text, is a simplified equation that can be
derived exactly– it consists of two terms.
1) The Surface term DGsurface ¼ an
2=3 represents the energetic cost of setting up an interface
between the clusters and ambient solution (or equivalently the interface between two liquid
phases of de-mixed components in phase separation). The prefactor a is related to the compo-
sition of the system. Consider a cluster of n molecules of volume vn ¼ nv1 where v1 is the aver-
age volume taken by 1 molecule in the clustered phase. For spherical clusters of constant
density v1 ¼ M=NA (M is molar mass,  is density and NA is Avogadro’s number) and thus:
4
3
pR3n ¼ vn
and 4pR2n ¼ An
Therefore,
Rn ¼
3v1
4p
 1=3
n1=3 and An ¼ 36pð Þ
1=3
v
2=3
1
n2=3
If the energy per unit area of the interface is s– then the surface energy term is
DGsurface ¼ sAn ¼ s 36pð Þ
1=3
v
2=3
1
n2=3
So that we recover the form DGsurface ¼ a n
2=3. The prefactor a ¼ s 36pð Þ1=3v
2=3
1
depends on the
specific interactions and geometric details of the interface between the two phases.
2) The bulk term, DGbulk ¼ bn represents the difference in free energy between a system with
all molecules in the ambient phase, and a system with n molecules in the clustered phase. In
this case, it can be shown (Abraham, 1974) that for a cluster of n molecules
DGbulk ¼ D n with D ¼ kBTLog
camb
csat
 
. Where camb is the ambient monomer concentration and
csat is the saturation concentration - the concentration that would be at equilibrium with the
clustered phase. Log refers to the natural logarithm (base ‘e’). D depends on both the ambient
concentration of monomers and the interactions of the monomers in the two phases and
changes sign at camb ¼ csat. DGbulk ¼ bn with the sign depending on whether camb < csat (positive
sign) or camb > csat (negative sign) Therefore, for a given set of interactions, the ambient concen-
tration alone can control which of the two phases is favoured and by how much. The system is
referred to as sub-saturated when camb < csat, and thus the bulk term DGbulk ¼ þbn. On the other
hand super-saturated systems, camb > csat, result in a bulk term DGbulk ¼ bn.
Therefore, if the system is sub-saturated DG ¼ an2=3 þ bn, both the terms add so that the free
energy continuously increases with increasing cluster size n. This energy function has no maxi-
mum, and therefore there is no nucleation barrier beyond which clusters stably grow. Any clus-
ter formed is energetically costly, and bigger clusters are increasingly more costly. Clusters that
form in sub-saturated state will be driven to dissipate. In a sub-saturated system, the distribu-
tion of cluster sizes is given by P nð Þ ¼ AeG=kBT (where A is a factor that normalizes the probabil-
ity distribution), and the free energy DG nð Þ ¼ kBTLog P nð Þð Þ (offset by a constant due to the
normalization factor A, see Materials and methods).
On the other hand, if the system is super-saturated, DG ¼ an2=3  bn with the two terms in
DG having opposite signs. This balance between a positive surface energy and a negative bulk
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 5 of 26
Research Communication Physics of Living Systems
the experimentally measured DG nð Þ ¼ kBTLog P nð Þð Þ we find the energetics of a condensing super-
saturated system. Since classical nucleation theory makes predictions on the distribution of sub-criti-
cal clusters, we consider the behavior of our experimentally measured free energy function
DG nð Þ ¼ kBTLog P nð Þð Þ for low n values(Log refers to the natural log (Base ‘e’)). The log-log plot of
our experimentally measured DG(n) reveals a linear asymptote of slope =g1 ¼ 2=3 for small n values
(Figure 1D). This evokes a system dominated by a surface energy (n2=3 / R2Þ for small clusters. We
then fitted the first few data points of DG(n), corresponding to the smallest clusters, to estimate a
surface energy term an2=3 and subtracted it off of the data ðDG(n)-an2=3Þ to obtain the resultant after
surface correction. The resultant was linear (g2=1) to within our experimental uncertainty suggestive
of a bulk (volumetric, n1 / R3Þ energy contribution (Figure 1E). Moreover the slope is negative, indi-
cating that the (negative) bulk energy term (-bn) minimizes the free energy. A positive surface ten-
sion balanced by negative bulk energy is the key signature of a super-saturated condensing system;
the combination gives rise to a well-defined maximum free energy representing the free energy bar-
rier for nucleation DG ncð Þð Þ, and the corresponding critical cluster size nC ¼
2a
3b
 
3
above which clus-
ters are thermodynamically stable and will spontaneously grow. By contrast, a sub-saturated system
has the same surface term an2=3
 

, but a positive (+bn) bulk term such that there is no maximum to
the free energy and therefore no regime for stable cluster growth (Slezov, 2009). Therefore, the
analysis of the cluster size distribution in unstressed cells reveals the precise energetics of a super-
saturated system undergoing first-order phase transition (Abraham, 1974; Slezov, 2009).
By fitting the data, plotted as -Log(P(n)) to the functional form DG nð Þ ¼ an2=3  bn(Figure 1F)
(where for the case described in Box 1, a ¼ 36pð Þ1=3
h i
sv
2=3
1
=kBT is the dimensionless surface energy,
b ¼ Log camb
csat
 
is the dimensionless bulk energy term and DG nð Þ is consequently in units of kBT), we
obtain the two parameters a ¼ 1:07  103 0:06 103ð Þ and b ¼ 4:3  106 3 107ð Þ (best fit,
mean  (s.e.m)) which determine the thermodynamic properties of the condensation process
(Figure 1G and Figure 1—figure supplement 4). Using these parameters, we can now extract two
important biophysical properties of the process: the critical radius and the nucleation barrier (see
Materials and methods). The nucleation barrier is DG ¼ 7.2 (±0.5) kBT, and the critical radius (i.e. the
radius above which clusters will spontaneously grow) is Rc=162 (±4) nm (mean  (s.e.m))
(Materials and methods).
Because the critical radius Rc is below the optical diffraction limit, this explains why a super-reso-
lution technique was required to measure it. However, we were surprised that the value was as big
as it is, because it is much higher than what would be predicted if a few monomers were sufficient to
contribution leads to a maximum in the free energy. An energy barrier and the critical cluster
size for the system are at that point where the free energy function is maximal: nC ¼
2a
3b
 
3
Below
this critical size, clusters formation and growth is energetically costly (positive slope DG), and
such ’sub-critical’ clusters are thermodynamically driven to dissolve. Above this critical size, clus-
ter growth is energetically favoured (negative slope DG; if a cluster grows to a size greater than
the critical size, it will grow at the cost of the monomer pool (and hence reduce the ambient
concentration). For the duration while a super-saturated concentration is maintained, the theory
has a simple prediction for the size distribution of sub-critical clusters. The sub-critical cluster
size distribution is a Boltzmann distribution (Slezov, 2009) (but with the negative sign of the
bulk term in DG in contrast to the sub-saturation distribution). P nð Þ ¼ AeDG=kBT (where A is a fac-
tor that normalizes the probability distribution) and DG nð Þ ¼ kBTLog P nð Þð Þ (offset by a constant
due to the normalization factor A, see Materials and methods).
Such super-saturated states are normally transient. Given the interactions and the ambient con-
centrations, the free energy change favors the addition of each molecule to a super-critical clus-
ter, thereby continuously decreasing the ambient concentration until it reaches the saturation
level. Therefore in unusual cases the super-saturated state could be maintained if super-satu-
rated clusters were removed from the system, this is the principle behind the so-called Szilard
model.
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 6 of 26
Research Communication Physics of Living Systems
nucleate a stable cluster. Our results suggest that the initial clusters likely form through a condensa-
tion of weakly interacting monomers.
We tested if these conclusions were generalizable to another cell type by performing our assay
on clusters traced with dendra2-synphilin in Neuro2A cells (neuronal precursor cells, Figure 1—fig-
ure supplement 5); we also tested labeling aggregates with an alternate tracer protein alpha Synu-
clein (Figure 1—figure supplement 2). In all these cases we arrived at the identical distribution,
suggesting the physical mechanism for sub-diffractive Synphilin1- or alpha Synuclein-marked aggre-
gation may apply to a range of mammalian cells.
In summary, we developed a high-resolution imaging assay to look at the distribution of aggre-
gate (cluster) sizes in fixed cell snapshots. We exploited the theoretical premise that in the distribu-
tion of cluster sizes below the critical size (sub-critical), the distribution can be approximated as a
Boltzmann distribution. From this distribution we get the free energy. The resulting free energy
terms extracted from the data were a surface tension term balanced by a linear bulk term, exactly as
expected for the condensation of a super-saturated system. The free energy calculation allows us to
determine the nucleation energy barrier and the critical cluster size (above which the clusters grow
stably) for the aggregation inside mammalian cells. We could also determine how these quantities
change under varying conditions. An important conclusion in this section is that even under normal
growth conditions mammalian cells are super-saturated.
Super-saturation can be tuned by the levels of endogenous aggregating
polypeptides
To test our model, we study how drug treatments affect its parameters. As noted before, the ener-
getics of nucleation and growth depend on two parameters corresponding to a bulk term and a sur-
face term. These parameters derive from the microscopic biochemical interactions within the system,
and should depend on the concentration of aggregating proteins (which affects the bulk term) and
on their energy of interactions.
A major constituent of Synphilin1-traced aggregates is believed to be endogenous misfolded pol-
ypeptides (Zaarur et al., 2008). We employed methods to pharmacologically increase or decrease
the cellular concentrations of these predicted constituents and measured the effect on cluster
parameters (Rc and nucleation barrier). To decrease the concentration of aggregating polypeptides
we partially inhibited translation with Rapamycin (Jefferies et al., 1997) which reduces the pool of
newly synthesized misfolded, therefore aggregation prone, polypeptides (Conn and Qian, 2013;
Sherman and Qian, 2013). We confirm the results with treatment by direct translation inhibitor
Cycloheximide. By contrast, to increase the concentration of misfolded aggregating polypeptides,
we incubated cells either with azetidine-2-carboxylic acid (AZC), a proline analogue that promotes
misfolding of newly synthesized proteins (Goldberg and St John, 1976), or with the proteasome
inhibitor MG132 that reduces degradation of misfolded-proteins (Nawaz et al., 1999).
In Figure 2A–F we find that Rapamycin increases the nucleation barrier and critical radius, consis-
tent with expectation for reduced super-saturation. A similar effect is also observed in treatments
with the translational inhibitor cycloheximide (Figure 2—figure supplement 1). In contrast, treat-
ment with either MG132 or AZC decreases the nucleation barrier and critical radius, consistent with
expectation for increased super-saturation. Therefore, over a range of complex pharmacological per-
turbations –with simple intuition of how the perturbation would affect the saturation– the measured
effects match the expectation from classical nucleation theory.
In summary, in this section we tested the effect of different pharmacological perturbations. We
also confirmed here that the expression of the labelled tracer (Synphilin1) is not the main driving
force for clustering, consistent with the previous characterization that the tracer labels aggregates
that are mostly composed of misfolded polypeptides (JA, 2006; Meriin et al., 2012; Park et al.,
2017; Tanaka et al., 2004). We find that the theoretical model holds robustly under different drug
treatments that globally affect protein quality control: a drug that reduces global protein synthesis,
thereby reducing the concentration of misfolded polypeptides is found to reduce super-saturation
(i.e. increase the nucleation barrier and Rc) while a drug that promotes misfolding of newly synthe-
sized protein is found to increase the super-saturation (i.e. decreasing the nucleation barrier, and
Rc).
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 7 of 26
Research Communication Physics of Living Systems
1000 2000
4
8
-L
o
g
(P
(n
))
n
 AZC
 Normal
1000 2000
4
8
-L
o
g
(P
(n
))
n
 MG132
 Normal
 
B
D
10 μm
Localizations/μm2
200010000
C
5μm
Untreated
Localizations/μm2
200010000
G
Mg132
180 min
Localizations/μm2
200010000
10 μm
A AZC
L
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 Rapamycin
 Normal
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I J
Figure 2. Super-saturation can be tuned by the levels of endogenous aggregative polypeptides and RuvBL-dependent mechanism clears super-critical
clusters: (A–F) Representative super-resolved reconstruction and free energy functional fit for AZC- (A and B), MG132-(C and D), and Rapamycin- (E and
F) treated cells. Distribution functions were computed from 2500 to 10,000 clusters from 7 to 10 cells in each condition. Red-hot colour code is used to
indicate the relative density of detections in A, C, E. Gray plot in B, D, F represents the functional fit for untreated cells for comparison. (G)
Representative super-resolution reconstruction for an untreated cell showing many sub-diffractive aggregates (dark red) but few large aggregates (red
hot). (H) Schematic of the observed effects of the different pharmacological treatments. (I) Representative super-resolution reconstruction for a RuvBL
depleted cell and zoomed view of large (red hot) aggregates. (J) –Log(P(n)) versus n curve from 7000 clusters from 9 RuvBL depletion cells shows almost
no effect on the sub-critical distribution. (K–M), quantification of the effect of the perturbations and comparisons of relative changes in the distributions
of aggregate size (violin plot, (K), Rc (L) and the measure nucleation barrier; (M) the range of values in L and M is chosen to illustrate the main
differences. Error bars in L and M represent s.e.m in fit estimation (Materials and methods). All cells imaged in this figure were fixed cells. Log refers to
the natural log (base ‘e’) (See Figure 2 – figure supplement 1 for combined effect of AZC and MG).
DOI: https://doi.org/10.7554/eLife.39695.008
The following figure supplement is available for figure 2:
Figure supplement 1. The effect of aggregation promoting amino acid substitute (AZC), proteasome inhibitor (MG132), translation inhibitor
cycloheximide and the HSP70 inhibitor (Ver155008):
DOI: https://doi.org/10.7554/eLife.39695.009
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 8 of 26
Research Communication Physics of Living Systems
RUVBL-dependent mechanism clears super-critical clusters
The picture emerging from our analysis is that even untreated cells are super-saturated. In super-sat-
urated systems if even one cluster reaches the critical size it should spontaneously grow; that cluster
will come to dominate the system and absorb monomers until the system is no longer super-satu-
rated. A violin plot of cluster sizes from untreated cells (Figure 2K, black) indicates that while a large
population of small cluster sizes is apparent (indicated by the width of the violin plot in Figure 2K),
there is a small minority of clusters (<5%) that have reached a size greater than Rc. Therefore,
despite the fact that clusters do reach the critical size, such a population of super-critical clusters
seems to be suppressed in healthy cells; this is corroborated by images of untreated cells that are
distinctly devoid of large super-critical clusters (Figure 2G). In the theory of first-order phase transi-
tion, this observation is suggestive of a model with strict requirements: There ought to be a clear-
ance mechanism that acts on the super-critical clusters without significantly affecting the sub-critical
distribution.
Because a AAA+ ATPase, RuvBL, was previously suggested as a potential protein disaggregase
in mammalian cells and in yeast (Zaarur et al., 2015), we tested whether RuvBL may be involved in
the clearance of super-critical clusters. Consistent with this hypothesis, we find that knocking down
RuvBL1 in untreated cells results in the appearance of large clusters (Figure 2I, compare to
untreated cell Figure 2G). A violin plot of cluster sizes from RuvBL knocked-down cells shows a clear
population of large cluster sizes. Some clusters have radii greater than 1m, a size range that we
observed previously only after hours of proteasome inhibition (Figure 2K). These results implicate
RuvBL in the clearance of large clusters from untreated cells (see Figure 3 for further tests of RuvBL).
Importantly, we find that upon RuvBL knockdown, Rc ¼ 157  6 nm did not change significantly
from Rc in control untreated cells (162  4 nm) (Figure 2J) suggesting that RuvBL knockdown did
not significantly change the sub-critical distribution. This observation implies that RuvbL did not
affect the concentration of aggregating molecules or their interactions, unlike, for instance,
3
6
Barrier
(KT)
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Gbarrier
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Normal
A C D
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nn n
3
6
Barrier
(KT)
Figure 3. The Szilard non-equilibrium steady state accounts for all genetic and pharmacological and genetic stresses. (A) Schematic depiction of Szilard
mechanism for maintenance of super-saturated steady state by simultaneous regulation of monomer creation and super-critical elimination. The
suggested mode of action of the stress conditions utilized in Figure 2 and the RUVBL depletion discussed in Figure 2, and Figure 3 are indicated. (B)
Schematic of predicted effect of Mg132 washout on sub-critical cluster size distribution and free energy function. (C, D) Data plots of DG (n) vs. n
measured before and after washout both without (C) and with (D) RuvBL depletion. Each curve is generated from 2500 to 6000 clusters from 6 to 10
cells in the various conditions. (E) Critical radii measured with and without RuvBL depletion, before and after MG132 washout. (F) Violin plots of cluster
sizes in the four conditions of (C–E) showing that the super-critical clearance is impeded in the case of RuvBL depletion compared to un-depleted cells.
In (B–D), Log refers to the natural log (base ‘e’).
DOI: https://doi.org/10.7554/eLife.39695.010
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 9 of 26
Research Communication Physics of Living Systems
proteasome inhibition, and AZC incubation which reduced Rc (Figure 2B, D, E). Our data indicate
that RuvBL-dependent clearance of clusters acts preferentially on clusters that have reached a size
above Rc, without changing the sub-critical distribution or the nucleation process.
We also tested whether the classical HSP70-mediated pathway for disaggregation was involved
at this stage. HSP70 is known to disaggregate amyloid fibrils (Gao et al., 2015) and the chemical
Ver155008 inhibits HSP70 (Massey et al., 2010). However, here, using HSP70 inhibitor Ver155008
we were not able to generate a substantial population of super-critical clusters (Figure 2—figure
supplement 1). This suggests that the RuvBL mechanism is likely distinct from HSP70 mediated
disaggregation.
In summary, the ultimate end point of the phase transition that occurs in super-saturated systems
should be the formation of a large macroscopic condensed phase. We found it very surprising that
cells are super-saturated yet they do not have many super-critical clusters under normal growth con-
ditions. We argue that there exists a mechanism that preferentially clears large aggregates without
significantly affecting the pre-nucleated distribution of aggregates. We identify a putative protein
chaperone (RuvBL) that is key to this clearance mechanism.
The Szilard model for non-equilibrium steady state accounts for the
genetic and pharmacological stresses tested
Without a specific mechanism in place to maintain the state, a super-saturated distribution is tran-
sient and unstable. Even if new monomers are continuously produced, super-critical clusters sponta-
neously absorb monomers faster than new clusters can form. One mechanism, attributed to Leo
Szilard (Farkas, 1927; Slezov, 2009), was proposed to maintain a super-saturated distribution at
steady state, through the preferential clearance of super-critical clusters.
The Szilard mechanism maintains a non-equilibrium steady state through the continuous produc-
tion of aggregating monomers, their constant thermodynamically driven condensation (governed by
the free energy function describe earlier) and a mechanism for preferential clearance of clusters at
sizes greater than the critical size. Our data suggest a Szilard-type model (Figure 3A) whereby a
RuvBL-dependent mechanism may help maintain cellular homeostasis in normal cells. Constituent
monomers – the concentration of which may be affected through modulation of protein misfolding,
damage, translation or degradation (e.g. through drug treatment or aberrant cellular processes) –
condense through weak biochemical interactions with their condensation limited by their surface to
volume ratio. At some point after the clusters reach a critical size beyond which their growth is fav-
oured, they are subject to RuvBL-mediated clearance. These elements together explain the striking
agreement between the distribution of sub-critical clusters and the energetics of steady state super-
saturation in first order phase transitions. It also accounts for the measured effects of pharmacologi-
cal treatments (e.g. in Figure 2).
One implication of the Szilard model is that accumulation of super-critical clusters could result
from two independent mechanisms: increase in super-saturation (for example by proteasome inhibi-
tion or by increased expression of polypeptides) or alternatively by decreasing clearance (e.g. RuvBL
knock down). To test this inter-dependence, we performed the treatment by proteasome inhibitor
MG132 followed by washout, in cells with or without RuvBL knockdown. In all cases, after MG132
washout the free energy barrier returned to close to that of normal, untreated cells, suggesting that
regardless of RuvBL knockdown, MG132 acted to increase the super-saturation in a reversible man-
ner (Figure 3C–E). However, after washout the clearance of the super-critical clusters (which existed
during MG132 treatment) was only possible in the controls with normal levels of RuvBL. On the other
hand, in the cells where RuvBL was knocked down, although the free energy barrier returned close
to normal untreated level, a population of super-critical clusters remained after MG132 wash-out,
corroborating the fact that RuvBL was necessary for the clearance of the super-critical clusters. These
experiments lend further support for RuvBL’s role as a part of a super-critical cluster clearance mech-
anism and help to demonstrate how cellular relaxation and adaptation after complex combinations
of perturbations can be fully explained by the Szilard steady state model.
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 10 of 26
Research Communication Physics of Living Systems
Live cell imaging data further support the model of super-critical
clusters as condensates
All the analysis and conclusions thus far were driven by a free energy function extracted from a distri-
bution of cluster sizes in fixed cell snapshots. This model has implications about the clusters, which
can be tested in living cells. First, we aimed to test whether the same free energy function describes
the distribution of clusters in live cells. This required the development of a light-sheet-based imaging
assay where the brightness of the cluster is used as a proxy for cluster size. The distribution obtained
by light sheet imaging is biased toward brighter (i.e. larger sized) clusters compared to super-resolu-
tion imaging. Nonetheless we are able to resolve enough of the sub-critical distribution and verify
that the same free energy function describes the live cell data. Secondly, we used this live cell data
to estimate the surface tension of the cluster-cytoplasm interface. We found that the surface tension
is comparable to previous estimates of phase-separated condensates in the literature. Third, we
measured the growth kinetics of the few super-critical clusters found in the living cells. We found
that the growth and behavior of the super-critical clusters was entirely consistent with the model –
suggested by our analysis in the sub-critical regime- of cluster formation by condensation. In particu-
lar, we found that growth and shrinkage was size dependent as expected from classical nucleation
theory. We also found clusters underwent merger events (~1 mergers visible per cell imaged over
ten minutes) as would be expected of condensates.
Cluster size quantification in living cells corroborate fixed cell data
To study the nucleation process directly in living cells, the relatively fast motion of clusters in living
cells precluded our previously developed quantitative live cell super-resolution approaches
(Cho et al., 2016; Cisse et al., 2013). Here, we develop a complementary, light sheet based,
approach to study aggregation directly in the living cells. We opted for a non-diffractive, lattice light
sheet (Chen et al., 2014) approach to selectively illuminate a thin optical sheet in the living cells; the
reduced background of excited molecules we anticipated would give us sufficient contrast to detect
sub-diffractive clusters as bright diffraction-limited spots.
We found that the light sheet reveals many condensates as diffraction-limited spots throughout
the cell (Figure 4A and Videos 1 and 2). Since light-sheet microscopy is not inherently a super-reso-
lution technique, the apparent spot size is not the physical size of the cluster and it is impossible to
accurately correlate the total intensity of the clusters with their real volume. However, since we have
3
6
-
L
o
g
(
P
(
N
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Total intensity (N, Counts)
C
005 00010
Nc =          = 1400+300( )32a
3b -
ΔGbarrier=6.6 + 0.7 kBT-
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0.0
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(N
)
Total intensity (N, Counts)
0 2000
  .01
1
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(
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(N, Counts)
BA
Live(Light sheet)
10 μm
Figure 4. Cluster size quantification in living cells corroborates fixed cell data and the estimation of surface tension at the condensate-cytoplasm
interface. (A) 2D maximum intensity projection of 3D direct imaging of Dendra2-Synphilin1 traced aggregates in a representative cell imaged with light
sheet microscope. (B) Using the relative intensities rather than the radius as a measure of aggregate size, we may plot distributions that reproduce all
the features of the fixed cell measurements (N=2800 aggregates from 22 cells). Insets: log-linear plot. (C) The free energy functional fit (yielding
a ¼ 0:166 :01 and b ¼ 0:011 :001(best fit  s.e.m)) of the live cell data corroborates the conclusions of the condensation through first order phase
transition. Here, the variable parameter N is an estimate of the number of fluorescent Dendra2-Synphilin imaged per aggregate and Log refers to the
natural log (base ‘e’). All cells imaged in this figure were live cells.
DOI: https://doi.org/10.7554/eLife.39695.011
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Research Communication Physics of Living Systems
established from fixed cell measurements that
out tracer protein Sypnhilin1 is homogenously
distributed throughout the volume of clusters over the range of cluster sizes (Figure 1—figure sup-
plement 3), the total fluorescence intensity of the directly illuminated, pre-converted (green state)
Dendra2-Synphilin1 signal can serve as an estimate of the number of fluorescent molecules.
We obtain a live cell cluster size distribution (Figure 4B and C) that corroborates our conclusions.
The distribution fits well to the functional form DG Nð Þ ¼ aN2=3  bN, and the measured nucleation
barrier in live cell is ~6.6 (±0.7) kBT in agreement with the 7.2 (±0.5) kBT barrier measured by fixed
cell super-resolution in Figure 1.
The critical cluster is estimated to have Nc = 1400 (±300) labeled, fluorescent molecules in a live
cell. Taken together with the super-resolution measured Rc, this suggests a spacing of (Nc/Rc) at
most one Dendra2-Synphilin every 15 nm. Therefore, given a Stokes radius of Dendra2 ~1.5 nm, the
labeled molecules occupy only about a thousandth of the volume of a cluster. This supports further
that the clusters are likely heterogeneous and composed of far more unlabeled endogenous proteins
than the fluorescent tracer (Synphilin 1) that labels aggregates.
Estimation of surface tension at the condensate-cytoplasm interface
The live cell measurements allow us to make bounded estimates for the surface tension of the con-
densate-cytoplasm interface. Estimates for the surface tension allow for direct comparison between
condensates formed in a wide range of systems, and in different studies. Briefly, the measured value
of a plays the role of a surface tension in the theory, a ¼
r2
1
s
kbT
 
, with r1 the length-scale of a mono-
mer (taken to be ~1nm), s the surface tension; we previously noted that our definition of n in fixed
cells (or N in live cells) were correct up to a multiplicative constant. While this does not affect our
ability to calculate the critical radius and nucleation barrier (see materials and methods), it does
impact our estimate of the individual parameter a. Nonetheless, we can still provide bounds on the
value of the surface tension at the condensate-cytoplasm interface.
In the fixed cell data we measure the radius R with high spatial resolution and then calculate R3
but ntot ¼ R
3 where  is the density of polypeptides in the cluster which is an unknown. In the live
cell measurements we measure the total intensity I and calculate N ¼ I=ISingle mol but again
ntot ¼ Nk with k unknown. So both N ¼ I=ISingle mol = ntot=k and n ¼ R
3 ¼ ntot= are only measures of
the total number of molecules up to a proportionality factor. Therefore from our fits we in fact
get a ¼ a2=3 and b ¼ b from the fixed cell data a ¼ ak2=3 and b ¼ bk from live cell data - where
starred parameters represent the real energetic terms if we had measured the total number of mole-
cules. Since surface tension is determined by a ¼
r2
1
s
kbT
 
, and we do not know a, we need to use
bounds on , k in order to estimate the surface tension.
For upper bounds - from live cell data we know that ntot is greater than the number of molecules
that are fluorescing (only Synphilin1-Dendra2). That is, the real parameter a is less than the mea-
sured parameter a. Consequently the surface tension calculated from the measurement over-esti-
mates the real surface tension and is an upper bound – since the measured parameter a (from live
cell data) was 0.166 at 310K (assuming ambient temperature as the temperature) and
using a ¼
r2
1
s
kbT
 
, this works out to s<6 104N=m. From fixed cell data, taking as input from the live
cell measurements that a critical cluster has at least 1400 molecules (the number of Synphilin
Video 1. Lattice light sheet imaging of Synphilin cluster
mergers in live cells - example 1.
DOI: https://doi.org/10.7554/eLife.39695.012
Video 2. Lattice light sheet imaging of Synphilin cluster
mergers in live cells - example 2.
DOI: https://doi.org/10.7554/eLife.39695.013
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 12 of 26
Research Communication Physics of Living Systems
molecules estimated by intensity measurements), and that the critical cluster size is measured to be
162 nm, we can estimate a lower bound on the density. That density is at
least 3:3 104 molecules per nm3. Since the measured value of a was 0.001 we can use a ¼ a2=3 to
get an upper bound on the real value of a and consequently on the surface tension this works out
to s<8 104N=m.
Lower bounds may be obtained by noting that the density of the cluster cannot be more than 1
molecule per nm3. This value corresponds to the size of proteins involved in the process. Using this
value of  ¼ 1 molecule per nm3 we can compute the value of a to be at least the measured value a
(a= 0.001 in fixed cells) and consequently establish a lower bound of s>4 106 N
m
:
Interestingly, the values s ~ 106 to 104N=m are similar to the order-of-magnitude estimate for
the surface tension of in vivo liquid droplets more apparent in large oocytes and embryos. For exam-
ple a surface tension around 105N=m was estimated for the nucleolar interface in oocytes
(Brangwynne et al., 2011) or 106N=m for germline P-granules liquid droplets interface with the
cytoplasm in c. elegans (Brangwynne et al., 2009). The comparable values of surface tensions sug-
gest that despite differences in their sizes, our diffraction-sized clusters may have the same droplet-
like properties as previously reported large in vivo condensates. It is also feasible that cluster forma-
tion mechanism described in this study may be in play in the formation of larger in vivo condensates
reported in other studies.
Live cell cluster dynamics reveal key signatures associated with
condensing systems
Nucleation and growth describes the evolution of a system toward matured, stable clusters. In our
live cell imaging, we expected most of the clusters to be unstable because they were either sub-criti-
cal or under the influence of RuvBL clearance. Consistent with this expectation, comparable to fixed
cells, we find that less than eight percent (<8%) of clusters were in the super-critical size range
needed for stability, and most of the tracked clusters did not last as long as the full duration of our
live cell experiments (6 min). Of the few that survived, we measured the dynamics of a representative
population: we investigated the growth and shrinkage dynamics of 30 individual clusters from seven
living cells imaged with the light sheet at 15 s time interval over 6 min. These represent a pool of the
largest clusters; smaller clusters than this pool did not last the full 6 min of imaging or could not be
tracked.
First, by normalizing the cluster intensity at t = 0, we find that individual clusters have gradually
grown or shrunk by up to 40% in the course of 6 min (Figure 5A). We color-coded the growth/
shrinkage dynamics with clusters growing more than 10% in red, and those shrinking more than 10%
in blue. Those clusters that have not changed in size by more than 10% after 6 min are in black. Strik-
ingly, the growth/shrinkage correlates directly with the original cluster intensity: Figure 5B shows
that growing clusters (red) were almost unanimously the largest clusters in the pool, while the shrink-
ing clusters (blue) were the smallest. The unchanged clusters had intensities N ~ 2000 close to the
estimated Nc, indicating that these stable clusters are likely around or above the critical size.
This coarsening behavior, that large clusters tend to grow larger while smaller clusters tend to
shrink, is a key dynamic signature of complex systems in phase transition, an example of which is the
well-known phenomenon of Ostwald ripening (Ostwald, 1897) where larger clusters, owing to the
lower curvature at their surface have a reduced pressure differential (Laplace pressure DP ¼ 2s=r)
across their surface and consequently reduced solubility relative to smaller clusters. Within the
framework illustrated in Figure 1 and Figure 4, coarsening can be understood by the fact that
smaller condensates have a higher surface to volume ratio and therefore a higher free energy than
large condensates; as such, above the critical barrier, large clusters spontaneously grow larger, and
in steady state this happens at the detriment of smaller aggregates which will shrink.
Instantaneously, any given cluster can exhibit growth and shrinkage steps. And a few small aggre-
gates will stochastically grow to reach super-critical sizes. Consistent with this view, in the time traces
of Figure 5B one of the smaller aggregates has grown (red) over the imaging window. These revers-
ible steps are consistent with a thermodynamically driven, probabilistic process.
Over the course of imaging, the overall growth or shrinkage seems roughly linear with time (N(t)
/ t) for the individual clusters. We note that since our super-resolution data shows that cluster size
scales with the cube of the average radius (Figure 1—figure supplement 3), our live cell data is
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 13 of 26
Research Communication Physics of Living Systems
B CA
...GrowthDimunition No change
0 100 200 300
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Intensity of c Intensity of ab + Intensity of c
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Figure 5. Live cell imaging of single aggregates growth and shrinking dynamics show ripening and coalescence. (A) Aggregate growth and diminution
kinetics over a period of 6 min from 30 long-lived aggregates from seven cells. Here, the intensity is normalized to the initial intensity. Color code: red
are growing intensity, blue are diminishing intensity, and black represent no change (<10%) between start and end time points. (B) The intensity time
traces of the individual aggregates show a clear difference in the global trend with the initially larger aggregates also corresponding to the growing
(red) aggregates, and initially smaller aggregates shrinking (blue). Instantaneously all aggregates exhibit individual steps of both growth and
diminution, and one small aggregate out of the 30, was seen to grow more than 10%. (C) Schematic depicting the expectations from Ostwald ripening:
This coarsening/ripening behavior that large aggregates grow larger while small aggregates diminish is a key dynamic signature of a fluid in phase
transition. (D and E) The aggregates coalesce. (D) A montage three aggregates successively coalescing into one aggregate over the period of ~6 min.
(E) The intensity trace of the three clusters in (D) shows that in each time upon merging the new droplet is the sum of the two precursor aggregates.
Also see Figure 5; Video 1 associated with 4D and 4E and Figure 5; Video 2 for more examples). All cells imaged in this figure were live cells.
DOI: https://doi.org/10.7554/eLife.39695.014
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Research Communication Physics of Living Systems
consistent with N(t) / R3 / t. Therefore, our observations of individual cluster growth and shrinkage
in live cell would be consistent with condensed phase coarsening with R / t 1/3, the prediction for
both diffusion-limited Ostwald ripening, or coarsening by Brownian motion-induced coalescence
(Berry et al., 2015; Ratke and Voorhees, 2002; Slezov, 2009).
In addition, we observe in the living cells that diffusing clusters, upon contact, merge into a single
condensate (Figure 5D and E and Videos 1 and 2). In 15 cells imaged for 6 min each, we manually
identified nine merger events, suggesting a rate of occurrence of about 1 in every 10 min. This coa-
lescence is another common feature of systems undergoing condensation, where the net attractive
interaction between monomers and the fact that the surface energy cost is minimized by fusion favor
coalescence upon contact. Together, the observations from intensity distributions in live cells that is
the corroboration of a thermodynamic free energy akin to condensation, the estimation of a surface
tension comparable to phase separated biomolecules in vivo (Brangwynne et al., 2009;
Brangwynne et al., 2011), the coexistence of fast stochastic dynamics with slow size-dependent
coarsening, and the incidents of coalescence – all provide support for the conclusion that aggregate
formation and growth is governed by the thermodynamics of a first order phase transition in live
mammalian cells.
Discussion
Aggregation of misfolded proteins is typically understood as sequential oligomerization in discrete,
often irreversible steps adding monomers to an already formed nucleus (Serio et al., 2000). How-
ever, how the original nucleus forms in live cells has not been clarified. Our work establishes that a
first-order phase transition is an appropriate thermodynamic framework to describe de novo forma-
tion and growth of protein aggregates in mammalian cells. Our results reveal that at the early
stages, the formation of misfolded protein clusters is akin to a first order phase transition leading to
the formation of a condensate. This link between condensation and early steps of aggregation pro-
vides a conceptual framework for our understanding of aggregation in vivo, with clear predictions
and implications that can be tested and falsified in experimental studies.
A key prediction from the existence of the free energy form is that super-saturation is being main-
tained in steady-state in the living mammalian cells. One testable implication is that even healthy
cells are already super-saturated and may have sub-diffractive condensates that may be impossible
to detect by conventional imaging, but that are readily apparent with the high-resolution micro-
scopes used here.
A requirement for physically maintaining a super-saturated steady state is that a mechanism exists
to recognize and clear condensates that are larger than a critical size. This expectation has led us to
identify the RuvBL-dependent pathway for aggregate clearance. It is possible that an accumulation
of super-critical clusters could result from the misregulation of RuvBL-dependent clearance of super-
critical clusters. We found that knocking down RuvBL was sufficient to increase super-critical clusters
in the cells. In future studies, it would be interesting to look for correlations between disease onset
and RuvBL expression level, or mutations.
Similarly, it has been hypothesized that intermediate aggregates could be more toxic to cells
than late stage aggregates in aggregation diseases (Cookson, 2005; Gosavi et al., 2002;
Karpinar et al., 2009; Lashuel et al., 2002a; Lashuel et al., 2002b; Pountney et al., 2004;
Ross and Poirier, 2004; Xu et al., 2002). If maturing condensates represent the toxic species, then
it would help explain the need for maintaining homeostasis by clearing condensates above a critical
size. The Szilard model offers a predictive quantitative framework for testing such hypotheses, since
it predicts and describes how alterations in cellular protein homeostasis would thermodynamically
alter the balance between condensate formation and clearance.
Most aggregates studied in vitro require higher than physiological concentrations of proteins for
de novo nucleation and formation of plaques, fibers or inclusions of homogeneous compositions
(e.g. with a single protein constituent). Often, however, the protein’s expression is not increased in
cells that contain visible aggregates in vivo, raising a question on whether there are missing nuclea-
tors that facilitate this transition. Rather, in vivo condensates have very high concentrations of
constituents, andcondensates can mature and acquire a variety of complex physical properties
(including gelation or solidification [Patel et al., 2015] and irreversibility) over long time scales.
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There is mounting evidence in the literature suggesting that in disease, intermediate steps of
aggregate formation may proceed through the type of nucleation process that we observe here. In a
classic study (Serio et al., 2000), Lindquist and colleagues examined the in vitro mechanism by
which a prion protein Sup35 forms self-seeded amyloid fibers. They found that variably sized spheri-
cal complexes (akin to condensates and apparent by high-resolution imaging (STEM and AFM)),
appear to be crucial intermediates in de novo amyloid nucleation (Serio et al., 2000). Similarly for
Huntingtin N terminal fragments, in vitro studies (Crick et al., 2013; Posey et al., 2018) show that
below the concentration required for growth of a structured fibrilar phase, there exists another satu-
ration point distinguishing monomers and small oligomers of <10 nm size from spherical complexes
of ~25 nm size (Posey et al., 2018); globular complexes have also been isolated from Huntingtin rat
models (Sathasivam et al., 2010). Intermediate steps are also suggested by fluorescence correlation
spectroscopy studies of nucleation of amyloids, where hints of a second nucleation barrier between
small multimers and large structured aggregates were seen (Garai et al., 2008).
In light of such precedence and the high concentrations needed for the nucleation
(To¨rnquist et al., 2018) of fibrils in vitro, it is plausible that, the micro-environment within in vivo
condensates such as the one found in our current study, could serve to provide the high concentra-
tions needed for a secondary nucleation (Buell et al., 2014; Buell et al., 2014) of fibers or plaques
with various properties (Vitalis and Pappu, 2011). Further, the regulatory template of the Szilard
mechanism - with a preferential regulation of super-critical clusters – could be useful in re-examining
previous results, such as for example, the regulated competition between fibrilar and amorphous
aggregation of Amyloid beta (Garai et al., 2018). It is also possible that mechanisms similar to those
described here may be relevant in other contexts (Cho et al., 2018; Chong et al., 2018;
Sabari et al., 2018).
Our assays and analytical framework also highlight various avenues where progress in the experi-
mental state-of-the-art in the near future may yield rich insights. On one hand, the super-resolution
methods are still limited by their localization accuracy (in our case ~20 nm); if the critical cluster size
is not greater, the sub-critical cluster sizes would not be readily quantifiable. Super-resolution techni-
ques are also limited in temporal resolution, making them unsuited for imaging fast moving sub-dif-
fractive clusters in living cell. On the other hand, the lattice light sheet approach we used for live cell
imaging is not sensitive enough to study detailed dynamics of the smallest clusters. And the gradual
photo-bleaching of the fluorescent labels limits how long individual clusters can be imaged in living
cells. Given these challenges there are still many questions made addressable by the ability to apply
thermodynamic principles to aggregation in living cells.
While our investigation has focused on aggregates related to Parkinson’s disease, we note that
the methodology can be readily extended to any protein that can be fluorescently tagged (for exam-
ple fused to the GFP-like Dendra2). Similar mechanisms may in fact apply in other cellular processes.
For example, there are large membraneless cellular organelles that have been shown to behave like
liquids, suggesting that their formation is akin to liquid-liquid phase separation. Applying the
approaches described in this paper would further define the biophysical properties underlying
membraneless organelle formation and also reveal regulatory mechanisms.
Materials and methods
Key resources table
Reagent type
(species) or
resource Designation Source or reference Identifiers Additional information
Cell line
(H. sapiens)
MCF10A ATCC ATCC:CRL10317
RRID: CVCL_0598
Cell line
(H. sapiens)
Neuro2A ATCC ATCC:CCL131
RRID: CVCL_0470
Continued on next page
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Research Communication Physics of Living Systems
Continued
Reagent type
(species) or
resource Designation Source or reference Identifiers Additional information
Transfected
construct
Synphilin-GFP Zaarur et al., 2008 n/a Generated by
Sherman lab -
published Zaarur et al., 2008,
backbone
pCXsbr
Transfected
construct
Human Alpha
Synuclein
Addgene 51437
Transfected
construct
Dendra 2 Clonetech USA PDendra2C
Transfected
construct
Synphilin-Dendra2 This Paper n/a Generated from
synphilin-gfp and
dendra two plasmid
above. Available
from Cisse lab
Transfected
construct
alpha Synuclein
Dendra2
This paper n/a Generated from
human alpha
Synuclein and
Dendra two plasmid
above. Available
from Cisse lab
Sequence-
based reagent
siGENOME
Non-Targeting
siRNA #5
Dharmacon D-001210–05
Sequence-
based reagent
siGENOME
RUVBL1 siRNA
Dharmacon (D-008977–04)
Chemical
compound, drug
Chemical
compound, drug
MG132 Sigma Aldrich M8699
Chemical
compound, drug
Rapamycin Sigma Aldrich R8781
Chemical
compound, drug
Cycloheximide Sigma Aldrich C7698
Chemical
compound, drug
Azetidine-2-
Carboxylic acid
Sigma Aldrich A0760
Chemical
compound, drug
Cholera Toxin Sigma Aldrich C8052
Chemical
compound, drug
Human Insulin Sigma Aldrich I9278
Chemical
compound, drug
Leboqitz L15
medium
Sigma Aldrich 11415064
Chemical
compound, drug
Hydrocortisone Sigma Aldrich H0888
Chemical
compound, drug
dbCAMP Sigma Aldrich D0627
Chemical
compound, drug
Ver155008 Sigma Aldrich SML0271
Chemical
compound, drug
Lipofectamine
RNAiMAX
Thermo Fisher 13778030
Chemical
compound, drug
Xtremegene 9 Sigma Aldrich 6365779001
Software,
algorithm
qSR Andrews et al. (2018) Software made
available on
repository - http://github.com/cisselab/qSR/
Continued on next page
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Continued
Reagent type
(species) or
resource Designation Source or reference Identifiers Additional information
Software,
algorithm
Lattice Light
sheet processing
code
Chen et al., 2014
Software,
algorithm
Multiple
Target
tracking(MTT)
Serge´ et al., 2008
Contact for reagent and resource sharing
’Further information and requests for resources and reagents should be directed to and will be ful-
filled by the Lead Contact, Ibrahim Cisse (icisse@mit.edu)
Experimental model and subject details
Cell lines were generated from MCF-10A (human breast epithelial) cells grown in 50:50 DMEM/F-12
medium supplemented with 5% horse serum, 20 ng/ml epidermal growth factor, 0.5 mg/ml hydrocor-
tisone (Sigma Aldrich), 10 mg/ml human insulin (Sigma Aldrich), and 100 ng/ml cholera toxin (Sigma
Aldrich). In all cases, medium was supplemented with Penicillin-Streptomycin and incubated at 37˚C
in an atmosphere of 5% CO2 in a water-saturated atmosphere.
For the Synphilin-Dendra2 cell line – The retroviral expression construct with C-terminally tagged
Synphilin one sub cloned into pCXbsr vector described previously (Zaarur et al., 2008) was used
with EGFP at the C-terminus of the construct replaced with Dendra2, PCR cloned from the P-Den-
dra2C plasmid purchased from Clontech, USA.
For the alpha Synuclein–Dendra2 cell lines – alpha Synuclein gene was copied by PCR from Addg-
ene plasmid #51437 and cloned into P-Dendra2C plasmid purchased from Clonetech, USA. For
MCF10A –alpha Synuclein cell line – alpha Synuclein-Dendra2 plasmid, was transiently transfected
using extremegene9 and selected using Kanamycin resistance cassette in MCF10A (ATCC, USA)
cells. The cell line was tested for mycoplasma contamination by the high-throughput sequencing
facility at the Koch Institute using the Lonza MycoAlert Plus kit. The cell line tested negative for
mycoplasma contamination. Cell line identity was authenticated by ATCC using STR profiling, and
gave a 94% match to ATCC cell line CRL-10317(MCF10A). For Neuro2A- alpha Synuclein-Dendra2
control – alpha Synuclein-dendra2 plasmid, described above was transiently transfected using
extremegene9 and selected using Kanamycin resistance cassette in Mouse neuroblastoma cell line -
Neuro2A (CCL-131, ATCC, USA)
Neuro2A was maintained in culture in growth medium consisting of 45% of DMEM high glucose
medium w/L-Glutamine (GIBCO, USA), 45% of OptiMEM1 medium (GIBCO, USA) and 10% of Fetal
bovine serum (GIBCO, USA) Supplemented by Penicillin-Streptomycin and incubated at 37C in an
atmosphere of 5% CO2 in a water saturated atmosphere.
Differentiation to neuronal state was achieved by simultaneous lowering of serum content to 1%
and addition of 0.5 mM dbcAMP (Sigma Aldrich, USA) as suggested in ATCC product manuals. In 2
days of growth, distinctly neuronal morphology was established in ~75% of the cells in culture and
alpha Synuclein expression was observed throughout the cell but was enhanced at the tips of the fin-
ger-like processes of the cell. The neuronal state of N2A cells under dbcAMP differentiation has
been established in the literature (Tremblay et al., 2010)
Method details
Genetic and pharmacological treatments
The various pharmacological and genetic stresses were applied as follows-
Naı¨ve (unstressed) growth – cells grown in the culture medium described above were imaged
without any stress. This condition was measured as control along with every other stress and on its
own on three separate occasions (independently cultured and plated imaging dishes).
Proteasome inhibition – cells were incubated for 0 to 4 hr using 2 mM MG132 (Sigma Aldrich,
USA) in normal growth medium. Additional tests were done with lower concentrations and slightly
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longer incubation times, 500 nM MG132 was the lowest attempted concentration that allowed
aggresome formation. This stress was measured on three separate occasions (independently cul-
tured and plated imaging dishes).
Rapamycin incubation: Cells were incubated for 12 hr in normal growth medium supplemented
with 100 nM rapamycin (Sigma Aldrich, USA) after being plated on the imaging coverslip. This stress
was measured on two separate occasions (independently cultured and plated imaging dishes).
Cycloheximide incubation: Cells were incubated in normal growth medium supplemented by 500
mg/ml of Cycloheximide for 3 hr. This experiment was repeated on two occasions (independently cul-
tured and plated imaging dishes)
Ver155008 incubation: Cells were incubated in normal growth medium supplemented by concen-
trations up to 50 mM in DMSO alongside DMSO control. Incubation was done for 3 hr and 9 hr.
Amino acid substitution: Cells were incubated for 3 hr in normal growth medium containing 5
mM Azetidine-2-carboxylic acid (Sigma Aldrich, USA). This stress was measured on its own on two
separate occasions separate occasions (independently cultured and plated imaging dishes), and also
as control dish for combination of amino acid substitution and proteasome inhibition on two sepa-
rate occasions (independently cultured and plated imaging dishes).
RUVBL depletion: For siRNA transfection, we used Lipofectamine RNAiMAX (Invitrogen) and fol-
lowed the manufacturer’s reverse-transfection protocol. For a well on a 24-well plate, we mixed 0.4
ml of the reagent with 2 ml of 10 mM siRNA in 100 ml of OptiMEM and added the mixture to 400 ml of
a cell suspension in the well. 24–28 hr later the transfection was stopped and the cells were plated
for an experiment conducted the next day. We used the following siRNAs purchased from Dharma-
con: siGENOME Non-Targeting siRNA #5 and siGENOME RUVBL1 siRNA (D-008977–04) this stress
was measured on two separate occasions (independently cultured and plated imaging dishes).
Cellular fixation
Fixation was carried out by 4% Paraformaldehyde (Electron Microscopy Sciences, USA) for 15 min at
room temperature. In tests to investigate possible fixation artefacts we varied fixation Paraformalde-
hyde concentrations and temperatures including a variety of fixation timescales from fixation in. 05%
paraformaldehyde at 4C for 16 hr to the conventional fixation for 15 min. Cells were then mostly
imaged immediately after fixation but were never stored longer than 5 days before imaging. The
storage was at 4C under Phosphate buffered saline in dark conditions. There was no noticeable dif-
ference between cells imaged immediately after fixation and a few days after. Different fixation rates
showed no difference in the resulting cluster size distributions:
Imaging
Super-resolution imaging
For imaging, Cells were plated on 25 mm round glass coverslips (CS-25R) from Warner Instruments
(Hamden, CT) for 12–24 hr in the specified growth conditions. Cells were either fixed and imaged or
imaged live after reaching 50–75% confluence. All imaging was carried out in Leibowitz’s L-15
medium. To conduct PALM Super resolution imaging, we used an optical system built using a Nikon
Eclipse Ti microscope with a 100  oil immersion objective (NA 1.40). Pre-converted Dendra2 was
excited by a 488 nm laser line. Photo-activation of Dendra2 was carried out with a 405 nm laser line
and in the post-converted state Dendra2 was excited by a 561 nm laser line. These laser lines were,
expanded, re-collimated and focussed on the back focal plane of the Microscope in an external opti-
cal path using an achromatic beam expander (AC254-040-A and AC508-300-A, from THORLABS,
Newton, NJ) and an achromatic converging lens (#45–354, from Edmund Optics, Barrington, NJ).
Image data was collected using an Andor iXon Ultra 897 EMCCD camera. The laser power densities
used for post-converted Dendra2 were 0.5 W/cm2 (405 nm) and 3.2 kW/cm2 (561 nm) on the image
plane.
For live cell imaging the L15 media was supplemented with 10% Fetal Bovine Serum (Thermo
Fisher). For both live and fixed cell imaging, the cells were maintained at 37˚C in a temperature con-
trolled platform (InVivo Scientific) on the microscope stage during image acquisition. Z-position of
the microscope stage was maintained during acquisition using the Perfect Focus System (PFS) on the
Nikon Ti Eclipse.
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For fixed cell super-resolution imaging, movies with 10,000 frames, each averaged over 50 ms of
exposure time, were acquired with both the excitation and photo-converting lasers on continuously.
Lattice light sheet imaging
For Lattice Light Sheet Microscopy (Chen et al., 2014), cells were plated on gelatine-coated cover-
slips 24–48 hr before imaging and grown as described above. Imaging took place in L15 medium
supplemented with 10% FBS. A lattice light sheet consisting of 61 Bessel beams was generated with
an annulus of inner/outer numerical aperture NA 0.44/0.55. Illumination power was 1.3 mW mea-
sured before the illumination objective. Volumetric image data with a temporal resolution of 15 s/
volume (300 frames) was acquired by stepping cells through the light sheet in intervals of 0.3 mm
with 50 ms exposure time using a sCMOS camera (Orca Flash v4.2, Hamamatsu). Images were proc-
essed (deskewed) using a modified version of MATLAB (The Mathworks) code supplied by
Chen et al. (2014). Analysis was performed on maximum intensity projections of images stacks.
Super-resolution reconstruction
To identify single molecules in raw images of photo-converted Dendra2 fluorescence, the intensity
signals were analysed using an adapted version of the multiple-target tracking algorithm (MTT)
(Serge´ et al., 2008) then we used our open software qSR for visualization, super-resolution recon-
struction and DBSCAN. Briefly, for each frame, the point-spread function (PSF) of spatially separated
individual fluorophores was detected and fitted to a two-dimensional Gaussian distribution. The cen-
tre of the fit yielded the position of single molecules with nanometre accuracy. Super-resolution
reconstruction images were generated by superimposing a 2D Gaussian curve with the same inten-
sity value central position and standard deviation as found by the fitting procedure. Finally, the posi-
tions of single molecules were fed into the DBSCAN (Ester et al., 1996) implementation custom
written to extract meaningful distribution functions from the resulting data. Representative super
resolved reconstructions along with zoom-ins showing DBSCAN efficacy in all measured conditions
are shown in Figure 1—figure supplement 1.
Quantification and analysis
DBSCAN image analysis
DBSCAN, density-based scanning is a powerful computational technique for identifying correlations
in a variety of data (Ester et al., 1996). Using two user chosen parameters, m and r, the algorithm
combs through a data set of spatial coordinates – corresponding here to the super resolved localiza-
tions from Dendra2 – classifying the points as belonging to clusters if there are at least m points
from that cluster within a radius r of the point. Our implementation was included in Andrews et al.
(2018) and Andrews et al. (2017).
Parameter choice will depend on the total density of localizations and the relative strength of
local density fluctuations constituting clusters, both of these are influenced by imaging conditions.
Therefore, parameters must be chosen by careful comparison to an unclustered control dataset
acquired keeping total density of localizations as close to constant as possible. Across all data sets
we consider the first 10,000 frames (50 ms integration time) for each cell in all experimental treat-
ments and with constant imaging conditions.
We chose r as 40 nm and m as 10. Our choice of parameters was based on running the algorithm
on cells transfected with plain Dendra2 as our unclustered control. While super-resolution maps
with ~50000 localizations in ~ 25mð Þ2 area for Dendra2 cells gave between 50 and 150 clusters/cell,
with the same localization density in Synphilin-Dendra2 cells we found of the order of 1000 clusters
per cell. Changing r and m by a factor of 2 did not significantly affect the number of clusters found.
Thus our parameter choice (and factors of two on either side of our parameter choice) was effec-
tively eliminating noise and not missing clusters. Lastly, we visually inspected the localization maps
and DBSCAN cluster allocations and never encountered a problem. Representative super resolved
reconstructions along with zoom-ins showing DBSCAN efficacy in all measured conditions are shown
in Figure 1—figure supplement 1.
Analysis of cluster size distributions (Super-resolution)
Computation of the cluster size distribution functions was carried out in the following steps:
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DBSCAN was run on 10,000 frames for each cell in a given experimental condition.
For each cluster identified by DBSCAN, the number of localizations making up the cluster and
their spatial spread as estimated by drawing a convex hull around the points (Radius R) were tabu-
lated. Data from all cells in similar conditions were collated. Since our uncertainty in super-resolved
molecular positions is ~20 nm we discarded all clusters (collections of points with at least m = 10
neighbours) with diameter spanning less than 50 nm.
Next for each cluster we calculated the quantity n ¼ R in nm=1nmð Þ3. In each experimental condi-
tion, we have ~ 10000 clusters collated from ~ 10 cells. In data from untreated cells, > 90% of these
clusters had n values less than n ¼ 2 106. In highly clustered experimental data sets such as 180
minutes post proteasome inhibition, the proportion of large clusters increased. However, the major-
ity of clusters were still less than n ¼ 2  106. The value of n corresponding to a critical size was
always less than n ¼ 2 106 depending on the experimental condition. The cluster size distribution
functions in the main text and this supplement were fit to the theoretical form solely in the sub-criti-
cal range where the theory is valid (which is also where the majority of our cluster data lay).
The cluster size distribution functions in each experimental condition were computed from nor-
malized histograms of the collated cluster n values from that experimental condition with a constant
bin size across all data sets (Dn ¼ 3 104). The main concern is to have enough data to be able to
choose sufficiently small bins to effectively sample the fastest variations in the underlying distribution
function without hitting a noise floor. This is the Nyquist criterion for binning. With more than 5000
clusters ranging for each condition from n ¼ 1:5 104 to n ¼ 2 106 (the sub-critical regime) we had
sufficient data that even bins of size Dn ¼ 5000– dividing the sub-critical regime into ~400 bins –
resulted in histograms that were noiseless enough to fit and sampling the distribution very accu-
rately. Data reported is with Dn ¼ 3 104 the results of fitting the distribution function are insensitive
to changing the bin size down to Dn ¼ 5000 (<2% change in estimated Rc).
For ease of presentation, we note that the probability distribution function is
Prob nð Þ ¼ AeG nð Þ where A enforces normalization. However A is determined by the fit parameters a
and b since
R nc
0
Prob nð Þ ¼ 1 implies ¼ 1=
R nc
0
eG nð Þ. Then Log Prob nð Þ ¼ G nð Þ  Log Að Þð , where Log
refers to the natural log (base ‘e’). Therefore, in order to read the nucleation barrier directly from
the –Log(P(n) curve, we must add an offset Log Að Þ. Equivalently this amounts to a self-consistent nor-
malization of our experimentally measured distribution function such that A is 1. This procedure just
contributes an offset to the –Log(P(n)) curves without affecting critical radius and permits ease of
presentation as it allows direct reading of the barrier height from the – Log(P(n)) graphs.
Fitting of the experimentally measured cluster size distribution functions to the theoretical func-
tional form was carried out using the Mathematica implementation of least squares linear regression
routine included in the LinearModelFit command. Errors in values of Rc reported standard error of
the mean from the best fit (computed, for instance using the MeanConfidenceBand object property
of the LinearModelFit package in Mathematica).
The range of n values for fitting data is important to determine. The theoretical form is only
expected to hold below the critical size and diverges above the critical size. This sets an upper
bound on range of data to use. However, the more data points you include the tighter the error
bars on the fit parameters. The fitting range was determined self consistently by fitting data up to
that value of n which was 80% of the critical radius predicted by the fit. In practice, this amounted to
fitting up to n~ 8 105 for the case of 180 min of proteasome inhibition (when the predicted critical
size was n ~ 1 106) and fitting up to n~ 1:5 106 for the case of untreated cells where the critical
size corresponded to n ~ 2 106. The larger error bars in the 3 hour proteasome inhibited case than
in the untreated cell reflect both the greater spread in the data (fewer total clusters) and smaller
available fitting range. The residuals in Fig. 1 depend slightly on the data range used to fit and sub-
tract the n2/3 term and consequently only qualitative conclusions (such as the sign of slope) should
be drawn from relative comparisons between data sets fit identically. Our procedure was to always
fit the range n < 2 105 in all data sets and using bin size 5000 in this range.
The distribution of sub-critical cluster sizes P(n) is a Boltzmann distribution only in terms of the
extensive variable ntot, the total number of polypetides in the cluster. Our analysis has been in terms
of the defined parameter n ¼ R
1 nm
 
3
: As defined, n should be proportional to the total number of
molecules in the cluster as we image only a fraction of fluorescently detected molecules which
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Research Communication Physics of Living Systems
constitute only one species in our aggregates (Figure 1—figure supplement 3). However, the criti-
cal radius and nucleation barrier may be computed immune to a multiplicative constant in the defini-
tion of n ¼ R
1 nm
 
3
. This can be seen by asking what would happen were we to misrepresent the
cluster size ntot by an arbitrary multiplicative factor k. Then ntot, the real cluster size would be
replaced by n
0
¼ kntot. The free energy measured in terms of n
0
would be DG n
0 

¼ b
0
n
0
þ a0n02=3. The
relation between primed parameters and the unprimed – true – parameters would be
b ¼ b0k and a ¼ a0k2=3. Now the true value of the barrier height is DG ntotcð Þ ¼ bntotc þ a ntotc
2=3 with
ntotc ¼
2a
3b
 
3
the critical size. If we used the scaled variables b’ and a’ we would get
DG n0c
 

¼ b0n0c þ a
0n0c
2=3= b0 2a
0
3b
0
 3
þa0 2a
0
3b0
 
3 2=3
On substitution, the factor k cancels out to yield DG n0c
 

¼ bnc þ a n
2
3
c ¼ DG ncð Þ. That is, even if
we had cluster size parameter n incorrect by a multiplicative factor, we can measure the barrier
height (in terms of KT assuming ambient temperature as the relevant factor for thermalization). Simi-
larly any multiplicative error made in converting R to n’ can be shown to cancel when converting n0c
back to Rc. For estimation of critical radius, we used the turning point of the fit function DG(n) to
estimate critical size and then converted from nc to Rc This procedure makes the determination of Rc
independent of any multiplicative factor in the definition of n as this same factor appears in nc and is
cancelled out on going back from nc to Rc.
Analysis of live cell (light sheet) data
Light sheet data was analyzed to extract both distribution of cluster intensity and time evolution.
. To calculate the intensity of the clusters in living cells, a three-dimension segmentation was
performed using standard Mathematica functions (using the MorphologicalComponents and
ComponentsMeasurements commands). For the instantaneous estimation of clusters sizes,
only the first time point of each time series was analysed as this corresponds to the least pho-
tobleaching at this stage. To aid the segmentation, a 20-pixel background subtraction was
performed on each image plane, however the actual intensity was calculated from the original
unprocessed 3D stack using the total intensity within the segmented domain coordinates.
Approximately 100–200 clusters were found in each cell.
. A control experiment was conducted by bleaching cells for 20 min when only single molecules
(with single steps blinking and photo-bleaching) were visible – a 20 pixel background subtrac-
tion was used and the intensity of ~100 single molecules were measured. The resulting aver-
age single molecule intensity (24 counts) was used to convert the cluster intensities into
estimated number of fluorescent molecules.
. The calculated cluster size converted into estimated number of fluorescent molecules was
binned in bins of 10 (binsize = 20 did not change the shape of the curve but at binsize = 5
there was noticeably more noise) and plotted as in Figure 4 in the main text and fit to the
same functional form as for the fixed cell super-resolution data.
To obtain the time trace of clusters sizes two challenges were considered: photo bleaching by
the light sheet illumination, and large scale motion of clusters during the measurement
interval.
. While the intensities in the first frame – used for the cluster size distribution of Figure 4- are
unaffected by bleaching, the intensity values in subsequent frames – used in Figure 5 – are
affected. In order to correct for photo bleaching the average intensity of an imaging plane was
measured as a function of time, and fit to an exponential. The exponential fit was used to cor-
rect the intensities at each time point. The data was acquired with very fine Z- steps (300 nm
step size); larger step sizes caused the bleaching rate to be bi-exponential, putatively due to
leaving Z-sections differentially bleached. We can see that our bleach correction is largely
effective by noting that that different clusters in the same region of the same cell had different
kinetics, some rising and some falling in intensity over the period of imaging.
. The motion of clusters during the measurement interval and in between time steps (15 s per
cell stack) necessitated that we go through the bleach corrected light sheet movies, following
individual clusters manually and using Mathematica (using the MorphologicalComponents and
ComponentsMeasurements commands) based segmentation to identify coordinates for inten-
sity calculations in ImageJ. The results from 30 such clusters are plotted in Figure 5A,B of the
main text. This procedure resulted in studying clusters that were trackable for the whole
movie.
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Acknowledgements
We thank Ammon Possey (WUSTL), Assaf Amitai (MIT), Ben Sabari (MIT), Gene Wei Li (MIT), Geral-
dine Seydoux (Johns Hopkins), Jeff Gore (MIT), Jeong-Mo Choi (WUSTL), Kabir Ramola (Brandeis),
Kandice Tanner (NCI/NIH), Kiersten Ruff (WUSTL), Miccah Hecht (MIT), Rick Young (MIT), Rohit
Pappu (WUSTL), Sina Wittman (MPI-CBG, Dresden), Tony Hyman (MPI-CBG, Dresden), Vivien Siegel
(MIT) and members of the Cisse´ lab at MIT for helpful comments and discussions. Research reported
in this publication was supported by the National Cancer Institute and the National Institutes of
Health through the NIH Director’s New Innovator Award Number DP2CA195769 to IIC. We acknowl-
edge HHMI for the license to build Lattice Light Sheet. The content is solely the responsibility of the
authors and does not necessarily represent the official views of the National Institutes of Health. This
work was also supported by funds from the MIT Department of Physics.
Additional information
Funding
Funder Grant reference number Author
National Institutes of Health DP2CA195769 Ibrahim I Cisse
The funders had no role in study design, data collection and interpretation, or the
decision to submit the work for publication.
Author contributions
Arjun Narayanan, Conceptualization, Software, Formal analysis, Investigation, Methodology, Writ-
ing—original draft, Writing—review and editing; Anatoli Meriin, Resources, Investigation, Methodol-
ogy, Writing—review and editing; J Owen Andrews, Software, Investigation, Writing—review and
editing; Jan-Hendrik Spille, Conceptualization, Software, Investigation, Methodology, Writing—
review and editing; Michael Y Sherman, Resources, Investigation, Methodology, Project administra-
tion, Writing—review and editing; Ibrahim I Cisse, Conceptualization, Formal analysis, Supervision,
Funding acquisition, Methodology, Writing—original draft, Project administration, Writing—review
and editing
Author ORCIDs
Arjun Narayanan http://orcid.org/0000-0002-2269-3253
Anatoli Meriin http://orcid.org/0000-0003-0087-814X
Ibrahim I Cisse http://orcid.org/0000-0002-8764-1809
Decision letter and Author response
Decision letter https://doi.org/10.7554/eLife.39695.018
Author response https://doi.org/10.7554/eLife.39695.019
Additional files
Supplementary files
. Transparent reporting form
DOI: https://doi.org/10.7554/eLife.39695.016
Data availability
All data generated or analyzed during this study are included in the manuscript and supporting files.
Source data files have been provided for Figures 1, 2, 3 and 4.
Narayanan et al. eLife 2019;8:e39695. DOI: https://doi.org/10.7554/eLife.39695 23 of 26
Research Communication Physics of Living Systems
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