BIOPHYSICS AND
COMPUTATIONAL BIOLOGY
Physical mechanisms of ESCRT-III–driven cell division
Lena Harker-Kirschnecka,b,c,1
, Anne E. Hafnera,b,c,1, Tina Yaoa,b
, Christian Vanhille-Camposa,b,c, Xiuyun Jianga,b,c
,
Andre Pulschenc,d, Fredrik Hurtigd
, Dawid Hryniuka,b, Siân Culleyb,c, Ricardo Henriquesb,c
, Buzz Baumb,c,d,
and Andela Šari´ca,b,c,2
aDepartment of Physics & Astronomy, University College London, London WC1E 6BT, United Kingdom; bInstitute for the Physics of Living Systems,
University College London, London WC1E 6BT, United Kingdom; cMedical Research Council Laboratory for Molecular Cell Biology, University College
London, London WC1E 6BT, United Kingdom; and dMedical Research Council Laboratory of Molecular Biology, University of Cambridge, Cambridge
CB2 0QH, United Kingdom
Edited by Ken Dill, Chemistry, Physics, Stony Brook University, Stony Brook, NY; received April 23, 2021; accepted November 15, 2021
Living systems propagate by undergoing rounds of cell growth
and division. Cell division is at heart a physical process that
requires mechanical forces, usually exerted by assemblies of cy-
toskeletal polymers. Here we developed a physical model for the
ESCRT-III–mediated division of archaeal cells, which despite their
structural simplicity share machinery and evolutionary origins
with eukaryotes. By comparing the dynamics of simulations with
data collected from live cell imaging experiments, we propose that
this branch of life uses a previously unidentified division mecha-
nism. Active changes in the curvature of elastic cytoskeletal fila-
ments can lead to filament perversions and supercoiling, to drive
ring constriction and deform the overlying membrane. Abscission
is then completed following filament disassembly. The model was
also used to explore how different adenosine triphosphate (ATP)-
driven processes that govern the way the structure of the filament
is changed likely impact the robustness and symmetry of the
resulting division. Comparisons between midcell constriction dy-
namics in simulations and experiments reveal a good agreement
with the process when changes in curvature are implemented at
random positions along the filament, supporting this as a possible
mechanism of ESCRT-III–dependent division in this system. Beyond
archaea, this study pinpoints a general mechanism of cytokinesis
based on dynamic coupling between a coiling filament and the
membrane.
cell division | archaea | ESCRT-III | membrane simulations | soft matter
C
ell division is one of the most fundamental requirements for
the existence of life on Earth. During division the material
from a single cell is divided into two separate daughter cells.
This is an inherently physical process. Living cells have evolved
multiple ways to apply mechanical forces for this purpose. In
general, division is thought to be achieved by proteins that assem-
ble into long polymeric ﬁlaments at the cytoplasmic side of the
cell membrane. These ﬁlaments then undergo a series of energy-
driven changes in their form and organization to deform the
associated membrane and/or guide cell wall assembly. However,
the physical mechanisms by which this type of nonequilibrium
protein self-assembly produces the mechanical work needed to
reshape and cut soft surfaces remain underexplored.
Although the mechanisms of division differ across the tree of
life, recent data support the idea that eukaryotic cells likely arose
from the symbiosis of an archaeal cell and an alphaproteobac-
terial cell, where the archaeal host gave rise to the eukaryotic
cell body and the associated proteobacteria went on to become
mitochondria (1–3). Because of this, many physical processes
that control eukaryotic cell division are likely to have originated
in archaea. In particular, ESCRT-III ﬁlaments, which drive cell
division in a subgroup of archaea called TACK (thaumarchaeota,
aigarchaeota, crenarchaeota and korachaeota) archaea, also cat-
alyze the ﬁnal step of cell division in many eukaryotes (4, 5).
Here we develop a physical model to study the dynamics of ar-
chaeal cell division by ESCRT-III ﬁlaments. In archaea, ESCRT-
III proteins polymerize into at least two distinct ﬁlamentous rings
that likely form a copolymer that is adsorbed on the cytoplasmic
side of the cell membrane. The ﬁrst ﬁlamenteous ring (called
CdvB) serves as a template for the assembly of a contractile
ring (made of CdvB1 and CdvB2 proteins) (Fig. 1A). Recently
it has been shown that the contractile CdvB1/2 ring is free to
exert forces to reshape the membrane only once the template
CdvB ring has been removed (6). As cytokinesis proceeds, the
contractile CdvB1/2 ESCRT-III ﬁlament is then disassembled.
Here we investigate different energy-driven protocols that can
lead to the contraction and disassembly of an ESCRT-III ring in
contact with a deformable cell. We quantify the rates, reliability,
and symmetry of the resulting cell division processes. We then
compare the dynamics of cell division predicted in simulations
with those observed via live imaging of the archeon Sulfolobus
acidocaldarius, the closest archaeal relative to eukaryotic cells
that can be easily cultured in a laboratory. This comparison
identiﬁes a single regime of ﬁlament remodeling that matches
the experimental data remarkably well.
Our simulations identify a physical mechanism for reshap-
ing and splitting cells in which division is driven by the su-
percoiling of the ﬁlament. This differs from models of division
described previously but, given the generality of our modeling
approach, suggests a possible role for this process in cytoskeletal-
induced membrane deformation events across biological systems.
Significance
Cell division is an essential requirement for life. Division re-
quires mechanical forces, often exerted by protein assemblies
from the cell interior, that split a single cell into two. Using
coarse-grained computer simulations and live cell imaging
we define a distinct cell division mechanism—based on the
forces generated by the supercoiling of an elastic filament as
it disassembles. Our analysis suggests that such a mechanism
could explain ESCRT-III–dependent division in Sulfolobus cells,
based on the similarity of the dynamics of division obtained
in simulations to those observed using live cell imaging. In
this way our study furthers our understanding of the phys-
ical mechanisms used to reshape cells across evolution and
identifies additional design principles for a minimal division
machinery.
Author contributions: B.B. and A.Š. designed research; L.H.-K., A.E.H., T.Y., C.V.-C., X.J.,
and D.H. performed research; A.P., F.H., S.C., and R.H. contributed new reagents/analytic
tools; L.H.-K., A.E.H., T.Y., C.V.-C., X.J., A.P., F.H., D.H., B.B., and A.Š. analyzed data; and
L.H.-K., B.B., and A.Š. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
This open access article is distributed under Creative Commons Attribution License 4.0
(CC BY).
1L.H.-K. and A.E.H. contributed equally to this work.
2To whom correspondence may be addressed. Email: a.saric@ucl.ac.uk.
This article contains supporting information online at https://www.pnas.org/lookup/
suppl/doi:10.1073/pnas.2107763119/-/DCSupplemental.
Published January 4, 2022.
PNAS 2022 Vol. 119 No. 1 e2107763119
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A
C
B
Fig. 1.
Computational model. (A) Division of an archaeon S. acidocaldarius. The cell membrane is indicated with a dashed line, the template filament
(CdvB) is fluorescently labeled in magenta, while the constricting ESCRT-III filament (CdvB1) is labeled in green. (B) The initial ESCRT-III filament state (CdvB
+ CdvB1/2) is modeled as a single helical filament with a target radius equal to the cell radius Rcell. The filament is attached to the inside of the fluid vesicle
that represents the archaeal cell. To constrict, upon CdvB degradation, the ESCRT-III filament (CdvB1/2) reduces its target radius to Rtarget, which results in
a new target state of a tighter helix. The filament model itself consists of triplet subunits that are connected to each other via nine bonds whose lengths
control the filament curvature (Inset and SI Appendix). (C) An example of a cell division simulation. The target radius of the filament is instantaneously
decreased to 5% of the original cell radius. The filament is then disassembled from both ends at a rate 102 × vdis = 6.7/τ (τ is the molecular dynamics unit
of time). The filament first forms a superhelix that consists of multiple short helices of alternating chiralities (shown in the box). As the superhelix contracts
and disassembles, it pulls the membrane into a tight neck, which spontaneously breaks (Movie S1).
In this way, our analysis should help inform efforts to design
synthetic nanomachinery that can drive the division of synthetic
cells (7–9).
Results
A Minimal Model of Cell Division. In the model, the ESCRT-III
ﬁlament (CdvB1/2) bound to the template (CdvB) is described
as an elastic helical polymer made of two full turns whose radius
of curvature matches the radius of the cell, Rcell (Fig. 1B).
The polymer is modeled via three-beaded monomers that are
connected by harmonic bonds to each other (Fig. 1 B, Inset).
The equilibrium lengths of the bonds determine the curvature
of the polymer (10). The archaeal cell is described as a vesicle
made of a coarse-grained, one-particle-thick membrane (11), in
which a single particle corresponds to a cluster of ∼10-nm-wide
lipid molecules. These particles interact via an anisotropic pair
potential that drives the self-assembly of ﬂuid membranes with
expected physiological bending rigidity. The outer side of the
ﬁlament (blue-colored beads in Fig. 1B) is adsorbed to the mem-
brane via a generic Lennard-Jones attractive potential, while
the inner side of the ﬁlament (red beads) interacts with the
membrane only via volume exclusion. The system is evolved
using molecular dynamics simulation with a Langevin thermostat
(see Materials and Methods and SI Appendix, section 1 for more
details). Such a model captures thermal ﬂuctuations that are
needed for the relaxation of the ﬁlament, the dynamic ﬁlament–
membrane attachment and detachment, and the spontaneous
membrane neck scission.
The removal of the template CdvB ﬁlament and subsequent
constriction of the ESCRT-III ﬁlament (CdvB1/2) are modeled
by shortening the equilibrium lengths of the bonds between the
ﬁlament’s subunits, which increases the ﬁlament curvature, from
a large radius of curvature Rcell to a small radius Rtarget. Fig. 1B
shows the ﬁlament in its initial and target geometrical states.
This change in target ﬁlament radius is expected to transform
the ﬁlament from a wide ring into a tight helix that will drag the
membrane with it. To test this idea, we instantaneously changed
the target radius of the ﬁlament to 5% of the cell radius and
followed the system as it evolved. Since ﬁlament disassembly is
needed for scission (6), as soon as the new equilibrium bond
lengths were imposed, the disassembly was initiated by severing
bonds between ﬁlament monomers sequentially from both ends
of the helix at a speciﬁed rate vdis.
Interestingly, instead of forming a single tight helix, which is its
target shape, upon constriction the ﬁlament rapidly transforms
itself into a collection of short tight helices with alternating
chirality separated by kinks, termed perversions (Fig. 1C). This
structure is called a hemihelix and it presents a local energy mini-
mum in which the system gets trapped (12–14). This shape arises
as the result of nonhomogeneous stresses in the ﬁlament, such
that the outer and inner portions of the ﬁlament are strained to
different extents as the ﬁlament undergoes a change in curvature.
Hemihelices, ﬁrst documented by Darwin in plant tendrils (15),
are ubiquitous in nature and have been reported to form in the
development of the gut tube (16), in synthetic elastomers (17,
18), and can be seen in everyday life when a wrapping ribbon is
induced to curl using scissors (19). Recently, this shape has also
been imaged in nanoscale biopolymers such as mitotic chromo-
somes in vivo (20) and, importantly for this analysis, hemihelices
are visible in many of the published in vitro images of ESCRT-
III and FtsZ ﬁlaments (see examples in SI Appendix, Fig. S13 or
ﬁgure 1b in ref. 21, ﬁgure 5 g–i in ref. 22, or ﬁgure 6 in ref. 23).
When attached to the cell, the hemihelix itself acquires a
superhelical shape to follow the cell curvature (Fig. 1C). This
effectively shortens the ﬁlament length and thereby pulls the
membrane with it. Over time, the ﬁlament further shortens as
it disassembles, until it becomes a single helix with a curva-
ture 1/Rtarget enveloped by a tight membrane neck. As this
helix disassembles, the membrane neck spontaneously breaks,
giving rise to two separate cells (Movie S1). To the best of our
knowledge, this mechanism of constriction—coiling of a coil—
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has not previously been considered as playing a potential role in
cytoskeletal ﬁlament-based membrane deformation in cells.
Characterizing the Reliability and Symmetry of Cell Division. We
next carried out a series of functional tests to determine how
reliable this process is as a division mechanism. Fig. 2A shows
the dependence of the probability of cell division on the amount
of the ﬁlament curvature change, Rtarget/Rcell, and the rate of
the ﬁlament disassembly, vdis. We see that division occurs only if
both the ﬁlament curvature change and its disassembly rate are
in the right regime. When the change in the ﬁlament curvature is
insufﬁcient, the resulting large hemihelical loops barely shorten
the ﬁlament and the ﬁlament does not have enough tension to
constrict the membrane to a width sufﬁciently narrow to induce
ﬁssion. As the ﬁlament disassembles in this case, the cell inﬂates
back to its original size (square labels in Fig. 2 A and B). In the
opposite regime, if the reduction in the ﬁlament curvature is too
large, the large tension stored in the ﬁlament drives its detach-
ment from the membrane before a substantial deformation of the
membrane can occur (circle labels in Fig. 2 A and B). The time
evolution of the ﬁlament tension and the tension transferred into
the membrane curvature (24) is shown in Fig. 2C for each case.
In the intermediate regime, the ﬁlament fulﬁls two conditions
that allow it to enable division: It has enough tension that it can
form a sufﬁciently tight constriction and it disassembles at a slow
enough rate to enable reaching of the tight neck (star symbols
in Fig. 2 A–C). However, if the rate of disassembly is too high,
the ﬁlament disassembles before a membrane bottleneck can be
formed that is sufﬁciently narrow to enable scission, leading to
division failure (diamond in Fig. 2 A–C). On the other hand,
in the absence of ﬁlament disassembly (vdis = 0), the ﬁlament
frequently blocks the membrane neck, preventing efﬁcient cell
division, even though there are instances in which the membrane
neck can still break, leaving the daughter cells connected by the
ﬁlament.
We also wanted to determine how the mechanism of division
inﬂuences division symmetry—since this is a parameter that we
are able to measure in experiments. We therefore test how evenly
the disassembled ﬁlament subunits are partitioned between the
daughter cells for different curvature changes and disassembly
rates, in the region of phase space in which division occurs.
This evenness is quantiﬁed via parameter E = 2Nsmall/Ntotal,
where Nsmall is the number of ﬁlament subunits in the less-ﬁlled
daughter cell and Ntotal is the total number of ﬁlament subunits.
As shown in Fig. 3, for small ﬁlament curvature reductions,
which are at the very boundary of the phase space in which divi-
sion occurs (down-pointing triangle label), the ﬁlament does not
constrict much and the division occurs because the membrane
wraps over the exposed membrane attraction sites generated via
local perversions. As a result, following division, one cell contains
substantially more of the ﬁlament content than the other. This
mechanism yields a successful division in only ∼70% of cases
(Fig. 2A). A similar effect is seen for protocols that include a
strong radius reduction (up-pointing triangle label in Fig. 3).
Here ﬁlament supercoils are generated very quickly so that the
membrane wraps over one side of the coiled ﬁlament and the
ﬁlament is inherited by just one of the two daughter cells. The
result is again a less reliable and more uneven division. In the
middle of the dividing region (star label in Fig. 2 and diamond
label in Fig. 3), the division machinery is evenly distributed
between the daughter cells. In this region of the phase diagram
division occurs with ∼100% probability.
Dynamical Curvature Change Protocols. The choice to induce in-
stantaneous changes in ﬁlament curvature (Fig. 4A) was inspired
by experimental observations in S. acidocaldarius, where the
A
C
B
Fig. 2.
Reliability of division. (A) The influence of the filament radius reduction, Rtarget/Rcell, and the rate of the filament disassembly, vdis, on the probability
of cell division. The color of each square represents the percentage of successful divisions out of 10 simulations performed with different random seeds.
(B) Snapshots of the representative simulations from A, as indicated by the respective symbols. (C) Time evolution of the average filament tension (Left) and
average membrane curvature (Right) for the four representative points from A, as indicated by the respective labels. The filament disassembly starts at the
vertical gray line in all the cases, and the shaded gray region marks the time range during which successful divisions occur (turquoise curve and star symbol).
All the curves show an average over 10 simulations.
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Fig. 3.
Symmetry of the division. (Left) The influence of the amount of the instantaneous target radius reduction and the rate of the filament disassembly
on the partitioning of ESCRT-III proteins between the daughter cells. The color of each square represents average value of 10 simulations performed with
different seeds. (Right) Representative simulation snapshots.
template CdvB ring was found to be rapidly degraded, which was
then assumed to trigger rapid curvature change of the constrict-
ing ring, akin to the release of a loaded spring (6). However,
the local constriction time is nonzero and is likely to be set by
the local presence of an enzyme Vps4 ATPase, which is needed
for division in Sulfolobus, as well as for force production by
ESCRT-III ﬁlaments in eukaryotes (25, 26). Pﬁtzner et al. (26)
recently found that Vps4 modiﬁes the composition of ESCRT-III
copolymers in a stepwise manner, thereby ordering the changes
in overall ﬁlament geometry to drive membrane remodeling. This
led us to investigate how different protocols of noninstantaneous
dynamical ﬁlament constriction inﬂuence the outcome of the
division process.
We tested two additional protocols: 1) Filament curvature is
changed in a sequential manner starting from one end of the
ﬁlament in a process that spreads at a rate vcurv (Fig. 4B), and
2) ﬁlament curvature is changed at random points along the
ﬁlament at a rate vcurv (Fig. 4C). In all cases the total change
in ﬁlament curvature was kept constant (see SI Appendix, Fig. S5
for the exploration of different amounts of curvature change) and
ﬁlament disassembly was initiated after the new target curvature
had been imposed throughout the whole ﬁlament. To compare
the effects of these different mechanisms of ﬁlament constriction
for each of the different protocols we tracked changes in cell
diameter over time.
As can be seen in Fig. 4A, Right, following an instantaneous
curvature change the cell diameter sharply decreases and then
slowly plateaus before the division occurs—as expected following
the release of energy stored in a tensed polymeric spring. The
smaller the target radius of the ﬁlament, the more energy is
stored in the ﬁlament, and the faster the cell diameter reaches its
equilibrium value. This behavior is in good agreement with the
dynamic data for cytokinesis in animal cells reported by Turlier
et al. (27).
The sequential and randomized protocols (Fig. 4 B and C)
follow the same qualitative curve only if the curvature change
is very fast, approaching the instantaneous limit. However, if
the curvature change is implemented more slowly, something
that is expected to mimic conditions in cells, the time evolution
of the cell diameter follows a concave curve, where the furrow
A
B
C
Fig. 4.
Different protocols for the curvature change. (A) Instantaneous: The target filament radius changes globally throughout the filament to Rtarget/Rcell,
as indicated in the key, within a single time step. (B) Sequential: The filament curvature change starts at one end of the filament and propagates at a rate
vcurv to the other end, here shown for Rtarget/Rcell = 5.5%. (C) Randomized: Random bonds along the filament constrict at a rate vcurv, here shown for
Rtarget/Rcell = 5.5%. In all the protocols, once the entire filament has transitioned, it is disassembled from both ends at a rate vdis. The value of vdis does
not influence the division curves (SI Appendix, Fig. S4). A–C, Right compare the normalized diameter of the cell at the midzone as a function of time. We
selected only simulations that led to division and averaged over simulation seeds and different disassembly rates.
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formation is signiﬁcantly delayed, after which it follows an almost
linear decrease before division occurs. The slower the constric-
tion rate is, the longer the delay in the furrow formation, which
indicates that a certain critical portion of the ﬁlament has to be
constricted to signiﬁcantly deform the membrane. This delayed
onset is less pronounced for the randomized protocol, since the
ﬁlament is transformed at random points. As a result, the tension
is distributed evenly across the midcell diameter ring, leading to
constriction that is faster than that seen when using the sequential
protocol.
These observations can be rationalized by looking at the
changes in ﬁlament geometry, which depends both on the proto-
col and on the rate of curvature change (SI Appendix, section 2).
The faster the curvature change is, the more perversions
the hemihelical ﬁlament contains (SI Appendix, Fig. S2), in
agreement with previous studies of hemihelix formation in elastic
materials (19). Importantly, the ﬁlament coiling in response
to implementation of the randomized protocol contains more
perversions (SI Appendix, Fig. S2) and as a consequence has a
smaller ﬁlament radius of gyration (SI Appendix, Fig. S3A) and
higher ﬁlament tension (SI Appendix, Fig. S3B) and therefore
drives a greater membrane deformation (SI Appendix, Fig. S3C)
than the ﬁlament coiled via the sequential protocol. This is
because it is energetically costly to position perversions close to
one another (14); hence, the clustered perversions formed in the
sequential protocol are more likely to relax than in the case where
they are randomly positioned throughout the polymer. Defect
relaxation requires the ﬁlament to detach from the membrane
and can lead to division failure (Fig. 5).
To further explore the differences between the sequential and
random constriction protocols, we characterized the extent to
which a robust cell division depends on the rate of curvature
change and the rate of ﬁlament disassembly, ﬁxing the amount of
curvature change to Rtarget/Rcell = 5.5% (Fig. 5 A and B). For
the case of sequential curvature change, the cell divides reliably
(Fig. 5A) and evenly (SI Appendix, Fig. S6A) only for very fast
curvature changes, which approach instantaneous constriction.
In that regime the new curvature and associated tension spread
quickly across the ﬁlament length, pulling the membrane with
it (Movie S2). However, if the rate of curvature change is de-
creased, the system enters a regime in which almost none of the
cells divide. In this regime the uneven distribution of tension
along the ﬁlament length comes into play as local perversions
in the ﬁlament have time to detach from the membrane and
to equilibrate while the rest of the ﬁlament is still transitioning
(Fig. 5C and Movie S3). If the rate of curvature change is further
decreased, division becomes more likely again, because the de-
tached portion of the ﬁlament has time to reattach and pull the
membrane with it.
For the randomized curvature change protocol (Fig. 5B
and Movie S4) the curvature and the associated tension are
distributed more evenly along the ﬁlament, independently
of the rate, enabling more effective ﬁlament constriction
(SI Appendix, Fig. S3) and resulting in a more reliable (Fig. 5B)
and even (SI Appendix, Fig. S6B) division overall. The random-
ized protocol is also less sensitive to the choice of the ﬁlament’s
target radius (SI Appendix, Fig. S5). From an energy perspective,
we found that both curving protocols dissipate a comparable
A
C
B
Fig. 5.
Reliability of division for noninstantaneous curvature change protocols. (A and B) The influence of the filament constriction rate, vcurv, and the
filament disassembly rate, vdis, on the probability of cell division for the sequential (A) and randomized (B) protocols. The color of each square represents
the amount of successful divisions out of 10 simulations performed with different seeds. (C) The representative examples of a successful and an unsuccessful
division. If the local helices fail to reattach to the membrane when forming (indicated by an arrow in Upper panel), division fails. If the helices manage to
reattach to the membrane (arrow in the Lower panel), division succeeds. All simulations are performed using Rtarget/Rcell = 5.5%, which divides cells with
100% reliability for the instantaneous protocol (Fig. 2).
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fraction of the energy that was invested into the curvature
change (SI Appendix, section 7 and Fig. S8). However, in the
radnomized protocol, the nondissipated portion of energy is
used more productively, such that more of it is converted into
the energy required to deform the membrane. Ultimately, our
model predicts that cells divide more successfully and evenly if
the constricting ﬁlament changes its curvature in a randomized
fashion, rather than sequentially from one ﬁlament end.
Comparison between Simulation and Experimental Data. To identify
which of the described constriction protocols best describes the
ESCRT-III–driven archaeal cell division, we compared the time
evolution of the midcell diameter collected in simulations with
similar measurements taken from live dividing S. acidocaldarius
cells. To do so, we analyzed cells imaged live using a membrane
dye from Pulschen et al. (28), as shown in Fig. 6A. This setup al-
lowed us to measure the intensity proﬁle of the membrane along
the division axis over time and hence extract the midcell (furrow)
diameter evolution (Fig. 6A and SI Appendix, Figs. S11 and S12).
Since cells can have varying initial diameters and can take varying
lengths of time to divide, we rescaled the midcell diameter with
the initial cell diameter and the time axis with the total division
time for each cell. We then aligned all the curves at the point
of 50% of the cell diameter decrease. Satisfyingly, all rescaled
cells appear to follow the same general trajectory as they divide,
enabling us to average the data to generate a single experimental
curve (Fig. 6B; see SI Appendix, sections 10 and 11 for details).
We then rescaled our simulations the same way to allow a direct
comparison between model and experiment.
As can be seen in Fig. 6D, in simulations based on instanta-
neous ﬁlament constriction the behavior of the furrow diameter
in time has a very different qualitative shape from the experi-
mental curve, irrespective of the amount of curvature change in
the ﬁlament. We considered the possibility that this discrepancy
arose because the simulated cells are effectively empty on the
inside and do not resist the fast initial cell constriction when
the target ﬁlament geometry is suddenly changed. To determine
whether bulk cytoplasm mass is likely to contribute in this way, we
repeated the instantaneous constriction protocol measurements
with cells in which the cytoplasm was modeled using volume-
excluded particles. As SI Appendix, Fig. S9 shows, under these
conditions the constriction curves did not change signiﬁcantly,
ruling this out as a contributing factor. Thus, the dynamics of the
process appear to be governed by ﬁlament tension alone.
A
D
B
E
C
F
Fig. 6.
Comparison with live cell experiment. (A) Time sequence of a dividing S. acidocaldarius cell. Bottom row shows the division axis along which we
measure the membrane intensity profile to determine the time evolution of the midcell (furrow) diameter. (Scale bar, 1 μm.) (B) The evolution of the
midcell diameter in time. The midcell diameter d is normalized by the initial cell diameter d0, while the time is normalized by the total division time tdivision.
Colored curves show the normalized measurements for individual cells (N = 23), and the black line shows the mean of all the experimentally measured
curves. (C) The average of the partitioning of the constricting filament proteins in the daughter cells in experiments (CdvB1/2) and in simulations for
noninstantaneous curvature change protocols that match the experimental curves for midcell evolution in time (102vcurv = 5/τ for the sequential and
102vcurv = 16/τ for the randomized protocol). (D–F) The normalized cell diameter evolution curves collected in simulations for different protocols (D,
instantaneous; E, sequential; F, randomized) and compared to the averaged experimental data (black curve). For the instantaneous protocol different
amounts of filament constriction Rtarget/Rcell are investigated. For the sequential and randomized protocols Rtarget/Rcell = 5.5% and the constriction rate
vcurv is varied, as shown. The disassembly rate does not influence the curves. All the simulation curves are averaged over at least 10 repetitions and the
shading shows 1 SD.
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BIOPHYSICS AND
COMPUTATIONAL BIOLOGY
By contrast, the relatively symmetric initial and ﬁnal plateaus
seen for slower, noninstantaneous ﬁlament curvature change
protocols resemble the membrane deformation trajectories seen
in experiments. The randomized protocol shows somewhat better
agreement with the experimental curves and, for a range of
simulation parameters, the normalized simulation and experi-
mental curves match remarkably well without any ﬁtting (blue
and pink curves in Fig. 6F). This randomized protocol also
yielded a reliable division (Fig. 5B) and led to the symmetric
partitioning of the division apparatus between the two daughter
cells (SI Appendix, Fig. S6B).
Further, we measured the evenness of ﬁlament protein
(CdvB1/2) partitioning in daughter cells in experiments and
compared this with our simulations, as seen in Fig. 6C. The
simulated data here are for the two best-matching curves of
Fig. 6 E and F (102vcurv = 5/τ for the sequential and 102vcurv =
16/τ for the randomized protocol). In the experiments, the
CdvB1/2 ﬁlament proteins are divided fairly evenly between the
daughter cells (Fig. 6C), in agreement with the behavior found
in simulations with the randomized protocol. Taken together,
these results suggest that a constriction protocol in which the
ﬁlament curvature is noninstantaneously changed at random
points throughout the ﬁlament length faithfully reproduces cell
division as seen in Sulfolobus.
Discussion
Here we develop a computational model for the dynamics of
archaeal cell division via ESCRT-III ﬁlaments to study the phys-
ical mechanisms that underlie the division process. In doing
so, we identify a cell division mechanism that is driven by the
supercoiling of a disassembling elastic ﬁlament. Our mesoscale
model allows for a direct connection between the geometrical
and mechanical properties of the ﬁlament and the resulting
experimentally observable cellular behavior. This model can now
be used to test hypothetical division mechanisms that cannot yet
be directly addressed in experiments and to make predictions
about what one expects to see once the necessary tools become
available.
One of the outstanding questions in the cytoskeletal and cell
division ﬁelds has long been whether cytoskeletal elements like
ESCRT-III are able to drive the entire process of cytokinesis, i.e.,
whether a single mechanism can be used to drive a membrane
tube with a micrometer-sized diameter (the approximate size of
a dividing Sulfolobus cell and a human midbody) to contract to
a diameter sufﬁciently small to allow for spontaneous scission.
Our model shows that this is possible and suggests a potential
mechanism for crossing the two important length scales involved:
the global curvature that arises due to the superhelical arrange-
ment of a coiled ﬁlament and the local curvature of the individual
coils. This supercoiling shortens the ﬁlament and guides the
initial cell constriction, while the membrane wrapping around
the individual tight coils creates a narrow neck that snaps after
the ﬁlament has completely disassembled. While perversions like
those predicted under this model of constriction can be clearly
seen in images of ESCRT-III ﬁlaments reported in in vitro studies
(SI Appendix, Fig. S13), as well as for FtsZ ﬁlaments (23), no one
has yet assigned them a potential function. Based on our analysis,
if this is how Sulfolobus cells divide, it should be possible to
see ESCRT-III ﬁlament supercoils in dividing Sulfolobus cells via
cryogenic electron microscopy experiments in the future. It will
also be fascinating to determine whether similar structures are
seen for other membrane-associated ﬁlaments.
Our analysis also suggests the time evolution of the furrow
diameter of dividing Sulfolobus cells is best explained by a ran-
dom model of ﬁlament curvature changes along the ﬁlament,
which we predict would be due to stochastic binding of the
Vps4 ATPase to the CdvB/B1/B2 copolymer. These random local
changes in ﬁlament geometry serve to spread tension, facilitating
a reliable and symmetric division. It can be imagined that such
a mechanism is also the easiest one for cells to implement, as it
does not rely on starting at a certain point within the ﬁlament.
Our simulations predicted that changing the ﬁlament’s
preferred curvature away from the ideal region causes a
more asymmetric division (see Fig. 3 for instantaneous and
SI Appendix, Fig. S5 for sequential and randomized protocols).
In experiments, asymmetric divisions occur when the CdvB2
protein is absent from the composite polymer ﬁlament. This
may change the preferred ﬁlament curvature and has been
found to cause ﬁlament detachment and slippage, followed by
asymmetric division (28). It has also been suggested that the loss
of CdvB1 might reduce ﬁlament tension, causing the observed
occasional division failure and reduced midzone constriction
rates (28). If this were the case, our simulations show how a
decrease in tension in the ﬁlament can render division unreliable
(SI Appendix, Fig. S7).
Thinking more broadly about division, we note that the im-
portant dynamic shape parameter used in this analysis—midzone
membrane constriction in time—which proved so useful in com-
paring simulations and experiments, has been subjected to a
thorough analysis in only a very small number of studies (27)
even in more standard model systems (29, 30). Our analysis shows
how extending this set of dynamic data will be very useful in
gaining a mechanistic understanding of division across systems
going forward, helping to reveal whether or not there are likely
to be general rules that reﬂect common mechanistic principles.
Thus, we believe our model can be used as a starting point
for the study of more complex division mechanisms that evolved
from this minimalistic archaeal division, such as severing of the
midbody in the last step of eukaryotic division, and may help
us to understand division of soft compartments by nanoscale
ﬁlaments in general. Finally, our model presents an excellent
playground for testing speciﬁc nonequilibrium protocols behind
bio-inspired nanomachines and their connection to the resulting
nanomachine function. We therefore hope that our near-minimal
model for cell division in this relatively simple archaeal cell sys-
tem will also be of interest to those aiming to achieve the scission
of synthetic cells, using reconstituted ESCRT-III ﬁlaments in
vesicles.
Materials and Methods
Simulation. The simulation setup—an elastic self-avoiding helical filament
that is coupled to the inside of a spherical membrane, representing the
archaeal cell—can be seen in Fig. 1B. The filament helix has two full turns
that consist of Ntotal = 480 subunits. The ratio between the helix width and
diameter (6.5σ/105σ ≈ 0.06) corresponds roughly to the experimentally
measured ratio (0.1 μm/1.25 μm = 0.08) (6).
We model the filament using the ESCRT-III model we developed in
Harker-Kirschneck et al. (10). It is built of three-beaded rigid subunits that
are bonded to each other via nine strong springs with spring constant
K = 600 kBT (Fig. 1 B, Inset), where kB is Boltzmann’s constant and T is
temperature. The equilibrium lengths of the individual springs determine
the target filament geometry (SI Appendix, section 1). The cell membrane
is simulated by a coarse-grained, one-particle-thick model [developed by
Yuan et al. (11)], in which a single particle corresponds to a lipid patch of
∼10 nm. These particles interact via an anisotropic pair potential that drives
the self-assembly of fluid membranes with bending rigidity of 15kBT. The
blue beads of the filament are attracted to the membrane via a Lennard-
Jones potential, while the red beads interact with the membrane only via
volume exclusion. A more detailed description of the simulation setup and
all the interactions can be found in SI Appendix, section 1. We also repeated
our main results using a triangulated membrane model within a Monte
Carlo scheme (31), to show that our results are robust against a different
membrane model (SI Appendix, section 9).
To change the filament curvature, the rest length of the bonds between
the subunits is adjusted to the target curvature. In the case of nonin-
stantaneous curvature change, the rate of the curvature change is deter-
mined by the number of bonds that are shortened per simulation timestep
(0.01τ); i.e., if we constrict the bonds between two subunits every nth
time step, the rate is vcurv = 1/(n(0.01τ)). To simulate filament disassembly,
Harker-Kirschneck et al.
Physical mechanisms of ESCRT-III–driven cell division
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every mth simulation time step one subunit is removed from each end of the
filament, making the disassembly rate vdis = 2/(m(0.01τ)).
To measure the diameter d of the membrane at the cell midzone as a
function of time, we collect all membrane particles that are located in a
cuboid that is fixed at the center of the simulation box and has a width of
1σ (the size of one membrane bead). The collected coordinates are then
projected onto a plane and the resulting data are fitted by a circle using the
Taubin method (32).
This membrane model has not been developed to capture the mem-
brane hydrodynamics (33); however, the timescales we describe (on the
orders of minutes) are much longer than those of the expected relax-
ation of hydrodynamics effects in the cell membrane or in the cytoplasm
(SI Appendix, section 8). This coarse-grained model is also not appropriate
for capturing fine geometries of the membrane neck scission, where molec-
ular details of the bilayer might become important. We nevertheless base
all our comparison with experiment, and our mechanistic conclusions, on
the first half of the cell division process, when the cell diameter constricts
up to 50%, well before the tight neck geometries.
Experiment. Sulfolobus cells were grown in standard media and imaged
using Nile Red for membrane staining, as described by Pulschen et al. (28).
This staining allowed us to measure the intensity profile of the membrane
along the division axis over time (SI Appendix, Figs. S11 and S12). The full
width at half maximum (FWHM) of this profile was used as a measure of
the midcell diameter of the dividing cells, a parameter that we can com-
pare well to our simulation results (for details see SI Appendix, section 10).
SI Appendix, section 11 describes the rescaling procedure of the data. It
is important to add that for the last part of the midcell evolution curve
the experimental uncertainty in measurement becomes larger due to the
resolution limit; hence, in all our results we focus on and discuss only the
first half of the division curves.
Data Availability. The simulation input files and codes are freely available
at https://github.com/cvanhille/ESCRTIII_CD_ex and at University College
London Research Data Repository: https://doi.org/10.5522/04/16601753.
ACKNOWLEDGMENTS. We acknowledge support from the Biotechnology
and Biological Sciences Research Council (L.H.-K.), Engineering and Physical
Sciences Research Council (A.E.H), University College London Institute for the
Physics of Living Systems (T.Y. and D.H.), Wellcome Trust Grant 203276/Z/16/Z
(to A.P., S.C., R.H., and B.B.), Volkswagen Foundation Grant Az 96727 (to A.P.,
B.B., and A.Š.), the Medical Research Council Grant MC_CF1226 (to R.H., B.B.,
and A.Š.), the Life Science Moore-Simons foundation grant (735929LPI), the
European Research Council Grant “NEPA” 802960 (to X.J. and A.Š.), the Royal
Society (C.V.-C. and A.Š.), and the UK Materials and Molecular Modelling Hub
for computational resources (EP/P020194/1).
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https://doi.org/10.1073/pnas.2107763119
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Physical mechanisms of ESCRT-III–driven cell division
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