COMMENTARY
Nucleus 4:3, 156–159; May/June 2013; © 2013 Landes Bioscience
Nuclear mechanics
Lamin webs and pathological blebs
Chase P. Broedersz1 and Clifford P. Brangwynne2,*
Lewis–Sigler Institute for Integrative Genomics and Joseph Henry Laboratories of Physics; Princeton University; Princeton, NJ USA; 2Department of Chemical
and Biological Engineering; Princeton University; Princeton, NJ USA
1
A
nomalies in the three-dimensional
shape of the nucleus are associated
with a number of genetic diseases. These
shape distortions include lobulated
structures, with localized bulges referred
to as nuclear blebs. Blebbing can result
from mutations in genes encoding lamin
intermediate filaments that form the
lamin cortex, a thin meshwork lining the
nuclear envelope. However, the biophysical origins of nuclear blebs remain a mystery. A recent study by Funkhouser et al.
provides a theoretical model in which
the lamin cortex is modeled as a thin,
inhomogeneous elastic shell. This model
shows that partial segregation of different lamin sub-networks—each with distinct mechanical properties—can lead
to shell morphologies similar to blebbed
nuclei in living cells.
Keywords: lamiopathies, progeria, nuclear membrane, shape, elasticity, filaments
Submitted: 04/26/13
Revised: 05/08/13
Accepted: 05/13/13
http://dx.doi.org/10.4161/nucl.25019
*Correspondence to: Clifford P. Brangwynne;
Email: [email protected]
Commentary to: Funkhouser CM, Sknepnek R,
Shimi T, Goldman AE, Goldman RD, Olvera de la
Cruz M. Mechanical model of blebbing in nuclear
lamin meshworks. Proc Natl Acad Sci U S A
2013; 110:3248-53; PMID:23401537; http://dx.doi.
org/10.1073/pnas.1300215110
156
The mechanical properties of cells are intimately tied to their biological function.
The dependence of biological function on
mechanics is now well established,1 including decisions as important as whether
a cell should grow or divide,2 where to
migrate,3 or how stem cells should differentiate,4 all strongly influenced by the
mechanical properties and structure of
cells and their surroundings. These effects
are most well-known in the context of the
cytoplasm, where actin, microtubules and
intermediate filaments (IFs) form a dense
interconnected mechanical scaffold. In
the nucleus, the importance of mechanics
has been increasingly appreciated over the
last decade. Indeed, mechanical forces are
associated with chromatin remodeling and
modulation of transcriptional activity.5,6
Nucleus
Moreover, as with the cytoplasm there are
a number of pathologies associated with
altered nuclear mechanics. However, elucidating the role of mechanics requires
new approaches in the nucleus, due to
its size, geometry and unique structural
features.
The nucleus typically contains no
microtubules, and while actin is present,
its form is poorly understood. Indeed,
despite recent advances in imaging actin
within living nuclei,7 there is still little
known about its potential mechanical
role. Instead, one of the key mechanical components of nuclei are the nuclear
lamins, members of the Type V intermediate filament protein superfamily. The
four major lamins can be grouped into
A and B types. A type lamins A (LA)
and C (LC) are encoded by the same
gene, while B type lamins B1 (LB1) and
B2 (LB2), are coded by different genes.8
Nuclear lamins form a dense meshwork
organized in a thin shell curving along
the inner membrane of the nuclear envelope.9-11 This lamina has a thickness of
only 10–80 nm, several orders of magnitude smaller than the typical nuclear
radius 5–10 μm. Fluorescence recovery
after photobleaching (FRAP) experiments
indicated that while nucleoplasmic lamins are dynamic, lamins within the cortex may be largely stable and immobile.12
This observation suggests that the integrity of the lamin meshwork is stabilized
by filament crosslinking, although little
is known about the way in which laminassociated proteins regulate the structure
of the lamina.13 Interestingly, reconstituted lamin networks—in the absence of
Volume 4 Issue 3
COMMENTARY
COMMENTARY
Figure 1. (A) Blebbing in nuclei of HeLa cells where lamin B1 is silenced. These cells exhibit distorted morphologies and segregation of lamin types similar to the theoretical results in (B). These
simulation results were obtained with a fraction of B-type nodes, f = 0.8, and show the nuclear
surface and cross-section. (A) adapted from reference 26, (B) adapted from reference 27.
auxiliary proteins—were found to form
predominantly elastic gels, which stiffen
strongly under strain and exhibit a large
mechanical resilience;14 these observations suggest substantial interactions that
prevent inter-filament sliding. Other in
vitro experiments on various IFs, including neurofilaments and vimentin, suggest
that divalent ions can facilitate crosslinks
between filaments,15,16 indicating that
electrostatic interactions could contribute
to IF network stability. Although much
remains to be understood, the lamin
meshwork appears to form a relatively
elastic solid-like cortical shell, which provides mechanical support to the nucleus.
Consistent with the idea that the lamin
cortex is an important structural component, various anomalies in the threedimensional shape of the nucleus are
caused by disease-associated mutations in
genes encoding for the basic constituents of
the lamina meshwork (for a recent review,
see ref. 17). While a normal nucleus typically exhibits a highly smooth, rounded
shape, such mutations can give rise to
severely mis-shapen nuclei; for example
cell nuclei from patients with HutchinsonGilford progeria syndrome exhibit highly
lobulated shapes, with localized bulges
typically referred to as “nuclear blebs”.18
These structures are reminiscent of cell
membrane blebs, widely observed both in
physiological and pathological contexts.
Like the nuclear blebs at the lamin cortex,
cytoplasmic blebs are associated with a
thin cortical shell, in this case comprised
www.landesbioscience.com
of an actomyosin network beneath the
cell surface. Local rupturing of mechanical connections between the membrane
and actomyosin cortex, together with
hydrostatic pressure on the membrane,
appears to underlie these highly dynamic
and repeated blebbing events, with actomyosin thought to be involved in reassembling and “repairing” the inflated
membrane surface on a timescale of
~1 min.19 Although nuclear blebs are reminiscent of these more well-understood
cytoplasmic blebs, the origins of nuclear
blebs are still poorly understood.
These pathological nuclear shape distortions could result from changes to the
elasticity of the lamin shell. Nuclear blebbing could thus be related to mechanical
instabilities of thin shells, well-known
from elasticity theory. A key parameter in
the analysis of such shells is the ratio of
the shell thickness, h, to its radius, R; for
thin shells h/R << 1, which has important
consequences for the resulting behavior.
In particular, the two dimensional deformation energy associated with stretching scales with h/R, while the bending
energy scales with (h/R)3.20 Although
elastic shells can undergo both stretching
and bending deformations, thin shells are
much more compliant to bending than
to stretching, since (h/R)3 << h/R. This
simple fact has myriad implications for the
three dimensional structures of deformed
shells, from the crumpling of dehydrated
pollen grains,21 to the indentation of
viruses under a localized stress.22
Nucleus
An important potential difference
between the nuclear cortex and a simple
elastic shell is that the nuclear lamina is
a composite material; this could be relevant, because material inhomogeneities
are known to have important implications for elastic instabilities.21,23,24 Lamins
LA and LB1 can interact with each other
both homotypically and heterotypically,25
but there is evidence that A- and B-lamins
form separate, but interconnected networks.26 Moreover, imaging reveals Aand B-rich microdomains, with some
partial overlap.10,26 It has also been suggested that B1-type lamins (LB1) play an
important role in organizing the A- and
B-type microdomains. For example, in
LB1 silenced cells, larger islands of A-type
domains were observed and the meshsize
of LB2 and A/C regions appeared to be
enlarged.26 Interestingly, blebs were found
to be enriched with A-type lamins and
lacking in B-type lamins (Fig. 1A), suggesting that segregation between the A
and B-type networks could lie at the origin of blebbing.
Motivated
by
these
observations, a recent computational study by
Funkhouser et al.27 proposed a two-component continuum elastic shell model
for the lamina. Each component is postulated to correspond to either of the
structurally dissimilar A or B-type lamins, and thus, each component is allowed
to have its own distinct mechanical and
morphological properties. The model
by Funkhouser et al. incorporates a reference shape (undeformed state) of the
lamina as a sphere with a radius of curvature R(0)A,B. Observations suggest that
the lamin density in A-enriched blebbed
regions appears to be reduced,26 which
could be caused by the blebbing event
itself. Alternatively, it could be an intrinsic
property of the A-type subnetwork. The
model of Funkhouser et al. assumes the
latter, imposing a larger radius of curvature for A-type regions R(0)A > R(0)B and a
larger meshsize (average spacing between
filaments). Thus, the two components of
the model shell not only have distinct elastic properties, but also distinct preferred
curved geometries.
Funkhouser et al. used a finite element
vertex model to describe this heterogeneous curved elastic system. Vertices are
157
distributed randomly over a 3D surface
with a spherical topology, while maintaining a fixed distance between the vertices.
Vertices are either A- or B-type lamins,
representing a region enriched with the
respective lamin type networks. To capture the stretching elasticity of the shell,
vertices are connected by A- or B-type
springs with a distinct stiffness and rest
length. Bending contributions are captured by an energy term that penalizes
departures from the preferred curvature
between the triangle elements belonging
to the apex of a vertex. This constitutes a
minimal numerical model to describe an
isolated, heterogeneous elastic shell in the
absence of pressures or tensions.
Starting with a fraction, f, of B-type
nodes randomly mixed with A-type
nodes, Funkhouser et al. employ a Monte
Carlo annealing procedure in which A
and B nodes are switched to relax the
node distribution as the temperature is
effectively reduced to zero (quenched
exponentially) through a sequence of
equilibrations. This procedure aims to
find the distribution of A- and B-type
nodes that minimizes the elastic energy.
Even though there is no penalty (or gain)
for mixing of A and B type elements in
their model, they find that the shell segregates into large A and B type domains.
The authors report that this segregation
depends only on the difference in preferred curvature between the two types
of elements (which can be tuned by varying a scaling factor of the metric tensor
M A for A-type nodes, holding MB = 1).
Such a segregation is energetically favorable since it reduces the amount of interface between A and B regions where large
deformations would be necessitated by
their different preferred curvatures. The
segregated two-component shells have
striking morphologies: For large differences in preferred curvature (M A = 2), the
shell has a wrinkled structure for B-type
fractions f < 0.5. This wrinkling hints
toward an elastic instability caused by the
constraints imposed on the expanding
A-regions by the surrounding B-regions.
By contrast, for higher B-type fractions
158
f > 0.5, A-type regions form smooth caplike protrusions, resembling more closely
typical morphologies of nuclear blebs, as
shown in Figure 1.
As pointed out by the authors, the
results of their Monte Carlo procedure
may depend on the details of the path
toward the lower energy states. In particular, when the computational system is
cooled down too fast, the distribution of A
and B components will essentially freeze
into a certain state of (partial) segregation.
The simulated shell morphologies thus
do not necessarily represent global energy
minima, but rather an energy minimization with a partially relaxed distribution of
A and B regions. Indeed, when the simulations are relaxed at a lower rate, fewer, but
larger blebs form. Clearly, the state with
the lowest elastic energy in this model
is obtained when the A and B regions
completely demix as to obtain two large
domains separated by a single interface.
A complete demixing is not typically
observed in cells.26 Funkhouser et al.
speculate that this could be due to the
limited mobility and turnover of filaments
in the blebs. It is certainly possible that
significant energy barriers prevent the system from relaxing to its fully segregated
ground state. It is puzzling though that
the system seems sufficiently dynamic
to reach this partially demixed state, but
then would appear to arrest completely.
Funkhouser et al. suggest that a model
that also includes the viscoelastic nature
of the lamina could explain this behavior.
Relaxation rates could effectively vanish
as the segregated domains become larger,
preventing the system from reaching
equilibrium on physiological time scales.
It would thus be interesting to consider
models that include aspects of the reorganization kinetics of the nuclear lamina,28
although the viscoelastic properties of the
lamina in living cells are unknown.
The segregation driven by differences
in the elasticity of the lamin sub-networks
proposed by Funkhouser et al. provides an
interesting perspective on the biophysical
origins of nuclear blebs. But it is important to recognize that the model contains
Nucleus
a range of geometrical and mechanical
parameters which are not well known
under in vivo conditions, and it remains
unclear whether such a mechanism is actually at play within living cells. Qualitatively
different models are conceivable. For
example, it may be possible that the lamina
itself is not the driving force for the formation of blebs. Instead, local defects in the
lamina could destabilize the laminar shape
against other forces, such as any osmotic
pressure difference between the nucleus
and the cytoplasm, or stresses arising from
the high density of compacted chromatin.
Indeed, a recent study observed nuclear
blebbing in mechanically compressed tissue culture cells29 and nuclear blebbing
has recently been shown to be a pathway
of mRNA export,30 demonstrating that
blebs can occur in cells in the absence of
lamin mutations. Moreover, a more complete, thermodynamic model would also
consider the entropy and energy of mixing of different lamin sub-networks, both
of which could counteract the tendency
toward a demixed state. It is also possible
that coupling between the lamina and
chromatin plays an important role in stabilizing the shape of the lamina and the
segregation dynamics of the lamins;26,31
an analogous arrest of a demixing phase
separation of lipid domains may arise from
coupling between the cell membrane and
underlying actin cortex.32 Future work
will investigate how these mechanical and
structural effects could give rise to the cell
and organism level phenotypes observed
in diseases such as Hutchinson-Gilford
progeria and Emery-Dreyfus muscular
dystrophy.
Disclosure of Potential Conflicts of Interest
No potential conflict of interest was
disclosed.
Acknowledgments
This work was supported by a LewisSigler fellowship (Ch.B.) and a NIH New
Innovator Award (Cl.B.). The authors
thank Ben Machta, Marina Feric and
Thoru Pederson for insightful comments
and discussions.
Volume 4 Issue 3
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