AbstractBlebs are membrane protrusions that appear during several physiological processes in eukaryotic cells. The phase behavior and kinetics of blebbing in cellular membrane is investigated computationally using a particle-based model for self-assembled lipid vesicles apposed to an elastic meshwork, mimicking a cell's cytoskeleton. We found that blebbing is induced when the cytoskeleton is subjected to a localized ablation, detachment from the membrane, or a uniform contraction. These results are in good agreement with experiments

Kumar, P.B. Sunil

Laradji, Mohamed

Spangler, Eric

Elsevier - Publisher Connector 

  Physics Procedia  57 ( 2014 )  38 – 42 
Available online at www.sciencedirect.com
1875-3892 © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Peer-review under responsibility of The Organizing Committee of CSP 2014 conference
doi: 10.1016/j.phpro.2014.08.128 
ScienceDirect
27th Annual CSP Workshops on “Recent Developments in Computer Simulation Studies in 
Condensed Matter Physics”, CSP 2014 
A computational study of blebbing in lipid membranes 
Eric Spanglera, P.B. Sunil Kumarb, and Mohamed Laradjia,* 
aDepartment of Physics, The University of Memphis, Memphis, Tennessee 38152, USA 
bDepartment of Physics, Indian Institute of Technology Madras, Chennai - 600 036, India 
Abstract 
Blebs are membrane protrusions that appear during several physiological processes in eukaryotic cells. The phase behavior and 
kinetics of blebbing in cellular membrane is investigated computationally using a particle-based model for self-assembled lipid 
vesicles apposed to an elastic meshwork, mimicking a cell’s cytoskeleton. We found that blebbing is induced when the 
cytoskeleton is subjected to a localized ablation, detachment from the membrane, or a uniform contraction. These results are in 
good agreement with experiments. 
© 2014 The Authors. Published by Elsevier B.V. 
Peer-review under responsibility of the Organizing Committee of CSP 2014 conference.  
Keywords: Lipid membranes; cytoskeleton, blebbing, molecular dynamics 
1. Introduction 
The coupling between the cortical actomyosin cytoskeleton (CSK) and the lipid bilayer of 
eukaryotic cells can lead to morpholigical changes to the plasma membrane in the form of 
transient exoplasmic spherical protrusion, commonly called blebs (Mohandas and Evans, 1994; 
Lim et al., 2002). Blebs occur in several cellular processes including cytokinesis, apoptosis, and 
cell motility. Recent experiments have shown that blebs occur in fibroblasts when the cortical 
CSK is subjected to a local ablation by laser (Tinevez et al., 2009) or when the CSK is 
compressed (Paluch et al., 2006). Red blood cells (RBCs) also undergo blebbing during their 
aging. Indeed, it is well documented that RBCs shed plasma membrane during the aging in the 
 
 
* Corresponding author. Tel.: 901-678-1676; fax: 901-678-4733. 
E-mail address: mlaradji@memphis.edu 
 14 The Authors. Published by Elsevi r B.V. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons. rg/licenses/by-nc-nd/3.0/).
Peer-review under responsibility of The Organizing Committee of CSP 2014 conference
 Eric Spangler et al. /  Physics Procedia  57 ( 2014 )  38 – 42 39
form of small vesicles about 100 nm in diameter, which is about the size of a single corral of the 
spectrin CSK of red blood cells (Backman et al., 1998).  
Up to now, very few theoretical and computational studies have been performed to investigate 
blebbing (Tinevez, 2009; Sens and Gov, 2007; Young and Mitran, 2010).  In this article, we 
present recent computational results of blebbing in self-assembled lipid bilayers coupled to an 
explicit CSK, using an efficient coarse-grained solvent-implicit molecular model (Spangler et al., 
2011).   
  
 
 
 
   
 
 
2. Model and method 
To model a system composed of a self-assembled lipid bilayer apposed to a CSK meshwork, 
which is akin to that of an RBC, we use a model recently developed by us (Revalee et al. 2008). 
In this model, a lipid molecule is modeled as a semi-flexible chain composed of one hydrophilic 
(h) bead, connected to two hydrophobic tail (t) beads.  The solvent is treated implicitly in this 
model. The lipid molecules spontaneously self-assemble through making the t-t interaction 
attractive. As shown in Fig. 1, the lipid bilayer vesicle, in this model, formed by the self-
assembly of the lipids is apposed with a semi-flexible polymer meshwork, mimicking the 
spectrin CSK of an RBC. Here, the CSK is composed of 162 vertices and is tessellated into 320 
triangular corrals. Most of the vertices (150) have six links, while 12 have 5 links, and each link 
is a semi-flexible chain composed of 8 to 22 beads called c. The CSK vertices are anchored to 
the bilayer through bola-like lipids, which mimics the more complex anchoring proteins.  
In this model, particles interact via the following potential, 
              U ri{ }( ) = U0 rij( )
i, j
 + Ubond ri,i+1( )
i
 + Ubend ri1,ri,ri+1( )
i
                                           (1) 
where ri is the position of bead i, and rij = ri  r j . U0 rij( ) is the interaction potential between 
two beads and is given by 
U0 r( ) =
Umax
 Umin
( ) rm  r( )
2
rm
2 +Umin
                             for r  rm
2Umin
 rc  r( )
3
rc  rm( )
3
+ 3Umax
 rc  r( )
2
rc  rm( )
2
   for  rm  r  rm
0                                                                             for r > rm
 
 
  
 
 
 
                   (2) 
 
where Umax
 > 0  for any pair. The self-assembly of the lipid molecules is realized through making 
the interaction between the tail beads attractive, i.e. Umin
 < 0  for  =  = t. Umin
 = 0  if
 or   t. The potential Ubond  ensures connectivity between consecutive beads belonging to a 
lipid molecule or CSK and is given by
Ubond (r) =
kbond
2
r  a( )2  (3)
Fig. 1. A cross-section of the initial configuration of a vesicle with CSK. The head and tail 
beads of lipids are red and blue, respectively. CSK beads are yellow. The junctions (black) 
beads connect the CSK to the lipid bilayer through bola-like lipids (green and orange). 
40   Eric Spangler et al. /  Physics Procedia  57 ( 2014 )  38 – 42 
 
where kbond  is a bond stiffness coefficient and a  is the bond length. Ubend  is a three-body 
potential to ensure bending stiffness of the chains and is given by, 
 
   Ubond ri1,ri,ri+1( ) =
kbend
2
cos0 
ri,i1 ri,i+1
ri,i1ri,i+1
 
 
 
 
 
	 
2
                                           (4) 
 
where kbend  is the bending stiffness coefficient of a lipid chain or a cytoskeletom, and 0  is a 
preferred splay angle. Here, we chose 0 =180
o  for all triplets.  
Specific values of the interaction parameters are Umax
hh =Umax
cc =Umax
ht =Umax
hc =Umax
tc =100, 
Umax
tt = 200, Umin
hh =Umin
cc =Umin
ht =Umin
hc =Umin
tc = 0 , kbond =100 /rm
2 ,  kbond =100 , a = 0.7rm , and 
rc = 2rm . More details about the model can be found in (Revalee et al., 2008; Spangler et al., 
2011). 
Particles are moved using molecular dynamics with a Langevin thermostat (Revalee et al., 
2008): r it = vit and mv i(t) = iU vi(t) +Wi(t), where m is the mass of a bead,  is the 
friction coefficient, and Wi(t)  is a random force, which satisfies Wi(t) = 0,  and 
Wi(t)W j (t') = 6kBT ij t  t '( ). This ensures that the dissipation-fluctuation theorem is not 
violated. The equations of motion are integrated using the velocity-Verlet method with 
 = 6m  with  = (rm
2m / )1/ 2, and rm  and   being our time and energy scales. All simulations 
are performed at kBT = 3 , at which the lipid bilayer is in the fluid phase (Spangler et al., 2011). 
The time step of the simulations, t = 0.02  and the number of lipids in a vesicle ranges between 
3.5 ×104and 2.5 ×105 . 
3. Results and discussion 
3.1. Phase diagram 
The equilibrium phase diagram of the system is shown in Fig. 2 in terms of the CSK’s corral 
stress-free area Acyto
(0)  and the parameter s = Alip /Acyto
(0) , which defines the mismatch between the 
area of the lipid vesicle per corral and the stress-free area of a corral. An s =1 corresponds to no 
mismatch, an s <1 corresponds to a CSK which is compressed within the vesicle, and an s >1 
corresponds to a stretched CSK. Fig. 2 shows that the system exhibits two equilibrium phases 
corresponding to (I) a uniform phase, in which the vesicle essentially has a spherical shape with 
thermally induced fluctuations, and (II) a blebbed phase in which the main vesicle is underlined 
with the CSK, and a bud or a bleb which is devoid from CSK. The bleb and main vesicle are 
connected by a neck with a diameter about the linear size of a corral. The inset of Fig. 2 shows 
that the transition line between the uniform and blebbed phase is consistent with s* ~ 1/ lcyto
(0)  
where lcyto
(0)  is a corral’s linear size. This is due to the interplay between the curvature (Helfrich’s) 
free energy of the vesicle and the elastic energy of the CSK (Spangler et al., 2011). 
 
 
 
 
 
Fig. 2.  (a) Phase diagram in terms of cytoskeleton corral 
stress-free area, Acyto
(0)  and mismatch parameter s (defined in 
text). The inset of (a) shows the transiltion line s* versus one 
over the linear size of a corral at rest. The blue line is a fit with 
the theory (see text above and ref. (Spangler et al., 2011)). (b) 
shows a uniform vesicle and (c) shows a vesicle with a single 
bleb.  
0 20 40 60 80 100
A
cyto 
[nm
2
]
1.5
2.0
2.5
3.0
s 
=
 A
lip
/ A
cy
to
0.10 0.15 0.20
1/l
cyto
1.6
1.8
2.0
2.2
s
Homogeneous vesicles
Blebbed vesicles
(0
)
(0)
*
(0)




	



 Eric Spangler et al. /  Physics Procedia  57 ( 2014 )  38 – 42 41
 
 
 
 
Fig. 3 shows the CSK elastic energy vs. the mismatch parameter, s, and configurations of the 
CSK within vesicle as a function of the mismatch parameter for the case of Acyto
(0) = 92rm
2 . This 
figures shows that the CSK elastic energy is minimized at a value, smin, slightly larger than 1. 
The increase in the CSK’s energy for s < smin  is due to its compression, while for s > smin , the 
high energy of the CSK is due to its stretching by the apposed lipid vesicle. We note that the 
sharp decrease in the CSK’s elastic energy implies that the transition from the uniform to the 
blebbed phase is first order. 
3.2. Kinetics of bleb formation and growth
We also investigated the kinetics of bleb formation as a result of localized ablation of the CSK. 
Here, an initially equilibrated vesicle in the uniform phase with the CSK’s coral size 
Acyto
(0) = 43.1rm
2, and with a mismatch parameter s =1.9, right below the transition line in Fig. 2.  
Fig. 3. The cytoskeleton elastic energy vs. the mismatch parameter for. Also 
shown are snapshots of the cytoskeleton for different values of s. The inset 
shows the actual corral area over the corral rest area vs. the mismatch parameter. 
The sharp decrease in the elastic energy is indicative of a first-order transition. 
Snapshot (a) corresponds to a compressed CSK. (b) corresponds to a stress-free 
CSK. (c) corresponds to a stretched CSK. (d) is a snapshot of the CSK right 
after the transition. The configuration of the CSK (d) is that of a stress-free 
CSK, similar to that of (b). 
 
0 0.5 1 1.5 2
A
lip
/A
cyto 
90
100
110
120
130
E
cy
to 0 0.5 1 1.5 2
s
0
1
2
A
cy
to
/ A
cy
to
(0)
(0
)
  

Fig. 4.  Top snapshot sequence of a vesicle undergoing blebbing as a result of a localized ablation of the CSK. The localized ablation is 
indicated by the arrow on left. Snapshots from left to right correspond to times t = 0, 1500, 3000, 6000, 9000, 24000, 46500, respectively.  
Bottom snapshot sequence shows views of the vesicle taken from inside it and showing evolution of the bleb. The location of the ablation 
(inidicated by the arrow). Snapshots from left to right correspond to t = 0, 1500, 7500, respectively. Only lipid head beads (red) and CSK 
beads (yellow) are shown in snapshots. Bottom right graph shows the velocity of the tip of the bleb versus time.
-20000 0 20000 40000
t[]
0
0.
00
2
0.
00
4
0.
00
6
V
bl
eb
[r
m
in
/
]
42   Eric Spangler et al. /  Physics Procedia  57 ( 2014 )  38 – 42 
The snapshot time series of the system resulting from a sudden ablation at t = 0 , shown in Fig. 4, 
demonstrates that the membrane caps right after the ablation, and exactly where the ablation is 
performed. The velocity of the bleb’s tip defined as v = d h( ) /dt , where h  is the distance 
between the bleb’s tip and its base, rapidly increases right after ablation of the CSK. The velocity 
reaches a maximum and then decays asymptotically to zero. The qualitative behavior of the blebs 
height vs. time is similar to that in the experimental study of (Charras et al, 2005). We also 
performed a series of computational experiments where the CSK is uniformly compressed or 
locally peeled from the bilayer, and found that blebbing can also occur in these situations. 
4. Conclusions 
We presented here a numerical study of blebbing of a model of a self-assembled lipid vesicle 
coupled to an explicit cytoskeleton. In this study, the solvent is accounted for implicitly, thus 
allowing us to perform large scale simulations and over long times. The phase behavior of the 
system, as expressed by the CSK corral size and by a mismatch parameter, s (defined by the area 
of the lipid bilayer over the area of a stress-free CSK), exhibits a uniform vesicle at low values of 
s and a blebbed vesicle at high values of s. In the uniform phase, the whole lipid membrane 
conforms to the CSK. However, in the blebbed phase, only part of the vesicle is apposed to the 
CSK, while part the other part of the lipid bilayer, i.e. bleb, is devoid of the CSK. The transition 
between the uniform phase and the blebbed phase is first order. From a series of computational 
experiments, we found that blebs occur when the lipid vesicle is subjected to a localized ablation, 
uniform compression or a localized peeling of the CSK. 
Acknowledgements 
This work was supported by the National Science Foundation (Grants No. DMR-0812470 and 
No. DMR-0755447) and the research corporation (Grant No. CC66879). 
References 
Backman, L., Jonasson, J.B., Hörstedt, P., 1998. Mol. Membr. Biol. 15, 27. 
Charras, G.T., Yarrow, J.C., Horton, M.A., Mahadevan, L., Mitchison, T.J., 2005. Nature, 435, 365.   
Lim, H.W.G., Wortis, M., Mukhopadhyay, R., 2002. Proc. Natl. Acad. Sci. USA 99, 16766. 
Mohandas, N., Evans, E., 1994. Anu. Rev. Biophys. Biomol. Struct. 23, 787. 
Paluch E., Sykes, C., Prost, J., Bornens, M., 2006. Trends Cell Biol. 16,5.  
Revalee, J.D., Laradji, M., Sunil Kumar, P.B., 2008. J. Chem. Phys. 128. 035102. 
Sens, P., Gov, N., 2007. Phys. Rev. Lett. 98, 018102. 
Spangler, E.J., Harvey, C.W., Revalee, J.D., Sunil Kumar, P.B., Laradji, M., 2011. Phys. Rev. E 84, 051906. 
Tinevez, J.-Y., Schulze, U., Salbreux, G., Roensch, J., Joanny, J.-F., Paluch, E., 2009. Proc. Natl. Acad. Sci. USA 106, 18581. 
Young, J., Mitran, S., 2010. J. Biomech. 43, 210. 
 


A Computational Study of Blebbing in Lipid Membranes 

Eric Spangler

P.B. Sunil Kumar

Mohamed Laradji

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Physics Procedia

A Computational Study of Blebbing in Lipid Membranes

Blebs are membrane protrusions that appear during several physiological processes in eukaryotic cells. The phase behavior and kinetics of blebbing in cellular membrane is investigated computationally using a particle-based model for self-assembled lipid vesicles apposed to an elastic meshwork, mimicking a cell\u27s cytoskeleton. We found that blebbing is induced when the cytoskeleton is subjected to a localized ablation, detachment from the membrane, or a uniform contraction. These results are in good agreement with experiments

Kumar, P. B.Sunil

University of Memphis Digital Commons

27th Annual CSP Workshops on  Recent Developments in Computer Simulation Studies in Condensed Matter Physics , CSP 2014 A computational study of blebbing in lipid membranes

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A Computational Study of Blebbing in Lipid Membranes

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