nanotubes from asymmetrically decorated vesicles

PAPER www.rsc.org/softmatter | Soft Matter

Nanotubes from asymmetrically decorated vesicles

S. Kremer,a C. Campillo,a F. Quemeneur,b M. Rinaudo,c B. P�epin-Donat*b and F. Brochard-Wyart*a

Received 6th April 2010, Accepted 12th October 2010

DOI: 10.1039/c0sm00212g

Hydrodynamic nanotube extrusion is used to characterize chitosan-decorated vesicles, which are

more robust to pH and salt shocks and exhibit specific behavior under osmotic pressure if compared

to their bare homologues. The vesicle attached to a micro-rod is submitted to a flow. Above

a threshold velocity, we observe the extrusion of a lipidic nanotube. We study how it grows and

relaxes when the flow is stopped. We find that extrusion forces for decorated vesicles are weaker

than for bare vesicles. We interpret these results using a model that introduces the spontaneous

curvature due to asymmetric adsorption of chitosan on the external leaflet of the bilayer, which

allows us to calculate the stationary length of the tube versus the flow velocity and to estimate the

spontaneous curvature c0.

Introduction

For living cells in which biological and physical properties are

reciprocally regulated, it appears that the first steps of many

biological processes are mainly controlled by the cells’ mechanical

properties. Therefore, it is of interest to develop models of cells

consisting in biomimetic objects. This approach may allow one to

decipher a particular biological process by studying how such

biomimetic objects respond in assays reconstituting biological

situations (adhesion to a substrate, movement in a flow.).1

Giant unilamellar vesicles (GUVs), which consist in a self-

closed phospholipidic membrane2 of micrometric size, are

considered as a first step to model a cell’s membrane. Never-

theless their poor resistance to external stresses limits their

relevance to mimicking real cells. To improve their mechanical

properties, one can act on their internal medium3 or on their

membrane.4 Here we study reinforcement by polymer decoration

of the membrane. Moreover, it is of particular biological rele-

vance since, in cells, the extracellular matrix covers the plasma

membrane.5 In addition, such polymer-coated vesicles may find

application as drug carriers because the polymer corona

improves their biocompatibility, enhancing their in vivo lifetime6

and may confer specific targeting character, in particular for

cancer therapy.7 Interaction of polymers with lipid membranes

has been extensively studied, both experimentally8 and theoreti-

cally.9 Adsorption of charged and neutral macromolecules on

lipid membranes renormalizes their curvature moduli.10 More-

over, asymmetric binding induces spontaneous curvature.11 If c is

the membrane curvature, its elastic deformation energy per unit

area is ½kðc� c0Þ2 where k is the bending modulus and c0 is the

spontaneous membrane curvature introduced by Helfrich12 to

aLaboratoire PCC Institut Curie, CNRS UMR 168, University Paris 6,75231 Paris Cedex 05, France. E-mail: [email protected] Electronique Mol�eculaire Organique et Hybride, UMR 5819SPrAM (CEA-CNRS-UJF), INAC/CEA-GRENOBLE, 38054GRENOBLE CEDEX 9, France. E-mail: [email protected] de Recherches sur les Macromol�ecules V�eg�etales (CERMAV-CNRS) affiliated with Joseph Fourier University, BP53, 38041 Grenoblecedex 9, France

946 | Soft Matter, 2011, 7, 946–951

describe asymmetric membranes, which are not flat at equilib-

rium. Spontaneous curvature has been shown to induce

membrane remodelling, involved in various biological processes

such as movement, division, extrusion of neuronal arbors and

vesicles trafficking.13

The present work deals with the mechanical properties of

DOPC giant vesicles decorated on their external surface by chi-

tosan. This pseudo-natural cationic polyelectrolyte obtained by

deacetylation of chitin extracted from crustaceous shells, cuticles

of insects and cell walls of some fungi,14 is recognized for its good

biocompatibility15 and degradability required for biological

applications.16 Its charge varies with pH as well as that of the

zwitterionic DOPC membrane.17 In the experimental conditions

of decoration adopted for the present study, the membrane and

polymer are respectively negatively and positively charged

leading to a strong electrostatic interaction between the zwit-

terionic DOPC and chitosan.17,18 We have already shown that

such chitosan-decorated vesicles exhibit enhanced resistance

against pH, salt shocks and specific behaviours under osmotic

deflation if compared to their bare homologues.19 Recently,

a modification of the electroformation technique has been

introduced to obtain GUVs decorated by chitosan on both sides

of the bilayer.20

We use the hydrodynamic nanotube extrusion technique,

a powerful tool to characterize membrane properties of vesicles21

and cells.22 The vesicle is attached to a micro-rod and submitted to

a hydrodynamic flow23 which produces Stokes forces of the order

of 10 pN, the range of forces exerted for example by molecular

motors in vivo.24 Above a threshold flow, a thin (�30 nm diameter)

membrane nanotube is extruded. For GUVs, nanotube extrusion

and retraction are governed by the bilayer’s bending energy and

membrane tension.25 The main interest of this technique is the

absence of force sensor in the experimental set-up. The friction

force applied on the vesicle is deduced from the Poiseuille flow

inside the micro-channel. We have recently used nanotube

extrusion to probe the membrane properties of biomimetic ‘‘gelly’’

liposomes containing a polyNIPAM internal medium.26

In this paper, we present the results of hydrodynamic nano-

tube extrusion experiments on chitosan-decorated GUVs to

This journal is ª The Royal Society of Chemistry 2011

investigate how the adsorbed polyelectrolyte changes the

mechanical properties of the vesicles.

Materials and methods

Chemicals for the preparation of chitosan decorated giant

unilamellar vesicles

1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dio-

leoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine rhoda-

mine B sulfonyl) (ammonium salt) were purchased from Avanti

Polar Lipids and dissolved separately in a chloroform–methanol

solution (9/1) at 10 mg mL�1. Fluorescently labelled lipids were

then mixed with DOPC in a weight ratio of 1 : 80 respectively

with total lipid concentration of 1 mg mL�1. Solutions are kept

at �20 �C until used. Sucrose, glucose, HCl and NaOH are

purchased from Sigma-Aldrich and used as received. Highly

purified 18.2 MU cm water is used for the preparation of all the

solutions.

Giant unilamellar vesicles (GUVs) are prepared from

a mixture of 1,2-dioleoyl-sn-glycero-3-phosphocholine and

1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(lissamine

rhodamine B sulfonyl) (ammonium salt), using the standard

electro-formation method:27 10 mL of lipids at 2 mg mL�1 are

deposited on two glass plates coated with indium tin oxide (ITO)

and hydrated under an AC field in a 200 mM sucrose solution at

room temperature.

Chitosan Kitomer (Marinard, Canada) is a linear random

b (1 / 4) copolymer of D-glucosamine and N-acetyl-D-glucos-

amine with a degree of acetylation DA ¼ 0.2 and a weight-

average molecular weight Mw ¼ 5 � 105. In order to observe the

decoration of GUVs by chitosan using fluorescence microscopy,

we label the chitosan with fluorescein28 as described in details in

our previous work.29

The complete solubilization of chitosan is obtained by addi-

tion of the stoichiometric amount of HCl to fully protonate the

NH2 groups of the chitosan macromolecules (final pH around

3.5). The solution is placed under constant stirring for 1 night at

room temperature until complete solubilization occurs. The

chitosan solution is diluted for vesicle incubation at 0.1 g L�1 in

a solution of 200 mM sucrose at pH ¼ 6.0.

The liposome suspension is added into the chitosan solution.

At this pH, the DOPC membrane and the polymer are respec-

tively negatively and positively charged.17,18 Back and forth

aspiration with a micropipette allows homogenization of the

mixture, which is left to rest for 30 min at room temperature for

incubation. We have shown that maximal coverage of the

membrane is reached after 30 min and that no detectable

desorption was observed after one hour in very dilute solution.

The coverage degree is estimated to be 0.3 chitosan monomeric

units adsorbed per accessible lipid (i.e. 0.11 mg m�2 assuming an

area-per-lipid head30 of 0.725 nm2).

Micro-rods and flow chamber

We applied the protocol previously used for bare-DOPC vesi-

cles.21 Micro-rods are made from glass capillaries using a hori-

zontal laser pipette puller (P-2000, Sutter Instrument Co.) and by

breaking off the tips with a micro forge at the desired diameter

(1–5 mm). Tips are immersed in a 0.1% w/v polylysine solution


(Sigma Diagnostic Inc.) for few minutes before use. Polylysine is

a positively charged polyelectrolyte and it is known that bare-

GUV membranes are slightly negatively charged.31 This allows

the vesicle to stick to the rod through electrostatic forces.

Although chitosan-decorated vesicles are positively charged, this

protocol is adapted in our experiments. This may be due to the

fact that polyelectrolyte adsorption at the vesicle interface of

opposite charge occurs with the progressive formation of a more

or less ordered patch-like surface structure consisting of a non-

uniform distribution of the surface charges (domains of stuck

chitosan, with a local positive charge excess, alternating with

domains of negatively charged bare membrane surface).27

The flow chamber is made from a channel-shaped piece of

PDMS sheet (Silgard 184, Dow Corning) stuck on a clean glass

cover slide (Fig. 1). The channel (section 150 � 103 mm2, length

1 cm) is filled with a glucose solution (200 mM, h ¼ 10�3 Pa s,

pH ¼ 6.0). Vesicles are suspended in a reservoir connected to the

end of the channel where the micro-rod is introduced. A vesicle is

picked up with the tip of the polylysine-coated micro-rod and

brought in the channel. The micro-rod is placed in the center of

the channel, to avoid wall effects and to minimize uncertainty in

velocity in the Poiseuille flow inside the channel. The other end of

the channel is connected to a syringe that pumps the liquid at

a given velocity. In our geometry, the Poiseuille flow velocities

ranges from 0 to a few 1000 mm s�1 and the Reynolds number is

very small (Re � 1). A step of flow velocity U is applied. When

U is larger than a threshold value, a tube is extracted. Stepwise

increases and decreases of flow velocity U can be applied.

Microscopy observations

Tube extrusion dynamics are observed using a microscope

(Axiovert S100, Zeiss) with 20X objective under bright field

illumination and monitored with a numerical camera (Photo-

metrics Cascade 512B). Sequences of interest are recorded and

analyzed using Metamorph, Molecular Devices.

Phase contrast microscopy observations are made using

a phase-contrast inverted microscope (Olympus CKX41)

equipped with 10X and 20X objectives and a numerical camera

AVT MarlinF080B (Imasys, Suresnes, France).

Confocal microscopy observations are performed with

a UltraView LCI Nipkow Disk scanner (PerkinElmer GmbH,

Rodgau-J€ugesheimf, Germany) attached to a Zeiss Axiovert 200

microscope (Zeiss GmbH, Heidelberg, Germany) equipped with

a C-Apochromat 63X, 1.2 NA water immersion objective. GUVs

observations are made at 488 nm excitation and 500LP emission

filters for the chitosan probed with fluorescein (Chit–Fluo) and at

568 nm excitation and 600/45BP emission filters for the 18 : 1

Liss Rhod PE lipids. Fluorescence acquisitions at these two

excitation wavelengths are made successively.

Results and discussion

Let us first review the main results of hydrodynamic tube

extrusion from bare vesicles.21,25 The extrusion of a membrane

nanotube can be seen as a first-order transition at a threshold

force f ¼ 2p(2ks)1/2 ¼ 2pk/r, where k z 4.10�20 J is the

bending rigidity of the membrane, s its tension and r the tube

radius (r ¼ (k/2s)1/2). Under a flow velocity U, the force on the

Soft Matter, 2011, 7, 946–951 | 947

Fig. 1 A) Experimental setup: chamber consisting in a micro-channel imprinted in PDMS stuck on glass. Zoom: sketch of a decorated vesicle anchored

to the micro-rod inside the channel subjected to a flow U. B) Videomicrograph of an extrusion experiment, scale bar: 15 mm.

Fig. 2 Tube extrusion and retraction dynamics from chitosan-decorated

GUVs: tube length versus time during retraction for six forces from 3 to

32 pN (from the same GUV with initial radius R¼ 15 mm). For extrusion

forces superior to 5 pN, tube extrusion is stopped for a maximal tube

length of 400 mm, which is simply the size of the camera field.

tethered vesicle (radius R) is the Stokes friction fv ¼ 6phUR (h is

the viscosity of water). At equilibrium fv ¼ f, leading to the

threshold velocity Uc given by:

Uc ¼ð2ksÞ1=2

3hR¼ k

3hRr(1)

The initial tension s0 is not imposed in our experiment, but is

known to range between 10�7 to 10�5 N m�1. From eqn (1), s0 sets

the initial threshold velocity Uc0. If U > Uc0, a tube is extruded at

a velocity L̇ ¼ dL/dt given by the force balance equation:

U � L̇ ¼ Uc0 (2)

As the tube grows, the excess surface area of the vesicle

decreases, and the membrane tension s increases. The relative

area extension DA/A is related to the membrane tension s by32:

DA

A¼ kBT

8pkln

�s

s0

�(3)

where kBT is the thermal energy. For a tube length L and

radius r, DA¼ 2pLr and A¼ 4pR2. As L grows, s increases and,

according to eqn (1), Uc increases until the growth stops when

Uc ¼ U. This fixes the membrane tension sN from eqn (1).

Inserting r and s into eqn (3) leads to:

LN ¼ s0U ln

�U

Uc0

�(4)

L

LN

¼ 1� exp

�� t

LN

ðU �Uc0Þ�

(5)

where the characteristic time s0 ¼ 3kBTR3h/2pk2 strongly

depends upon the size R and the curvature modulus k of the

vesicle. The extrusion time deduced from eqn (5)

s ¼ U �Uc0

LNxs0

�1þ ln

U

Uc0

�depends weakly upon U. When

we stop the flow, the force balance equation becomes L̇ ¼ �Uc

and leads to:

L ¼ s0U exp��t

s

�� sUc0 (6)

This approximate solution describes well the retraction

dynamics that starts at L ¼ LN and L̇ ¼ �U and ends at L ¼0 and L̇ ¼ �Uc0 after a time sret z sln(U/Uc0). Experiments by

948 | Soft Matter, 2011, 7, 946–951

Borghi et al.21 on nanotube extrusion from DOPC vesicles have

confirmed the validity of eqn (4), (5) and (6) which led to

a measurement of k ¼ 10kBT for such liposomes.

We now describe nanotube extrusion from chitosan-decorated

GUVs: the variation of the extruded tube length L as a function

of time is observed during hydrodynamic tube extrusion and

retraction experiments.

First of all, while retraction curves follow the expected expo-

nential behavior of eqn (6) as illustrated in Fig. 2, extraction

regimes for applied forces higher than 5 pN are characterized by

an erratic tube growth, which does not follow the expected

exponential behavior (eqn (5)). This systematically observed

phenomenon could be attributed to polymer accumulation at the

neck of the tube or to transient pores induced by the increase of

the membrane tension during tube extrusion. Betterton and

Brenner33 have shown that for charged vesicles, holes in the

membrane decrease the counterions’ electrostatic energy and

transient pores are favoured. From this reference, we calculate

that the electrostatic contribution to the surface tension is 2 �10�5 N m�1 (we measured a surface charge density of 7 � 10�4 C

m�2,26 and calculated a Debye length of 30 nm from the estimated

salt concentration in the solution of 10�4 mol L�1). Therefore, the

increase of s due to nanotube extrusion (of the order of 5 � 10�5

N m�1 for a tube length of 100 mm) at sufficiently high velocity

contributes to decrease the barrier energy to form a hole.

Nevertheless, we have no direct evidence of these transient pores

because of their milliseconds lifetime.34 Because the extrusion is


Fig. 4 a) Osmotic deflation of a chitosan-decorated vesicle at pH ¼ 6.0

induced by a glucose gradient: the vesicle remains globally spherical while

ejecting many membrane tethers. b) Observation by confocal microscopy

of GUVs decorated with chitosan at pH ¼ 6.0 connected by a sponta-

neously-formed tube. We visualize independently the lipid membrane

labelled with rhodamine (b) and the chitosan decoration labelled with

fluorescein (c). Scale bar: 10 mm.

erratic, we use the tube retraction where no such effects can occur

to characterize the mechanical properties of the decorated

membrane. We measure the plateau value of the tether length

LN(U) by decreasing U step by step. As shown in eqn (6) for tube

retraction, the asymptotical limit at infinite times provides

a measurement of the threshold extrusion velocity Uc0. This

parameter is calculated from the slope of L(t) at the end of

retraction.

The values of Uc0 obtained for chitosan-decorated vesicles are

much lower than for bare vesicles. Indeed, for the curves of

Fig. 2, we measure an average velocity Uc0 ¼ 0.34 � 0.15 mm s�1

corresponding to a Stokes force f ¼ 0.1 � 0.04 pN dramatically

lower than 5 pN reported by Borghi et al.21 This explains why

tubes can be extruded at speeds of the order of a few mm s�1

whereas for bare vesicles, the velocities are ten times larger. Fig. 3

shows the evolution of the tube length versus time for decreasing

flow velocities. This allowed us to investigate the evolution of LN

versus flow velocity using classical theoretical framework (eqn

(4)). Fitting the curve LN(U) with eqn (4) leads to s0 ¼ 2.7 s and

Uc0 ¼ 9.2 � 10�2 mm s�1 and, from this value, we obtain

a membrane tension of s0 ¼ 1.5 � 10�10 N m�1. We never

observed the large membrane fluctuations that should occur at

such a low membrane tension. This clearly shows evidence that

the model used for DOPC bare vesicles is not suitable to describe

the behaviour of chitosan-decorated vesicles.

To interpret the low force needed to extrude membrane

nanotubes from chitosan-decorated vesicles, we introduce

a spontaneous curvature c0 induced by the membrane asymmetry

of chitosan-coated vesicles. Indeed, only their external leaflet,

which interacts with the polyelectrolyte solution, is decorated.

Fig. 4 shows the homogeneity of this decoration at the optical

scale. Besides, we have demonstrated that the curvature of the

membrane had no effect on the polymer decoration for vesicles

with radii ranging from 2.5 mm to 100 nm,29 therefore we make

the assumption that the polymer decoration rate is independent

on the membrane curvature.

With a spontaneous curvature term c0, the free energy of the

vesicle F is given by:

F

2prL¼ k

2

�1

r� c0

�2

þ s0 ¼ k

2r2� kc0

rþ s (7)

s ¼ s0 + kc20/2 is the global membrane tension. In a micropipette

experiment, s would be fixed by the aspiration pressure. s0 is the

Fig. 3 Tube length versus time for step-by-step decreasing forces: after

a tube length of 400 mm is reached for a Stokes force of 10.2 pN, the fluid

velocity is progressively reduced to observe the evolution of the

stationary length for different Stokes forces (values in grey varying from

10.2 to 0 pN), R ¼ 15 mm.


tension of the bare lipid membrane and kc20/2 corresponds to the

energy required to keep it flat. The derivation of free energy at

constant volume U ¼ 2pr2L provides an expression of the

extrusion force:

f ¼�

vF

vL

�U

¼ 2p�k

r� kc0

�¼ 2p

� ffiffiffiffiffiffiffiffi2ksp

� kc0

�(8)

Thus, for s < kc20/2, f < 0 and the vesicle spontaneously ejects

tubes without being submitted to an external force as predicted

previously.35 When s > kc20/2 the tether extrusion requires the

application of an external force. In this latter case, two situations

can arise depending on the bare membrane tension s00 ¼ s0(t ¼ 0)

at the beginning of the extrusion experiment. When s00 [ kc20/2

the effect of spontaneous curvature can be neglected and the

analysis presented above for membrane without spontaneous

curvature is valid. When s00 � kc20/2 the effect of spontaneous

curvature has to be considered.

In the following, we assume that spontaneous curvature effect

dominates at the beginning of extrusion (s ¼ s0 + kc20/2 with s’0

� kc20/2). The threshold extrusion velocity Uc0 is given by the

equality of extrusion and Stokes forces:

6phRUc0y2ps00c0

(9)

For U > Uc0 we consider two new cases according to whether

s0N is small or large compared to kc20. At low velocity of extrusion

(s0N � kc20/2), the equilibrium between extrusion force for

s0 ¼ s0N (eqn (8) with the square root term simplified) and Stokes

force gives:

6phRUy2ps0Nc0

(10)

Eqn (9) and (10) lead to:

s0Ns00¼ U

Uc0

(11)

and tube radius r is given by:

1

r¼ c0 þ

3hRU

k(12)

Replacing in the Helfrich relation, eqn (3), sN/s0 and the

radius r by their respective expressions given by eqn (11) and

(12), we finally obtain:

LN ¼1

2s0

�U*

c þU�ln

U

Uc0

(13)

Soft Matter, 2011, 7, 946–951 | 949

Fig. 5 Stationary length of the tube as a function of flow velocity (data

from 4 different vesicles). From the inflexion point of the curve, we

estimate the characteristic velocity Uc* (14 mm s�1 for vesicle #2: ves2),

the intersection between fit extrapolation (grey line) and axe LN ¼0 corresponds to

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Uc0U*

c

pand gives the value of Uc0 (1.75 mm s�1 for

ves2), data are fitted by eqn (13) with the value of Uc* and Uc0 obtained

previously, black plot. Inset: LN(U) for chitosan decorated vesicles and

for bare vesicles (open circles, data from Borghi et al.21 fitted by eqn (4)).

Fig. 6 Uc* versus 1/R curve gives a value for the spontaneous curvature

c0 ¼ 9.4 � 0,6 mm�1 (eqn (14)).

where

U*c ¼

kc0

3hR(14)

and

s0 ¼3kBTR3h

2pk2(15)

Eqn (13) is valid for U < Uc*. LN(U) varies logarithmically with

an inflexion point for U ¼ Uc*.

At large velocities, for U [ Uc* where sN [ kbc20, the

expression of the extrusion force is approximately:

f ¼ 2pffiffiffiffiffiffiffiffiffiffiffi2ksN

p¼ 2p

k

r(16)

Equilibrium between extrusion force and Stokes friction leads

to:

sN ¼ð3hRUÞ2

2k(17)

and

1

r¼ 3hRU

k(18)

From eqn (10), always valid for s0 ¼ kc20/2, we can determine

sN/s0:

sN

s0

¼ 3hRU2

2kc0Uc0

(19)

Anew, replacing sN/s0 and the tether radius r in the Helfrich

relation by their respective expressions given by eqn (18) and

(19), we obtain finally:

LN ¼ s0UlnUffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2Uc0U*c

p (20)

At large velocities, the law for LN(U) is identical to the

classical law (eqn (4)) with a renormalized threshold velocity

U�

c0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Uc0U*

c

p.

To summarize, as a function of U, LN is given by eqn (13) for

U > Uc0 up to Uc*, corresponding to the inflexion point in the

curve LN(U). For U > Uc*, LN is given by eqn (20).

Let us now interpret our experiments in this framework. A

membrane with a spontaneous curvature can spontaneously eject

membrane tubes if the extrusion force is negative, i.e. at low

tension s < kc20/2 (eqn (8)). Osmotic deflation of a vesicle provides

a way to decrease its membrane tension. Fig. (4) shows osmoti-

cally deflated vesicles decorated with chitosan: lipidic tubes

spontaneously form. This evidences that this type of chitosan-

decorated membrane exhibits a spontaneous curvature and

justifies the use of the model described above.

In the case of hydrodynamic tether extrusion at small but

positive extrusion forces, let us interpret our measures of LN as

a function of flow velocities U. Fig. 5 presents the values of LN

versus U for 4 different vesicles. The inflexion point of the curves

estimated graphically gives the characteristic velocity Uc* ¼11.8 � 2.6 mm s�1. The black line is an adjustment with eqn (13)

for one of the vesicles presented (vesicle 2). For U > Uc*, the

intersection between fit extrapolation (grey line) and axe LN ¼0 corresponds to

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Uc0U*

c

p.

950 | Soft Matter, 2011, 7, 946–951

The spontaneous curvature c0 is calculated from eqn (14): the

slope of Uc* versus 1/R curve (Fig. 6) gives a value for the

spontaneous curvature c0¼ 9.4� 0.6� 10�3 nm�1, assuming that

k z 10 kBT. This allows calculation of s0 and f0 from eqn (9) and

(8), for the different vesicles presented here, s0 lies between 0.8

and 3.7 � 10�7 N m�1 and f0 between 0.4 and 3.4 � 10�1 pN. The

values of Uc0 are coherent with values obtained at the end of

retraction curves presented in Fig. 2 (average value: 0.34 mm s�1).

The measurements of s0 are also in agreement with usual values

of membrane tension. Finally, the values of f0 are much lower

than for bare vesicles.

Conclusion

Chitosan-decorated vesicles show anomalous tether dynamics.

First, the extrusion is erratic. We propose that this behaviour is

the signature of transient pores, which have been predicted to

arise for charged lipid membranes by Brenner.33 Second, the

extrusion forces are extremely small and the stationary length

versus velocity do not fit classical extrusion laws observed for

bare vesicles. We ascribe these findings to the contribution of


spontaneous curvature induced by the adsorption of chitosan

only on the external membrane leaflet. We extend the static

model35 to the dynamics of tube formation from membranes with

a spontaneous curvature. This allows to analyze the LN(U)

curves and derive the spontaneous curvature. We further confirm

the existence of a spontaneous curvature by the direct fluores-

cence microscopy observation of spontaneous tethers formed

when the membrane tension is decreased (negative extrusion

force) by osmotic deflation.

In the future, checking if transient pores are indeed opened

upon extrusion can be considered using chitosan-decorated

vesicles with higher internal viscosity leading to pores of larger

sizes and life times.

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