The physics of membrane tubes: soft templates for studying cellular membranes Aur´ elien Roux * Lipid membranes under shear or tension can form surprising, cylindrical structures called membrane tubes with diameters varying between a few hundreds of nanometers to a few tens of nanometers. These structures can be formed in multiple ways, and provide a clear signature of membrane fluidity and elasticity. In vivo, tubular structures are used during intracellular transport to exchange material between compartments, and their formation depends upon the same principles as in vitro. Recent studies of the specific physico-chemical properties of membrane tubes have shed light on how tubular structures are formed in vivo. In addition, the controlled formation of such membrane tubes in vitro has proven to be an elegant way to study many dynamic processes during membrane trafficking. Introduction All living cells are enclosed by a lipid membrane, which consists of an auto-assembled phospholipid bilayer. To maintain cell integrity, this envelope must be impermeable to cell contents, but the lipid membrane also has very specic mechanical properties: it is an auto-sealable 2D uid, which is easy to bend yet hard to stretch. Typically, lipid membranes can only be stretched until the area is only a few percent greater than the relaxed area. Membranes break at tensions in the range of 10 3 to 10 2 Nm 1 , making them more resistant than rubber at the same scale. Nevertheless, because the membrane is so thin, it can easily bend to curvatures below a 100 nm radius. Lipid membranes are thus easily deformed by the Brownian motion of the surrounding uid, and these striking uctuations provide a signicant component of membrane tension. While membrane uctuations were one of the earliest behaviours to be studied, it can be challenging to measure these uctuations well enough to accurately determine physical membrane prop- erties (tension, bending rigidity). The astonishing mechanical properties of lipid membranes also make them susceptible to deforming into tubular structures. In many cases the action of a point force or area difference between the two leaets will cause a lipid membrane to sponta- neously deform into a cylindrical structure with dimensions (length, but more importantly radius) directly linked to mechan- ical parameters. Moreover, the one-dimensional nature of these cylinders simplies the free energy equation of the membrane, enabling simple theory and analytical analysis of the equations. Thus, membrane tubes are frequently structures of choice for studying membrane mechanics. The primary goal of this article is to review the discovery of membrane tubules and their biological relevance, and also to describe simple theories of membrane tubulation. In addition, we will extensively describe experiments in using membrane tubes to study processes occurring in cell membranes. Biological relevance and occurrence Tubular structures were rst observed when the eukaryotic cell structure was examined by electron microscopy in the 1950s and 60s. These observations led to the notion that eukaryotic cells were compartmentalized into organelles with specialized functions and structures. As most of these organelles are separated from their environment by a lipid membrane, the shape and structure of these organelles are highly dependent on the membrane. Membrane tubes or tubules, as they are called in biology, are common structures in many cellular organelles. They can be divided into two categories: - the rst class consists of tubules that are part of one organelle structure, and thus stable with time and of rather controlled size (10–100 nm). We will call them structural tubules. One of the most well described organelles, the endoplasmic reticulum, consists almost entirely of a tubular network that lls up the inner volume of any eukaryotic cell. 1 Other tubular structures can be seen in organelles such as mitochondria 2 (functioning in ATP and energy production) and the Golgi apparatus (which serves in protein tagging and sorting for secretion). Some tubular structures are specic to cell types involved in a particular physiological role. For example in muscle cells, invaginations of the plasma membrane called T-tubules serve to conduct the action potential from nerves directly to contractile bers within the cells. 3 Another example is the microvillar, mono-disperse tubules that form a highly dense Biochemistry Department, University of Geneva, Science II, 30 quai Ernest Ansermet, CH-1211 Geneva 4, Switzerland. E-mail: [email protected]; Web: http://cms. unige.ch/sciences/biochimie/-Aurelien-Roux-Lab; Fax: +41 22 379 64 70; Tel: +41 22 379 35 32 Cite this: Soft Matter, 2013, 9, 6726 Received 19th February 2013 Accepted 16th May 2013 DOI: 10.1039/c3sm50514f www.rsc.org/softmatter 6726 | Soft Matter , 2013, 9, 6726–6736 This journal is ª The Royal Society of Chemistry 2013 Soft Matter REVIEW Published on 20 May 2013. Downloaded by Georgetown University Library on 04/10/2013 08:41:33. View Article Online View Journal | View Issue
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Soft Matter
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Biochemistry Department, University of Gen
CH-1211 Geneva 4, Switzerland. E-mail: a
unige.ch/sciences/biochimie/-Aurelien-Roux-L
379 35 32
Cite this: Soft Matter, 2013, 9, 6726
Received 19th February 2013Accepted 16th May 2013
DOI: 10.1039/c3sm50514f
www.rsc.org/softmatter
6726 | Soft Matter, 2013, 9, 6726–67
The physics of membrane tubes: soft templates forstudying cellular membranes
Aurelien Roux*
Lipid membranes under shear or tension can form surprising, cylindrical structures called membrane tubes
with diameters varying between a few hundreds of nanometers to a few tens of nanometers. These
structures can be formed in multiple ways, and provide a clear signature of membrane fluidity and
elasticity. In vivo, tubular structures are used during intracellular transport to exchange material
between compartments, and their formation depends upon the same principles as in vitro. Recent
studies of the specific physico-chemical properties of membrane tubes have shed light on how tubular
structures are formed in vivo. In addition, the controlled formation of such membrane tubes in vitro has
proven to be an elegant way to study many dynamic processes during membrane trafficking.
Introduction
All living cells are enclosed by a lipid membrane, which consistsof an auto-assembled phospholipid bilayer. To maintain cellintegrity, this envelope must be impermeable to cell contents,but the lipid membrane also has very specic mechanicalproperties: it is an auto-sealable 2D uid, which is easy to bendyet hard to stretch. Typically, lipid membranes can only bestretched until the area is only a few percent greater than therelaxed area. Membranes break at tensions in the range of 10�3
to 10�2 N m�1, making them more resistant than rubber at thesame scale. Nevertheless, because the membrane is so thin, itcan easily bend to curvatures below a 100 nm radius. Lipidmembranes are thus easily deformed by the Brownian motionof the surrounding uid, and these striking uctuations providea signicant component of membrane tension. Whilemembrane uctuations were one of the earliest behaviours tobe studied, it can be challenging to measure these uctuationswell enough to accurately determine physical membrane prop-erties (tension, bending rigidity).
The astonishing mechanical properties of lipid membranesalso make them susceptible to deforming into tubular structures.In many cases the action of a point force or area differencebetween the two leaets will cause a lipid membrane to sponta-neously deform into a cylindrical structure with dimensions(length, but more importantly radius) directly linked to mechan-ical parameters. Moreover, the one-dimensional nature of thesecylinders simplies the free energy equation of the membrane,enabling simple theory and analytical analysis of the equations.
Thus, membrane tubes are frequently structures of choicefor studying membrane mechanics. The primary goal of thisarticle is to review the discovery of membrane tubules and theirbiological relevance, and also to describe simple theories ofmembrane tubulation. In addition, we will extensively describeexperiments in using membrane tubes to study processesoccurring in cell membranes.
Biological relevance and occurrence
Tubular structures were rst observed when the eukaryotic cellstructure was examined by electron microscopy in the 1950sand 60s. These observations led to the notion that eukaryoticcells were compartmentalized into organelles with specializedfunctions and structures. As most of these organelles areseparated from their environment by a lipid membrane, theshape and structure of these organelles are highly dependent onthe membrane. Membrane tubes or tubules, as they are calledin biology, are common structures in many cellular organelles.They can be divided into two categories:
- the rst class consists of tubules that are part of one organellestructure, and thus stable with time and of rather controlled size(10–100 nm).Wewill call them structural tubules. One of themostwell described organelles, the endoplasmic reticulum, consistsalmost entirely of a tubular network that lls up the inner volumeof any eukaryotic cell.1 Other tubular structures can be seen inorganelles such as mitochondria2 (functioning in ATP and energyproduction) and the Golgi apparatus (which serves in proteintagging and sorting for secretion). Some tubular structures arespecic to cell types involved in a particular physiological role. Forexample in muscle cells, invaginations of the plasma membranecalled T-tubules serve to conduct the action potential from nervesdirectly to contractile bers within the cells.3 Another example isthe microvillar, mono-disperse tubules that form a highly dense
This journal is ª The Royal Society of Chemistry 2013
brush covering the luminal side of epithelial cells in the intestine.Microvilli are lled with cytoskeletal laments,4 and increase thecell surface area in contact with the gut media. Similartubular structures are found in nerve cells in the inner ear as partof the sound-responsive element. These tubules are associatedinto pyramidal bundles, the size of which determines thefrequency at which the bundle vibrates resonantly and the celldetects sound.5
- the second class of tubules are highly dynamic and transient(formed and disappearing in a fewminutes), and their movementis frequently driven by the cytoskeleton. These tubules were onlyrecently discovered, as exchanges between organelles had beenthought to be predominantly mediated by small sphericalmembrane carriers (50–100 nm vesicles) that bud from and fusewith organelles. By tagging proteins carried by these vesicles withthe Green Fluorescent Proteins (GFP), cell biologists discoveredthat highly dynamic membrane tubules were also responsible forthese exchanges.6 These tubules grow along cytoskeletal la-ments and are highly dynamic,7 moving quickly (up to severalmicrons per second), and breaking and fusing frequently.Tubules have been observed emerging from the Golgi apparatus,as well as from the endosomes (the rst compartment to receivemembrane carriers budding from the plasma membrane), andare believed to occur on all intracellular traffic routes. Impor-tantly, the formation of these tubes has been shown to depend onthe amount of cargo to transport8 and requires specic proteins.9
Filopodia and other evaginations also belong to this categoryas they are highly dynamic. These evaginations mostly formthrough the action of actin when extensions of the cell cortexprotrude out from the cell and deform themembrane. Signalingmolecules are found at the tip of these tubules allowing them toguide the migration of the cell.
It has been a long-standing question how these cylindricalstructures could be generated and maintained, but it is onlyrecently that progress has been made. Importantly, it wasshown that the components within structural tubules oforganelles are also highly dynamic, and their stable shaperesults from a dynamic equilibrium in the turnover of theircomponents. Thus, despite the obvious differences betweenstructural and highly dynamic tubules, the mechanismscontrolling their behavior share many similarities.
In this review, we will describe the physical principles by whicha at membrane can be deformed into a highly curved cylindricalone. Essentially twomainmechanisms have been described: localapplication of a force normal to the membrane plane, or gener-ation of a spontaneous curvature. Each principle can be applied toseveral cases, and we will illustrate these by taking examples fromso-matter experiments and biological systems. Finally, we willreview recent technical use of membrane nanotubes to studymembranes in a physical, biological or chemical context.
Membrane tube formation by force
The rst observation of a tubular deformation of a membraneunder force was observed on red blood cells submitted to shearow,10 and it allowed one of the rst measurements of thestretching modulus of lipid membranes. As described in the
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following, shear ow has been widely used to pull tubes out ofvarious membranes, but other micromanipulation techniquessuch as optical tweezers, micropipettes, and protein generatedforces have also been used. In the following, we review some ofthe techniques that are used to extract tubules, as well as bio-logical relevance of this mode of membrane deformation. First,though, we describe theoretically the formation of a tube from alipid membrane by the local application of a force.
Theory
The cylindrical shape taken by a at membrane acted on by alocal point force arises from the peculiar mechanical propertiesof lipid membranes: if a point force is applied to a solid elasticsheet such as a rubber membrane, the elastic sheet deformsinto a funnel-like shape: a catenoid. Application of the forcetends to increase the surface of the elastic sheet. The exactshape of the catenoidal deformation minimizes the shear,bending and dilational stresses within the sheet while con-necting the application point of the force to the rest of theelastic sheet. This shape is strictly constrained by the fact thatthe sheet is a solid.
In contrast, in a lipid membrane the molecules in eachleaet canmove within the plane of themembrane and the lipidmembrane cannot support shear stresses. As a result, the shapeof a lipid membrane depends only upon competition betweenthe dilational (area) and bending stresses. Clearly, the best wayto minimize the area increase would be to form a very narrowtube (effectively a line with zero area) connecting the applica-tion point to the rest of the membrane, but this would cause avery large bending energy. In contrast, the best way to minimizethe bending energy would be to form a large tube, but thiswould greatly increase the membrane area. Thus, the equilib-rium tube radius results from a compromise between thestretching energy and the bending energy costs. However,the fact that a tube (rather than a catenoid) forms relies on theuidity of the membrane.
The elastic energy of a lipid membrane is usually describedby the Canham–Helfrich equation:11
Eel ¼ sDAþðA
k
2J2 dA
where sDA is the energy associated with membrane stretching,s is the membrane tension and DA the change in its surfacearea. The energetic cost associated with membrane bending isthe integral of the local curvature Jmultiplied by the membranebending rigidity k over the whole membrane area A. This rigiditydepends on the lipid composition of the membrane.
This equation can be used to calculate the energy associatedwith any shape, and can also be used to nd the equilibriummembrane shape by minimizing the free energy. However, thiscan be a non-trivial problem as the membrane shape has to beconsidered in 3D, and most cases can only be solvednumerically.
However, for a membrane tube of length L under the pullingforce F (equilibrium force), the Canham–Helfrich equationsimplies dramatically. As the curvature of the tube, neglecting
the complex problems of the extremities, is J ¼ 1/Rt, Rt beingits radius, and DA ¼ 2pRtL, the free energy of the tube is thengiven by:
Etube ¼ 2pRtL(s + k/(2Rt)2) � FL (1)
By minimizing the free energy of the tube with respect toRt
12–14 one then obtains a simple relationship between theradius, the force, tension and rigidity:
Rt ¼ffiffiffiffiffiffiffiffiffiffik=2s
pand F ¼ 2p
ffiffiffiffiffiffiffiffi2ks
p(2)
For standard values of rigidity and tension (a few tens of kTsfor k and 10�6 to 10�4 Nm�1 for tension), the tube radius rangesfrom 10 nm to 200 nm, and forces are between 1 pN and 50 pN.These values correspond well to the size of membrane struc-tures and protein-generated forces found in cells, and thusforce-generated tubules are very interesting structures to studymembrane traffic processes (see below).
However, the simplicity of these results hides the complexshape of the tube ends connected to the at membrane and tip.Numerical calculations show13,14 that the base of the tube followsthe shape of a half-catenoid, and where the catenoid converts to acylinder the tube is slightly more constricted, with a radius that is8–10% smaller than Rt. While the tube tip has a slightly largerradius than the tube, there is again a small constriction at thebase of the tip equivalent to the one at the top of the catenoid.The dynamics of tube extraction also shows non-trivial behavior:when rst pulling on the at membrane, the force increaseslinearly with the distance, until it reaches the equilibrium forceF ¼ 2p
ffiffiffiffiffiffiffiffi2ks
p. At this point, themembrane forms a pure catenoid,
but by pulling a little further, the force reaches a maximum(about 8–10% above the equilibrium force), and a shape transi-tion occurs when the catenoid contracts back and a tube appearsat the top of the catenoid. Aer this shape transition, the forcedrops back to the equilibrium force, and if the tension is keptconstant, the force is then independent of tube length.
However, even if the exact shape of the tube and its extractiondynamics are complex, the typical size of the tube (its radius) andthe force require to maintain it are easily measured in experi-ments (see eqn (2)), and thus, tubules have been widely used toprobe the membrane parameters in various experimental situa-tions, as described below. The tube extraction technique is notonly useful to measure membrane parameters, but is also amechanism by which living cells create membrane cargoes.Finally, tubules have been used in vitro to understand how thespecic properties of lipid membranes are used in cells to allowthe formation of membrane carriers in membrane traffic.
Micromanipulation
As stated above, membrane tube formation was rst observedunder shear ow. This technique has been used to study thedynamics and limiting factors of tube extraction under highows.15 When tubes are pulled fast (a few tens of microns persecond), a gradient of tension, and thus a gradient of radii,appears along the tube. A signature of this gradient is theretraction speed of the tube: it is non-linear with the retracted
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fraction of the tube as the speed depends on the tensiongradient.15 Techniques to pull tubes more quickly providedinsight into why this tension gradient arises. Very fast pullingrates (above 100 microns per second) were achieved by aspira-tion of the membrane with a very thin pipette, or using a pipetteto aspirate a bead glued to the membrane, and by pulling thisrapidly it was possible to break the membrane by extraction.The neck connecting the at part of themembrane to the tube isa place where the two leaets of the membrane have to ow atdifferent speeds in order to accommodate the change incurvature. At rates higher than 10 microns per s, the membraneow differs so greatly between the two leaets that it generates ameasurable friction,12 and at even higher rates it can evendestabilize the membrane.
However, the dynamics of extraction reveals that undercellular conditions and in most in vitro experiments, tubes areeasily formed and do not break. For example, micropipettepulling can be used to create extensive networks of membranetubes connecting Giant Unilamellar Vesicles (GUVs)16 usingelectric pulses to fuse membranes. These networks of nano-conduits can be used for femtoliter chemical reactions, wheremixing of substrates is achieved by using a micropipette toincrease pressure in one GUV, thereby pushing its contents toanother through the tube.17 Also, by intelligent design of thenetwork geometry, it is possible to create stable membrane tubenodes,18 a proof that fusion, even in these highly curvedmembrane structures, is not spontaneous.
In most cases, the limiting factor for tube extraction is theforce required to pull on the membrane locally. This force istypically in the range of a few tens of piconewtons,13 and thuscompatible with forces exerted by proteins in vivo. In order toverify these theoretical ndings (see eqn (2)) and study theconditions of tube pulling, researchers have started using opticaltweezers to pull membrane tubes (see Fig. 1B and 2G). Bygraing a polystyrene or silica bead onto the membrane, andthen manipulating the bead with optical tweezers, it has beenpossible tomeasure the force needed to pull tubes out of cells19,20
or articial membrane reservoirs such as GUVs.21–23 Theseexperiments conrmed that the tube-formation force is in therange of a few tens of piconewtons, and showed that theformation of the tube happens with a shape transition correlatedwith a force overshoot, as predicted by theory. However, thisforce overshoot depends on the size of the adhesion patch.23
One of the difficulties in these experiments is that force andradius depend on both the tension and rigidity, so measuringthe force or radius alone does not allow a full determination ofthe membrane's mechanical properties. However, by assuminga standard value for the membrane bending rigidity (20 kT),tube pulling from cells with optical tweezers provides a directand easy way to measure membrane tension.19,24–26
To fully verify the theory, one must control membranetension while measuring the force. Using GUV micropipetteaspiration to control membrane tension, and optical tweezers tomeasure the tube force it was possible to verify that the squareof the force is proportional to s as predicted by eqn (2).27,28 Theslope was proportional to the membrane rigidity, and thusprovided a direct measurement of the GUV membrane rigidity.
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Fig. 1 (A) Different modes of membrane tube formation in cells. (B) In vitro set-up for pulling a membrane tube from a giant liposome with control of membranetension (micropipette aspiration) and force measurement (optical tweezers).
Fig. 2 Examples of membrane tubules: (A) dynamin-coated tubules observed byDIC, bar 10 microns. (B) Dynamin-coated tubule as observed by negative stainelectron microscopy, bar 100 nanometers. (C) Membrane tubules extracted froma giant liposome (in the center) along microtubules by kinesins, as seen by DIC(bar 10 microns). (D) Membrane tubules extracted from a purified Golgimembrane by kinesins as seen by electron microscopy (bar 100 nanometers). (E)Membrane tubules grown out of liposomes by amphiphysin, a BAR domaincontaining protein, as seen by negative stain EM (bar, 100 nanometers). (F)Growth of membrane tubules induced by Arf1p-GTP as observed by live DICimaging, bar 10 microns. (G) Dynamin nuclei (green) partially coating a tubuleextracted from a giant liposome using the set-up described in Fig. 1B.
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Also, by measuring the rigidity k and controlling tension s
through pipette aspiration, this technique can be used tocontrol and measure the radius of the tube with one nmprecision, and has been a powerful tool to study processes at thesub-cellular scale, including curvature-dependent sorting oflipids and proteins, and curvature-dependent recruitment ofproteins.
Interestingly, the ability of a point force to deform a lipidmembrane into a tube is used by cells in intracellular trafficand motility.
Molecular motors and cytoskeleton extraction
Since membrane tubes formation only require the applicationof a moderate force on the membrane, any protein or complexable to generate such forces can form tubules in vivo. Thecytoskeleton, a system of polymerizing laments and associatedmolecular motors that are responsible for cell architecture andmotility, can generate such tubes.
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As discussed earlier, two kinds of tubes are seen in vivo:structural tubules that are part of essential shaping of organ-elles or cells and dynamic tubules, involved in membranetraffic, cell motility and signaling.
Tubules formed by growing laments. For structuraltubules, the action of growing laments against the membraneplays a key role. For example, the fact that sensory cilia andother stable extensions like microvilli contain bundles of actinimmediately suggested that membrane tubule formation mightresult from the force generated by the growth of these laments.This could only be true if the polymerization energy of actin andmicrotubules is sufficient to overcome the bending energy of asingle tube. Furthermore, as predicted from the force value (seeeqn (2)), high tension should inhibit the formation of thesetubules. Both effects were rst demonstrated in vitro by recon-stitution of microtubule polymerization into Giant UnilamellarVesicles. Observations29 showed that microtubules had tobundle in order to spontaneously deform the membrane into atube, even though the polymerization energy of a singlemicrotubule (around 10 kT per dimer30) is sufficient fordeforming a membrane at low tension. Interestingly, thebundling occurred because the deformation of the GUV into a
lemon-like shape triggered the growing microtubules to orientalong the longest axis. Furthermore, at high membranetensions, microtubule buckling was observed becausethe deformation force exceeded the buckling threshold ofthe MTs.30
Actin laments can also deform the membranes intotubules,31,32 but must form bundles to do so since a single actinlament cannot provide enough force to deform membranes(1 kT nm�1 or a few pN,33). Membrane tubules obtained in vitroare different from lopodia seen in vivo. In vivo, the lamentsconstantly grow and shrink dynamically whereas in vitro, a forceequilibrium leads to laments of xed length.32 When actin andpolymerizing factors are added to giant liposomes, inwardlopodia structures begin to grow. These tubules are lled withactin bundles, and all stop growing at the same time and to thesame length. This is thought to result from a mechanicalequilibrium. As the membrane deformation could increase themembrane tension,34 growth would stop when the polymerizingforce of bundles and membrane tube force reach equilibrium.
It is important to note that in these structural tubules, thewidth is linked to the size of the bundle and not to membranerigidity and tension as for a tube formed by a point force (seeeqn (2)). More surprisingly, it has been proposed that the exactshape of such structures and their length distribution dependon growing/shrinking rates of the laments.35 In this model,membrane mechanics plays a minor role, and it is mostlycytoskeletal parameters (polymerization and depolymerizationrates, cross-linking density, etc.) that set the shape.
Tubules grown by pulling motors. Another way in which cellsextract membrane tubes is by the force exerted by molecularmotors. There are several types of molecular motors, and eachone is associated with a specic type of cytoskeletal lament.For example, kinesins and dyneins are associated with micro-tubules. Soon aer the discovery of these motors (originallyimplicated in the movement of axonal transport), it wasproposed that they could participate in the formation of thecomplex network of tubules of the endoplasmic reticulum: longtubules growing at the speed of microtubule associated motorsgrew from puried endoplasmic reticulum membranes thatwere deposited onto a network of microtubules in vitro,resembling the architecture of ER seen in vivo.36 It was thuspostulated that the constant pulling of motors could dynami-cally maintain a tubular network structure. As well as structuraltubules lled with cytoskeletons, some ER tubules might alsoform via a dynamical equilibrium of forces.
However a contradiction was raised against this hypoth-esis.13 The strongest motors are able to generate a maximumforce of 5–6 pN, and the minimum force needed to extract atube is 5–8 pN, even if tension is very low (less than 10�7 Nm�1).Most of the time, for tension approaching the in vivo range(around 10�5 N m�1) the force is actually more than 20 pN (seeeqn (2)). As one motor cannot form a tube on its own, a clus-tering must occur.
The formation of tubes by motor pulling was reconstitutedin vitro with puried motors, membranes and microtubules37
(see Fig. 1A, 2C and D), and as predicted, the clustering ofmotors was required to initiate tube formation. Surprisingly,
6730 | Soft Matter, 2013, 9, 6726–6736
however, if the density of individual, un-clusteredmotors on themembrane was raised above a threshold value,38 dynamicclustering of motors can occur and tubules can then grow. Asexpected from theory, this threshold is dependent onmembrane tension, as more motors are needed for pulling atube of higher tension.38 But what causes dynamic clustering?Motors at the tip of the tube are heavily loaded which reducestheir speed. Motors back from the tip of the tube can move atfull speed along the microtubule and catch up with the slower-moving motors at the tip. Since motors have an intrinsicprobability of detaching (actually dependent on their load), adynamic cluster forms at the tip, constantly lled with motorscoming from the back of the tube, and constantly losing motorsas they detach. The exact dynamics of this cluster was theoret-ically determined,39,40 and experiments showed that the speedand number of motors in the cluster are linked, and on average4–5 motors pull a the tip.39,40
Dynamic tubules seen in vivo are formed in a similarmanner: they are mostly observed when looking at membranecomponents implicated in specic membrane traffic routes. Forexample, many highly dynamic tubules are observed growingfrom endosomes. They grow mostly on microtubules and actin,at the speed of motors.41 At the Golgi, many tubules areobserved with various membrane trafficking markers. Generallyspeaking, membrane tubules formed by pulling motors areoen seen when the tight regulation of a specic route is per-turbed. For example, extensively long tubules are seen wheneither the amount of cargo (proteins transported within themembrane carrier)8 or the molecular machinery recruitingthe motors to the membrane is increased.9 Similarly, tubules atthe plasma membrane42 or at the Golgi43 are increased andlengthened by a specic block in the ssion machinery. Ahypothesis of dynamic tubule formation can thus be proposed;initiation of the bud is generated by a cluster of motors, andthen the ssion machinery can precisely control the length ofthe carrier, from spheres if ssion occurs just aer pulling tointerconnected networks (ER-like) if ssion occurs at very latestages. Looking globally at all the routes of intracellular traffic,membrane deformation generated by motor pulling forcesseems quite general: even membrane coats that are thought toscaffold the membrane (see below) are oen linked to molec-ular motors,44 suggesting that motor pulling could activelyparticipate in the formation of the buds. Moreover, it is thoughtthat the forces generated by pulling on the bud structures arenecessary for the ssion reaction.45,46
Polymerization induced tubes
Another way to form tubules by force is by scaffolding: in thismechanism, the membrane is forced to adopt the shape ofpolymerizing proteins binding to it. The most well-knownexample is clathrin, a protein which binds to the membraneand polymerizes into soccer ball-like structures made of hexa-gons and pentagons. These structures are involved in theformation of carriers from the plasmamembrane (endocytosis).Another protein, dynamin, which mediates the ssion of theneck of clathrin buds, is also able to deform the membrane into
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tubules. In vivo it polymerizes into a helical structure of 14dimers per turn that wraps around the neck of clathrin budsand drives ssion by constricting. In vitro, if sufficiently highconcentrations are used, dynamin can deform membranes intolong tubules (several tens of microns) coated with a continuoushelix of dynamin (see Fig. 1A, 2A and B). Unlike tubules createdby pulling, the radius of dynamin-coated tubules does not resultfrom a competition between stretching and bending energies.Instead, the radius (10 nm) is xed by the helical structure of thepolymer, and does not vary with bending rigidity or membranetension. Importantly, the force needed to extract the tube islinked to the polymerization energy. Just as for polymerizingmicrotubules and actin laments, dynamin must generateenough force through its polymerization to deform themembrane into a tube. If dynamin fully covers the tube, the freeenergy of the tube can be written as:
Etube ¼ 2pRdL(s + k/(2Rd)2) � FL � PL (3)
where Rd is the constant radius imposed by dynamin, and P thepolymerization force of dynamin. At equilibrium Etube is inde-pendent of length, L, and:
F ¼ pk/Rd + 2pRds � P (4)
This gives a direct experimental test of the theory, as the tubeforce is linear with tension instead of the square root of tensionas for a free tube. Furthermore, both Rd and P can be deter-mined from a plot of F versus s. A recent study measured apolymerization force of approximately 20 pN for a dynaminconcentration of 10 micromolar.47 This is equivalent to a poly-merizing energy of 3.5 kT nm�1, and is indeed between thepolymerizing energy of actin (1 kT nm�1 per lament33) andmicrotubules (around 10 kT nm�1)30. These observationsconrm that dynamin can deform the membrane by a scaf-folding mechanism when the membrane tension is sufficientlylow and the dynamin concentration is sufficiently high. As tubeforce varies with tension (see eqn (2)), above 10�6 N m�1,tension should block tubulation because the force needed toform a tube exceeds the polymerization force of dynamin.
However, dynamin is a special case because it polymerizesinto a helical structure, while other scaffolding proteins typi-cally deform the membrane into a spherical bud. In vivo tubulesare common structures that are usually formed by proteins thatcreate a spontaneous curvature, rather than pulling or scaf-folding the membrane.
Membrane tube formation by spontaneouscurvatureTheory
Another way to form tubules is through the spontaneouscurvature. For example, proteins that bind to only one leaet ofthe membrane can insert between the lipids. This causes twoeffects. Firstly, insertions can create local kinks in themembrane by working like wedges. If the protein does notinsert deeply into the lipid layer, it pushes the lipid headgroups
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apart, and forces the membrane to bend locally. Secondly, if theprotein inserts into the leaet, it causes the surface of thisleaet to expand. To accommodate the area difference of thetwo leaets, the membrane will bend, acquiring the sponta-neous curvature (the unstressed state of the membrane iscurved).
Although these two mechanisms may seem similar, thewedge-like action is a local effect while the area-difference is aglobal effect. As a consequence, the wedge-like effect can be verystrong, even at low protein densities,48 and while high proteindensities are required for the area difference to create evenmodest curvatures.
Because most proteins which tubulate membranes usuallywork at low protein density and create curvatures in the range of10–100 nm radii, it is believed that they generally act as wedge-like structures, rather than by creating an inter-leaet areadifference. The effect of wedge-like inclusions can be describedtheoretically in terms of a local effective spontaneous curvatureC0, which corresponds to the shape of the membrane in theabsence of applied stresses.48 Including this property in the freeenergy of a force-pulled tube gives a free energy:
Etube ¼ 2pRtL(s + k/2[1/Rt2 � 2C0ft/Rt
2] + cDf2/2) � FL (5)
where ft is the surface density of the protein in the tube, and Df
the difference of protein densities between the tube and the atpart of the membrane. Thus, one can see that the term 2C0ft/Rt
2
is the total effect of proteins on the curvature of the tube, andthat the term cDf2/2 is an entropic term opposing strongdifferences of protein densities between the tube and the atpart of the membrane. By minimizing the free energy withrespect to Rt, the radius, force, tension, and rigidity can berelated by:
with keff ¼ k[1 � kC0/c], and ff the protein density on the atpart of the membrane. The theory predicts that the presence ofthe protein on the membrane reduces both the radius and theforce required to hold the tube, thereby rendering themembranemore susceptible to bending. Furthermore, the forcedrops to zero below a threshold value of the tension, s* ¼k/2C0
2ff2, if ff is small. Thus, for tensions below s*, the inclu-
sions will drive spontaneous tube formation, without needingany external force.
We now describe experiments showing that the asymmetricinsertion of amphipathic polymers and protein motifs into lipidmembranes creates tubular structures growing from a reservoirmembrane, and is generally well described by this simpletheoretical model.
Experiments
Protein insertion. Induction of a spontaneous curvaturegenerally leads to membrane tubulation, as tubes can concen-trate the curvature without a big change of volume. As describedabove, the spontaneous curvature can be produced in two ways.Firstly, an area difference will be created if there is a change in
the number of molecules in each leaet, or the modication ofthe average area of molecules in one of the 2 leaets. Alterna-tively, the insertion of molecules can create local kinks in themembrane, especially if they do not insert deeply into the leaetthereby pushing apart the lipid headgroups but not the tails.
Tubulation by insertion. Amphipathic molecules can insertinto the membrane, but generally their hydrophilic partprevents them from crossing the membrane and they are typi-cally restricted to the outer leaet. As would be expected, theirinsertion breaks the symmetry of the bilayer and creates aspontaneous curvature. For example, tubule growth has beenobserved when amphipathic polymers are added to a at lipidmembrane.49 The dynamics of growth and retraction as well asthe tubule size are consistent with pure spontaneous curvatureinduction resulting from a chemical equilibrium between bulksolution and membrane-bound forms of the polymer. Also, atlonger times the membrane deformation continues until pearlsform on the tubes, resembling beads connected by tinymembrane necks.49,50 As the polymer is unstructured, in thiscase the spontaneous curvature is thought to be primarily dueto an increased area in the outer leaet.
Many proteins contain amphipathic segments, and so it isnot surprising that their insertion can induce membranecurvature. The rst examples were discovered during studies ofclathrin-associated proteins that contain a BAR (Bin-Amphi-physin-Rvs) domain.51 This protein domain forms a crescent-shaped dimer, but is thought to tubulate membranes because ofN-terminal amphipathic helices that insert into the outerleaet. Amphiphysin was found to tubulate charged liposomes(see Fig. 1A and 2E) while mutations in the N-term of theamphipathic helix of endophilin, a member of the BAR familyclose to amphiphysin, completely abolished the tubulationin vitro. However, it is not yet clear if these molecules tubulatemembranes by increasing the area difference between the twoleaets, or by acting as a wedge. Simulations suggest that thesize and depth of the insertion will strongly inuencethe mechanism:52 if the amphipathic peptide inserts into theheadgroup region, then it creates a signicant local curvaturewithout a substantial change to the area of the leaet. Incontrast, if the peptide inserts deeper into the membrane,pushing the acyl chains apart, it will act less as a wedge whileincreasing the area difference. At the density at which theseproteins are found in the membrane, it is unlikely that they cancreate enough area difference to substantially change thespontaneous curvature and it therefore thought that theytubulate membranes via a wedge-like insertion mechanism.
It has long been debated whether BAR domains act ascurvature-sensing modules, meaning they selectively bind tohighly curved membranes, or whether the domain is a curva-ture-inducing module that binds to any membrane and theninduces curvature by forming a curved scaffold around themembrane (see eqn (5) and (6)). In theory, the two cases can bedistinguished from the force vs. tension curve. If BAR domaininsertion induces a spontaneous curvature, the force shouldevolve linearly with the square root of tension (eqn (6)). Incontrast, if BAR domains act as scaffolds that require a poly-merization process/interactions between membrane-bound
6732 | Soft Matter, 2013, 9, 6726–6736
proteins, the force should depend linearly on tension (see eqn(4)). A recent report48 showed that at very low bound densities ofthe BAR domain, no deviation in the force–tension curve is seenif a tube is pulled out of the GUV, using the micropipette/opticaltweezer technique. However, the protein binds preferentially tothe tube. Thus, in the low concentration regime, the BARdomain behaves as a pure curvature-sensingmodule, binding tothe highly curved membrane, but not signicantly changing theforce required to maintain the tube. The low density limit (ff z0) of the theory described above predicts this behavior. Incontrast, when the concentration of the BAR domain is high, itbinds to both the at and curved regions of the membrane. Theradius is then xed by the protein coat and the force is linearwith tension, consistent with a scaffolding mechanism seen fordynamin. Thus, depending on its membrane-bound density,the BAR domain can act as a curvature-sensor at low densitiesand as a curvature-inducer at high densities. At intermediateconcentrations, the BAR domain displays a combination ofboth behaviors – the concentration on the tube is higher andthe force required to maintain the tube is lower. Thusthe mechanical action of the BAR domain, as well as its struc-ture, is dual.
Many other proteins have been shown to induce similartubulation of liposomes. One of the striking examples is the Arffamily of proteins, a group of small GTPases that bind to themembrane in the GTP-bound form. In the GDP-bound state, anamphipathic helix is buried in a hydrophobic pocket of theprotein. Transient interaction with the membrane mediates theexchange of GDP to GTP, expelling the amphipathic helix fromthe pocket which then inserts into the membrane. Sar1p, amember of the Arf family, was the rst shown to induce theformation of tubules from articial liposomes.53 This behavioris thought to contribute to curvature generation during theformation of COPII vesicles. COPII is a proteinaceous coatassembly that is recruited to the membrane by Sar1p and formsa membrane carrier between the Golgi apparatus and thereticulum. Other members of the Arf family (Arf1, 3 etc.54–56)have also been shown to tubulate liposomes (see Fig. 1A and2F). As the structural feature (amphipathic helix) common to Arfmembers is also present in many other small GTPases that bindtransiently to the membrane, such as Rab proteins and Ras-Rallike proteins, it is expected that these proteins can also partic-ipate in curvature generating processes.
A recently discovered amazing case of membrane tubulationis the reticulons. The reticulons are resident, membrane-embedded proteins of the endoplasmic reticulum that arerequired to create the amazing three-dimensional tubularnetwork of the reticulum.57 They have recently been recon-stituted in articial membranes, and they then create tubules,showing that they are sufficient to curve the membrane.58 Evenif the density required for tubulation is higher in articialmembranes than in cells, it is expected on the basis of theirstructure that the global effect of the reticulons is to induce avery high spontaneous curvature of the membrane, which isbest transmitted to the membrane in the form of a membranetube.18 However, the effective spontaneous curvature of theseproteins has never been measured, and it would be a source of
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very interesting information in order to understand better howthese proteins cause such extensive membrane deformations.
Lipid modifying enzymes. Another way to induce the spon-taneous curvature is through enzymes which modify the lipidshape. Most phospholipids have a cylindrical prole and favor aat membrane, provided that the number of lipids in bothleaets is equal. However, acyl-chain removal or headgroupcleavage can convert a lipid into a conical shape that is moresimilar to a detergent molecule. The best known example isPhospholipase A2,59 which removes one of the two acyl-chainsof phospholipids. When phospholipase A2 is only present onone side of the membrane, it converts lipids on that side to aconical shape, which then forces the membrane to curve.Perturbation of its activity60 disrupts tubulation of the Golgiboth in vivo and in vitro, suggesting that its enzymatic activity isneeded to induce tubules. However this activity may not besolely responsible for the observed tubulation as many othercytosolic factors present both in vivo and in vitro could generatetubules. In reconstituted systems with pure proteins and lipids,PlA2 aids the formation and budding of lipid domains,61 but itis not clear howmuch of the curvature results from PlA2 activityversus the line tension at domain interfaces.
In conclusion, many proteins can deform the membraneinto tubular structures, which are a common cellular structure.Proteins can create tubes by exerting a local pulling force on themembrane, by polymerizing onto the membrane into a cylin-drical coat, or by a wedge-like effect creating a spontaneouscurvature. An important feature of these tubules is their size,which is generally less than 100 nm in radius. This curvedgeometry also inuences the lipid composition, and can recruitspecic proteins to the membrane. In recent studies, articialmembrane tubes proved to be very convenient tools for thestudy of these curvature-dependent processes.
Membrane tubes as curved templates for thestudy of curvature dependent-processes
Early studies of intracellular structures by electron microscopyrevealed a diverse range of membrane shapes encompassingspheres, tubes, at disks and many others. This naturally leadto the idea that shape might play an intrinsic role in organellefunctions. For example, membrane curvature was proposed totrigger binding of molecules specic to the function of theorganelle, leading scientists to search for proteins that couldbind specically to highly curved membranes.62 Furthermore,because the membrane is uid, it was proposed that thecurvature could induce a lateral segregation of lipids.63
Curvature-dependent lipid sorting
The discovery that lipid composition was correlated withmembrane curvature is quite recent, because of the difficultiesof isolating specic membrane cargoes from donor or othermembranes. Most of the fractions obtained by cell fractionationassays are contaminated with lipids of various sources (othercell compartments, lipid bodies, blood or culture media),rendering mass-spectrometry analysis quite difficult.
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In a breakthrough paper,64 the composition of Golgi-derivedCOP I vesicles and its donor membrane (Golgi cisternae) wasanalysed by mass-spectrometry. The vesicles showed a cleardecit in long acyl-chain lipids, establishing that lipids aresorted during the formation of transport vesicles. However, thisraised the question of whether lipid sorting resulted fromprotein activity, or via a physico-chemical mechanism.
Part of the answer came from in vitro studies in whichmembrane tubes were extracted from articial liposomes. Bygraing puried kinesins, molecular motors walking alongmicrotubules, onto GUVs, it is possible to form very longtubules by placing the GUVs onto a network of microtu-bules.37–39 Fluorescently labelled lipids were then used to visu-alize any differences between the membrane composition of thehighly curved tubules and relatively at GUV membrane. ForGUVs containing sphingomyelin, phosphocholine and choles-terol,28 tubules and GUVs showed clear differences in lipidcomposition. Since the GUV membrane appeared homoge-neous, these observations strongly suggested that membranecurvature alone could drive lipid sorting.
Further mechanistic insight was obtained from an in vitrostudy,65 where the micropipette/optical tweezers technique wasused to form tubes from GUVs with different lipid composi-tions. This approach allowed tube curvature to be directlymeasured either by force or uorescence. The authors foundthat the sorting effect was only observed when the GUVexhibited macroscopic phase separation, or if its composition isclose to a phase transition, i.e. for non-segregating composi-tions that are close to compositions where macroscopic phaseseparation is observed. They also found that the tube force wassmaller than expected at small radii, suggesting a reduction ofmembrane rigidity at high curvature. This observation wasconsistent with the observation that the lipids that wereexcluded from the tube (sphingomyelin and cholesterol)increase membrane rigidity, even at low concentrations. Bytting the force curve to the keff corresponding to the changinglipid composition of the tube, they showed that curvature-induced lipid sorting minimizes the free energy of the tube.
However, theoretical estimates had previously suggested thatlipids are too small to feel the curvature of the tube:66–68 thebending energy for one lipid can be approximated by U ¼ k/2 �a/Rt
2, where a is the area covered by one lipid (0.5 nm2), and Rtthe radius of the tube (typically 20 nm). k is usually close to20 kT, whichmeans that the curvature energy stored in one lipidis approx. kT/40, far below the thermal energy of kT. Thus,entropy should win and curvature would not induce signicantsegregation of lipids. However, this treatment does not considerthat in compositions close to the phase transition, lipids mayorder themselves on distances longer than the molecular size topossibly form highly transient domains on the order of a fewnm2. In a at membrane these domains are too labile to createmacroscopic phase separation, but in a curved membrane thesmall energy per lipid may be sufficient to cause them to coa-lesce into macroscopic domains.
Thus direct lipid sorting by curvature requires themembrane composition to be nely tuned. For a membranecomposition close to phase separation, lipid sorting can be
strong with up to a tenfold difference in lipid composition.Interestingly, experiments suggest the composition of the cellplasma membrane may indeed be close to a phase transition.Compared to lipids, proteins are much larger and thus areexpected to be far more sensitive to curvature. Thus, protein–membrane interactions can indirectly drive curvature-depen-dent lipid sorting.
Curvature-dependent protein binding
Many protein domains have been found to promote lipidmembrane binding. Many of these protein domains interactspecically with a single type of lipid headgroup. For instance,the Pleckstrin Homology domain, PH, binds the biphosphatedinositol head of phosphatidyl-(4,5)bisphosphate (PIP2).However, other protein domains have been shown to bind tolipid membranes in a curvature-dependent manner: forexample, in vitro the ArfGAP1 Lipid-Packing Sensor (ALPS)binds only to Small Unilamellar Vesicles with a radius less than50 nm.69 ALPS sequences form amphipathic helices that bind tolipid-packing defects between lipid headgroups when themembrane is curved. Bin-Amphiphysin-Rvs (BAR) domains alsocontain amphipathic helices, but their curvature-sensingproperties are thought to come from their crescent shapeddimeric form.70 Experiments using in vitro membrane tubeshave been critical to the understanding of the curvature-sensingproperties of these two domains.
ArfGAP1 plays a crucial role in initiating the disassembly ofthe protein coat surrounding COP I vesicles. To do so, it mustpreferentially bind to the highly curved membrane of the budwhere it then catalyses the release of the protein, Arf. However,when the bud is still connected to the donor membrane prior tossion, it should still be sufficiently curved to recruit ArfGAP1,and so it was unknown why ArfGAP1 only induces coat disas-sembly aer the bud has detached from the plasmamembrane.71 Ambroggio et al. were able to resolve this mysteryby pulling tubules from GUVs coated with Arf and ArfGAP1.72
They observed that although ArfGAP1 bound efficiently andspecically to the tube, it did not efficiently remove Arf from thetube. For tubes longer than 30microns, they observed a gradientof Arf along the tube, with a higher concentration at the basethan the tip. This showed that Arf was being removed from thetube, but that this loss was compensated by Arfmolecules boundto the GUV diffusing into the tube. Thus, before a bud separatesfrom the donor membrane, the removal of Arf by ArfGAP1 in thebud is compensated by diffusion of Arf from the membranereservoir. As soon as ssion occurs, though, Arf detaches and thecoat is released. Using long tubes allowed the authors tomeasure diffusion of molecules in a unconventional way,making the point that a chemical reaction (GTP hydrolysisinduced by ArfGAP1) could be compensated by diffusion. Noother method could have provided such information.
Curvature-dependent nucleation of dynamin
Dynamin, which can polymerize into a helix squeezing amembrane tube, is a unique example of a membrane-deformingscaffold. While some proteins of the BAR domain family can
6734 | Soft Matter, 2013, 9, 6726–6736
form helical scaffolds as well,73,74 only dynamin can generate apolymerization force sufficient to deform the membrane.47
However, at low concentrations, the polymerization force is tooweak to be able to deform a at membrane into a tube. But if atube is already formed, dynamin polymerization can stillsqueeze it to a radius of 10 nm, as it requires less energy than toform a tube de novo (see Fig. 2G). To be precise, if the poly-merization energy of dynamin (which depends on bulkconcentration) overcomes the energy required to squeeze thetube (which depends on the difference between the initialradius and the nal radius of the dynamin helix), the dynaminwill polymerize. Thus, for any concentration of dynamin, thereis a threshold radius, below which dynamin can polymerize,and above which it cannot. The threshold radius depends onthe bulk concentration of dynamin. For dynamin concentra-tions thought to be similar to physiological values (0.5 micro-molar), the threshold radius is 20 nm, twice the inner radius ofa dynamin helix.47 In vivo, when dynamin polymerization isinhibited, CCPs have necks of approx. 20 nm.75 Thus, thenucleation of dynamin at the neck of CCPs is probablycontrolled by curvature, which provides a specic way, yetprotein-independent mechanism to recruit dynamin at itsphysiological target.
Conclusions
This review article has described the discovery of membranetubes, and a simple theory describing their formation bydifferent mechanisms. Membrane tubes are by far the easiestmembrane deformation to form, and thus oen occur in vivo orin vitro. They have a clear role in the organelle shape andmembrane traffic in cells, and are also very useful tools to studythe dynamics and mechanics of lipid membranes both in vitroand in vivo. Overall, membrane tubes are visible signatures oflipid membranes unconventional properties which living cellsexploit to protect themselves from the environment.
Acknowledgements
I deeply thank Gil Toombes for his careful correction of thismanuscript and useful comments. I also deeply thank PierreNassoy, the tube master, for being such a great source ofinspiration.
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