Lipid Polymorphisms and Membrane Shape

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Vadim A. Frolov1,2,3, Anna V. Shnyrova1,2, and Joshua Zimmerberg4

1Unidad de Bioﬁsica (Centro Mixto CSIC-UPV/EHU), Leioa 48940, Spain 2Departamento de Biochimica y Biologı´a Molecular, Universidad del Pais Vasco, Leioa 48940, Spain 3IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain 4Program in Physical Biology, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892 Correspondence: [email protected]

Morphological plasticity of biological membrane is critical for cellular life, as cells need to quickly rearrange their membranes. Yet, these rearrangements are constrained in two ways. First, membrane transformations may not lead to undesirable mixing of, or leakage from, the participating cellular compartments. Second, membrane systems should be metastable at large length scales, ensuring the correct function of the particular organelle and its turnover during cellular division. Lipids, through their ability to exist with many shapes (polymorphism), provide an adequate construction material for cellular membranes. They can self- assemble into shells that are very ﬂexible, albeit hardly stretchable, which allows for their far-reaching morphological and topological behaviors. In this article, we will discuss the importance of lipid polymorphisms in the shaping of membranes and its role in controlling cellular membrane morphology.

ipids are natural molecules whose ability to volumetric shape of lipid molecules is different Lself-assemble in dynamic macrostructures in different phases. This plasticity in molecular in water has been recognized as one of the im- shape was discovered in the ﬁrst X-ray diffrac- portant mechanisms of evolution (Luisi et al. tion structural determinations of lipid/water 1999; Hanczyc and Szostak 2004). This ability mixtures under different osmotic stresses, and is driven by the amphiphilic nature of lipid the investigators used the appropriate term molecules which tend to aggregate so that the from crystallography, polymorphism, to de- hydrophobic (tails) and the hydrophilic (heads) scribe the “crystallization into two or more parts of the lipid are well separated, and the area chemically identical but crystallographically of the dividing surface is held by the hydropho- distinct forms” (Random House Dictionary, bic effect (Tanford 1980). 2nd ed.) (Luzatti et al. 1968). Amongst many Because lipid assemblies “hate edges,” they of such structures, the bilayer plays the most tend to form various closed structures or phases important role in our life. Besides forming the extended over the space, in which the average core of cellular membranes, it is quickly gaining

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V.A. Frolov et al.

technological popularity. Lipid capsules or To balance dynamics and stability, cells closed bilayer vesicles are widely used in cos- employ different lipid species in the membrane metics, drug delivery, etc., primarily because (Dowhan 1997). Although the core phospho- of their natural biological compatibility (Hafez lipids, such as PC, assemble stable lipid bilayers and Cullis 2001). These vesicles can be con- at physiological temperatures, many of cellu- structed from lipids or similar amphiphiles that lar lipids intrinsically destabilize bilayers and, sense the environment, temperature (through when purified, do not form bilayer phases at thermal expansion), pH (through protonation physiological conditions (Cullis and de Kruijff of the heads), and so on, so that they can be 1979). Such “nonbilayer” lipids as PE and destabilized and release their content at the tar- DAG, however, are important membrane con- get place (Hafez and Cullis 2001). Lipid sacs can stituents: they mediate proteolipid interactions also have different shapes (such as spherical, within the lipid bilayer (Dowhan 1997; Lee polyhedral, and tubular vesicles) which may 2004; Ces and Mulet 2006) and increase mor- be important for the flow properties of vesicular phological plasticity of the lipid bilayer (Hafez suspensions (Florence et al. 2004). Hence, the and Cullis 2001). The behavior of individual main technological interest resides in making lipid species can be regulated: charged lipid spe- the lipid vesicle shape and topology switchable cies, such as PS, can switch its “bilayer” identity (i.e., the regulation of the shape of the lipid at elevated pH or Ca2þ (Hafez and Cullis 2001; bilayer). Fuller et al. 2003; Zimmerberg et al. 2006). Nev- Living cells have to solve the same task on a ertheless, the overall lipid mixture of cells is daily basis. Cellular membranes are extremely always balanced to form metastable lipid bi- dynamic, as cells (and biological matter in gen- layers. Microorganisms living at different tem- eral) are in constant flux. This motion has both peratures alter the ratio between bilayer and constitutive aspects that tend toward homeo- nonbilayer lipids dependently on the growth stasis, and regulated aspects that are governed temperature (de Kruijff 1997). Besides dynamic by signaling networks. Consequently, cellular regulation of the bulk lipid composition, cells membranes preserve their morphology at large specifically create nonuniform distribution of scale, forming organelles with distinct shape lipids within membrane organelles. First, in and function, whereas at smaller scales the most of the membrane systems, except endo- membranes are constantly remodeled to main- plasmic reticulum (van Meer et al. 2008), there tain dynamic material exchange between dif- is substantial compositional asymmetry be- ferent membrane formations (Paiement and tween the two monolayers: for example, in Bergeron 2001; McMahon and Gallop 2005). plasma membrane such active lipid species as This remodeling, however, may not interfere PS and PE are accumulated in the monolayer with the barrier function and the overall struc- facing the cytoplasm (Hafez and Cullis 2001; tural stability of the membranes. This combi- Janmey and Kinnunen 2006; van Meer et al. nation of flexibility and the resistance against 2008). Second, lipids and proteins can segregate rupture is brought by the lipid bilayer. Despite laterally by forming domains of distinct compo- the extreme protein crowding, the lipid bilayer sitions and functions (Lingwood et al. 2009). remains the structural core of cellular mem- These three factors, large amounts of nonbilayer branes. The protein area occupancy in mem- lipids, trans-bilayer asymmetry, and lateral in- branes generally does not exceed 20% (Dupuy teractions and segregation of protein and lipid and Engelman 2008), so that the mean distance species in the cellular membranes, provide a between membrane-inserting parts of the pro- basis for the active involvement of lipids in cel- teins is 10 nm, more than 10 lipid molecules lular morphogenesis, as we describe below. (Phillips et al. 2009). Thus, lipids “glue” the The morphological activity of the lipid membrane components together and in the bilayer is regulated by special enzymes main- same time actively participate in membrane taining or changing the lipid distribution in remodeling (Chernomordik and Kozlov 2003). the membrane. This way, the lipid content of

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Lipid Polymorphisms and Membrane Shape

the membrane can be matched to the cellular profile, which determines the redistribution of “morphological” needs and to the physiological stresses across the lipid bilayer (Marsh 2007). function of a particular membrane compart- By looking at the cross section of the lipid ment, making lipids the mediators of the struc- bilayer, several distinct regions dominated by ture/function relationships at the organelle the proper set of forces become noticeable. level (Shnyrova et al. 2009). Some fundamental The most important region for the structural principles linking the molecular identity of lipid stability of the monolayer is the one near the species and their function are embedded into interface dividing the hydrophilic and hydro- the molecular architecture of the lipids. There- phobic parts of the lipids. Even a small increase fore, lipids can be designed (synthesized, me- in the area of this dividing surface leads to tabolized, or intracellularly remade) to have a hydrophobic tail exposure, a process that is predictable morphological behavior. very costly energetically. Thus, the lipid monolayers are hardly expandable as lipids are held MOLECULAR ORGANIZATION OF LIPID together by the hydrophobic effect resulting POLYMORPHISM from the high negative pressure peaked at the dividing surface (Fig. 1). Changes in the divid- Forces Driving Self-Assembly ing surface affect the membrane morphology of Lipid Bilayers the most so that this region is a general target Although the intrinsic wish of lipids to avoid for proteins that control membranes via hydro- direct exposure of the oily tails to water can be phobic insertion (Campelo et al. 2008). intuitively understood, this wish can be fulfilled For a “relaxed” lipid monolayer at equili- in various ways. The result will be determined brium, with no external forces applied, the lat- Ðeral force balance requires the pressure integral by a complex balance of repulsive and attractive h=2 forces between lipid molecules in the lipid h=2 pdz to be zero. Thus the condensing effect monolayer. Figures 1 and 2 illustrate this notion of negative pressure in the dividing surface is by using the concept of bilayer pressure (p) balanced by the repulsive interactions in both the head-group and tail regions. Let us consider the forces existing in the head-group membrane z region. Although, attractive hydrogen bonding Head groups Dividing surface and electrostatic attractions are present, the Acyl chains steric and electrostatic repulsions dominate in p p (z) these areas of the lipid bilayer. The lipid heads T are the ones most susceptible for external perturbations brought by the environment bathing Figure 1. Lateral pressure profile across the lipid the membrane. Hence, changes in the polar bilayer. For each monolayer, three clear regions can heads often result in imbalances in the pressure be distinguished. In the head-group region, a repul- profile that interfere with the stability and mor- sive component from the entropic, steric, and elec- phology of the lipid bilayer. The most receptive trostatic interactions is dominant. The hydrophobic effect, which holds the membrane together, manifests are charged head groups whose electrostatic itself as a strong attractive force (negative pressure response depends on the pH and ionic compo- values) in the head/tail dividing surface. Finally, sition of the bathing solution. Specialized pro- there is a repulsive component from the entropic tein domains, such as PH or ENTH domains, and steric interactions in the acyl chains region. At have been evolved to specifically recognize ino- equilibrium, the lateral force balance sets the pressure sitol head groups, such domains are commonly integral zero. However, uneven distribution of the found in proteins controlling membrane positive and negative pressure over z (illustrated by blue arrows) leads to the integral torque intending remodeling in cells (Lemmon 2003). to bend a monolayer (red arrow). In symmetric As regards to the acyl chain region, it is the case, the torques in two monolayers cancel each other core of the lipid bilayer that consists of the resulting in the flat bilayer configuration. tightly packed yet highly mobile lipid tails

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V.A. Frolov et al. Geometry

z z z

Packing p(z) p(z) p(z) Polymorphism

Lamellar Lamellar Nonlamellar

Figure 2. Molecular geometry of lipids and membrane stored stress. Monolayers made of cylindrical molecules of zero SC can form nonstressed lamellas (first column, green lipid). However, for nonzero SC, lipid molecules have to be reshaped to fit into a flat state, leading to membrane stress (second column, orange lipid). When the packing parameter of the lipid is too far from unity, the stress accumulated in the resulting bilayer is too big; hence the transition of the lamella into a nonlamellar (e.g., HII) phase is favorable. The transition begins when small interlammellar contacts having characteristic hourglass shape form (third column, red lipid), lipids with negative SC promotes formation of these localized nonbilayer structures.

resembling a fluid phase. Here again there is an each monolayer, and if so, it tends to bend the overall repulsive force which is a balance lipid monolayer (Fig. 1). The torque reflects between attractive weak van der Waals forces the pressure distribution along the membrane and repulsive entropic forces, each of which normal. For bulkier tails the large entropic depend on the tail chemistry and their inter- repulsion force is distributed over the whole actions (Marsh 2007). Cellular membranes tail region, so that the bearing point is shifted display considerable variety of acyl chain com- upward to the heads’ part; the resulting torque binations, controlled by specialized enzymes tends to bend the monolayer (Fig. 1). For a sym- (Dowhan 1997; van Meer et al. 2008). The spe- metrical bilayer made of two equivalent mono- cific enzymes acting on the lipid tails, such as layers the torques act in the opposite directions phospholipases (PLAs), are intimately involved intending to tear the bilayer apart. However, in creation of membrane morphology (Brown creating a hydrophobic void inside a bilayer et al. 2003). cost substantial energy (Gruner 1989), thus As mentioned above, at equilibrium the up to a critical value the torque results in crea- lateral force balance requires the pressure tion of elastic stress stored in the flat bilayer. integralÐ to be zero. However, the torque The amount of the stored stress depends on h=2 (T h=2 pzdz) might remain unbalanced in the lipids’ “molecular shape,” characterized by

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Lipid Polymorphisms and Membrane Shape

the relative bulkiness of their head groups and the fluid-disordered lamella phase (Ld), where, tails. Let us analyze this in detail. as in bulk fluid phase, there is no long-range correlation between mobility of the lipid tails (Mouritsen and Jorgensen 1994). In this article, Lipid Molecular Shape and Membrane we mostly focus on the L phase as the basis for Stored Stress d understanding the morphological dynamics of Toparameterize the concepts of lipid molecular cellular membranes. If V is to remain constant, shape, one assigns a specific packing parameter the transformation of the conically shaped lipid P (P ¼ V=al, where V is the specific volume into a cylindrical one will cause the averaged occupied by the tails, a is the area per lipid mol- stretching or compressing of the acyl tails (Fig. ecule in the dividing surface, and l is the effec- 2, orange and red geometries), which leads to tive length of the tails’ region) to lipids of membrane stress. The amount of stress is indi- certain “shape” (Israelachvili 1992). As in the cated by how far the P is from unity, many cellu- fluid state, where lipids rotate freely, P describes lar lipids, such us DAG and DOPE, destabilize a shape with revolution symmetry; that is, P bilayer (lamellar) state at physiological condi- 1 to cylinders (e.g., dioleoylphosphocholine or tions, asthey tend to form nonbilayer structures. DOPC), P . 1 to cones (e.g., dioleoylphospho- tidylethanolamine or DOPE), and P , 1to Nonbilayer Lipid Structures inverse cones (e.g., lysophosphocholine or LPC). Importantly, P characterizes a situation The transformation of the lipid bilayer (lamellar of zero monolayer torque, when the curvature phase) into nonbilayer structures (phases) is the of the monolayer surface corresponds to the classical manifestation of lipid polymorphism intrinsic wishes of the lipids. This curvature, (de Kruijff 1997). The transformation is driven termed spontaneous curvature (SC) or intrinsic by the stored stress, which is augmented with curvature, characterizes the intrinsic shape of temperature as it increases the repulsive pres- the monolayer of zero bending stress (Gruner sure in the tail region and, thus, the bending tor- 1985). Naturally occurring cellular lipids have que. At a certain point the stored stress exceeds a a very wide range of spontaneous curvatures critical value and a new phase nucleates (Fig. 2, (from diacylglycerol (DAG) [Leikin et al. third column) which frees the stressed lipid by 1996] to LPC [Fuller and Rand 2001]) owing placing it in an environment with less torque. to the great variety of the fatty acids available For positive P, various nonbilayer “inverse” for the acyl chain combinations. The SC of a phases form, characterized by periodic arrange- multicomponent monolayer is well approxi- ment of curved lipid monolayers, illustrating mated by the sum of the SCs of all of its compo- the rich landscape of lipid polymorphism (de nents (Kumar 1991). This additivity indicates Kruijff 1997; Shearman et al. 2006). that lipid tails may be considered as a uniform For the inverse hexagonal (HII) phase, mono- fluid-like oily phase whose density is similar layers are arranged in long cylinders whose to that of a 3D fluid mixture of the correspond- geometry directly reports the SC when the cou- ing fatty acids (e.g., May et al. 2004). pling between cylinders is relaxed by the addi- Monolayers made of cylindrical molecules tion of a hydrocarbon solvent (Rand et al. of zero SC can form nonstressed bilayers 1990). The SC of many biologically important (Fig. 2, first column). However, for nonzero lipids, such as DAG or DOPE, fits an HII ar- SC, lipid molecules have to be reshaped to fit rangement much better than a flat bilayer; be- into a flat state (Fig. 2, second and third col- cause of the excess of stored stress they alone umn). A fundamental constraint here is that do not form any lamellar phase. Studies of the tails’ volume V should remain constant dur- the pathway of lamellar to HII transition pro- ing such reshaping because of fluid-like nature vided the first conjecture on why cells need of the tails’ region. We note here that the simple nonbilayer lipids at all: this transition is nucle- “oil phase” approximation works the best for ated through localized connections between two

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V.A. Frolov et al.

closely apposed bilayers, mimicking membrane z fusion events (Fig. 2, third column). These connections are characterized by a high monolayer p(z) curvature suitable for nonbilayer lipids. As the formation of such connections from cylindri- z cal lipids is much more energetically costly, the intimate involvement of nonbilayer lipids in topological membrane remodeling, fusion, and p(z) fission was predicted and later confirmed experimentally (reviewed in Chernomordik et al. 1987; Chernomordik and Kozlov 2003). Con- Figure 3. Curvature emergence through trans-mem- sequently, though nonbilayer phases are not brane asymmetry. Lipid bilayers made of two dif- present widely in vivo, nonbilayer lipids play a ferent monolayers generally have an asymmetric key role as morphological elements required to pressure profile, the difference in the pressure distribu- support the dynamic organization of cellular tion along the membrane normal z (indicated by blue membrane systems. We propose the term “lipid arrows) leads to the different monolayer torques (red morphogen” to capture this idea that the stresses arrows), the monolayer with the bigger torque “wins,” described above are embodied into the stressed and the bilayer bends to restore the torque balance. lipid that then organizes membrane structure during topological transformations in biology. two monolayers, each having the specific SC and bending resistance, dictated by the lipid composition. Although the range of SC in phos- Membrane Asymmetry and Curvature pholipids is sufficiently large, their bending Besides producing the various lyotropic phases resistance is mainly independent on their SC described above, lipid polymorphism manifests (Fuller and Rand 2001). Hence, in most cases, itself in the morphological complexity shown the SC of the bilayer is defined by the sum of by individual lipid lamella (bilayers) made of SC of its monolayers (similarly to the SC of monolayers with different properties. In this each of the monolayers, dictated by the sum of case, the stored stress is unevenly distributed the SC of their lipids). between the monolayers and a new pathway for The energy scale for the bending of a lipid the membrane stored stress relaxation emerges. bilayer from its spontaneous state is set mostly The simplest example illustrating the conse- by the lipid tails. During any deformation, the quences of an asymmetric stress distribution is spatial constraints imposed on the tails change a bilayer made of monolayers of different SC and the corresponding repackaging energy can (Fig. 3). In the flat configuration, the bending be estimated by simple Flory analysis (Rawicz torque is nonbalanced even at small stresses, but et al. 2000). Far more sophisticated approaches equilibriumcanbeachievedviamembranebend- are needed to account for great variety of exper- ing. Even when one monolayer is not stressed, imentally observed phenomena (see Marrink the stresses in the opposite one cause the bilayer et al. 2009), yet for small deformations of the to bend. This is because of monolayer coupling lipid molecule the associated work can be (Sheetz and Singer 1974), as we described above, estimated by a simple quadratic approxima- the formation of voids inside the bilayer is ener- tion (implemented by W. Helfrich): Eb 2 kc 2 getically prohibited. Hence a trans-membrane (C 2 C0) , where C is the mean curvature of asymmetry, ordifferences in the elastic properties the dividing surface (equals to 0 for symmetric of the two monolayers, is a requirement for the monolayer), C0 is the SC, and kc is the bending emergence of bilayer curvature. modulus which is a material constant character- In this case, the spontaneous curvature of an izing the flexibility of particular tails. Measure- asymmetric lipid bilayer is the result of a force ments of kc and the characterization of its lipid balance between the intrinsic wishes of the dependence have been approached in numerous

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Lipid Polymorphisms and Membrane Shape

studies using different methodologies (Marsh between membrane monolayers, but also by 2006). In agreement with the general “oil phase” nonlocal factors. approximation of the bilayer interior, kc varies One of these nonlocal factors is related to only moderately with lipid composition, with the difference in area between the inner and 25 kBT being the rough median (Marsh 2006). outer monolayers of the bilayer (Dobereiner Shortening of lipid tails and introduction of et al. 1997). As monolayers are hardly expand- double bonds soften the bilayer, whereas tails able, changes in the area difference between ordering and condensation increase kc by sev- the two lead to bending because of the bilayer eral fold (Henriksen et al. 2006; Marsh 2006; coupling. In lipid vesicles, this effect is seen as Marsh 2007; Bashkirov et al. 2008). Neverthe- membrane budding. The budding can be in- less, the energies and the associated forces duced by temperature or addition of lipids to remain notably low: lipid bilayers are extremely the outer monolayer (i.e., by factors changing bendable. The softness of the lipid bilayer is the monolayers area balance), in this case be- indicated by large temperature-driven fluctua- cause of relative expansion of the outer mono- tions of the shape of freely suspended mem- layer (Dobereiner et al. 1997; Papadopulos brane objects (e.g., Dobereiner et al. 2003). et al. 2007). To compensate, the vesicle is trans- This softness, combined with high structural formed into a chain of smaller vesicles to match stability, is crucial importance for the biological the new area disparity. With time, lipid flip-flop functionality of lipid bilayer. However, we can diminish the area difference and the mem- acknowledge here that the bending rigidity brane shape may relax to the initial spherical increases dramatically with lateral ordering of configuration. the tails in fluid-ordered (Oradd et al. 2009) Other nonlocal factors include lateral mem- and crystalline bilayers, so that those phases brane tension and pressure differences between are much less prone for morphological and the vesicle interior and exterior. Because of the topological remodeling. nonlocal nature of these factors, the shape of To summarize, lipid bilayers possess closed membrane systems is determined via extreme morphological plasticity because of global minimization of the elastic energy, where small kc and a wide variety of SC. Thus lipids the effects of tension, pressure and nonlocal can be considered as small elastic blocks which elasticity is accounted for via the corresponding molecular shape is ultimately revealed at large Lagrange multipliers. Theoretical and experi- scale via the self-assembly process. Although mental studies performed mostly on giant uni- these blocks can be easily assembled into curved lamellar vesicles (GUVs) have revealed complex patches of lipid bilayer (Fig. 3B), such patches shape diagrams (by analogy the with phase dia- are yet to be pieced together to form a stable grams) of closed lipid bilayers (Lipowsky 1995; membrane configuration. Its shape and stability Dobereiner et al. 1997; Majhenc et al. 2004). will depend on how the bilayer edges, which The rich morphology of closed membrane presence was neglected in the above analysis, shapes illustrates another dimension of lipid are concealed from exposure to water. polymorphism displayed in closed lamellas. The extreme responsiveness of the morphology of lipid vesicles to various external perturba- Closed Membranes and Shape Diagrams tions provides the basis of the morphological In most cases the stationary membrane forma- activity of lipids in cellular systems. tions are closed structures with no open edges. Edges, such as pores or localized breaches in CHANGING MEMBRANE MORPHOLOGY membrane monolayers, form only transiently during topological remodeling of membranes As we have described above, lipids themselves or pathological processes. The shape of the can assemble into a wide variety of stable closed membrane bilayer, such as a vesicle, is morphologies. Yet it is apparent that external determined not only by the local force balance energy sources are required to make those

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V.A. Frolov et al.

morphologies alive (i.e., to support dynamic from a flat lipid bilayer. The force which is transformations of the membrane shape). Pro- required to pull a tube from a GUV (Koster teins use different strategies to transform the et al. 2005) or plasma membrane (Sun et al. energy (available from conformational changes 2005) is on the order of tens of picoNewtons. or nucleotide hydrolysis) into membrane defor- This force is set by the membranepffiffiffiffiffiffiffiffiffiffi tension and mations. All these strategies had to evolve in tight bending rigidity (F ¼ 2p 2kcs) and thus can cooperation with lipids, as the latter define the be further increased by augmenting the lateral energy landscape for the protein action. Mecha- membrane tension and/or the bending rigidity. nistically, lipid–protein cooperation is imple- Already for typical tensions and bending mented in two principal modes (Zimmerberg rigidity, whose ratio determinespffiffiffiffiffiffiffiffiffiffiffiffi the characteris- and Kozlov 2006). Proteins can perform “tuning” tic curvature scale here (r ¼ kc=2s), the pull- of membrane shape by matching the membrane ing force is comparable with those produced by composition and morphology. Here membrane few molecular motors (Shaklee et al. 2008). shape is ultimately determined by lipids and Changing kc will give rise to the different tube membrane asymmetry. Alternatively, proteins geometry and will require different amount of like molecular motors or scaffolds can directly motors to pull the tube. This way creation of a “force” membrane remodeling. Here, as the tubular geometry can be performed by motors recent experiments have shown, the final shape combined with lipids. is function of membrane elasticity (Bashkirov The same similarity is noticeable when the et al. 2008). Therefore, the effect of lipids is specific (per unit area) energy of the tube for- directly linked to the two main constituencies mation is compared with the energy available of lipid polymorphism: molecular shape and from polymerization of proteins which squeeze elasticity. Multiple experimental observations the tube by forming a cylindrical scaffold on its confirm the crucial involvement of lipid poly- surface, such as dynamin, or push the tube by morphisms in membrane remodeling performed forming a thin filament inside it, such as actin by various protein machines. or tubulin (Shnyrova et al. 2009). The polymerization energy per protein unit ranges from 1 k T for actin (Footer et al. 2007) to 4–10 Forcing Shape B kBT for tubulin and dynamin (Dogterom et al. The high morphological plasticity of the fluid 2005; Bashkirov et al. 2008; Roux et al. 2010), (Ld) lipid bilayer is seemingly indicative of its well corresponding to the specific elastic energy low resistance to deformations imposed by for the tubes of tens of nm in diameter. Again, proteins. However, at biologically relevant cur- increasing the elastic resistance of the tube vatures and length-scales this high compliance membrane leads to a different final geometry is not obvious: the curvatures of cellular tubulo- (Bashkirov et al. 2008) illustrating the pro- vesicular compartments reach high values and teolipid cooperativity described above. the amount of proteins participating in mem- Finally, the energy required to make a spher- brane remodeling is restricted by the size of the ical vesicle can be estimated as 500 kBT inde- membrane objects and membrane crowding. pendently on the vesicle radius as it scales Whenever direct force measurements become with area: E ¼ 8pkc. In turn, if the vesicle is possible in reconstituted systems, the results formed by a set of coat proteins and adaptors, show that protein action is in scale with mem- the available energy will depend on the coat brane resistance, meaning that the proteins size. The two energies crossover when the vesicle do not dominate the elastic resistance of lipid diameter approaches 100 nm (Dobereiner et al. bilayer in determining overall membrane struc- 1993; Nossal 2001) indicating, once again, ture. This scaling can be illustrated in several protein–lipid cooperativity at a physiologically examples. relevant length scale. One of the typical events in membrane The above energy estimates assume “direct remodeling is the formation of a thin tube forcing” of membrane shape, where the stresses

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Lipid Polymorphisms and Membrane Shape

induced by an external force are uniformly dis- A tributed over the lipid molecules. However, proteins further cooperate with lipids to optimize the deformation process: They minimize the elastic stresses by tuning the membrane composition to the morphological demand (Fig. 4).

Very stressed Tuning of Membrane Shape Creating Membrane Asymmetry As described above, membrane asymmetry is the driving force of the morphological transformations of a lipid bilayer. Lipid head groups Nonstressed are the part of the monolayer most susceptible for external perturbations. The repulsive inter- B actions between the negatively charged lipids (such as phosphatidylserine (PS) or cardiolipin (CL) depend on the protonation of the charged residues. Neutralization of the charge in CL by applying acidic pH weakens the electrostatic repulsion and causes the decrease of the effective area CL occupies in a monolayer (Khalifat et al. 2008). Consequently, localized application of acidic pH to a GUV containing CL leads to inward membrane invagination and formation of tubes mimicking the mitochondrias cristae. Figure 4. Forcing and tuning of the membrane In turn, expansion of the PS-containing mono- shape. (A) Pulling a cylindrical membrane tube layer by application of basic pH leads to outward from a spherical vesicle by an external force; the force invagination and rapid growth of the mem- creates the high elastic stress (red) in the cylindrical brane protrusion (Fournier et al. 2009). Special- regions, and the stress is also evident from dramatic ized proteins involved in membrane remodeling transformation of lipid molecules in the cylinder generally have strong afﬁnity to charged lip- seen in the red cross section. (B) The force-induced stress can be relaxed by tuning molecular compo- ids. Such proteins might cause similar changes sition of the membrane to its shape: Lipids with con- in lipid head groups which might impact the ical shape (left cross section) or shallow insertion membrane curvature creation (Zimmerberg of a protein domain (right cross section) relax the et al. 2006). neighbor lipid molecules and diminish the integral Localized changes in membrane composi- elastic stress. tion can also be produced by enzymes medi- ating lipid metabolism and interconvertion in cells. Some of them (e.g., PLA2) are critically PLA2 activity, whereas sphingomyelinase con- involved in membrane trafﬁcking (Brown et al. vert sphingomyelins to ceramides. Accordingly, 2003) and creation of cellular membrane mor- the opposite membrane curvatures have been phologies (Christiansson et al. 1985). PLA2 produced by these enzymes in GUV. Further- (Staneva et al. 2004) and sphingomyelinase more, the activity of these enzymes is, in turn, (Holopainen et al. 2000) morphological activity modulated by nonbilayer lipids (Urbina et al. have been reconstituted with GUVs. These 2010). enzymes produce lipids with opposite packing Nevertheless, the curvature effect was not parameter: Lysolipids are the by-product of a direct consequence of the production of

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lipids with opposite SC. The enzyme adsorp- examples of lipid-driven morphology in vivo tion causes changes in the area of the outer are yet to be revealed. monolayer (Papadopulos et al. 2007). The reaction products, such as ceramides, tend to Protein Insertion aggregate forming rigid membrane domains (Holopainen et al. 2000). Thus the morpholog- The current paradigm supported by numerous ical activity of the enzymes relies not only theoretical and experimental results states that on the localized changes in membrane asymme- hydrophobic insertion is the most powerful try, but also on nonlocal elastic response and tool in creation of membrane curvature (Zim- domain-driven membrane morphology (see merberg and Kozlov 2006; Campelo et al. below). 2008). Most of the protein machinery medi- In principle, membrane asymmetry can also ating membrane remodeling in cells rely on be caused by clustering of lipids with certain membrane-inserting domains, its critical in- spontaneous curvature. Asymmetric clustering volvement in formation of membrane tubes of cholesterol by proteins orchestrating mem- and vesicles as well as in topological membrane brane vesiculation, such as viral matrix protein remodeling, fusion, and fission has been well (Shnyrova et al. 2007) or caveolin (Martin and established (reviewed in McMahon and Gallop Parton 2005), can contribute to the creation of 2005; Zimmerberg and Kozlov 2006). The basis the vesicle morphology. More interestingly, of the insertion action is evident from the pres- such clustering can be promoted by the mem- sure profile: It forces a hydrophobic wedge brane curvature itself. inside the lipid bilayer acting against the attractive pressure (Fig. 4) and thus pushes lipids away. Yet the curvature activity of the insertion Curvature-Composition Coupling depends on how it modifies the pressure profile On the basic level, the composition-morphol- (Zemel et al. 2005; Campelo et al. 2008). The ogy link corresponds to the curvature-coupl- most effective are shallow insertions that pen- ing hypothesis (Leibler 1986). The coupling is etrate slightly below the dividing surface and revealed as lateral redistribution of lipids or thus cause tilting of the tails of neighboring lipid–protein complexes in a curved membrane lipids (Fig. 4B). This tilt results in very high so that the SC of the lipid bilayer approaches its effective curvature of the proteolipid complex geometric curvature (Sorre et al. 2009; Bash- consisting of the inserting domain and its kirov et al. 2010; Capraro et al. 2010). This redis- boundary lipids. For the ENTH domain of tribution leads to lowering of the membrane epsin, the adaptor protein is responsible for energy and thus “auto-tuning” of membrane membrane curvature creation during endocy- shape (Fig. 4B). Furthermore, the feedback be- tosis, this curvature being similar in magnitude tween curvature and composition are multiple. to those created by DOPE or lysolipids (Capraro Enzyme activity (Urbina et al. 2010), protein et al. 2010). The interaction between the protein insertion and polymerization all are depend inserting motifs and lipid polymorphism is evi- on curvature (McMahon and Gallop 2005; Drin dent from the experiments demonstrating the and Antonny 2010; Roux et al. 2010). These effect of membrane-inserting peptides on the effects are also coupled to component demix- phase behavior of lipids. And vice versa, lipids ing in heterogeneous membranes (Sorre et al. significantly modulate the insertion profile and 2009). the structure of the inserting protein domains Hence, both the initiation of membrane (Marsh 2008). Thus, the curvature created by transformation and the final membrane geom- hydrophobic insertion is the result of proteo- etry depends on the coupling between sponta- lipid collaboration in which nonbilayer lipids neous and geometric curvatures, opening a and protein domains specialized on membrane new “lateral” dimension for lipid polymor- remodeling are peers. Spatial coordination of phism (Shnyrova et al. 2009). However, clear multiple insertions by the scaffold proteins

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Lipid Polymorphisms and Membrane Shape

provides a general foundation of the shape polymorphism play any role in this process? creation in cells. SC of lipids becomes an important parameter in regulation of the main driving force of the domain-driven budding, the line tension Nonlocal Elasticity in Shape Tuning (Dobereiner et al. 1993; Staneva et al. 2004). Besides changing the local membrane asymme- For most of the studied cases in which the fluid try, each insertion expands the lipid monolayer phase coexistence involves the so-called fluid it inserts into. This expansion significantly ordered and fluid disordered phases, the thick- impacts the shape transformation (Mui et al. ness of the former is greater which leads to the 1995; Holopainen et al. 2000; Papadopulos membrane height mismatch at the phase boun- et al. 2007). However, unlike changes in SC, dary (Kuzmin et al. 2005). Nonbilayer lipids are this effect can be counterbalanced by lipid flip- ideally suited for lowering the energy of this flop. Elegant experiments on GUV showed how mismatch by providing a smooth transition the initial adsorption or insertion of a flippase between membrane regions of different thick- into the outer monolayer of a GUV caused ness. Thus, they accumulate in the boundary vesicle budding because of expansion of the region and effectively lower the line tension. outer monolayer. Subsequent increase in the The stimulating effect of domain budding by flip-flop rate, caused by the actual flippase lipids with large SC has been reconstructed activity, led to shape restoration (Papadopulos experimentally (Dobereiner et al. 1993). In cells, et al. 2007). it is now clear that a 100-nm vesicle has a dis- Importantly, the same shape transforma- tinctly different lipid composition than its tion can be performed by different means. An parent membrane, along with a different degree instructive example is the membrane tubulation of lipid ordering (as determined by dyes), sug- or transition from a closed spherical shape to gesting that phase separation and its consequent cylindrical shapes. Cylindrical geometry can line tension between domains give rise both to be imposed by changes in SC of outer mono- budding and lipid sorting (Klemm et al. 2009). layer (proteins [e.g., synaptotagmin]; Martens This efficient “boundary” effect plays a very et al. 2007) as well as by changes in the area dif- important role in the latest class of membrane ference between the inner and outer monolayers transformations involved in cellular membrane (Mui et al. 1995). Thus the hydrophobic inser- morphogenesis: topological remodeling. tion in combination with nonlocal elasticity and flip-flop provide a versatile set for the regu- TOPOLOGICAL PLASTICITY lation of membrane morphology, essentially OF MEMBRANES based on intrinsic polymorphic behavior of lipid bilayer vesicles. To preserve the compartmentalization of the intracellular space, lipid bilayers of cellular membranes must maintain their structural Domain-Driven Shape stability. Lipid lamellae made of lipids with The final tool in lipid-driven membrane mor- small SC are stable formations under physio- phogenesis is provided via the ability of lip- logical conditions. They provide a foundation ids to phase separate into fluid-coexistence for the barrier function of cellular membranes regimes. The domain boundary provides the and repel each other at close contact so that driving force for membrane budding even for membrane vesicles do not merge spontane- a symmetric lipid bilayer. Domain-driven bud- ously. However, cellular membranes contains ding, predicted theoretically (Lipowsky 1992), sufficient amounts of nonbilayer lipids. Figure 2 has been studied in different lipid systems and shows how such lipids can promote localized the involvement of fluid domains in protein- destabilization of lamellar phase and forma- driven membrane morphogenesis has been tion of nonbilayer connections between the op- shown (Shnyrova et al. 2007, 2009). Does lipid posed lipid bilayers. This is the scenario for the

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Lipid Polymorphisms and Membrane Shape

Vadim A. Frolov, Anna V. Shnyrova and Joshua Zimmerberg

Cold Spring Harb Perspect Biol 2011; doi: 10.1101/cshperspect.a004747 originally published online June 6, 2011

Subject Collection The Biology of Lipids

Role of Lipids in Virus Replication Membrane Organization and Lipid Rafts Maier Lorizate and Hans-Georg Kräusslich Kai Simons and Julio L. Sampaio Model Answers to Lipid Membrane Questions Shotgun Lipidomics on High Resolution Mass Ole G. Mouritsen Spectrometers Dominik Schwudke, Kai Schuhmann, Ronny Herzog, et al. Glycosphingolipid Functions Glycosphingolipid Functions Clifford A. Lingwood Clifford A. Lingwood Regulation of Cholesterol and Fatty Acid Phosphoinositides in Cell Architecture Synthesis Annette Shewan, Dennis J. Eastburn and Keith Jin Ye and Russell A. DeBose-Boyd Mostov Lipid-Mediated Endocytosis Synthesis and Biosynthetic Trafficking of Helge Ewers and Ari Helenius Membrane Lipids Tomas Blom, Pentti Somerharju and Elina Ikonen Fluorescence Techniques to Study Lipid Lipid Polymorphisms and Membrane Shape Dynamics Vadim A. Frolov, Anna V. Shnyrova and Joshua Erdinc Sezgin and Petra Schwille Zimmerberg Lysosomal Lipid Storage Diseases Specificity of Intramembrane Protein−Lipid Heike Schulze and Konrad Sandhoff Interactions Francesc-Xabier Contreras, Andreas Max Ernst, Felix Wieland, et al. Distribution and Functions of Sterols and Dynamic Transbilayer Lipid Asymmetry Sphingolipids Gerrit van Meer J. Thomas Hannich, Kyohei Umebayashi and Howard Riezman

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