Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape

Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes.     

Molecular theory of lipid-protein interaction and the Lalpha-HII transition.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the HII lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor Lalpha phase coexists with a peptide-rich HII phase.     

Interactions of cholesterol with lipid bilayers: the preferred configuration and fluctuations.

The free energy difference associated with the transfer of a single cholesterol molecule from the aqueous phase into a lipid bilayer depends on its final location, namely on its insertion depth and orientation within the bilayer. We calculated desolvation and lipid bilayer perturbation contributions to the water-to-membrane transfer free energy, thus allowing us to determine the most favorable location of cholesterol in the membrane and the extent of fluctuations around it. The electrostatic and nonpolar contributions to the solvation free energy were calculated using continuum solvent models. Lipid layer perturbations, resulting from both conformational restrictions of the lipid chains in the vicinity of the (rigid) cholesterol backbone and from cholesterol-induced elastic deformations, were calculated using a simple director model and elasticity theory, respectively. As expected from the amphipathic nature of cholesterol and in agreement with the available experimental data, our results show that at the energetically favorable state, cholesterol's hydrophobic core is buried within the hydrocarbon region of the bilayer. At this state, cholesterol spans approximately one leaflet of the membrane, with its OH group protruding into the polar (headgroup) region of the bilayer, thus avoiding an electrostatic desolvation penalty. We found that the transfer of cholesterol into a membrane is mainly driven by the favorable nonpolar contributions to the solvation free energy, whereas only a small opposing contribution is caused by conformational restrictions of the lipid chains. Our calculations also predict a strong tendency of the lipid layer to elastically respond to (thermally excited) vertical fluctuations of cholesterol so as to fully match the hydrophobic height of the solute. However, orientational fluctuations of cholesterol were found to be accompanied by both an elastic adjustment of the surrounding lipids and by a partial exposure of the hydrophobic cholesterol backbone to the polar (headgroup) environment. Our calculations of the molecular order parameter, which reflects the extent of orientational fluctuations of cholesterol in the membrane, are in good agreement with available experimental data.     

Electrostatic free energy and spontaneous curvature of spherical charged layered membrane

A biophysical model for the equilibrium curvature of a composite membrane element is derived taking into account the mechanical bilayer properties and the adjacent charged protein layers. The minimum of the total free energy density with respect to the curvature of such a membrane curved was estimated from the sum of the electrostatic free energy density of the charges of the membrane and the elastic surface energy density due to bending the lipid bilayer membrane. It was shown that the equilibrium curvature, i.e. the spontaneous curvature, of such a charged composite sandwich-like membrane depends inversely on the bending stiffness of the lipid membrane itself and directly on the charge amount inside and outside the membrane to the second power. Furthermore the geometric and electrostatic structure of the protein layers and the physico-chemical environment conditions are involved. Corresponding to the model developed a "standard RBC" membrane element has a negative spontaneous curvature, accounting for a discocyte RBC shape. The shape change from a discocyte to a more stomatocytic shape (increase in the negative spontaneous curvature) after reducing the charges in the glycocalyx is also explained within this model.     

Small scale membrane mechanics

Large scale changes to lipid bilayer shapes are well represented by the Helfrich model. However, there are membrane processes that take place at smaller length scales that this model cannot address. In this work, we present a one-dimensional continuum model that captures the mechanics of the lipid bilayer membrane at the length scale of the lipids themselves. The model is developed using the Cosserat theory of surfaces with lipid orientation, or ‘tilt’, as the fundamental degree of freedom. The Helfrich model can be recovered as a special case when the curvatures are small and the lipid tilt is everywhere zero. We use the tilt model to study local membrane deformations in response to a protein inclusion. Parameter estimates and boundary conditions are obtained from a coarse-grained molecular model using dissipative particle dynamics (DPD) to capture the same phenomenon. The continuum model is able to reproduce the membrane bending, stretch and lipid tilt as seen in the DPD model. The lipid tilt angle relaxes to the bulk tilt angle within 5–6 nm from the protein inclusion. Importantly, for large tilt gradients induced by the proteins, the tilt energy contribution is larger than the bending energy contribution. Thus, the continuum model of tilt accurately captures behaviors at length scales shorter than the membrane thickness.     

Inclusion-induced bilayer deformations: effects of monolayer equilibrium curvature

The energetics of protein-induced bilayer deformation in systems with finite monolayer equilibrium curvature were investigated using an elastic membrane model. In this model the bilayer deformation energy delta G(def) has two major components: a compression-expansion component and a splay-distortion component, which includes the consequences of a bilayer curvature frustration due to a monolayer equilibrium curvature, c(0), that is different from zero. For any choice of bilayer material constants, the value of delta G(def) depends on global bilayer properties, as described by the bilayer material constants, as well as the energetics of local lipid packing adjacent to the protein. We introduce this dependence on lipid packing through the contact slope, s, at the protein-bilayer boundary. When c(0) = 0, delta G(def) can be approximated as a biquadratic function of s and the monolayer deformation at the protein/bilayer boundary, u(0): delta G(def) = a(1)u(0)(2) + a(2)u(0)s + a(3)s(2), where a(1), a(2), and a(3) are functions of the bilayer thickness, the bilayer compression-expansion and splay-distortion moduli, and the inclusion radius (this expression becomes exact when the Gaussian curvature component of delta G(def) is negligible). When c(0) not equal 0, the curvature frustration contribution is determined by the choice of boundary conditions at the protein-lipid boundary (by the value of s), and delta G(def) is the sum of the energy for c(0) = 0 plus the curvature frustration-dependent contribution. When the energetic penalty for the local lipid packing can be ignored, delta G(def) will be determined only by the global bilayer properties, and a c(0) > 0 will tend to promote a local inclusion-induced bilayer thinning. When the energetic penalty for local lipid packing is large, s will be constrained by the value of c(0). In a limiting case, where s is determined only by geometric constraints imposed by c(0), a c(0) > 0 will impede such local bilayer thinning. One cannot predict curvature effects without addressing the proper choice of boundary conditions at the protein-bilayer contact surface.     

Amphipathic helixes and plasma lipoproteins: Thermodynamic and geometric considerations

In this paper analyses are made of the thermodynamic and geometric properties of the predicted association between amphipathic helixes and phospholipid vesicles. From thermodynamic considerations it is proposed that a major driving force for such an association is the negative free energy gained by the transfer of a number of hydrophobic residues (contained within the non-polar faces of amphipathic helixes), from water to the interior of a phospholipid bilayer. The mechanism proposed is that in the aqueous state a potentially amphipathic sequence forms a non-helical hydrophobic patch on the surface of the apolipoprotein. Formation of an amphipathic helix and simultaneous burial of the hydrophobic residues in the surface of a phospholipid bilayer provides the driving force for lipid association. From this model an estimate of the upperlimit for the hydrophobically driven free energy of lipid association (?40?65 kcal/mol) is calculated for the 4 apolipoproteins with known sequences.On the basis of geometrical considerations a model for an intermediate state of high density lipoprotein (HDL) synthesis is proposed. This model consists of a cholesterol-containing phospholipid bilayer disc whose ‘naked’ hydrophobic edges are shielded from the aqueous phase by amphipathic helixes of the apolipoproteins. Exposure of these ‘bicycle tire’ micelles to the enzyme lecithin: cholesterol acyl transferase (LCAT) is postulated to result in the formation of mature spherical HDL particles with cholesteryl ester forming a neutral lipid core.     

Factors influencing local membrane curvature induction by N-BAR domains as revealed by molecular dynamics simulations

N-BAR domains are protein modules that bind to and induce curvature in membranes via a charged concave surface and N-terminal amphipathic helices. Recently, molecular dynamics simulations have demonstrated that the N-BAR domain can induce a strong local curvature that matches the curvature of the BAR domain surface facing the bilayer. Here we present further molecular dynamics simulations that examine in greater detail the roles of the concave surface and amphipathic helices in driving local membrane curvature. We find that the strong curvature induction observed in our previous simulations requires the stable presentation of the charged concave surface to the membrane and is not driven by the membrane-embedded amphipathic helices. Nevertheless, without these amphipathic helices embedded in the membrane, the N-BAR domain does not maintain a close association with the bilayer, and fails to drive membrane curvature. Increasing the membrane negative charge through the addition of PIP₂ facilitates closer association with the membrane in the absence of embedded helices. At sufficiently high concentrations, amphipathic helices embedded in the membrane drive membrane curvature independently of the BAR domain.     

Continuum solvent model studies of the interactions of an anticonvulsant drug with a lipid bilayer

Valproic acid (VPA) is a short, branched fatty acid with broad-spectrum anticonvulsant activity. It has been suggested that VPA acts directly on the plasma membrane. We calculated the free energy of interaction of VPA with a model lipid bilayer using simulated annealing and the continuum solvent model. Our calculations indicate that VPA is likely to partition into the bilayer both in its neutral and charged forms, as expected from such an amphipathic molecule. The calculations also show that VPA may migrate (flip-flop) across the membrane; according to our (theoretical) study, the most likely flip-flop path at neutral pH involves protonation of VPA pending its insertion into the lipid bilayer and deprotonation upon departure from the other side of the bilayer. Recently, the flip-flop of long fatty acids across lipid bilayers was studied using fluorescence and NMR spectroscopies. However, the measured value of the flip-flop rate appears to depend on the method used in these studies. Our calculated value of the flip-flop rate constant, 20/s, agrees with some of these studies. The limitations of the model and the implications of the study for VPA and other fatty acids are discussed.     

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.     

Membrane perturbation induced by interfacially adsorbed peptides

The structural and energetic characteristics of the interaction between interfacially adsorbed (partially inserted) alpha-helical, amphipathic peptides and the lipid bilayer substrate are studied using a molecular level theory of lipid chain packing in membranes. The peptides are modeled as "amphipathic cylinders" characterized by a well-defined polar angle. Assuming two-dimensional nematic order of the adsorbed peptides, the membrane perturbation free energy is evaluated using a cell-like model; the peptide axes are parallel to the membrane plane. The elastic and interfacial contributions to the perturbation free energy of the "peptide-dressed" membrane are evaluated as a function of: the peptide penetration depth into the bilayer's hydrophobic core, the membrane thickness, the polar angle, and the lipid/peptide ratio. The structural properties calculated include the shape and extent of the distorted (stretched and bent) lipid chains surrounding the adsorbed peptide, and their orientational (C-H) bond order parameter profiles. The changes in bond order parameters attendant upon peptide adsorption are in good agreement with magnetic resonance measurements. Also consistent with experiment, our model predicts that peptide adsorption results in membrane thinning. Our calculations reveal pronounced, membrane-mediated, attractive interactions between the adsorbed peptides, suggesting a possible mechanism for lateral aggregation of membrane-bound peptides. As a special case of interest, we have also investigated completely hydrophobic peptides, for which we find a strong energetic preference for the transmembrane (inserted) orientation over the horizontal (adsorbed) orientation.     

Minimum Membrane Bending Energies of Fusion Pores

Membranes fuse by forming highly curved intermediates, culminating in structures described as fusion pores. These hourglass-like figures that join two fusing membranes have high bending energies, which can be estimated using continuum elasticity models. Fusion pore bending energies depend strongly on shape, and the present study developed a method for determining the shape that minimizes bending energy. This was first applied to a fusion pore modeled as a single surface and then extended to a more realistic model treating a bilayer as two monolayers. For the two-monolayer model, fusion pores were found to have metastable states with energy minima at particular values of the pore diameter and bilayer separation. Fusion pore energies were relatively insensitive to membrane thickness but highly sensitive to spontaneous curvature and membrane asymmetry. With symmetrical bilayers and monolayer spontaneous curvatures of ?0.1 nm^?1 (a typical value) separated by 6 nm (closest distance determined by repulsive hydration forces), fusion pore formation required 43–65 kT. The pore radius of ~2.25 nm fell within the range estimated from conductance measurements. With bilayer separation >6 nm, fusion pore formation required less energy, suggesting that protein scaffolds can promote fusion by bending membranes toward one another. With nonzero spontaneous monolayer curvature, the shape that minimized the energy change during fusion pore formation differed from the shape that minimized its energy after it formed. Thus, a nascent fusion pore will relax spontaneously to a new shape, consistent with the experimentally observed expansion of nascent fusion pores during viral fusion.     

Molecular mechanisms of spontaneous curvature and softening in complex lipid bilayer mixtures

Membrane reshaping is an essential biological process. The chemical composition of lipid membranes determines their mechanical properties and thus the energetics of their shape. Hundreds of distinct lipid species make up native bilayers, and this diversity complicates efforts to uncover what compositional factors drive membrane stability in cells. Simplifying assumptions, therefore, are used to generate quantitative predictions of bilayer dynamics based on lipid composition. One assumption commonly used is that “per lipid” mechanical properties are both additive and constant—that they are an intrinsic property of lipids independent of the surrounding composition. Related to this is the assumption that lipid bulkiness, or “shape,” determines its curvature preference, independently of context. In this study, all-atom molecular dynamics simulations on three separate multilipid systems were used to explicitly test these assumptions, applying methodology recently developed to isolate properties of single lipids or nanometer-scale patches of lipids. The curvature preference experienced by populations of lipid conformations were inferred from their redistribution on a dynamically fluctuating bilayer. Representative populations were extracted by both structural similarity and semi-automated hidden Markov model analysis. The curvature preferences of lipid dimers were then determined and compared with an additive model that combines the monomer curvature preference of both the individual lipids. In all three systems, we identified conformational subpopulations of lipid dimers that showed non-additive curvature preference, in each case mediated by a special chemical interaction (e.g., hydrogen bonding). Our study highlights the importance of specific chemical interactions between lipids in multicomponent bilayers and the impact of interactions on bilayer stiffness. We identify two mechanisms of bilayer softening: diffusional softening, driven by the dynamic coupling between lipid distributions and membrane undulations, and conformational softening, driven by the inter-conversion between distinct dimeric conformations.     

Theory of cation-phospholipid-induced shape changes in a lipid bilayer couple

A quantitative model of ion binding and molecular interactions in the lipid bilayer membrane is proposed and found to be useful in examining the factors underlying such membrane characteristics as shape, sidedness, stability and vesicle size at various cation concentrations. The lipid membrane behaves as a bilayer couple whose preferential radius of curvature depends on the expansion or contraction of one monolayer relative to the other. It is proposed that molecular packing may be altered by electrostatic repulsion of adjacent like-charged phospholipid headgroups, or by bringing two headgroups closer together by divalent cation crossbridging. The surface concentrations of each type of cation-phospholipid complex can be described by simple binding equilibria and the Gouy-Chapman-Stern formulation for the surface potential in a diffuse double layer. The asymmetric distribution of acidic phospholipids in most biological membranes can account for the differential effects of identical ionic environments on either side of the bilayer. The fraction of vesicle material which tends to have a right-side-out orientation may be approximated by a normal distribution about the mean curvature. The theory generates vesicle sidedness distributions that, when fitted to experimental results from human erythrocyte membranes, provide an alternative method of estimating intrinsic cationphospholipid dissociation constants and other molecular parameters of the bilayer. The results also corroborate earlier suggestions that the Gouy-Chapman theory tends to overestimate free counter-ion concentrations at the surface under large surface potentials.     

DNA-lipid complexes: stability of honeycomb-like and spaghetti-like structures.

A molecular level theory is presented for the thermodynamic stability of two (similar) types of structural complexes formed by (either single strand or supercoiled) DNA and cationic liposomes, both involving a monolayer-coated DNA as the central structural unit. In the "spaghetti" complex the central unit is surrounded by another, oppositely curved, monolayer, thus forming a bilayer mantle. The "honeycomb" complex is a bundle of hexagonally packed DNA-monolayer units. The formation free energy of these complexes, starting from a planar cationic/neutral lipid bilayer and bare DNA, is expressed as a sum of electrostatic, bending, mixing, and (for the honeycomb) chain frustration contributions. The electrostatic free energy is calculated using the Poisson-Boltzmann equation. The bending energy of the mixed lipid layers is treated in the quadratic curvature approximation with composition-dependent bending rigidity and spontaneous curvature. Ideal lipid mixing is assumed within each lipid monolayer. We found that the most stable monolayer-coated DNA units are formed when the charged/neutral lipid composition corresponds (nearly) to charge neutralization; the optimal monolayer radius corresponds to close DNA-monolayer contact. These conclusions are also valid for the honeycomb complex, as the chain frustration energy is found to be negligible. Typically, the stabilization energies for these structures are on the order of 1 k(B)T/A of DNA length, reflecting mainly the balance between the electrostatic and bending energies. The spaghetti complexes are less stable due to the additional bending energy of the external monolayer. A thermodynamic analysis is presented for calculating the equilibrium lipid compositions when the complexes coexist with excess bilayer.     

Cholesterol and phosphatidylethanolamine lipids exert opposite effects on membrane modulations caused by the M2 amphipathic helix

Membrane curvature remodeling induced by amphipathic helices (AHs) is essential in many biological processes. Here we studied a model amphipathic peptide, M2AH, derived from influenza A M2. We are interested in how M2AH may promote membrane curvature by altering membrane physical properties. We used atomic force microscopy (AFM) to examine changes in membrane topographic and mechanical properties. We used electron paramagnetic resonance (EPR) spectroscopy to explore changes in lipid chain mobility and chain orientational order. We found that M2AH perturbed lipid bilayers by generating nanoscale pits. The structural data are consistent with lateral expansion of lipid chain packing, resulting in a mechanically weaker bilayer. Our EPR spectroscopy showed that M2AH reduced lipid chain mobility and had a minimal effect on lipid chain orientational order. The EPR data are consistent with the surface-bound state of M2AH that acts as a chain mobility inhibitor. By comparing results from different lipid bilayers, we found that cholesterol enhanced the activity of M2AH in inducing bilayer pits and altering lipid chain mobility. The results were explained by considering specific M2AH-cholesterol recognition and/or cholesterol-induced expansion of interlipid distance. Both AFM and EPR experiments revealed a modest effect of anionic lipids. This highlights that membrane interaction of M2AH is mainly driven by hydrophobic forces. Lastly, we found that phosphatidylethanolamine (PE) lipids inhibited the activity of M2AH. We explained our data by considering interlipid hydrogen-bonding that can stabilize bilayer organization. Our results of lipid-dependent membrane modulations are likely relevant to M2AH-induced membrane restructuring.     

Role of helix 0 of the N-BAR domain in membrane curvature generation

A group of proteins with cell membrane remodeling properties is also able to change dramatically the morphology of liposomes in vitro, frequently inducing tubulation. For a number of these proteins, the mechanism by which this effect is exerted has been proposed to be the embedding of amphipathic helices into the lipid bilayer. For proteins presenting BAR domains, removal of an N-terminal amphipathic α-helix (H0-NBAR) results in much lower membrane tubulation efficiency, pointing to a fundamental role of this protein segment. Here, we studied the interaction of a peptide corresponding to H0-NBAR with model lipid membranes. H0-NBAR bound avidly to anionic liposomes but partitioned weakly to zwitterionic bilayers, suggesting an essentially electrostatic interaction with the lipid bilayer. Interestingly, it is shown that after membrane incorporation, the peptide oligomerizes as an antiparallel dimer, suggesting a potential role of H0-NBAR in the mediation of BAR domain oligomerization. Through monitoring the effect of H0-NBAR on liposome shape by cryoelectron microscopy, it is clear that membrane morphology is not radically changed. We conclude that H0-NBAR alone is not able to induce vesicle curvature, and its function must be related to the promotion of the scaffold effect provided by the concave surface of the BAR domain.     

Mechanisms of membrane deformation

Membrane traffic requires the generation of high-curvature lipid-bound transport carriers represented by tubules and vesicles. The mechanisms through which membranes are deformed has gained much recent attention. A major advance has been the demonstration that direct interactions between cytosolic proteins and lipid bilayers are important in the acquisition of membrane curvature. Rather than being driven only by the formation of membrane-associated structural scaffolds, membrane deformation requires physical perturbation of the lipid bilayer. A variety of proteins have been identified that directly bind and deform membranes. An emerging theme in this process is the importance of amphipathic peptides that partially penetrate the lipid bilayer.     

Coupling between lipid shape and membrane curvature

Using molecular dynamics simulations, we examine the behavior of lipids whose preferred curvature can be systematically varied. This curvature is imposed by controlling the headgroup size of a coarse-grained lipid model recently developed by us. To validate this approach, we examine self-assembly of each individual lipid type and observe the complete range of expected bilayer and micelle phases. We then examine binary systems consisting of lipids with positive and negative preferred curvature and find a definite sorting effect. Lipids with positive preferred curvature are found in greater proportions in outer monolayers with the opposite observed for lipids with negative preferred curvature. We also observe a similar, but slightly stronger effect for lipids in a developing spherical bud formed by adhesion to a colloid (e.g., a viral capsid). Importantly, the magnitude of this effect in both cases was large only for regions with strong mean curvature (radii of curvature <10 nm). Our results suggest that lipid shape must act in concert with other physico-chemical effects such as phase transitions or interactions with proteins to produce strong sorting in cellular pathways.