Statistical Thermodynamics of Amphiphile Self-Assembly: Structure and Phase Transitions in Micellar Solutions

Ben‐Shaul, Avinoam; Gelbart, William M.

doi:10.1007/978-1-4613-8389-5_1

Cited by 74 publications

(81 citation statements)

References 199 publications

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“…We confirm some of the key assumptions underlying our mean-field model by carrying out Monte Carlo simulations of a minimal molecular model of MPPN organization, which we formulate following previous work on viral capsid symmetry [13]. Finally, we use our mean-field model of MPPNs to calculate [12,14,15] the MPPN self-assembly phase diagram as a function of protein concentration, bilayer-protein contact angle, and protein size. We show that our model correctly predicts, with all model parameters determined directly from experiments, the observed [4] symmetry and size of MPPNs formed from MscS.…”

supporting

confidence: 67%

“…Phase diagram.-Based on our mean-field model of MPPNs we construct the MPPN phase diagram from [12] the statistical thermodynamics of amphiphile selfassembly in dilute aqueous solutions [14,15]. Let N n denote the total number of proteins bound in MPPNs with n proteins each and N w the total number of solvent molecules, which we take [4,7] to be dominated by contributions due to water.…”

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

“…We assume here that all proteins in the system are incorporated into MPPNs, a point we return to below. In the dilute limit c 1 with no interactions between MPPNs we have [14,15] the mixing entropy…”

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

“…This then allows [14,15] construction of the Helmholtz free energy F = E − T S with E = N w n Φ(n)E min (n), in which the minimum MPPN energy E min (n) is determined by our mean-field model of MPPNs via Eqs. (1)-(3).…”

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

“…Our model accounts for the energy cost of proteininduced lipid bilayer bending deformations [9][10][11] and topological defects in protein packing in MPPNs [12,13], and the statistical thermodynamics [12][13][14][15] of MPPN self-assembly. With all model parameters determined directly from experiments, our model correctly predicts the observed [4] symmetry and size of MPPNs formed from MscS.…”

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

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Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Kahraman

Haselwandter

2016

Phys. Rev. Lett.

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In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S. A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the observed symmetry and size of MPPNs. Our model suggests how key lipid and protein properties can be modified to produce a range of MPPN symmetries and sizes in experiments. Utilization of MPPNs for high-resolution structural studies requires [4] control over the symmetry and size of MPPNs. In this Letter we develop a physical description of MPPNs which establishes a quantitative link between the shape of MPPNs and key molecular properties of their constituents. We first describe a simple meanfield model of MPPNs inspired by previous work on membrane budding [9-11] and viral capsid self-assembly [12]. Our mean-field model of MPPNs accounts for the lipid bilayer bending deformations induced by MscS [3,5,6] and the MscS packing defects resulting from the spherical topology of MPPNs, and yields the MPPN energy as a function of the number of MscS per MPPN without any free parameters. We confirm some of the key assumptions underlying our mean-field model by carrying out Monte Carlo simulations of a minimal molecular model of MPPN organization, which we formulate following previous work on viral capsid symmetry [13]. Finally, we use our mean-field model of MPPNs to calculate [12,14,15] the MPPN self-assembly phase diagram as a function of protein concentration, bilayer-protein contact angle, and protein size. We show that our model correctly predicts, with all model parameters determined directly from experiments, the observed [4] symmetry and size of MPPNs formed from MscS. Our results suggest that the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects.Mean-field model.-The membrane-spanning region of MscS [5,6] has an approximately conical shape [3,16] with radius ρ i ≈ 3.2 nm in the lipid bilayer midplane and bilayer-protein contact angle α ≈ 0.46-0.54 rad, yielding [3] protein-induced lipid bilayer bending deformations [see Fig. 1(b)]. The preferred MscS arrangement minimizing bilayer bending energy is expected [9-11] to be a uniform hexagonal lattice. Our simple mean-field model of MPPNs therefore considers, on the one hand, contri-

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supporting

confidence: 67%

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

Section: Fig 2: (Color Online) Minimized Total Mppn Energy Eminmentioning

confidence: 99%

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Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Kahraman

Haselwandter

2016

Phys. Rev. Lett.

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Advances in the Molecular Simulation of Microphase Formers

Zhang¹

2022

Reviews in Computational Chemistry

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HIV TAT Forms Pores in Membranes by Inducing Saddle‐Splay Curvature: Potential Role of Bidentate Hydrogen Bonding

et al. 2008

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The TAT protein transduction domain (PTD) of the human immunodeficiency virus (HIV-1) can cross cell membranes with unusual efficiency [1] and has many potential biotechnological applications. [2][3][4] Extant work has provided important clues to the molecular mechanism underlying the activity of this peptide, which consists of 11 amino acids, 8 of which are cationic and 6 of these are arginines. TAT PTD synthesized with d-amino acids enters cells as efficiently as the native form, [5] thereby indicating that the mechanism of transduction is receptor independent; this conclusion is consistent with recent results that suggest that the TAT PTD may enter cells through receptor-independent macropinocytosis.[6] Substitution of any of the PTDs cationic residues with neutral alanine decreases activity, while substitution of neutral residues has no effect. [5] This indicates the importance of electrostatic interactions between cationic TAT PTD and anionic phospholipid membranes. Recent work has shown that the physics of electrostatic interactions can drive a rich polymorphism of self-assembled structures that depend on parameters such as charge density [7,8] and intrinsic membrane curvature. [9,10] However, although arginine-rich polycations can enter cells, cationic polylysine cannot. [11] This shows that electrostatic interactions alone are insufficient for PTD activity and that the arginine residues play a specific, essential role.We use confocal microscopy and synchrotron X-ray scattering (SAXS) to study the interaction of the TAT PTD with model membranes at room temperature. We find that the transduction activity correlates with induction of negative Gaussian ("saddle-splay") membrane curvature, which is topologically required for pore formation. Moreover, we show that the TAT PTD can drastically remodel vesicles into a porous bicontinuous phase with analogues in block-copolymer systems, [12][13][14] and we propose a geometric mechanism facilitated by both electrostatics and bidentate hydrogen bonding. The latter is possible for the TAT PTD but not for similarly cationic, nonarginated polypeptides.Cell membranes are composed of lipids that have fundamentally different interactions with cationic macroions such as TAT PTD. We examine representative model membranes composed of lipids with different charges and intrinsic curvatures: 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) have zwitterionic headgroups, while 1,2-dioleoyl-sn-glycero-3-[phospho-l-serine] (sodium salt) (DOPS) and 1,2-dioleoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (sodium salt) (DOPG) have anionic headgroups; all have zero intrinsic curvature [15] (C 0 = 0, "cylinder-shaped") except for DOPE, which has negative intrinsic curvature (C 0 < 0, "cone-shaped"). When rhodamine-tagged TAT PTD (Rh-PTD) is applied to the exterior of giant unilamellar vesicles (GUVs, diameters of 5-30 mm) with low DOPE content (0 and 20 %), rhodamine fluorescence is seen only outside the GUVs (Figure 1 a), thereby indi...

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Statistical Thermodynamics of Amphiphile Self-Assembly: Structure and Phase Transitions in Micellar Solutions

Cited by 74 publications

References 199 publications

Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Advances in the Molecular Simulation of Microphase Formers

HIV TAT Forms Pores in Membranes by Inducing Saddle‐Splay Curvature: Potential Role of Bidentate Hydrogen Bonding

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