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Cellular processes are controlled by the thermodynamics of the underlying biomolecular interactions. Frequently, structural investigations use one monomeric binding partner, while ensemble measurements of binding affinities generally yield one affinity representative of a 1:1 interaction, despite the majority of the proteome consisting of oligomeric proteins. For example, viral entry and inhibition in SARS-CoV-2 involve a trimeric spike surface protein, a dimeric angiotensin-converting enzyme 2 (ACE2) cell-surface receptor and dimeric antibodies. Here, we reveal that cooperativity correlates with infectivity and inhibition as opposed to 1:1 binding strength. We show that ACE2 oligomerizes spike more strongly for more infectious variants, while exhibiting weaker 1:1 affinity. Furthermore, we find that antibodies use induced oligomerization both as a primary inhibition mechanism and to enhance the effects of receptor-site blocking. Our results suggest that naive affinity measurements are poor predictors of potency, and introduce an antibody-based inhibition mechanism for oligomeric targets. More generally, they point toward a much broader role of induced oligomerization in controlling biomolecular interactions., Competing Interests: Competing interests statement:P.K. is a nonexecutive director, shareholder of and consultant to Refeyn Ltd., J.L.P.B. and W.B.S. are shareholders of and consultants to Refeyn Ltd. W.B.S. and P.K. received the University of Oxford’s COVID-19 Research Response Fund. P.K. has filed a patent for the contrast enhancement methodology and its application to mass measurement of single biomolecules. G.R.S. is on the GSK Vaccines Scientific Advisory Board, a founder shareholder of RQ biotechnology and Jenner investigator. Oxford University holds intellectual property related to the Oxford-AstraZeneca vaccine.

Mass photometry (MP) is a rapidly growing optical technique for label-free mass measurement of single biomolecules in solution. The underlying measurement principle provides numerous advantages over ensemble-based methods but has been limited to low analyte concentrations due to the need to uniquely and accurately quantify the binding of individual molecules to the measurement surface, which results in diffraction-limited spots. Here, we combine nanoparticle lithography with surface PEGylation to substantially lower surface binding, resulting in a 2 orders of magnitude improvement in the upper concentration limit associated with mass photometry. We demonstrate the facile tunability of degree of passivation, enabling measurements at increased analyte concentrations. These advances provide access to protein-protein interactions in the high nanomolar to low micromolar range, substantially expanding the application space of mass photometry.

Hepatitis B virus (HBV) displays remarkable self-assembly capabilities that interest the scientific community and biotechnological industries as HBV is leading to an annual mortality of up to 1 million people worldwide (especially in Africa and Southeast Asia). When the ionic strength is increased, hepatitis B virus-like particles (VLPs) can assemble from dimers of the first 149 residues of the HBV capsid protein core assembly domain (Cp149). Using solution small-angle X-ray scattering, we investigated the disassembly of the VLPs by titrating guanidine hydrochloride (GuHCl). Measurements were performed with and without 1 M NaCl, added either before or after titrating GuHCl. Fitting the scattering curves to a linear combination of atomic models of Cp149 dimer (the subunit) and T = 3 and T = 4 icosahedral capsids revealed the mass fraction of the dimer in each structure in all the titration points. Based on the mass fractions, the variation in the dimer-dimer association standard free energy was calculated as a function of added GuHCl, showing a linear relation between the interaction strength and GuHCl concentration. Using the data, we estimated the energy barriers for assembly and disassembly and the critical nucleus size for all of the assembly reactions. Extrapolating the standard free energy to [GuHCl] = 0 showed an evident hysteresis in the assembly process, manifested by differences in the dimer-dimer association standard free energy obtained for the disassembly reactions compared with the equivalent assembly reactions. Similar hysteresis was observed in the energy barriers for assembly and disassembly and the critical nucleus size. The results suggest that above 1.5 M, GuHCl disassembled the capsids by attaching to the protein and adding steric repulsion, thereby weakening the hydrophobic attraction.

The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent, such as RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with a combinatorial number of intermediates. Hence, the mechanism of the reaction is poorly understood. In this paper, we combined solution small-angle X-ray scattering (SAXS), cryo-transmission electron microscopy (TEM), and computational modeling to determine the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by SAXS and cryo-TEM. To analyze the data, we performed Langevin dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures consistent with the experimental data. We found that close to physiological ionic strength, [Formula: see text] VLPs coexisted with VP1 pentamers. At lower or higher ionic strengths, incomplete particles coexisted with pentamers and [Formula: see text] particles. Including the simulated structures was essential to explain the SAXS data in a manner that is consistent with the cryo-TEM images., (© 2023. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)

BiP (immunoglobulin heavy-chain binding protein) is a Hsp70 monomeric ATPase motor that plays broad and crucial roles in maintaining proteostasis inside the cell. Structurally, BiP is formed by two domains, a nucleotide-binding domain (NBD) with ATPase activity connected by a flexible hydrophobic linker to the substrate-binding domain. While the ATPase and substrate binding activities of BiP are allosterically coupled, the latter is also dependent on nucleotide binding. Recent structural studies have provided new insights into BiP's allostery; however, the influence of temperature on the coupling between substrate and nucleotide binding to BiP remains unexplored. Here, we study BiP's binding to its substrate at the single molecule level using thermo-regulated optical tweezers which allows us to mechanically unfold the client protein and explore the effect of temperature and different nucleotides on BiP binding. Our results confirm that the affinity of BiP for its protein substrate relies on nucleotide binding, by mainly regulating the binding kinetics between BiP and its substrate. Interestingly, our findings also showed that the apparent affinity of BiP for its protein substrate in the presence of nucleotides remains invariable over a wide range of temperatures, suggesting that BiP may interact with its client proteins with similar affinities even when the temperature is not optimal. Thus, BiP could play a role as a "thermal buffer" in proteostasis., (© 2023 The Protein Society.)

We review recent advances in our ability to characterise biomolecular structure, interactions and associated dynamics by mass photometry (MP), the label-free detection and mass measurement of individual biomolecules in solution. Molecular counting and identification provides direct access to relative abundance, and thereby affinities, while associated dynamics yield on- and off-rates. The molecular resolution afforded by MP enables these measurements as a function of stoichiometry and assembly at equilibrium, as opposed to the majority of existing solution-based methods. Together with future improvements in terms of assays and technological performance, MP is likely to provide mechanistic details of complex biomolecular processes., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships that may be considered as potential competing interests. Philipp Kukura reports a relationship with Refeyn Ltd. that includes: board membership, consulting or advisory, and equity or stocks., (Copyright © 2022 The Authors. Published by Elsevier Ltd.. All rights reserved.)

There are ∼10 30 possible intermediates on the assembly path from hepatitis B capsid protein dimers to the 120-dimer capsid. If every intermediate was tested, assembly would often get stuck in an entropic trap and essentially every capsid would follow a unique assembly path. Yet, capsids assemble rapidly with minimal trapped intermediates, a realization of the Levinthal paradox. To understand the fundamental mechanisms of capsid assembly, it is critical to resolve the early stages of the reaction. We have used time-resolved small angle X-ray scattering, which is sensitive to solute size and shape and has millisecond temporal resolution. Scattering curves were fit to a thermodynamically curated library of assembly intermediates, using the principle of maximum entropy. Maximum entropy also provides a physical rationale for the selection of species. We found that the capsid assembly pathway was exquisitely sensitive to initial assembly conditions. With the mildest conditions tested, the reaction appeared to be two-state from dimer to 120-dimer capsid with some dimers-of-dimers and trimers-of-dimers. In slightly more aggressive conditions, we observed transient accumulation of a decamer-of-dimers and the appearance of 90-dimer capsids. In conditions where there is measurable kinetic trapping, we found that highly diverse early intermediates accumulated within a fraction of a second and propagated into long-lived kinetically trapped states (≥90-mer). In all cases, intermediates between 35 and 90 subunits did not accumulate. These results are consistent with the presence of low barrier paths that connect early and late intermediates and direct the ultimate assembly path to late intermediates where assembly can be paused.

Understanding viral assembly pathways is of critical importance to biology, medicine, and nanotechology. Here, we study the assembly path of a system with various structures, the simian vacuolating virus 40 (SV40) polymorphs. We simulate the templated assembly process of VP1 pentamers, which are the constituents of SV40, into icosahedal shells made of N = 12 pentamers ( T = 1). The simulations include connections formed between pentamers by C-terminal flexible lateral units, termed here "C-terminal ligands", which are shown to control assembly behavior and shell dynamics. The model also incorporates electrostatic attractions between the N-terminal peptide strands (ligands) and the negatively charged cargo, allowing for agreement with experiments of RNA templated assembly at various pH and ionic conditions. During viral assembly, pentamers bound to any template increase its effective size due to the length and flexibility of the C-terminal ligands, which can connect to other VP1 pentamers and recruit them to a partially completed capsid. All closed shells formed other than the T = 1 feature the ability to dynamically rearrange and are thus termed "pseudo-closed". The N = 13 shell can even spontaneously "self-correct" by losing a pentamer and become a T = 1 capsid when the template size fluctuates. Bound pentamers recruiting additional pentamers to dynamically rearranging capsids allow closed shells to continue growing via the pseudo-closed growth mechanism, for which experimental evidence already exists. Overall, we show that the C-terminal ligands control the dynamic assembly paths of SV40 polymorphs.

Viruses are remarkable self-assembled nanobiomaterial-based machines, exposed to a wide range of pH values. Extreme pH values can induce dramatic structural changes, critical for the function of the virus nanoparticles, including assembly and genome uncoating. Tuning cargo-capsid interactions is essential for designing virus-based delivery systems. Here we show how pH controls the structure and activity of wild-type simian virus 40 (wtSV40) and the interplay between its cargo and capsid. Using cryo-TEM and solution X-ray scattering, we found that wtSV40 was stable between pH 5.5 and 9, and only slightly swelled with increasing pH. At pH 3, the particles aggregated, while capsid protein pentamers continued to coat the virus cargo but lost their positional correlations. Infectivity was only partly lost after the particles were returned to pH 7. At pH 10 or higher, the particles were unstable, lost their infectivity, and disassembled. Using time-resolved experiments we discovered that disassembly began by swelling of the particles, poking a hole in the capsid through which the genetic cargo escaped, followed by a slight shrinking of the capsids and complete disassembly. These findings provide insight into the fundamental intermolecular forces, essential for SV40 function, and for designing virus-based nanobiomaterials, including delivery systems and antiviral drugs.

For many viruses, capsids (biological nanoparticles) assemble to protect genetic material and dissociate to release their cargo. To understand these contradictory properties, we analyzed capsid assembly for hepatitis B virus; an endemic pathogen with an icosahedral, 120-homodimer capsid. We used solution X-ray scattering to examine trapped and equilibrated assembly reactions. To fit experimental results, we generated a library of distinct intermediates, selected by umbrella sampling of Monte Carlo simulations. The number of possible capsid intermediates is immense, ∼10 30 , yet assembly reactions are rapid and completed with high fidelity. If the huge number of possible intermediates were actually present, maximum entropy analysis shows that assembly reactions would be blocked by an entropic barrier, resulting in incomplete nanoparticles. When an energetic term was applied to select the stable species that dominated the reaction mixture, we found only a few hundred intermediates, mapping out a narrow path through the immense reaction landscape. This is a solution to a viral application of the Levinthal paradox. With the correct energetic term, the match between predicted intermediates and scattering data was striking. The grand canonical free energy landscape for assembly, calibrated by our experimental results, supports a detailed analysis of this complex reaction. There is a narrow range of energies that supports on-path assembly. If association energy is too weak or too strong, progressively more intermediates will be entropically blocked, spilling into paths leading to dissociation or trapped incomplete nanoparticles, respectively. These results are relevant to many viruses and provide a basis for simplifying assembly models and identifying new targets for antiviral intervention. They provide a basis for understanding and designing biological and abiological self-assembly reactions.

Hepadnaviruses are hepatotropic enveloped DNA viruses with an icosahedral capsid. Hepatitis B virus (HBV) causes chronic infection in an estimated 240 million people; woodchuck hepatitis virus (WHV), an HBV homologue, has been an important model system for drug development. The dimeric capsid protein (Cp) has multiple functions during the viral life cycle and thus has become an important target for a new generation of antivirals. Purified HBV and WHV Cp spontaneously assemble into 120-dimer capsids. Though they have 65% identity, WHV Cp has error-prone assembly with stronger protein-protein association. We have taken advantage of the differences in assemblies to investigate the basis of assembly regulation. We determined the structures of the WHV capsid to 4.5-Å resolution by cryo-electron microscopy (cryo-EM) and of the WHV Cp dimer to 2.9-Å resolution by crystallography and examined the biophysical properties of the dimer. We found, in dimer, that the subdomain that makes protein-protein interactions is partially disordered and rotated 21° from its position in capsid. This subdomain is susceptible to proteolysis, consistent with local disorder. WHV assembly shows similar susceptibility to HBV antiviral molecules, suggesting that HBV assembly follows similar transitions. These data show that there is an entropic cost for assembly that is compensated for by the energetic gain of burying hydrophobic interprotein contacts. We propose a series of stages in assembly that incorporate a disorder-to-order transition and structural shifts. We suggest that a cascade of structural changes may be a common mechanism for regulating high-fidelity capsid assembly in HBV and other viruses. IMPORTANCE Virus capsids assemble spontaneously with surprisingly high fidelity. This requires strict geometry and a narrow range of association energies for these protein-protein interactions. It was hypothesized that requiring subunits to undergo a conformational change to become assembly active could regulate assembly by creating an energetic barrier and attenuating association. We found that woodchuck hepatitis virus capsid protein undergoes structural transitions between its dimeric and its 120-dimer capsid states. It is likely that the closely related hepatitis B virus capsid protein undergoes similar structural changes, which has implications for drug design. Regulation of assembly by structural transition may be a common mechanism for many viruses., (Copyright © 2019 American Society for Microbiology.)

This paper presents the computer program D+ (https://scholars.huji.ac.il/uriraviv/book/d-0), where the reciprocal-grid (RG) algorithm is implemented. D+ efficiently computes, at high-resolution, the X-ray scattering curves from complex structures that are isotropically distributed in random orientations in solution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures (containing over 100 protein subunits), a hybrid method can be used to avoid numerical artifacts. In the hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. This article describes how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a Protein Data Bank file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+ . A Python wrapper (https://scholars.huji.ac.il/uriraviv/book/python-api) is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, a large number of tests are presented. The results of D+ are compared with those of other programs when possible, and the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number is demonstrated. D+ and its source code are freely available for academic users and developers (https://bitbucket.org/uriraviv/public-dplus/src/master/).

Multivalent ions affect the structure and organization of virus nanoparticles. Wild-type simian virus 40 (wt SV40) is a nonenveloped virus belonging to the polyomavirus family, whose external diameter is 48.4 nm. Calcium ions and disulfide bonds are involved in the stabilization of its capsid and are playing a role in its assembly and disassembly pathways. Using solution small-angle X-ray scattering (SAXS), we found that the volume of wt SV40 swelled by about 17% when both of its calcium ions were chelated by ethylene glycol-bis(2-aminoethylether)- N , N , N ', N '-tetraacetic acid and its disulfide bonds were reduced by dithiothreitol. By applying osmotic stress, the swelling could be reversed. DNA-containing virus-like particles behaved in a similar way. The results provide insight into the structural role of calcium ions and disulfide bonds in holding the capsid proteins in compact conformation., Competing Interests: The authors declare no competing financial interest.

Exposure of a protein to cosolutes, like denaturants, changes its folding equilibrium. To determine the ensemble of protein conformations at equilibrium, in the presence of weakly interacting cosolutes, we present a two-stage analysis of solution X-ray scattering data. In the first stage, Guinier analysis and Kratky plot revealed information about the compactness and flexibility of the protein. In the second stage, elastic network contact model and coarse-grained normal mode analysis were used to generate an ensemble of conformations. The scattering curves of the conformations were computed and fitted to the measured scattering curves to get insights into the dominating folding states at equilibrium. Urea and guanidine hydrochloride (GuHCl) behaved as preferentially included weakly interacting cosolutes and induced denaturation of hen egg-white lysozyme, which served as our test case. The computed models adequately fit the data and gave ensembles of conformations that were consistent with our measurements. The analysis suggests that in the presence of urea, lysozyme retained its compactness and assumed molten globule characteristics, whereas in the presence of GuHCl lysozyme adopted random coiled conformations. Interestingly, no equilibrium intermediate states were observed in both urea and GuHCl., Competing Interests: The authors declare no competing financial interest.

Crystallization is a fundamental and ubiquitous process that is well understood in the case of atoms or small molecules, but its outcome is still hard to predict in the case of nanoparticles or macromolecular complexes. Controlling the organization of virus nanoparticles into a variety of 3D supramolecular architectures is often done by multivalent ions and is of great interest for biomedical applications such as drug or gene delivery and biosensing, as well as for bionanomaterials and catalysis. In this paper, we show that slow dialysis, over several hours, of wild-type Simian Virus 40 (wt SV40) nanoparticle solution against salt solutions containing MgCl 2 , with or without added NaCl, results in wt SV40 nanoparticles arranged in a body cubic center crystal structure with Im3m space group, as a thermodynamic product, in coexistence with soluble wt SV40 nanoparticles. The nanoparticle crystals formed above a critical MgCl 2 concentrations. Reentrant melting and resolubilization of the virus nanoparticles took place when the MgCl 2 concentrations passed a second threshold. Using synchrotron solution X-ray scattering we determined the structures and the mass fraction of the soluble and crystal phases as a function of MgCl 2 and NaCl concentrations. A thermodynamic model, which balances the chemical potentials of the Mg 2+ ions in each of the possible states, explains our observations. The model reveals the mechanism of both the crystallization and the reentrant melting and resolubilization and shows that counterion entropy is the main driving force for both processes.

In many biochemical processes large biomolecular assemblies play important roles. X-ray scattering is a label-free bulk method that can probe the structure of large self-assembled complexes in solution. As we demonstrate in this paper, solution X-ray scattering can measure complex supramolecular assemblies at high sensitivity and resolution. At high resolution, however, data analysis of larger complexes is computationally demanding. We present an efficient method to compute the scattering curves from complex structures over a wide range of scattering angles. In our computational method, structures are defined as hierarchical trees in which repeating subunits are docked into their assembly symmetries, describing the manner subunits repeat in the structure (in other words, the locations and orientations of the repeating subunits). The amplitude of the assembly is calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the grids of larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures, we developed a hybrid method that sums grids of smaller subunits in order to avoid numerical artifacts. We developed protocols for obtaining high-resolution solution X-ray scattering data from taxol-free microtubules at a wide range of scattering angles. We then validated our method by adequately modeling these high-resolution data. The higher speed and accuracy of our method, over existing methods, is demonstrated for smaller structures: short microtubule and tobacco mosaic virus. Our algorithm may be integrated into various structure prediction computational tools, simulations, and theoretical models, and provide means for testing their predicted structural model, by calculating the expected X-ray scattering curve and comparing with experimental data.

Using small-angle X-ray scattering, we determined the three-dimensional packing architecture of the minichromosome confined within the SV40 virus. In solution, the minichromosome, composed of closed circular dsDNA complexed in nucleosomes, was shown to be structurally similar to cellular chromatin. In contrast, we find a unique organization of the nanometrically encapsidated chromatin, whereby minichromosomal density is somewhat higher at the center of the capsid and decreases towards the walls. This organization is in excellent agreement with a coarse-grained computer model, accounting for tethered nucleosomal interactions under viral capsid confinement. With analogy to confined liquid crystals, but contrary to the solenoid structure of cellular chromatin, our simulations indicate that the nucleosomes within the capsid lack orientational order. Nucleosomes in the layer adjacent to the capsid wall, however, align with the boundary, thereby inducing a 'molten droplet' state of the chromatin. These findings indicate that nucleosomal interactions suffice to predict the genome organization in polyomavirus capsids and underscore the adaptable nature of the eukaryotic chromatin architecture to nanoscale confinement.

Remarkably, uniform virus-like particles self-assemble in a process that appears to follow a rapid kinetic mechanism. The mechanisms by which spherical viruses assemble from hundreds of capsid proteins around nucleic acid, however, are yet unresolved. Using time-resolved small-angle X-ray scattering (TR-SAXS), we have been able to directly visualize SV40 VP1 pentamers encapsidating short RNA molecules (500mers). This assembly process yields T = 1 icosahedral particles comprised of 12 pentamers and one RNA molecule. The reaction is nearly one-third complete within 35 ms, following a two-state kinetic process with no detectable intermediates. Theoretical analysis of kinetics, using a master equation, shows that the assembly process nucleates at the RNA and continues by a cascade of elongation reactions in which one VP1 pentamer is added at a time, with a rate of approximately 10(9) M(-1) s(-1). The reaction is highly robust and faster than the predicted diffusion limit. The emerging molecular mechanism, which appears to be general to viruses that assemble around nucleic acids, implicates long-ranged electrostatic interactions. The model proposes that the growing nucleo-protein complex acts as an electrostatic antenna that attracts other capsid subunits for the encapsidation process.

It is well-known that phospholipids in aqueous environment self-assemble into lamellar structures with a repeat distance governed by the interactions between them. Yet, the understanding of these interactions is incomplete. In this paper, we study the effect of temperature on the interlamellar interactions between dipolar membranes. Using solution small-angle X-ray scattering (SAXS), we measured the repeat distance between 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) bilayers at different temperatures and osmotic stresses. We found that when no pressure is applied the lamellar repeat distance, D, decreases and then increases with increasing temperature. As the osmotic stress increases, D decreases with temperature and then increases to a limited extent, until at sufficiently high pressure D decreases with temperature in all the examined range. We then reconstructed experimentally the equation of state and fit it with a modified interaction model that takes into account the temperature dependence of the fluctuation term. Finally, we showed how the thickness of DLPC membranes decreases with temperature.

Like-charged solid interfaces repel and separate from one another as much as possible. Charged interfaces composed of self-assembled charged-molecules such as lipids or proteins are ubiquitous. The present study shows that although charged lipid-membranes are sufficiently rigid, in order to swell as much as possible, they deviate markedly from the behavior of typical like-charged solids when diluted below a critical concentration (ca. 15 wt %). Unexpectedly, they swell into lamellar structures with spacing that is up to four times shorter than the layers should assume (if filling the entire available space). This process is reversible with respect to changing the lipid concentration. Additionally, the research shows that, although the repulsion between charged interfaces increases with temperature, like-charged membranes, remarkably, condense with increasing temperature. This effect is also shown to be reversible. Our findings hold for a wide range of conditions including varying membrane charge density, bending rigidity, salt concentration, and conditions of typical living systems. We attribute the limited swelling and condensation of the net repulsive interfaces to their self-assembled character. Unlike solids, membranes can rearrange to gain an effective entropic attraction, which increases with temperature and compensates for the work required for condensing the bilayers. Our findings provide new insight into the thermodynamics and self-organization of like-charged interfaces composed of self-assembled molecules such as charged biomaterials and supramolecular assemblies that are widely found in synthetic and natural constructs.

Interactions between charged and neutral self-assembled phospholipid membranes are well understood and take into account temperature dependence. Yet, the manner in which the structure of the membrane is affected by temperature was hardly studied. Here we study the effect of temperature on the thickness, area per lipid, and volume per lipid of charged membranes. Two types of membranes were studied: membranes composed of charged lipids and dipolar (neutral) membranes that adsorbed divalent cations and became charged. Small-angle X-ray scattering data demonstrate that the thickness of charged membranes decreases with temperature. Wide-angle X-ray scattering data show that the area per headgroup increases with temperature. Intrinsically charged membranes linearly thin with temperature, whereas neutral membranes that adsorb divalent ions and become charged show an exponential decrease of their thickness. The data indicate that, on average, the tails shorten as the temperature rises. We attribute this behavior to higher lipid tail entropy and to the weaker electrostatic screening of the charged headgroups, by their counterions, at elevated temperatures. The latter effect leads to stronger electrostatic repulsion between the charged headgroups that increases the area per headgroup and decreases the bilayer thickness.

In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ∼10 M(-1). One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The ion-dipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The ion-dipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications., (© 2011 American Chemical Society)