Where Do the Ions Reside in a Highly Charged Droplet?

Aqueous droplets in atmospheric and electrosprayed aerosols are charged due to presence of multiple ionic species. We examine the ion spatial distribution and the surface electric field in aqueous charged nanodrops by using atomistic modeling and analytical theory. We find that in nanoscopic liquid drops the concentration of simple ions is higher in the outer droplet shells, reduces gradually toward the drop center, and dies-off toward the vapor-droplet interface. The behavior of the ion spatial distribution is supported by a general analytical theory that takes into account a fluctuating droplet interface, an effective screening length of the charges and the finite size of a solvated ion. We compute the electric potential and the electric field near the droplet surface using a multipole expansion. We emphasize the significance of the fluctuations of the normal component of the electric field in ion evaporation via the Born model. In the presence of a highly charged peptide, we find that the peptide is situated mainly in the droplet interior and occasionally near the droplet surface. The simple ions are mainly near the droplet surface. The study provides insight into droplet chemistry and electrospray ionization mass spectrometry findings.

Strengths and Weaknesses of Molecular Simulations of Electrosprayed Droplets.

The origin and the magnitude of the charge in a macroion are critical questions in mass spectrometry analysis coupled to electrospray and other ionization techniques that transfer analytes from the bulk solution into the gaseous phase via droplets. In many circumstances, it is the later stages of the existence of a macroion in the containing solvent drop before the detection that determines the final charge state. Experimental characterization of small (with linear dimensions of several nanometers) and short-lived droplets is quite challenging. Molecular simulations in principle may provide insight exactly in this challenging for experiments regime. We discuss the strengths and weaknesses of the molecular modeling of electrosprayed droplets using molecular dynamics. We illustrate the limitations of the molecular modeling in the analysis of large macroions and specifically proteins away from their native states. Graphical Abstract ᅟ.

Interplay of self-association and conformational flexibility in regulating protein function.

Many functional roles have been attributed to homodimers, the most common mode of protein self-association, notably in the regulation of enzymes, ion channels, transporters and transcription factors. Here we review findings that offer new insights into the different roles conformational flexibility plays in regulating homodimer function. Intertwined homodimers of two-domain proteins and their related family members display significant conformational flexibility, which translates into concerted motion between structural domains. This flexibility enables the corresponding proteins to regulate function across family members by modulating the spatial positions of key recognition surfaces of individual domains, to either maintain subunit interfaces, alter them or break them altogether, leading to a variety of functional consequences. Many proteins may exist as monomers but carry out their biological function as homodimers or higher-order oligomers. We present early evidence that in such systems homodimer formation primes the protein for its functional role. It does so by inducing elevated mobility in protein regions corresponding to the binding epitopes of functionally important ligands. In some systems this process acts as an allosteric response elicited by the self-association reaction itself. Our analysis furthermore suggests that the induced extra mobility likely facilitates ligand binding through the mechanism of conformational selection.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Macroion-Solvent Interactions in Charged Droplets.

Macroion-droplet interactions play a critical role in many settings such as ionization techniques of samples in mass spectrometry analysis and atmospheric aerosols. The droplets under investigation are composed of a polar solvent, primarily water, a charged macroion, and, possibly, buffer ions. We present highlights of our research on the relation between the charge state of a macroion and the droplet morphologies. We have determined that, depending on the charge on the macroion and certain macroscopic properties of the solvent, such as its dielectric constant and surface tension, a droplet may obtain striking conformations such as droplets with extruded tails, "pearl-necklace" conformations, and multipoint "star" shapes. The shapes of the droplet containing the macroion influence the charging mechanism of the macroion in a reciprocal manner. Understanding of the macroion-droplet interactions plays a central role in explaining the origin and the magnitude of the charge in spectra obtained in electrospray ionization mass spectrometry experiments and in controlling the stability of complexes of nucleic acids and proteins in droplets.

When droplets become stars: charged dielectric droplets beyond the Rayleigh limit.

When a nano-drop comprising a single spherical central ion and dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. In contrast, conducting droplets, will undergo fission. Here we report combined atomistic molecular dynamics and continuum modelling study of star formation of droplets that contain a highly charged ion. We assume that in the continuum model the dielectric response is linear. In this linear continuum model, which is an extension of Rayleigh model, the energy of the drop is comprised of terms analogous to those in Rayleigh model, which are surface energy and electrostatic energy of dielectric droplet charged by a central point charge. We present the stability analysis of the continuum model to determine the threshold of instability. Indeed we find that the model accounts well for the onset of the instabilities. Molecular dynamics show that the number of points of the star-shaped nano-drops depends only on the surface tension, dielectric constant and size of the droplet, and on the magnitude of the charge of the central ion, but not on its sign. Intuitively, it is expected that when a spherical dielectric drop becomes unstable it would transform into a non-spherical finite shape of the same volume as the initial spherical shape with the point charge located in the drop interior. To test whether the extended Rayleigh model can account for the observed droplet shapes, we performed numerical simulations of the linear continuum model. Contrary to the expectations, the simulations of the extended Rayleigh model does not reproduce the stable star shapes found in the atomistic simulations, not even when we account for the bending rigidity and spontaneous curvature of the surface. We argue that the assumption that the dielectric response is linear breaks down if the droplet surface approaches the central macro-ion, where the electric field strength is such that dielectric saturation sets in. We envisage that for certain solvents, these stars could be made permanent by cross-linking, opening the way to the production of a novel class of highly-non-convex colloids.

Advances in Modeling the Stability of Noncovalent Complexes in Charged Droplets with Applications in Electrospray Ionization-MS Experiments.

Electrospray ionization mass spectrometry is used extensively to measure the equilibrium constant of noncovalent complexes. In this Perspective, we attempt to present an accessible introduction to computational methodologies that can be applied to determine the stability of weak noncovalent complexes in their journey from bulk solution into the gaseous state. We demonstrate the usage of the methods on two typical examples of noncovalent complexes drawn from a broad class of nucleic acids and transient protein complexes found in aqueous droplets. We conclude that this new emerging direction in the use of simulations can lead to estimates of equilibrium constant corrections due to complex dissociation in the carrier droplet and finding of agents that may stabilize the protein interfaces.

Interplay of buried histidine protonation and protein stability in prion misfolding.

Misofolding of mammalian prion proteins (PrP) is believed to be the cause of a group of rare and fatal neurodegenerative diseases. Despite intense scrutiny however, the mechanism of the misfolding reaction remains unclear. We perform nuclear Magnetic Resonance and thermodynamic stability measurements on the C-terminal domains (residues 90-231) of two PrP variants exhibiting different pH-induced susceptibilities to aggregation: the susceptible hamster prion (GHaPrP) and its less susceptible rabbit homolog (RaPrP). The pKa of histidines in these domains are determined from titration experiments, and proton-exchange rates are measured at pH 5 and pH 7. A single buried highly conserved histidine, H187/H186 in GHaPrP/RaPrP, exhibited a markedly down shifted pKa ~5 for both proteins. However, noticeably larger pH-induced shifts in exchange rates occur for GHaPrP versus RaPrP. Analysis of the data indicates that protonation of the buried histidine destabilizes both PrP variants, but produces a more drastic effect in the less stable GHaPrP. This interpretation is supported by urea denaturation experiments performed on both PrP variants at neutral and low pH, and correlates with the difference in disease susceptibility of the two species, as expected from the documented linkage between destabilization of the folded state and formation of misfolded and aggregated species.

The Landscape of Intertwined Associations in Homooligomeric Proteins.

We present an overview of the full repertoire of intertwined associations in homooligomeric proteins. This overview summarizes recent findings on the different categories of intertwined associations in known protein structures, their assembly modes, the properties of their interfaces, and their structural plasticity. Furthermore, the current body of knowledge on the so-called three-dimensional domain-swapped systems is reexamined in the context of the wider landscape of intertwined homooligomers, with a particular focus on the mechanistic aspects that underpin intertwined self-association processes in proteins. Insights gained from this integrated overview into the physical and biological roles of intertwining are highlighted.

Variation of droplet acidity during evaporation.

Variation of acidity and associated chemical changes of macromolecules in evaporating droplets is of central importance in electrosprayed aerosols. We study changes in acidity during evolution of a droplet that is composed of solvent and a charge binding macromolecule. We analyze the acidity of the droplet using analytical theory and stochastic modeling. We derive a universal relation for the minimum pH of a droplet in the presence of a protein and the results are confirmed by the stochastic modeling of ubiquitin and lysozyme at varying values of pH. We establish that in acidic droplets, once the number of solvated charges reaches the macroion charge, the further droplet evaporation, counter-intuitively, reduces the number of charges on the macromolecule and increases the droplet pH.

Intertwined associations in structures of homooligomeric proteins.

Intertwined homo-oligomers are complexes comprising identical protein subunits, where small segments or compact protein substructures (domains) are exchanged between the subunits. Using a formal definition of intertwined homo-oligomers, we survey the Protein Data Bank for all such complexes. Results show that intertwining occurs in 13,442 (24%) of all surveyed structures. A majority (∼72%) exchanges one contiguous chain segment of varying length. Another ∼10%, exchange structural domains, and the remaining ∼20% display complex intertwining topologies. Smaller proteins are more often intertwined, and intertwining is dominant in solution homodimers. These findings and analyses of various properties of the major category of intertwined complexes, their interfaces and quaternary context, support the physiological role of intertwining in promoting homooligomer stability. Furthermore, the number of different intertwining modes observed in families of related proteins is limited, and likely specific to the protein fold. These findings yield unique insights into the role of intertwining in homomeric association.

Classification of the ejection mechanisms of charged macromolecules from liquid droplets.

The relation between the charge state of a macromolecule and its ejection mechanism from droplets is one of the important questions in electrospray ionization methods. In this article, effects of solvent-solute interaction on the manifestation of the charge induced instability in a droplet are examined. We studied the instabilities in a prototype system of a droplet comprised of charged poly(ethylene glycol) and methanol, acetonitrile, and water solvents. We observed instances of three, previously only conjectured, [S. Consta, J. Phys. Chem. B 114, 5263 (2010)] mechanisms of macroion ejection. The mechanism of ejection of charged macroion in methanol is reminiscent of "pearl" model in polymer physics. In acetonitrile droplets, the instability manifests through formation of solvent spines around the solvated macroion. In water, we find that the macroion is ejected from the droplet through contiguous extrusion of a part of the chain. The difference in the morphology of the instabilities is attributed to the interplay between forces arising from the macroion solvation energy and the surface energy of the droplet interface. For the contiguous extrusion of a charged macromolecule from a droplet, we demonstrate that the proposed mechanism leads to ejection of the macromolecule from droplets with sizes well below the Rayleigh limit. The ejected macromolecule may hold charge significantly higher than that suggested by prevailing theories. The simulations reveal new mechanisms of macroion evaporation that differ from conventional charge residue model and ion evaporation mechanisms.

Manifestations of charge induced instability in droplets effected by charged macromolecules.

Ion-release processes from droplets that contain excess charge are of central importance in determining the charge-state distributions of macromolecules in electrospray ionization methods. We develop an analytical theory to describe the mechanism of contiguous extrusion of a charged macromolecule from a droplet. We find that the universal parameter determining the system behavior is the ratio of solvation energy per unit length to the square of the ion charge density per unit length. Systems with the same value of the ratio will follow the same path in the course of droplet evaporation. The analytical model is compared with molecular simulations of charged polyethylene glycol macroion in aqueous droplets, and the results are in excellent agreement.

Multiple replica repulsion technique for efficient conformational sampling of biological systems.

Here, we propose a technique for sampling complex molecular systems with many degrees of freedom. The technique, termed "multiple replica repulsion" (MRR), does not suffer from poor scaling with the number of degrees of freedom associated with common replica exchange procedures and does not require sampling at high temperatures. The algorithm involves creation of multiple copies (replicas) of the system, which interact with one another through a repulsive potential that can be applied to the system as a whole or to portions of it. The proposed scheme prevents oversampling of the most populated states and provides accurate descriptions of conformational perturbations typically associated with sampling ground-state energy wells. The performance of MRR is illustrated for three systems of increasing complexity. A two-dimensional toy potential surface is used to probe the sampling efficiency as a function of key parameters of the procedure. MRR simulations of the Met-enkephalin pentapeptide, and the 76-residue protein ubiquitin, performed in presence of explicit water molecules and totaling 32 ns each, investigate the ability of MRR to characterize the conformational landscape of the peptide, and the protein native basin, respectively. Results obtained for the enkephalin peptide reflect more closely the extensive conformational flexibility of this peptide than previously reported simulations. Those obtained for ubiquitin show that conformational ensembles sampled by MRR largely encompass structural fluctuations relevant to biological recognition, which occur on the microsecond timescale, or are observed in crystal structures of ubiquitin complexes with other proteins. MRR thus emerges as a very promising simple and versatile technique for modeling the structural plasticity of complex biological systems.

Mechanism and energy landscape of domain swapping in the B1 domain of protein G.

Three-dimensional domain swapping has emerged as a ubiquitous process for homo-oligomer formation in many unrelated proteins, but the molecular mechanism of this process is still poorly understood. Here we present a mechanism for the swapping reaction in the B1 domain of the immunoglobulin G binding protein from group G of Streptococcus (GB1). This is a particularly attractive system for investigating the swapping process, as the swapped dimer formed by the quadruple mutant (L5V/F30V/Y33F/A34F) of GB1 was recently shown to exist in equilibrium with a monomer-like conformation over time scales of minutes. According to our mechanism, swapping in GB1 starts from the C-terminus of the polypeptide chain and progresses by exchanging an increasing portion of the chains until a stable conformational state is reached. This exchange process does not involve unfolding. Rather, the conformational changes of individual monomers and their association are tightly coupled to minimize solvent exposure and maximize the total number of native contacts at all times, thereby closely approximating the minimum energy path of the reaction. Using detailed atomic descriptions, we compute the complete free-energy profiles of the exchange reaction for the GB1 quadruple mutant that forms swapped dimers and for the wild-type protein, which is monomeric. In both GB1 forms, intermediates sample a surprisingly wide range of nearly isoenergetic association modes and hinge conformations, indicating that the exchange reaction is a non-specific process akin to encounter complex formation where the amino acid sequence plays a marginal role. The main role of the mutations in the swapping process is to destabilize the GB1 monomer state, while stabilizing the swapped dimer conformation, with non-native intersubunit interactions, fostered by mutant side chains, contributing significantly to this stabilization. Our findings are rationalized in terms of a generic swapping mechanism that involves the association of activated molecular species, and it is argued that a similar mechanism may apply to swapping in other protein systems.

Membrane curvature alters the activation kinetics of the epithelial Na+/H+ exchanger, NHE3.

The epithelial Na(+)/H(+) exchanger, NHE3, was found to activate slowly following an acute cytosolic acidification. The sigmoidal course of activation could not be explained by the conventional two-state model, which postulates that activation results from protonation of an allosteric modifier site. Instead, mathematical modeling predicted the existence of three distinct states of the exchanger: two different inactive states plus an active form. The interconversion of the inactive states is rapid and dependent on pH, whereas the conversion between the second inactive state and the active conformation is slow and pH-independent but subject to regulation by other stimuli. Accordingly, exposure of epithelial cells to hypoosmolar solutions activated NHE3 by accelerating this latter transition. The number of surface-exposed exchangers and their association with the cytoskeleton were not affected by hypoosmolarity. Instead, NHE3 is activated by the membrane deformation, a result of cell swelling. This was suggested by the stimulatory effects of amphiphiles that induce a comparable positive (convex) deformation of the membrane. We conclude that NHE3 exists in multiple states and that different physiological parameters control the transitions between them.

LAMP proteins are required for fusion of lysosomes with phagosomes.

Lysosome-associated membrane proteins 1 and 2 (LAMP-1 and LAMP-2) are delivered to phagosomes during the maturation process. We used cells from LAMP-deficient mice to analyze the role of these proteins in phagosome maturation. Macrophages from LAMP-1- or LAMP-2-deficient mice displayed normal fusion of lysosomes with phagosomes. Because ablation of both the lamp-1 and lamp-2 genes yields an embryonic-lethal phenotype, we were unable to study macrophages from double knockouts. Instead, we reconstituted phagocytosis in murine embryonic fibroblasts (MEFs) by transfection of FcgammaIIA receptors. Phagosomes formed by FcgammaIIA-transfected MEFs obtained from LAMP-1- or LAMP-2- deficient mice acquired lysosomal markers. Remarkably, although FcgammaIIA-transfected MEFs from double-deficient mice ingested particles normally, phagosomal maturation was arrested. LAMP-1 and LAMP-2 double-deficient phagosomes acquired Rab5 and accumulated phosphatidylinositol 3-phosphate, but failed to recruit Rab7 and did not fuse with lysosomes. We attribute the deficiency to impaired organellar motility along microtubules. Time-lapse cinematography revealed that late endosomes/lysosomes as well as phagosomes lacking LAMP-1 and LAMP-2 had reduced ability to move toward the microtubule-organizing center, likely precluding their interaction with each other.