Variation of Surface Propensity of Halides with Droplet Size and Temperature: The Planar Interface Limit.

The radial number density profiles of halide and alkali ions in aqueous clusters with equimolar radius ≲1.4 nm, which correspond to ≲255 H2O molecules, have been extensively studied by computations. However, the surface abundance of Cl-, Br-, and I- relative to the bulk interior in these smaller clusters may not be representative of the larger systems. Indeed, here we show that the larger the cluster is, the lower the relative surface abundance of chaotropic halides is. In droplets with an equimolar radius of ≈2.45 nm, which corresponds to ≈2000 H2O molecules, the polarizable halides show a clear number density maximum in the droplet's bulk-like interior. A similar pattern is observed in simulations of the aqueous planar interface with halide salts at room temperature. At elevated temperature the surface propensity of Cl- decreases gradually, while that of I- is partially preserved. The change in the chaotropic halide location at higher temperatures than the room temperature may considerably affect photochemical reactivity in atmospheric aerosols, vapor-liquid nucleation and growth mechanisms, and salt crystallization via solvent evaporation. We argue that the commonly used approach of nullifying parameters in a force field in order to find the factors that determine the ion location does not provide transferable insight into other force fields.

Limitations of Atomistic Molecular Dynamics to Reveal Ejection of Proteins from Charged Nanodroplets.

Atomistic molecular dynamics (MD) is frequently used to unravel the mechanisms of macroion release from electrosprayed droplets. However, atomistic MD is currently feasible for only the smallest window of droplet sizes appearing at the end steps of a droplet's lifetime. The relevance of the observations made to the actual droplet evolution, which is much longer than the simulated sizes, has not been addressed yet in the literature. Here, we perform a systematic study of the desolvation mechanisms of poly(ethylene glycol) (PEG), protonated peptides of different compositions, and proteins, to (a) obtain insight into the charging mechanism of macromolecules in larger droplets than those that are currently amenable to atomistic MD and (b) examine whether currently used atomistic MD modeling can establish the extrusion mechanism of proteins from droplets. To mimic larger droplets that are not amenable to MD modeling, we scale down the systems, by simulating a large droplet size relative to the macromolecule. MD of PEG charging reveals that, above a critical droplet size, ions are available near the backbone of the macromolecule, but charging occurs only transiently by transfer of ions from the solvent to the macroion, while below the critical size, the capture of the ion from PEG has a lifetime sufficiently long for the extrusion of a charged PEG from the aqueous droplet. This is the first report of the role of droplet curvature in the relation between macroion conformation and charging. Simulations of protonated peptides with a high degree of hydrophobicity show that partial extrusion of a peptide from the droplet surface is rare relative to desolvation by drying-out. Different from what has been presented in the literature, we argue that atomistic MD simulations have not sufficiently established the extrusion mechanism of proteins from droplets and their charging mechanism. We also argue that release of highly charged proteins can occur at an earlier stage of a droplet's lifetime than predicted by atomistic MD. In this earlier stage, we emphasize the key role of jets emanating from a droplet at the point of charge-induced instability in the release of proteins.

Atomistic Modeling of Jet Formation in Charged Droplets.

The first atomistic simulations that reveal the mechanism of Rayleigh fission are presented. It is demonstrated that simple ion or macroion ejection takes place through droplet deformation from a spherical into a distinct "tear" shape that contains a conical protrusion. We assert that the latter state is a free-energy minimum along an order parameter that measures the degree of droplet asphericity. The charged droplet's long-time evolution proceeds by alternating between the two minima above and below the critical value that are reached through solvent evaporation and ion ejection, respectively. For the first time, this mechanism allows one to explain the nature of the progeny droplets and the percentage of charge lost during fission. The cone half angle is estimated and found to be in good agreement with the value predicted from the solution of the electrostatic equation for the dielectric liquid. It is found that the conical deformation is independent of the effect of electrohydrodynamic forces reported in experiments. Contrary to the experimental observations of two diametrically opposite jets for droplets suspended in the electric field, we find that a single jet is formed at the Rayleigh limit. The study provides insight into the mechanism of capture of a macroion in jets appearing in electrospray ionization mass spectrometry (ESI-MS) experiments and may explain the tolerance of the ESI-MS spectrum to salt contamination of the sample.

Salt Enrichment and Dynamics in the Interface of Supercooled Aqueous Droplets.

The interconversion reaction of NaCl between the contact-ion pair (CIP) and the solvent-separated ion pair (SSIP) as well as the free-ion state in cold droplets has not yet been investigated. We report direct computational evidence that the lower is the temperature, the closer to the surface the ion interconversion reaction takes place. In supercooled droplets the enrichment of the subsurface in salt becomes more evident. The stability of the SSIP relative to the CIP increases as the ion-pairing is transferred toward the droplet's outer layers. In the free-ion state, where the ions diffuse independently in the solution, the number density of Cl- shows a broad maximum in the interior in addition to the well-known maximum in the surface. In the study of the reaction dynamics, we find a weak coupling between the interionic NaCl distance reaction coordinate and the solvent degrees of freedom, which contrasts with the diffusive crossing of the free energy barrier found in bulk solution modeling. The H2O self-diffusion coefficient is found to be at least an order of magnitude larger than that in the bulk solution. We propose to exploit the enhanced surface ion concentration at low temperature to eliminate salts from droplets in native mass spectrometry ionization methods.

Conical Shape Fluctuations Determine the Rate of Ion Evaporation and the Emitted Cluster Size Distribution from Multicharged Droplets.

The ion evaporation mechanism (IEM) is perceived to be a major pathway for disintegration of multi-ion charged droplets found in atmospheric and sprayed aerosols. However, the precise mechanism of IEM and the effect of the nature of the ions in the emitted cluster size distribution have not yet been established despite its broad use in mass spectrometry and atmospheric chemistry over the past half century. Here, we present a systematic study of the emitted ion cluster distribution in relation to their spatial distribution in the parent droplet using atomistic modeling. It is found that in the parent droplet, multiple kosmotropic and weakly polarizable chaotropic ions (Cs+) are buried deeper within the droplet than polarizable chaotropic ions (Cl-, I-). This differentiation in the ion location is only captured by a polarizable model. It is demonstrated that the emitted cluster size distribution is determined by dynamic conical deformations and not by the equilibrium ion depth within the parent droplet as the IEM models assume. Critical factors that determine the cluster size distribution such as the charge sign asymmetry that have not been considered in models and in experiments are presented. We argue that the existing IEM analytical models do not establish a clear difference between IEM and Rayleigh fission. We propose a shift in the existing view for IEM from the equilibrium properties of the parent droplet to the chemistry in the conical shape fluctuations that serve as the centers for ion emission. Consequently, chemistry in the conical fluctuations may also be a key element to explain charge states of macromolecules in mass spectrometry and may have potential applications in catalysis due to the electric field in the conical region.

Low Density Interior in Supercooled Aqueous Nanodroplets Expels Ions to the Subsurface.

The interaction between water and ions within droplets plays a key role in the chemical reactivity of atmospheric and man-made aerosols. Here we report direct computational evidence that in supercooled aqueous nanodroplets a lower density core of tetrahedrally coordinated water expels the cosmotropic ions to the denser and more disordered subsurface. In contrast, at room temperature, depending on the nature of the ion, the radial distribution in the droplet core is nearly uniform or elevated toward the center. We analyze the spatial distribution of a single ion in terms of a reference electrostatic model. The energy of the system in the analytical model is expressed as the sum of the electrostatic and surface energy of a deformable droplet. The model predicts that the ion is subject to a harmonic potential centered at the droplet's center of mass. We name this effect "electrostatic confinement". The model's predictions are consistent with the simulation findings for a single ion at room temperature but not at supercooling. We anticipate this study to be the starting point for investigating the structure of supercooled (electro)sprayed droplets that are used to preserve the conformations of macromolecules originating from the bulk solution.

Relation between Ejection Mechanism and Ion Abundance in the Electric Double Layer of Droplets.

Charged droplets have been associated with distinct chemical reactivity. It is assumed that the composition of the surface layer plays a critical role in enhancing the reaction rates in the droplets relative to their bulk solution counterparts. We use atomistic modeling to relate the localization of ions in the surface layer to their ejection propensity. We find that ion ejection takes place via a two-stage process. First, a conical protrusion emerges as a result of a global droplet deformation that is insensitive to the locations of the single ions. The ions are subsequently ejected as they enter the conical regions. The study provides mechanistic insight into the ion-evaporation mechanism, which can be used to revise the commonly used ion-evaporation models. We argue that atomistic molecular dynamics simulations of minute nanodrops do not sufficiently distinguish the ion-evaporation mechanism from a Rayleigh fission. We explain mass spectrometry data on the charge state of small globular proteins and the existence of supercharged droplet states that have been detected in experiments.

Molecular Characterization of the Surface Excess Charge Layer in Droplets.

The surface excess charge layer (SECL) in droplets has often been associated with distinct chemistry. We examine the effect of the nature of ions in the composition and structure of SECL by using molecular dynamics. We find that in the presence of simple ions the thickness of SECL is invariant not only with respect to droplet size but also with respect to the nature of the ions. In the presence of simple ions, this layer has a thickness of ∼1.5-1.7 nm but in the presence of macroions it may extend to ∼2.0 nm. The proportion of ions contained in SECL depends on the nature of the ions and the droplet size. For the same droplet size, I- and model H3O+ ions show considerably higher concentration than Na+ and Cl- ions. We identify the maximum ion concentration region, which, in nanodrops, may partially overlap with SECL. As the relative shape fluctuations decrease when microdrop size is approached, the overlap between SECL and maximum ion concentration region increases. We suggest the extension of the bilayer droplet structure assumed in the equilibrium partitioning model of Enke to include the maximum ion concentration region that may not coincide with SECL in nanodrops. We compute the ion concentrations in SECL, which are those that should enter the kinetic equation in the ion-evaporation mechanism, instead of the overall drop ion concentration that has been used.

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.

Effect of the chemical environment of the DNA guanine quadruplex on the free energy of binding of Na and K ions.

Guanine quadruplex (G-quadruplex) structures play a vital role in stabilizing the DNA genome and in protecting healthy cells from transforming into cancer cells. The structural stability of G-quadruplexes is greatly enhanced by the binding of monovalent cations such as Na+ or K+ into the interior axial channel. We computationally study the free energy of binding of Na+ and K+ ions to two intramolecular G-quadruplexes that differ considerably in their degree of rigidity and the presence or absence of terminal nucleotides. The goal of our study is two-fold. On the one hand, we study the free energy of binding every ion, which complements the experimental findings that report the average free energy for replacing Na+ with K+ ions. On the other hand, we examine the role of the G-quadruplex structure in the binding free energy. In the study, we employ all-atom molecular dynamics simulations and the alchemical transformation method for the computation of the free energies. To compare the cation-dependent contribution to the structural stability of G-quadruplexes, we use a two-step approach to calculate the individual free energy difference ΔG of binding two Na+ and two K+ to two G-quadruplexes: the unimolecular DNA d[T2GT2(G3T)3] (Protein Data Bank ID 2M4P) and the human telomeric DNA d[AGGG(TTAGGG)3] (PDB ID 1KF1). In contrast to the experimental studies that estimate the average free energy of binding, we find a varying difference of approximately 2-9 kcal/mol between the free energy contribution of binding the first and second cation, Na+ or K+. Furthermore, we found that the free energy of binding K+ is not affected by the chemical nature of the two quadruplexes. By contrast, Na+ showed dependency on the G-quadruplex structure; the relatively small size allows Na+ to explore larger configurational space than K+. Numerical results presented here may offer reference values for future design of cationic drug-like ligands that replace the metal ions in G-quadruplexes.

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.

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.

"Star" morphologies of charged nanodrops comprised of conformational isomers.

We study the spatial distribution of conformational isomers surrounding a central macroion in a charged droplet with linear dimensions in the nanometer range. Dimethyl carbonate and formic acid are selected as typical solvents that undergo isomerization and a charged buckyball (C60) is selected as a representative example of a macroion. The study is performed by atomistic molecular dynamics simulations. We find that when the charge of the buckyball is above a threshold value, it induces the formation of concentric shells of different conformational isomers surrounding the macroion. The presence of layers with different dielectric properties necessitates the use of different state equations for the solvent polarization in each layer. We find that at a high charge state of the buckyball, the nearest layer to the macroion comprises the conformers with the highest dipole moment. The interface of the outer layers of conformers is characterized by "ray"-forming structures of the higher dielectric constant isomers penetrating into the layer of the lowest dielectric constant isomers. For high values of the solvent dielectric constant, the charged droplet acquires a "star"-like global shape. We demonstrate that these distinct droplet structures are a manifestation of charge-induced instability. We describe this simulation-based phenomenology by an analytical theory that supports this conclusion. The findings suggest new experimental research venues that may explore the reactivity and assembly of molecules within regions of different dielectric properties in droplets.

What factors determine the stability of a weak protein-protein interaction in a charged aqueous droplet?

Maintaining the interface of a weak transient protein complex transferred from bulk solution to the gaseous state via evaporating droplets is a critical question in the detection of the complex association (dissociation) constant by using electrospray ionization mass spectrometry (ESI-MS). Here we explore the factors that may affect the stability of a protein-protein interaction (PPI) using atomistic molecular dynamics (MD) modelling of a complex of ubiquitin (Ub) and the ubiquitin-associated domain (UbA) (RCSB PDB code ) and a non-covalent complex of diubiquitin (RCSB PDB code ) in aqueous droplets. A general method is presented to determine the protonation states of the complexes we investigate in particular, and that of a protein in general, under various pH conditions that an evaporating droplet acquires due to its change in size. We find that the combination of high temperature and high charge states of the protein complexes may destabilize the interface by creating new interfaces instead of a direct rupture of the initial stable interface. We provide evidence that highly charged protein complexes are found in droplets that form conical extrusions of the solvent on the surface due to charge-induced instability. This distinct droplet morphology leads to a higher solvent evaporation rate that assists in transferring the complex in the gaseous state without dissociation. The conical solvent protrusions expose on the droplet surface certain amino acids that otherwise would be solvated in a droplet with the protein complex of low charge states. The new vapor-protein interface does not have a direct effect on the stability of the PPI. A common way in experiments to stabilize the protein complexes in droplets is to reduce the protonation state of the proteins. Here we find that weakly bound protein complexes even at high protonation states can be stabilized by the presence of a small number of counterions, without affecting the protonation state of the protein. Our findings may provide guiding principles in ESI-MS experiments to stabilize weak transient PPIs.

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.

Charging and Release Mechanisms of Flexible Macromolecules in Droplets.

We study systematically the charging and release mechanisms of a flexible macromolecule, modeled by poly(ethylene glycol) (PEG), in a droplet by using molecular dynamics simulations. We compare how PEG is solvated and charged by sodium Na+ ions in a droplet of water (H2O), acetonitrile (MeCN), and their mixtures. Initially, we examine the location and the conformation of the macromolecule in a droplet bearing no net charge. It is revealed that the presence of charge carriers do not affect the location of PEG in aqueous and MeCN droplets compared with that in the neutral droplets, but the location of the macromolecule and the droplet size do affect the PEG conformation. PEG is charged on the surface of a sodiated aqueous droplet that is found close to the Rayleigh limit. Its charging is coupled to the extrusion mechanism, where PEG segments leave the droplet once they coordinate a Na+ ion or in a correlated motion with Na+ ions. In contrast, as PEG resides in the interior of a MeCN droplet, it is sodiated inside the droplet. The compact macro-ion transitions through partially unwound states to an extended conformation, a process occurring during the final stage of desolvation and in the presence of only a handful of MeCN molecules. For charged H2O/MeCN droplets, the sodiation of PEG is determined by the H2O component, reflecting its slower evaporation and preference over MeCN for solvating Na+ ions. We use the simulation data to construct an analytical model that suggests that the droplet surface electric field may play a role in the macro-ion-droplet interactions that lead to the extrusion of the macro-ion. This study provides the first evidence of the effect of the surface electric field by using atomistic simulations. Graphical Abstract ᅟ.

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.

Stability of a Transient Protein Complex in a Charged Aqueous Droplet with Variable pH.

Electrospray ionization mass spectrometry (ESI-MS) has the potential to become a high-throughput robust experimental method for the detection of protein-protein equilibrium constants. Poorly understood processes that affect the stability of weak noncovalent protein complexes in the intervening droplet environment are a significant factor that precludes the advancement of the method. We use molecular dynamics to study the stability of a ubiquitin and ubiquitin-associated domain complex (RCSB PDB code 2MRO ) in an aqueous droplet with changing size and charge concentration. We present evidence that a weak protein complex changes conformation and may dissociate in shrinking droplets. Then, the droplets containing these dissociated proteins divide. Our findings suggest that in some cases ESI-MS does not measure the correct association constants. The study intends to stimulate research for systematic development of experimental protocols that stabilize weakly bound protein interfaces in droplets.

Characterization of "Star" Droplet Morphologies Induced by Charged Macromolecules.

"Star" morphologies of charged liquid droplets are distinct droplet conformations that, for a certain charge squared to volume ratio, have lower energy than their spherically shaped analogues. For these shapes to appear, the charge should be carried by a single ionic species. A typical example of a charge carrier that we employ in this study is a fully charged double-stranded oligodeoxynucleotide (dsDNA) in an aqueous and an acetonitrile droplet. We characterize the structure and dynamics of the star-shaped droplets. We find that by increasing the charge squared to volume ratio, the droplet evolves from spherical to "spiky" shapes, by first passing from droplet sizes that undergo enhanced shape fluctuations relative to those of the larger spherical droplets. These fluctuations mark the onset of the instability. We also find that in the spiky droplet, the orientation of the solvent molecules in the first shell about the dsDNA is very close to that in the bulk solution. However, this orientation is substantially different farther away from the dsDNA. With regards to dynamics, the motion of the spikes is reflected in the autocorrelation functions of rotationally invariant order parameters that show a damped oscillator form of decay, indicative of the elastic motion of the spikes. We compare the formation of spikes with that of the ferrofluids and the dielectric materials in an electric field, and we conclude that they represent a different entity that deserves its own characterization. The study provides insight into the manner in which the charge distribution may give rise to well-controlled droplet morphologies and calls for experiments in this direction.