MacroionâSolvent Interactions in Charged Droplets - The Journal of

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Macroion−Solvent Interactions in Charged Droplets Styliani Consta,*,† Myong In Oh,† Mahmoud Sharawy,† and Anatoly Malevanets‡ †

Department of Chemistry, The University of Western Ontario, London, Ontario, Canada N6A 5B7 Department of Electrical and Computer Engineering, The University of University of Western Ontario, London, Ontario, Canada N6A 5B9

‡

ABSTRACT: 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.

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INTRODUCTION The study of the interactions of simple ions with solvent molecules in finite sized systems has been a highly active area of research in computations1−7 and experiments8,9,9−12 over several decades. The considerable volume of research in this field is outside of the scope of this article; thus, our referenced articles are only indicative and certainly constitute a small sample. On the other end, macroion−solvent interactions in clusters are relatively less studied by spectroscopic and computational methods. This Review Article discusses the general features of macorion−droplet interactions that we have identified by molecular simulations13 and continuum modeling.14 Examples of macroions that are studied experimentally and computationally are proteins,15−17 nucleic acids,18−21 their complexes22 and assemblies,23 as well as colloidal particles.24 The size of these clusters is determined by the size of the macroion, which may be substantial relative to the amount of the solvent (a typical value of a protein radius is 2 nm) and the surrounding solvent layers. We will use the term “droplet” for a macroion−solvent finite-sized system in order to distinguish it from the clusters of several tens of solvent molecules. The macroions are multiply charged, but additionally, droplets may also contain other simpler ions. Droplets with macroions are often generated by electrospray ionization (ESI),25,26 or they may be naturally found in atmospheric aerosols that contain biological material.27 We note here that the electrosprayed droplets have much higher charge than the atmospheric aerosols.28 This Review draws its examples from droplet−macorion interactions that have applications in ESI-MS.25,29 ESI operates © XXXX American Chemical Society

by spraying a solution composed of solvent, macroions, buffer, and possibly other additives into a chamber where there is an electric potential difference.26 The spraying creates a mist of highly charged droplets, which are composed of solvent, macroions, and other simpler ions. The droplets undergo a cascade of solvent evaporation and disintegration events30−32 that finally lead to desolvated macroions. The dried macroions may be analyzed or selected by mass spectrometry (MS). The key question in the ESI-MS experiments is the origin and the magnitude of the charge state of a macroion that is detected in the gaseous state by MS.33 It has been demonstrated that the droplet environment plays a decisive role in the charging of the macroions;34−36 therefore, it is critical to understand the macroion−droplet interactions. Another important question in the use of ESI-MS is how to stabilize the protein complexes and assemblies as they are transferred from the bulk solution into the gaseous state for MS analysis.17,23,37 The droplet environment where these complex structures reside may affect their interactions and, therefore, alter the measured ratio of bound to unbound species relative to that in the bulk solution.16,17,19,23,37−43 The insight obtained on the subject of the macroion−droplet interactions may also find applications in other ionization methods44−47 such as thermospray,48 sonic spray,49 and matrix-assisted ionization.50,51 Exploration of the role of the droplet environment in the charging mechanism of macroions has its roots in the pioneering works of J. Fenn and Received: February 8, 2018 Revised: March 15, 2018 Published: March 21, 2018 A

DOI: 10.1021/acs.jpca.8b01404 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Classes of stable droplet-chain conformations. The drawn macromolecule is only a schematic representation of a macroion in a droplet. The solvent boundary is shown by the dashed line. The polarization charge on the droplet surface is shown by positive signs when the macroion is positively charged. (a) Gradual expulsion of a linear macroion from a droplet. This process occurs below the Rayleigh limit. (b) “Pearl-necklace” droplet conformation. The charge within each “pearl” is below the Rayleigh limit. (c) Formation of conical protrusions of the solvent surrounding a macroion. (d) Atomistically modeled extrusion of poly(ethylene glycol) from an aqueous droplet65 that corresponds to (a). The blue spheres represent Na+ ions, and the red dots represent H2O molecules. (e) Droplet comprised of approximately 1200 water molecules and 2LJL15+.13,66 Each spherical lobe is found below the Rayleigh limit, as in the schematic (b). (f) Droplet comprised of water (red dots), a negatively charged 20mer dsDNA (ds stands for double-stranded), and Na+ ions (purple spheres).67 It corresponds to schematic (c). Details are described in the text.

co-workers,36,52−54 who devoted considerable efforts to devise possible mechanisms that could explain the MS observations. Unfortunately, Fenn’s intuitive guesses on the mechanism of charge transfer on a macroion lacked direct evidence at the time. As the complexity of the systems studied today by MS increases,55,56 the question of the origin of the charge state of the macroion is still in the forefront of MS and gaseous ions research. In this article we highlight our contributions in advancing the understanding of macroion−droplet interactions. Because the droplets are multiply charged, the first fundamental question to be addressed is that of the condition of droplet stability. The problem of the stability of a charged conducting droplet was first studied theoretically by Lord Rayleigh.32,57,58 In the Rayleigh model, the energy of a droplet (E) in a macroscopic (continuum) description is expressed as the sum of the surface energy (Esurf = σA) and the electrostatic

(

1

E = σA +

1 QΦ 2

(1)

where Q, σ, A, and Φ are the droplet charge, the surface tension coefficient, the surface area, and the electrostatic potential on the surface, respectively. The model considers that the droplet undergoes small shape fluctuations, where the volume is maintained constant but the surface area may vary. The Rayleigh model gives rise to a dimensionless parameter, which is called the fissility parameter (X), defined as X=

Q2 64π 2σε0R3

(2)

A linear stability analysis of the model shows that if X is less than unity then the system is stable. At X = 1, the droplet is at the Rayleigh limit. Above the Rayleigh limit (X > 1), the spherical droplet is unstable; therefore, it has to change into another form. In conducting droplets, the instability is

)

energy Eelec = 2 Q Φ

B


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fields that we have used are the CHARMM General Force Field79,80 for modeling of the ubiquitin−ubiquitin associated domain protein complex (RCSB PDB81 code 2MRO82) and the noncovalent complex of diubiquitin (RCSB PDB code 2PEA83) in TIP3P water. We used the TIP3P water model due to the fact that the OPLS-AA and CHARMM models for the other molecules in the system were developed to work well with TIP3P. PEG has been modeled with a united atom OPLS model65 and with all-atom OPLS73,74 with consistent findings. The simulations were performed using the molecular simulation packages NAMD,84 CHARMM,85 and GROMACS86,87 and with our own codes.14,88 The systems were simulated by molecular dynamics (MD)89 using the Verlet90 and velocity Verlet91 algorithms. The time step used for our simulations was 0.5 or 1.0 fs. We performed both constanttemperature and constant-energy simulations. We performed constant-temperature simulations using either Nosé−Hoover dynamics92,93 or the Lowe−Andersen thermostat.94 Equilibrium MD runs of a droplet of specific size were performed by placing the droplets in a spherical cavity. The cavity is a spherical potential that confines evaporating molecules within a volume. The radius of the cavity should accommodate the largest fluctuation of the droplet and also the dimensions of a possibly extruded linear macroion. Water evaporation from the droplet in the vacant space of the cavity establishes an equilibrium vapor pressure. The size of the spherical cavity and the temperature determine the average size of the connected droplet. Typical sizes of systems that we studied with equilibrium calculations were aqueous droplets composed of a few thousand water molecules and the macroion, which corresponds to a droplet radius of approximately 3 nm. In equilibrium simulations, we studied a sequence of droplet sizes. A major challenge in the simulations of droplets with macroions is to determine the charge state of a macroion. Details of the method have been presented elsewhere.72,75,88 Here, we only outline the method. The maximum charge state of a droplet is determined by the Rayleigh limit (X = 1 in eq 2). The Rayleigh limit indicates that different size droplets have different acidity. The study of the sodiation or lithiation of PEG is facilitated by the fact that the transfer of sodium ions between the solvent and the PEG is modeled adequately using the molecular mechanics force fields. However, the charge state of proteins or of their complexes is determined by protonation. If the simple charge carriers, such as the commonly used ammonium acetate, were to participate in protonation reactions, then the simulations would require an approach that involves the quantum mechanical modeling of protonation reactions. Modeling of the protonation reactions is not feasible for most of the systems except for small clusters containing a handful of molecules using quantum mechanical methods95,96 or of larger systems using quantum mechanics/molecular mechanics methods. To address this challenge, we introduce a multiscale modeling approach. In the macroscopic level, we use the charge balance equation in the droplet that equates the Rayleigh limit charge (X = 1 in eq 2) of the entire droplet to the sum of the charge of the protein and those of the other ions present such as ammonium and acetate. The concentration of every species involved in this equation is a function of pH. For the specific pH, the charge state of the protein is determined. In the next stage, we perform MD simulations starting from different initial conditions of the droplet−protein system within the cavity. This methodology can be used to determine (a) possible dissociation of protein complexes transferred from the

manifested by the droplet fission. Rayleigh theory provides a remarkably accurate prediction for the charge-induced instability of droplets containing free ions,59−61 even for nanoscopic droplets.62−64 The Rayleigh criterion has been extended for a droplet with a central nonfissile charge.14 In this model the energy expression has the same terms (surface energy and electrostatic energy) as the Rayleigh model, but the electrostatic energy is that of a dielectric droplet. Above a threshold value of the chargesquared-to-volume ratio, the instability is manifested by droplet deformations (without fission). We will discuss this model in the following sections. We have found that the macroion−droplet interactions lead to classes of stable droplet shapes13,65,68,69 (Figure 1) above and below the Rayleigh limit of the corresponding spherical conducting57 and dielectric droplet.14 Figure 1a−c shows schematic representations of the droplet−macroion shapes while Figure 1d,e shows examples from atomistic simulations where these morphologies have been realized. Below the Rayleigh limit, a droplet is spherical. Figure 1a shows that a linear macroion may extrude from this spherical droplet13,65,69,70 for certain values of the ratio of solvation energy over charge density-squared69 of the linear chain. Figure 1b shows that the solvent may solvate a macroion by forming a “pearl-necklace” conformation. The charge within each subdroplet (“pearl”) is below the Rayleigh limit. The interplay among several factors, which are (i) the tendency of the solvent to form spherical droplets in order to minimize the surface energy, (ii) the constraint that the charge of each subdroplet should be below the Rayleigh limit, (iii) the solvation energy of the chain, and (iv) the length of the chain and the distribution of charge, may lead to the formation of two subdroplets at the termini of a chain,68 as shown in Figure 1e, more than two subdroplets along the chain backbone, or a single droplet in the interior of a chain. The subdroplets do not have to attach to each other. The segment of the chains that are exposed to the vapor is still partially solvated. Figure 1c shows a “spiky” droplet shape that evolves from a spherical unstable droplet. The spiky droplet appears after the droplet crosses an instability point that exhibits enhanced shape fluctuations.71 Examples of systems where we have encountered the spiky shapes are proteins72 and nucleic acids.67 Figure 1f shows an example of a negatively charged dsDNA with Na+ counterions in an aqueous droplet. We will analyze the interactions that lead to these shapes later in the discussion.

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MODELING AND SIMULATION METHODS Equilibrium Simulations. Charged droplets composed of various one-component solvents such as water,13,64,65 methanol,73 acetonitrile,74 or their mixtures74 have been simulated. The charge carriers in the droplets are macroions and other simple ions. We have studied linear macroions such as poly(ethylene glycol) (PEG),65 model linear macroions,69 a highly charged poly histidine,13 dsDNA (double-stranded DNA),67 or compact macroions such as complexes of proteins.72,75 The solvents and the macroions are modeled by fully atomistic molecular models using established force fields. The water molecules are often represented by the TIP3P model76 (three-site transferable intermolecular potential). The PEG, acetonitrile, and methanol molecules have been modeled using the OPLS-AA (Optimized Potential for Liquid Simulations-All Atom)77,78 force field, where all hydrogen atoms are explicitly represented.74 Other examples of force C


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The Journal of Physical Chemistry A bulk solution into the gaseous state and (b) possible changes in the conformations of the macroions in their transfer from bulk solution into the gaseous state. The time of the MD simulations inside of the cavity is determined by a cutoff time. This cutoff time is determined from a separate set of simulations of the evaporation rate of the droplet of the specific size. Depending on the competition of the evaporation and dissociation rates, one may find the change in the ratio of the bound and unbound species. The details of how we estimate this ratio can be found in refs 72 and 75. This multiscale method can be applied to find out whether a macromolecule changes its conformation during the droplet lifetime. The equilibrium runs in a cavity allow one to sample the conformational changes of a macroion and, therefore, determine whether the conformation will change within the cutoff time (determined by solvent evaporation) after which the droplet will have a substantially different size. Nonequilibrium Simulations. Nonequilibrium simulations intend to explore complex dynamic processes that occur in the evaporating droplets. 65 The exact experimental conditions of temperature and pressure under which the evaporation and desolvation of the gas-phase ions in nanoscopic droplets take place are still unknown.97,98 For this reason, one may consider comparing simulations at constantenergy and constant-temperature conditions. The simulation protocol in terms of the setup of the MD simulations is the same as that described in the equilibrium simulations. In the nonequilibrium simulations, the droplet is placed in vacuo. Constant-temperature simulations are usually carried out by coupling the integration algorithm to a heat bath. The temperature control in our simulations is performed either by Nosé−Hoover dynamics or the Lowe−Andersen thermostat.94 When constant-energy simulations are performed, the connected part of the droplet cools down because of solvent evaporation. Here we note that the constant energy simulation in vacuo represents better the experimental conditions at the latest stage of droplet desolvation under conditions of very low pressure, where the droplet is not constantly thermalized due to collisions with the gas.

simulation runs lead to consistent findings in terms of the charge state of PEG and its extrusion mechanism from a droplet.64,65,73,102 Therefore, the simulation results are robust with respect to the fine details of the force field. A sequence of steps in the extrusion mechanism of sodiated PEG is described in Figure 4. We note that a noncharged PEG in a neutral H2O droplet lies on its surface. The sequence of simulation snapshots shown in Figure 4 started from a droplet of approximately 6500 H2O molecules with 16 Na+ ions and a PEG64 (Figure 2a). These system parameters correspond to a

RESULTS AND DISCUSSION Extrusion of a Linear Macroion from a Droplet. Droplet−linear macroion interactions may lead to extrusion of a macroion from a droplet. We carried out detailed investigation of the extrusion mechanism of the sodiated or lithiated PEG. We note that the simulations that we have performed for the extrusion of macroions from droplets are for sizes of systems that contain up to approximately 7000 H2O molecules, which corresponds to an approximate radius of 4 nm. We elected to study the droplet−sodiated PEG interactions for several reasons: (a) PEG−ion interactions have been extensively studied in MS experiments;29,36,99−101 therefore, we can compare the final charge of PEG bare of solvent to MS measurements.64,65,102 The comparison between our findings and the charge states from MS experiments indicates that the interactions of PEG with water and Na+ can be modeled reliably with the existing force fields65,73,102 (b) The sodiation (lithiation) of PEG has the advantage that it can be directly observed in molecular mechanics simulations relative to the protonation of proteins that may require sophisticated QM/MM (quantum mechanics/molecular mechanics) modeling methods. (c) We have used different molecular models such as united atom and all-atom modeling to represent the methylene groups of PEG. All of the

charge-squared-to-volume ratio of the droplet considerably below the Rayleigh limit. The release of the sodiated PEG from an aqueous droplet is the result of a series of chemical events. The sodiation of PEG does not occur in any droplet size but in a droplet size that reaches a critical Na+ concentration. This concentration is approximately that of 20 Na+ ions in a droplet of 6500 H2O molecules, as was found in our previous simulations,73 or higher. In Figure 2b, the first sodiation occurs when 16 Na+ ions remain in approximately 3500 H2O molecules. When a Na+ ion is captured by the PEG, it becomes coordinated by the oxygen sites of the monomers (Figure 2b). The PEG segment that encloses the Na+ ion exposes its hydrophobic methylene group to the aqueous surface, resulting in a weaker interaction with the solvent molecules present at the droplet surface. Once one sodiated segment of PEG is released, it remains extended at an equilibrium position. To a first approximation, this position is determined by the balance between the solvation interactions between the attached segment of PEG to the droplet surface and the electrostatic repulsion between the extruded sodiated segment of PEG and the rest of the charged droplet.74 This cycle of sodiation and partial releases repeats until PEG64 is charged with four Na+ ions, and then, it is completely detached from the parent droplet. The sodiated segment can easily detach from the

Figure 2. Typical snapshots of PEG64 sodiation and ejection from a charged aqueous droplet. The Na+ ions are represented by blue spheres. The numbers of water molecules remaining in the main droplet are shown. The numbers of remaining Na+ ions in the droplet are (a) 16, (b) 15, (c) 14, and (d) 12. The duration of the process shown is approximately 65 ns at T = 300 K.

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D


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The Journal of Physical Chemistry A droplet, as shown in Figure 2c,d. Our previous simulations65,102 and analytical theory70 have shown that, depending on the amount of remaining charges in the droplet, a sodiated PEG may entirely leave the droplet or stay partially attached to the droplet and dry out. The radius of the droplet remains approximately constant throughout the sodiation and release of PEG. As shown in Figure 2b−d, only ∼8% of the water molecules evaporated during the charge and release of the sodiated PEG. In summary, the mechanism that we observe by the example of PEG is the following: The PEG sodiates in a stepwise process, and the sodiated segments are released faster (due to lower activation energy) than the water-solvated Na+ ion release. The study of the charging of PEG reveals a charging-induced extrusion mechanism, which we have abbreviated as the CI-EM.70 We expect that linear macromolecules with the solvation properties of PEG will also be released via an extrusion mechanism. We have also examined several other macromolecules in order to find the general patterns in the droplet shapes. In 2010, we examined a completely charged polyhistidine in an aqueous droplet.13 We found that when the charge of the corresponding spherical droplet is above the Rayleigh limit, the system stabilizes by forming conical extrusions on its surface, as shown in Figure 1c. We will discuss this spiky form of droplet shape in the following sections. The study of a possible extrusion mechanism of a protein from a droplet is a very challenging question. Differently from PEG, which is a flexible macroion with welldefined conformation on the droplet surface74 or interior,74 proteins may have a certain structure in an aqueous solution even when they are found in highly charge states. Thus, there are two obstacles to tackle in the study: (a) the force fields have not been optimized to account for the various protein conformations in the various charge states besides the native charge state and (b) the sampling of the protein conformations in solution (droplet or bulk) is very demanding at best. The droplet environment has different acidity from that of the parent bulk solution; therefore, the protonation state of the protein may change within the droplet88 depending on the dynamics of the various processes (proton transfer reactions, solvent and ion evaporation). Whether the protein conformation will change within the droplet lifetime is another challenging question. To address this question, one possible way is to implement the multiscale methodology that we devised to study the stability of protein complexes.72,75 In a simplified model that does not consider the deprotonation of a protein, the conformation of a protein may change dramatically in a small droplet due to a charge-induced instability that may cause the extension of the chain. This process is similar to the dissociation of the DNA67 or that of the fission of a droplet due to a high charge. We think that a very likely solvent distribution along the backbone of a charged protein is that where each termini of the extended protein is surrounded by a droplet (Figure 1e). This conformation also appears in highly charged PEG in methanol; therefore, it is a general solvation pattern68 that may appear in general in the solvation of a charged finite rod of a certain length. An extended conformation of a protein like that of 2LJL15+ may result from a more compact protein that may undergo charge-induced unfolding in a droplet. Analytical Modeling of the Extrusion of a Chain from a Droplet. When droplets undergo small fluctuations from the spherical shape, they are accessible to analytical modeling using methods of electrostatics. Here we present an analytical model

that we have developed to obtain insight into the location of a macorion in a droplet. We emphasize here that in the analytical model the strength of the interactions between the droplet and the macroion are variable. Finally, we determine the extrusion mechanism for a range of macroion−droplet interactions. Details of the models are found in refs 69 and 70. In the model, we express the total energy of the macromolecule (Etotal) as the sum of the electrostatic energy (Eelec) and the solvation energy Etotal = Eelec + (L − λ)v0

(3)

where L is the length of the macromolecule, λ is the length of the extruded segment of the macromolecule from the surface of the droplet, and v0 is the solvation energy per unit length of the macromolecule. A schematic illustration that shows the parameters of the model is shown in Figure 4a. The justification for the solvation energy term is presented in ref 70. We note here that, unlike the Rayleigh model, in the presented model the surface tension is not included in the expression of the energy. The omission of the surface energy from the model is justified by the fact that simulations of charged PEG in aqueous droplets65,69,102 revealed that in the course of droplet evaporation the solvated segment carries charge smaller than that given by the Rayleigh formula; therefore, the droplet remains spherical. In the equations that follows, we consider that the charge of the droplet is carried by the macroion only. The generalization of the model when there is additional free charge is described in ref 70. The electrostatic energy of a conductor is given in general by Eelec =

∑

1 ϕ′q 2 i i

(4)

where qi denotes the charge of the atomic site i and ϕi′ is the electrostatic potential at the position of the corresponding charge i without that of qi. We evaluate the electrostatic energy of a conducting sphere and a linear charged macromolecule by utilizing the method of image charges.103 In the model, the chain is released from the droplet as a rigid segment. In the electrostatic energy, we take into account the images that are induced by all of the charge distribution along an extruded linear macromolecule. By taking the derivative of the total energy (eq 3) with respect to λ equal to zero finds 4πεv0

R 2R + λ ln + λ R R ζ ⎡L − λ R + λ⎤ λ +⎢ + ln ⎥ ⎣ R R ⎦R + λ

−Bex = −

2

(

∂E total ∂λ

)

= 0 , one

=

(5)

where ζ is the charge density (charge per unit length) of the macroion. Equation 5 dictates two order parameters λ/L and L/R to describe the extrusion of a chain from a droplet. The molecular interactions of the macroion with the droplet are included in the parameter Bex, which is the ratio of the solvation energy to the squared charge density of the macroion. For various macromolecule−droplet interactions, one may build the extrusion path in the λ/L and L/R coordinates. This phase diagram as a function of the two order parameters is shown in Figure 3. The gray region represents the points that correspond to the maxima of Etotal. The curved lines show the path of the extrusion of the macroion from the droplet. E


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mechanisms coupled to droplet evaporation where the droplet shrinks and the macroion emerges from the droplet and (b) extrusion mechanisms where the droplet radius remains approximately constant and the macroion extrudes. These extrusion mechanisms have been described in ref 70.

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MACROIONS SOLVATED IN THE INTERIOR OF A DIELECTRIC DROPLET Linear Electrostatic Model of the Droplet Energy. For a point charge in the interior of a dielectric droplet, one may develop a linear continuum model that will allow for analysis of the stability of a charged dielectric droplet. In this model, we consider a droplet with a fluctuating shape that maintains its volume but may change its surface area. In macroscopic modeling, the energy of a droplet is written as the sum of the electrostatic (Eelec) and the surface energy (Esurf) E = Esurf + Eelec (6)

Figure 3. Phase diagram of the extrusion mechanisms of a chain extrusion from a droplet in the space defined by the degree of extrusion of the chain from a droplet ξ = λ/L (x-axis) and L/R (y-axis) The colored lines represent the various degrees of interactions of the macroion with the droplet as it is expressed in Bex The color coding of the lines is shown by the color bar of the Bex values. The gray region corresponds to maxima of the energy (eq 3) that are found by solving ∂E total = 0. ∂λ

In the analysis that we highlight in the next paragraphs, we find the difference in energy between a spherical droplet and a droplet that deviates from a sphere. The surface energy is expressed as the product of the surface area (A) times the surface tension (σ). The surface is given by

In order to compare the analytical theory with the simulation findings, we used the PEG backbone with assigned charge on the atomic sites. In that way, we could change the charge at will. This modified PEG molecule, denoted as m-PEG, does not keep all of the features of the real PEG. The real PEG resides entirely on the surface of the droplet, while the m-PEG may be found partially solvated inside of the droplet because of its higher charge (shown in Figure 4b). Snapshots included in

ρ(θ , ϕ) = R +

∑

al , mlYl , ml(θ , ϕ) (7)

l > 0, ml

where (θ,ϕ) is the spherical angle, ρ(θ,ϕ) is the distance from the center, Yl,m(θ,ϕ) denote the spherical harmonics functions of rank m and order l, and al,ml are the expansion coefficients. R is the l = 0 term in the expansion of ρ(θ,ϕ) in terms of Yl,m(θ,ϕ). We note that R is not necessarily equal to the radius of the spherical shape. Following several algebraic steps,32 we arrive at the following expression for the surface area A = 4πR2 +

∑ l > 0, ml

|al , ml|2 +

1 2

∑ l > 0, ml

l(l + 1) al , ml|2 (8)

103

Following textbook electrostatics, the electrostatic energy (Ediel) of a linear (polarizable) dielectric with free charge is given by 1 dr D · E Ediel = (9) 2 3 / V

∫

where D is the electric displacement and E is the electric field caused by the free charge. Equation 9 includes the response of the dielectric; therefore, its polarization may involve “stretching” and displacement of the dielectric molecules as we bring the free charge into the dielectric (or the dielectric into the free charge). When a spherical charge is surrounded by a dielectric with dielectric permittivity εI embedded into a dielectric with dielectric permittivity εE, eq 9 yields the energy of the system given by

Figure 4. (a) Schematic illustration that shows the parameters that are used in the analytical model (eq 3) that describes the extrusion of a linear macroion. R is the radius of the droplet, and λ is the length of the extruded segment of the macromolecule from the droplet. The system is a conductor; therefore, the charge is found on its surface, as indicated by the schematic. (b) Aqueous droplet composed of 2400 H2O molecules and an m-PEG48 with charge +7 e. The charge is uniformly distributed along the chain instead of being carried out by Na+ ions. It is noted that the distributed charge along the chain is higher than the maximum charge state of a sodiated (or lithiated) mPEG48. We note here that m-PEG is used as an example of a general macroion where the charge can be varied at will.

Ediel = −

1 2

∫ /V dr (ε E − ε I)E·E0 3

(10)

The difference in energy (δEdiel) (where the energy is composed of the surface energy and the electrostatic energy as written in eq 6) between a spherical shape and a deformed shape to a linear approximation is given by γ δEdiel = ∑ [(l − 1)(l + 2) + 4XS(ε I /ε E , l)]|al ,m|2 2 l > 0, m

Figure 3 show the two states in which the m-PEG can be found, solvated in the interior of the droplet and extruded. The extrusion path follows one of the curved lines, depending on the strength of the interaction between the m-PEG and the aqueous droplet. The gray region indicates an activation barrier. Using this analytical model, we have identified (a) extrusion

(11) F


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The Journal of Physical Chemistry A where S is given by S(ε , l) = (ε − 1)

l(l − 1) − (l + 1)(l + 2) εl + l + 1

(12)

In eq 12, ε = ε /ε . The details of the algebra that leads to eq 11 are described in ref 14. We note here that the electrostatic energy includes the response of the dielectric, therefore, the energy due to solvation. We contrast this equation with eq 3 for a linear chain in a spherical conducting droplet. In eq 3, we separate the electrostatic energy from the solvation energy. Equation 11 holds for any system parameters Q, R, σ for which the linear approximations are valid. In simulations, the onset of instability is marked by enhanced shape fluctuations of the droplet. By comparison with simulations, we have found that eq 11 predicts very well the onset of charge-induced instability14,71 for aqueous droplets. The closeness of the prediction for other solvents is still to be examined. Stable Droplets beyond the Instability Point. When the charge-squared-to-volume ratio of a spherical droplet exceeds a certain value predicted by eq 11, then a spherical droplet becomes unstable. To accommodate the instability, the unstable droplet deforms into a stable nonspherical shape that exhibits conical solvent protrusions on the droplet surface. Examples of a nonfissile macroion is a fully charged nucleic acid67,71 or a charged protein.13 The conical protrusions of the solvent may appear along the backbone of a linear macroion, or they may form a three-dimensional “star” shape when the macroion is spherical. Because of the common features of the spiky shapes regardless of the fine details in the structure of the macroion, we will use here the example of a spherical structureless macroion residing in the center of an aqueous droplet. A collection of typical droplet morphologies in the presence of a central macroion of various charges is shown in Figure 5. The charge of the corresponding spherical droplet is above the Rayleigh limit, and the central charge is nonfissile. Analysis of the structure of these systems has shown that they are composed of a region closest to the central macroion that is characterized by saturation of the polarization of the solvent.14,71 The spikes are formed beyond the saturated core and show an elastic motion.71 To explore the physical origin of the star formations, we have also performed continuum modeling.14 A key question that we address is whether the observed droplet morphology can be explained exclusively on the basis of macroscopic properties of the liquid, such as the dielectric constant, the surface tension, and possibly the bending rigidity and the radius of spontaneous curvature, or the molecular details of the liquid matter.14 In the continuum model, the energy of the drop was expressed exactly like that in eq 6 (as the sum of the surface energy and electrostatic energy). In the model, Esurf = σA and Eelec is given by eq 9. In the computations that we performed, the surface deformations were not linearized differently from the algebraic steps that lead to eq 11. The calculations of the free energy of a deformed droplet were performed by changing the shape using a Monte Carlo method.14 We note that in the continuum model we assume that the dielectric response is linear. This assumption may break down close to the central macroion. However, we think that the findings of the basic model that we are using are not affected by improvements in the expression of the dielectric constant. Our simulations reveal a problem with the linear dielectric continuum model: we find that above the Rayleigh limit the I

E

Figure 5. Typical snapshots of charged aqueous droplets at T = 300 K. All of the droplets are composed of 2148 TIP3P-H2O molecules and have an embedded model spherical ion. The charge at the instability limit for these droplets is Q ≈ 13.9. All of the droplets are charged above the Rayleigh limit.

electrostatic energy tends to decrease as we allow the minimum value of r(θ,ϕ) to go to zero. In every observed case of the system starting from a spherical droplet, we find that the surface evolves into an irregular shape where some r(θ,ϕ) goes to zero (at which point we terminate the simulation). We have not observed any metastable states even close to the boundary of stability of charged droplets. The failure of the linear dielectric continuum model suggests that we cannot reproduce the equilibrium shapes observed in the atomistic simulations on the basis of the surface tension and dielectric constant alone. However, by testing, we found that the presence of a soft core potential provides shapes that are reminiscent of the star shapes. Typical snapshots of the shapes that include the soft-core potential are shown in Figure 6. There are still open questions regarding the continuum modeling of the star-shaped droplets. The fact that these shapes have been found in simulations for a variety of solvents and shapes of the central ions shows that the finding is robust and that it will be also present in macroscopic droplets. The energy components that should enter the macroscopic equations are still to be discovered. Conical protrusions of aqueous droplets have been found by simulations of neutral droplets in an uniform external electric field104,105 and on hydrophilic surfaces with the application of a uniform external electric field.106 In those simulations, the external field is uniform; therefore, the droplet deformations involve the development of two conical protrusions at the end points of an oval-shaped droplet where the major axis is aligned with the electric field. Analysis of the conical protrusions of a droplet in an external electric field is found in the seminal works of G. I. Taylor107 and extension by Ramos and G


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agreement between the de la Mora model and the average charge state of the proteins detected in the positive ion mode. In order to use the Rayleigh limit expression, the model considers that the mass density of the globular protein be the same as that of water, and it also implicitly assumes that the last layer of water surrounding the macroion is uniformly spread on the surface of the protein. Transfer of the charge on the macroion when the last layer of solvent surrounds the macroion may be one of the mechanisms where a globular protein acquires its charge. In our previous research, we have introduced deprotonation of a protein as another possible mechanism that determines the final charge state of a protein.88 We found in the literature that several proteins have been reported with an average charge state higher than that predicted by de la Mora’s model. Examples of such proteins are the PHBH in ref 113, 2PEA in ref 35, and Urease α18β18 and Urease α24β24 in ref 112. Moreover, the maximum charge state of a protein (which is different from the average charge state) is often above the Rayleigh limit of the corresponding aqueous spherical droplet. In our previous studies, we have examined a diubiquitin complex (RCSB PDB code 2PEA83), which has been detected at a charge state of +14 e by using cryogenic ion mobility-MS (cryo-IM-MS).35 The charged 2PEA was formed under native ESI conditions. The relation Zr = 0.078M0.5 predicts a charge state of +10 e for the 2PEA. In simulations that we performed, we showed that the 2PEA at +14 e requires several layers of water in order to become spherical. Therefore, the droplet should have passed via star shapes in the drying process. We simulated the 2PEA in an aqueous droplet of 800 H2O molecules as described in ref 72. Indeed, as shown in Figure 7, we found that the droplet morphology is characterized by conical protrusions of water.

Figure 6. Shapes observed in simulated annealing of droplets with a core stabilizing potential. Panel (a) corresponds to the droplet charge Q = 6e, and panel (b) corresponds to the droplet charge Q = 10e. Details of the computations are found in ref 14.

Castellanos.108 In the systems that we investigate, the electric field is generated by a macroion, which is internal in the droplet, and thus, the field is nonuniform. An evident consequence of that is that we have larger variability in the shapes of the deformed droplets. In a continuum description, in all cases, the energy of the system is the sum of the electrostatic energy and the surface energy. The relation of the conical protrusions that we have found to that of the ferrofluids in a magnetic field109 and to the aformationed works is still to be examined. Effects of the Star-Shaped Morphology. Even though the star-shaped droplets have not been observed experimentally as of yet, we think that they may play a role in determining the macroion charge state in evaporating droplets and that they may be also potentially utilized in material science and catalysis applications. In relation to ESI experiments, it is very likely that spiky structures appear in the transfer of a droplet from the bulk solution into the gaseous state. The question on the origin of the charge states of globular proteins has been discussed over decades in ESI-MS.25,33,36,110−113 Of course, the charge state of a protein can be manipulated by changing the experimental conditions such as the surface tension of the droplets by using different solvents and cosolvents or various buffers. A collection of the most abundant charge state and the maximum charge state of a variety of proteins measured in the positive and a few in the negative ion mode of ESI is presented in Table 1112 of the article of Heck and van den Heuvel. These measurement are made in the Heck laboratory by nanoflow ESI from 50 mM aqueous ammonium acetate at neutral pH. A model proposed by de la Mora36 has often be used to explain the final charge state of a protein that is transferred into the gaseous state by the ESI process. The model assumes that when a droplet comprises the compact macroion and a layer of water surrounding the macroion, the droplet will sustain as many charges as those predicted by the Rayleigh limit. This composition of course occurs in the latest stage of a droplet’s lifetime. The model proposes that in the final stage of solvent evaporation the ions will be transferred on the compact protein. Consequently, the charge on the protein will be equal to the charge predicted by the Rayleigh limit of a liquid droplet of the size of the protein. Using the Rayleigh limit expression (X = 1 in eq 2), de la Mora provided an empirical relation Zr = 0.078M0.5 between the protein charge Zr with its molar mass M. Figure 2 in the article of Heck and van den Heuvel shows good

Figure 7. Typical snapshot showing the star formation of a charged aqueous droplet, comprised of 2PEA in a charge state of +14 e and 833 H2O molecules. The ubiquitin molecules are colored red and blue, and the water molecules are colored transparent green.

The findings suggest two possible mechanisms for the charging of 2PEA. These mechanisms may hold for other proteins as well. The first mechanism that we propose is that 2PEA acquired a charge state of +14 e in a larger droplet88 than that comprised the 2PEA surrounded by a single layer of water. This larger droplet may have also contained co-ions (although unlikely). As the droplet shrinks, co-ions are released and the only ion left in the droplet may be the macroion. We argue that the droplets may be found in stable spiky states without undergoing deprotonation. We think that this may happen because the spikes delay the release of protons for two reasons: (a) the spikes dictate the pathways for ion release but the spikes H


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The Journal of Physical Chemistry A may not extend out from the charged amino acids that may potentially release the protons and (b) the location of the spikes changes via birth and death processes. An alternate mechanism that we propose is that of the protonation of 2PEA in a droplet where 2PEA may be found in a charge state below +14 e with ammonium ions. If solvent evaporation is faster than ion release, the droplet may obtain a transient spiky shape. At this state, the release of simple ions is delayed13 relative to a droplet with only simple ions. The examples of these two mechanisms indicate that the spiky solvent protrusion may play a role in the charging mechanism of the proteins. Another potential application of the star-shaped droplets may be found in material science. The droplet star shapes have the same morphology as branched colloidal nanocrystals.114−116 The fabrication of monodisperse nanocrystal building blocks of complex geometry is a coveted goal in the assembly of functional nanostructures. We think that it is experimentally possible to generate solid highly nonconvex colloids by adjusting the charge state of the central macroion. Once the star structure is stabilized, possibly by polymerization, the central charge can be neutralized with well-established experimental techniques.117

force field (ReaxFF)118 may be a promising approach to this problem. We have proposed that, in a different mechanism from that proposed by de la Mora,36 a globular protein may obtain its final charge state (which is close to the Rayleigh limit) by release of protons from a higher charge state acquired in an earlier stage of the droplet’s lifetime.88 This mechanism has been supported by analytical theory and numerical modeling88 but still needs to be explored in experiments. Another important study would be to compare the solvation of proteins and other macromolecules in a droplet to that in the bulk solution.4,5 It is intriguing that many times in the field of MS the origin of the conformational stability of proteins between the bulk solution and the gaseous state has been attributed to the high dielectric constant of water relative to that of vacuo. It is worth exploring this thought considering that computations report a very low dielectric constant of water on the surface of macroions119 and therefore not a considerable difference between the water dielectric constant and the vacuo. The efforts of many scientists in experiments and computations will soon lead to the understanding of the general mechanisms of macroion charging in a droplet.

CONCLUSIONS Considerable progress has been made using molecular simulations and analytical theory in unraveling the macorion−droplet interactions. These interactions include extrusion of a linear macroion from a droplet, formation of a “pearlnecklace” droplet conformation, and “star”-shaped droplets. These classes are universal for macroions of different levels of complexity ranging from simple macroions to assemblies of proteins. Extrusion of a linear macroion from a droplet has been evidenced for PEG by atomistic simulations and experiments.29,36,54,65 An analytical theory that considers the solvation energy of a macroion in a droplet and its electrostatic energy allowed us to identify extrusion mechanisms69,70 and test them using simulations of a model linear macroion. A pearl-necklace droplet conformation may emerge due to the interplay of a number of factors, which are (i) the tendency of the solvent to form spherical droplets in order to minimize the surface energy, (ii) the constraint that the charge of each subdroplet (pearl) should be below the Rayleigh limit, (iii) the solvation energy of the chain, and (iv) the length of the chain and the distribution of charge. A charged spherical droplet composed of a solvent and a nonfissile macroion (spherical or linear) above its Rayleigh limit deforms into a stable star-like shape. Nucleic acids and proteins are examples of macroions that may give rise to the spiky shapes. In the pearl-necklace conformation, a subdroplet may also transform into a star shape; therefore, there may be more than one star-shaped region along a chain. We think that the spiky structures may affect the charge state of a macroion. Regarding the intriguing finding of star-shaped droplets, there are still a number of questions to be answered. We need to discover the energy terms that are required in the continuum modeling to reproduce the multipoint droplet shapes. We also need to establish the relation between the number of points of the starshaped droplets and the Thomson problem of the distribution of electrons in a spherical shell. The relation between the angle of the Taylor cone107 and the observed angles of the spikes is yet to be investigated. Simulating the protonation reactions in a droplet environment is still a challenging task. Modeling using the reactive

Corresponding Author

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AUTHOR INFORMATION

*E-mail: [email protected]. ORCID

Styliani Consta: 0000-0001-8869-4155 Notes

The authors declare no competing financial interest. Biographies Styliani Consta received her P.h.D degree from the University of Toronto under the supervision of Prof. Raymond Kapral. Consta was a Marie Curie Fellow in the group of Computational Physics of Prof. Daan Frenkel at AMOLF (FOM Institute for Atomic and Molecular Physics), Amsterdam. Her faculty position is in the Department of Chemistry of the University of Western Ontario, London, Ontario. Consta’s research interests are found in the study of the stability of charged droplets, charging of macromolecules, and methods of statistical mechanics for studying the dynamics of complex chemical and biochemical systems. The studies on charged droplets have direct applications in electrospray mass spectrometry. Myong In Oh received his B.Sc. degree in Chemistry from the University of Western Ontario in 2013. His undergraduate research was on experiments in the optimization and characterization of absorber and buffer layers for CZTS solar cells. He is currently finishing his Ph.D. degree under the supervision of S. Consta at the University of Western Ontario. His research interests are in the modeling of charging mechanisms of macromolecules in droplets, interactions of protein complexes in droplets and bulk solution, and computations of equilibrium constants of noncovalently bound macromolecules. Mahmoud Sharawy received his B.Sc. degree with Honors Specialization in Chemistry from the University of Western Ontario in 2012. In his undergraduate research, he synthesized and characterized new lanthanide compounds as potential contrast agents for MRI. Then, he joined the group of S. Consta in 2013. He is now completing his Ph.D. in Theoretical and Computational Chemistry. His research interests are in the interactions of nucleic acids in solution. Anatoly Malevanets received his Ph.D. in Chemical Physics from the University of Toronto under the supervision of Prof. Raymond Kapral. He continued his studies as a postdoctoral follow at the University of I


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beyond pattern recognition to harvest the structural information encoded in vibrational spectra. J. Chem. Phys. 2016, 144, 074305. (13) Consta, S. Manifestation of Rayleigh Instability in Droplets Containing Multiply Charged Macroions. J. Phys. Chem. B 2010, 114, 5263−5268. (14) Oh, M. I.; Malevanets, A.; Paliy, M.; Frenkel, D.; Consta, S. When droplets become stars: charged dielectric droplets beyond the Rayleigh limit. Soft Matter 2017, 13, 8781−8795. (15) Schmidt, C.; Robinson, C. V. Dynamic protein ligand interactions−insights from MS. FEBS J. 2014, 281, 1950−1964. (16) Barylyuk, K.; Balabin, R. M.; Grünstein, D.; Kikkeri, R.; Frankevich, V.; Seeberger, P. H.; Zenobi, R. What happens to hydrophobic interactions during transfer from the solution to the gas phase? The case of electrospray-based soft ionization methods. J. Am. Soc. Mass Spectrom. 2011, 22, 1167−1177. (17) Loo, J. A. Studying noncovalent protein complexes by electrospray ionization mass spectrometry. Mass Spectrom. Rev. 1997, 16, 1−23. (18) Light-Wahl, K. J.; Springer, D. L.; Winger, B. E.; Edmonds, C. G.; Camp, D. G.; Thrall, B. D.; Smith, R. D. Observation of a small oligonucleotide duplex by electrospray ionization mass spectrometry. J. Am. Chem. Soc. 1993, 115, 803−804. (19) Chen, F.; Gülbakan, B.; Weidmann, S.; Fagerer, S. R.; Ibáñez, A. J.; Zenobi, R. Applying mass spectrometry to study non-covalent biomolecule complexes. Mass Spectrom. Rev. 2016, 35, 48−70. (20) Beverly, M. B. Applications of mass spectrometry to the study of siRNA. Mass Spectrom. Rev. 2011, 30, 979−998. (21) Gabelica, V.; De Pauw, E.; Rosu, F. Interaction between antitumor drugs and a double-stranded oligonucleotide studied by electrospray ionization mass spectrometry. J. Mass Spectrom. 1999, 34, 1328−1337. (22) Smith, R. D.; Light-Wahl, K. J.; Winger, B. E.; Loo, J. A. Preservation of non-covalent associations in electrospray ionization mass spectrometry: Multiply charged polypeptide and protein dimers. Org. Mass Spectrom. 1992, 27, 811−821. (23) Mehmood, S.; Allison, T. M.; Robinson, C. V. Mass spectrometry of protein complexes: From origins to applications. Annu. Rev. Phys. Chem. 2015, 66, 453−474. (24) Adamson, B. D.; Miller, M. E.; Continetti, R. E. The aerosol impact spectrometer: a versatile platform for studying the velocity dependence of nanoparticle-surface impact phenomena. EPJ Techn. Instrum. 2017, 4, 2. (25) Dole, M.; Mack, L.; Hines, R.; Mobley, R.; Ferguson, L.; Alice, M. d. Molecular beams of macroions. J. Chem. Phys. 1968, 49, 2240− 2249. (26) Kebarle, P.; Verkerk, U. H. Electrospray: from ions in solution to ions in the gas phase, what we know now. Mass Spectrom. Rev. 2009, 28, 898−917. (27) Després, V.; Huffman, J. A.; Burrows, S. M.; Hoose, C.; Safatov, A.; Buryak, G.; Fröhlich-Nowoisky, J.; Elbert, W.; Andreae, M.; Pöschl, U.; et al. Primary biological aerosol particles in the atmosphere: a review. Tellus, Ser. B 2012, 64, 15598. (28) Mather, T.; Harrison, R. Electrification of volcanic plumes. Surv. Geophys. 2006, 27, 387−432. (29) Wong, S. F.; Meng, C. K.; Fenn, J. B. Multlple charging in electrospray ionization of poly(ethylene glycols). J. Phys. Chem. 1988, 92, 546−550. (30) Iribarne, J. V.; Thomson, B. A. On the evaporation of small ions from charged droplets. J. Chem. Phys. 1976, 64, 2287−2294. (31) Thomson, B.; Iribarne, J. Field induced ion evaporation from liquid surfaces at atmospheric pressure. J. Chem. Phys. 1979, 71, 4451− 4463. (32) Consta, S.; Malevanets, A. Disintegration mechanisms of charged nanodroplets: novel systems for applying methods of activated processes. Mol. Simul. 2015, 41, 73−85. (33) Felitsyn, N.; Peschke, M.; Kebarle, P. Origin and number of charges observed on multiply-protonated native proteins produced by ESI. Int. J. Mass Spectrom. 2002, 219, 39−62.

Oxford in the research group of Prof. Julia Yeomans. Later, he worked as a researcher in the Hospital for Sick Children in Toronto. Malevanets developed the multiparticle collision dynamics method, which is a mesoscale modeling technique for hydrodynamic flows used in chemistry and polymer physics. His research interests cover Monte Carlo techniques for large biochemical systems, modeling of protein interactions, and chemical reactions.

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ACKNOWLEDGMENTS S.C. thanks Prof. R. Kapral, Department of Chemistry, University of Toronto, Prof. D. Frenkel, Department of Chemistry, University of Cambridge, Prof. S. S. Xantheas, Pacific Northwest National Laboratory, and Prof. D. Russell, Department of of Chemistry, Texas A&M University, for discussions on different aspects of the stability of charged systems. S.C. acknowledges an NSERC-Discovery grant (Canada) and a Marie Curie International Incoming Fellowship of the European Commission Grant Number 628552, held in the Department of Chemistry, University of Cambridge. M.I.O. acknowledges financial support from the Alexander Graham Bell Canada Graduate Scholarships-Doctoral Program (CGS D) of NSERC, Canada. Sci-Net, SHARCNET, and Compute Canada are acknowledged for providing the computing facilities.

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REFERENCES

(1) Gorlova, O.; DePalma, J. W.; Wolke, C. T.; Brathwaite, A.; Odbadrakh, T. T.; Jordan, K. D.; McCoy, A. B.; Johnson, M. A. Characterization of the primary hydration shell of the hydroxide ion with H2 tagging vibrational spectroscopy of the OH−-(H2O) n= 2, 3 and OD−-(D2O) n= 2, 3 clusters. J. Chem. Phys. 2016, 145, 134304. (2) Fournier, J. A.; Wolke, C. T.; Johnson, M. A.; Odbadrakh, T. T.; Jordan, K. D.; Kathmann, S. M.; Xantheas, S. S. Snapshots of proton accommodation at a microscopic water surface: Understanding the vibrational spectral signatures of the charge defect in cryogenically cooled H+ (H2O) n= 2−28 clusters. J. Phys. Chem. A 2015, 119, 9425−9440. (3) Perera, L.; Berkowitz, M. L. Stabilization energies of Cl-, Br-, and I- ions in water clusters. J. Chem. Phys. 1993, 99, 4222−4224. (4) Lynden-Bell, R.; Rasaiah, J.; Noworyta, J. Using simulation to study solvation in water. Pure Appl. Chem. 2001, 73, 1721−1731. (5) Bagchi, B.; Jana, B. Solvation dynamics in dipolar liquids. Chem. Soc. Rev. 2010, 39, 1936−1954. (6) Miller, M. A.; Bonhommeau, D. A.; Moerland, C. P.; Gray, S. J.; Gaigeot, M.-P. Dynamics and thermodynamics of decay in charged clusters. Mol. Phys. 2015, 113, 2428−2434. (7) Miller, M. A.; Bonhommeau, D. A.; Heard, C. J.; Shin, Y.; Spezia, R.; Gaigeot, M.-P. Structure and stability of charged clusters. J. Phys.: Condens. Matter 2012, 24, 284130. (8) Miller, D. J.; Lisy, J. M. Hydrated Alkali-Metal Cations: Infrared Spectroscopy and ab Initio Calculations of M+ (H2O) x= 2−5Ar cluster ions for M= Li, Na, K, and Cs. J. Am. Chem. Soc. 2008, 130, 15381−15392. (9) Wang, X.-B. Cluster Model Studies of Anion and Molecular Specificities via Electrospray Ionization Photoelectron Spectroscopy. J. Phys. Chem. A 2017, 121, 1389−1401. (10) Ross, M. W.; Berkdemir, C.; Castleman, A., Jr Strong-Field Ionization and Coulomb Explosion of Chlorine Weakly Bound to Small Water Clusters. J. Phys. Chem. A 2012, 116, 8530−8538. (11) Chakrabarty, S.; Williams, E. R. The effect of halide and iodate anions on the hydrogen-bonding network of water in aqueous nanodrops. Phys. Chem. Chem. Phys. 2016, 18, 25483−25490. (12) Wolke, C. T.; Fournier, J. A.; Miliordos, E.; Kathmann, S. M.; Xantheas, S. S.; Johnson, M. A. Isotopomer-selective spectra of a single intact H2O molecule in the Cs+ (D2O) 5H2O isotopologue: Going J


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The Journal of Physical Chemistry A (34) Barylyuk, K.; Gülbakan, B.; Xie, X.; Zenobi, R. DNA Oligonucleotides: A Model System with Tunable Binding Strength to Study Monomer−Dimer Equilibria with Electrospray IonizationMass Spectrometry. Anal. Chem. 2013, 85, 11902−11912. (35) Servage, K. A.; Silveira, J. A.; Fort, K. L.; Clemmer, D. E.; Russell, D. H. Water-mediated dimerization of ubiquitin ions captured by cryogenic ion mobility-mass spectrometry. J. Phys. Chem. Lett. 2015, 6, 4947−4951. (36) Fernandez de la Mora, J. Electrospray ionization of large multiply charged species proceeds via Dole’s charged residue mechanism. Anal. Chim. Acta 2000, 406, 93−104. (37) Boeri Erba, E.; Barylyuk, K.; Yang, Y.; Zenobi, R. Quantifying protein-protein interactions within noncovalent complexes using electrospray ionization mass spectrometry. Anal. Chem. 2011, 83, 9251−9259. (38) Hilton, G. R.; Benesch, J. L. P. Two decades of studying noncovalent biomolecular assemblies by means of electrospray ionization mass spectrometry. J. R. Soc., Interface 2012, 9, 801−816. (39) Erba, E. B.; Zenobi, R. Mass spectrometric studies of dissociation constants of noncovalent complexes. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2011, 107, 199−228. (40) Gülbakan, B.; Barylyuk, K.; Zenobi, R. Determination of thermodynamic and kinetic properties of biomolecules by mass spectrometry. Curr. Opin. Biotechnol. 2015, 31, 65−72. (41) Ngounou Wetie, A. G.; Sokolowska, I.; Woods, A. G.; Roy, U.; Loo, J. A.; Darie, C. C. Investigation of stable and transient proteinprotein interactions: Past, present, and future. Proteomics 2013, 13, 538−557. (42) Yamaguchi, K. Cold-spray ionization mass spectrometry: principle and applications. J. Mass Spectrom. 2003, 38, 473−490. (43) Yao, Y.; Richards, M. R.; Kitova, E. N.; Klassen, J. S. Influence of Sulfolane on ESI-MS Measurements of Protein-Ligand Affinities. J. Am. Soc. Mass Spectrom. 2016, 27, 498−506. (44) Monge, M. E.; Harris, G. A.; Dwivedi, P.; Fernaandez, F. M. Mass spectrometry: recent advances in direct open air surface sampling/ionization. Chem. Rev. 2013, 113, 2269−2308. (45) Sakairi, M.; Kambara, H. Atmospheric pressure spray ionization for liquid chromatography/mass spectrometry. Anal. Chem. 1989, 61, 1159−1164. (46) Bruins, A. P.; Covey, T. R.; Henion, J. D. Ion spray interface for combined liquid chromatography/atmospheric pressure ionization mass spectrometry. Anal. Chem. 1987, 59, 2642−2646. (47) Kambara, H. Sample introduction system for atmospheric pressure ionization mass spectrometry of nonvolatile compounds. Anal. Chem. 1982, 54, 143−146. (48) Blakley, C.; Vestal, M. Thermospray interface for liquid chromatography/mass spectrometry. Anal. Chem. 1983, 55, 750−754. (49) Hirabayashi, A.; Sakairi, M.; Koizumi, H. Sonic spray ionization method for atmospheric pressure ionization mass spectrometry. Anal. Chem. 1994, 66, 4557−4559. (50) Devereaux, Z. J.; Reynolds, C. A.; Fischer, J. L.; Foley, C. D.; DeLeeuw, J. L.; Wager-Miller, J.; Narayan, S. B.; Mackie, K.; Trimpin, S. Matrix-Assisted Ionization on a Portable Mass Spectrometer: Analysis Directly from Biological and Synthetic Materials. Anal. Chem. 2016, 88, 10831−10836. (51) Peacock, P. M.; Zhang, W.-J.; Trimpin, S. Advances in ionization for mass spectrometry. Anal. Chem. 2017, 89, 372−388. (52) Fenn, J. B. Ion formation from charged droplets: roles of geometry, energy, and time. J. Am. Soc. Mass Spectrom. 1993, 4, 524− 535. (53) Fenn, J. B.; Rosell, J.; Meng, C. K. In electrospray ionization, how much pull does an ion need to escape its droplet prison? J. Am. Soc. Mass Spectrom. 1997, 8, 1147−1157. (54) Nohmi, T.; Fenn, J. B. Electrospray mass spectrometry of poly (ethylene glycols) with molecular weights up to five million. J. Am. Chem. Soc. 1992, 114, 3241−3246. (55) Heck, A. J. Native mass spectrometry: a bridge between interactomics and structural biology. Nat. Methods 2008, 5, 927.

(56) Marsh, J. A.; Hernández, H.; Hall, Z.; Ahnert, S. E.; Perica, T.; Robinson, C. V.; Teichmann, S. A. Protein complexes are under evolutionary selection to assemble via ordered pathways. Cell 2013, 153, 461−470. (57) Rayleigh, L. XX On the equilibrium of liquid conducting masses charged with electricity. Philos. Mag. 1882, 14, 184−186. (58) Hendricks, C.; Schneider, J. Stability of a conducting droplet under the influence of surface tension and electrostatic forces. Am. J. Phys. 1963, 31, 450−453. (59) Duft, D.; Lebius, H.; Huber, B. A.; Guet, C.; Leisner, T. Shape Oscillations and Stability of Charged Microdroplets. Phys. Rev. Lett. 2002, 89, 084503. (60) Duft, D.; Achtzehn, T.; Muller, R.; Huber, B. A.; Leisner, T. Coulomb fission: Rayleigh jets from levitated microdroplets. Nature 2003, 421, 128−128. (61) Achtzehn, T.; Müller, R.; Duft, D.; Leisner, T. The Coulomb instability of charged microdroplets: dynamics and scaling. Eur. Phys. J. D 2005, 34, 311−313. (62) Consta, S. Fragmentation reactions of charged aqueous clusters. J. Mol. Struct.: THEOCHEM 2002, 591, 131−140. (63) Consta, S.; Mainer, K. R.; Novak, W. Fragmentation mechanisms of aqueous clusters charged with ions. J. Chem. Phys. 2003, 119, 10125−10132. (64) Sharawy, M.; Consta, S. Effect of counterions on the charging mechanisms of a macromolecule in aqueous nanodrops. J. Chem. Phys. 2014, 141, 104321. (65) Consta, S.; Chung, J. K. Charge-induced conformational changes of PEG-(Na(n)(+)) in a vacuum and aqueous nanodroplets. J. Phys. Chem. B 2011, 115, 10447−10455. (66) Singarapu, K. K.; Tonelli, M.; Chow, D. C.; Frederick, R. O.; Westler, W. M.; Markley, J. L. Structural Characterization of Hsp12, the Heat Shock Protein from Saccharomyces cerevisiae, in Aqueous Solution Where It Is Intrinsically Disordered and in Detergent Micelles Where It Is Locally α-Helical. J. Biol. Chem. 2011, 286, 43447−43453. (67) Sharawy, M.; Consta, S. How do non-covalent complexes dissociate in droplets? A case study of the desolvation of dsDNA from a charged aqueous nanodrop. Phys. Chem. Chem. Phys. 2015, 17, 25550−25562. (68) Consta, S.; Malevanets, A. Classification of the ejection mechanisms of charged macromolecules from liquid droplets. J. Chem. Phys. 2013, 138, 044314. (69) Consta, S.; Malevanets, A. Manifestations of Charge Induced Instability in Droplets Effected by Charged Macromolecules. Phys. Rev. Lett. 2012, 109, 148301. (70) Consta, S.; Oh, M. I.; Malevanets, A. New mechanisms of macroion-induced disintegration of charged droplets. Chem. Phys. Lett. 2016, 663, 1−12. (71) Sharawy, M.; Consta, S. Characterization of “Star” Droplet Morphologies Induced by Charged Macromolecules. J. Phys. Chem. A 2016, 120, 8871−8880. (72) Oh, M. I.; Consta, S. What factors determine the stability of a weak protein-protein interaction in a charged aqueous droplet? Phys. Chem. Chem. Phys. 2017, 19, 31965−31981. (73) Soltani, S.; Oh, M. I.; Consta, S. Effect of solvent on the charging mechanisms of poly (ethylene glycol) in droplets. J. Chem. Phys. 2015, 142, 114307. (74) Oh, M. I.; Consta, S. Charging and Release Mechanisms of Flexible Macromolecules in Droplets. J. Am. Soc. Mass Spectrom. 2017, 28, 2262−2279. (75) Oh, M. I.; Consta, S. Stability of a Transient Protein Complex in a Charged Aqueous Droplet with Variable pH. J. Phys. Chem. Lett. 2017, 8, 80−85. (76) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926−935. (77) Chandrasekhar, J.; Spellmeyer, D. C.; Jorgensen, W. L. Energy Component Analysis for Dilute Aqueous-Solutions of Li+, Na+, F-, and Cl- Ions. J. Am. Chem. Soc. 1984, 106, 903−910. K


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The Journal of Physical Chemistry A (78) Jorgensen, W. L.; Tirado-Rives, J. The OPLS Force Field for Proteins. Energy Minimizations for Crystals of Cyclic Peptides and Crambin. J. Am. Chem. Soc. 1988, 110, 1657−1666. (79) Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; et al. CHARMM general force field: A force field for drug-like molecules compatible with the CHARMM all-atom additive biological force fields. J. Comput. Chem. 2009, 31, 671−690. (80) Yu, W.; He, X.; Vanommeslaeghe, K.; MacKerell, A. D. Extension of the CHARMM general force field to sulfonyl-containing compounds and its utility in biomolecular simulations. J. Comput. Chem. 2012, 33, 2451−2468. (81) Berman, H. M.; Westbrook, J.; Feng, Z.; Gilliland, G.; Bhat, T. N.; Weissig, H.; Shindyalov, I. N.; Bourne, P. E. The protein data bank. Nucleic Acids Res. 2000, 28, 235−242. (82) Nowicka, U.; Zhang, D.; Walker, O.; Krutauz, D.; Castañeda, C. A.; Chaturvedi, A.; Chen, T. Y.; Reis, N.; Glickman, M. H.; Fushman, D. DNA-Damage-Inducible 1 Protein (Ddi1) Contains an Uncharacteristic Ubiquitin-like Domain that Binds Ubiquitin. Structure 2015, 23, 542−557. (83) Ryabov, Y.; Fushman, D. Structural Assembly of Multidomain Proteins and Protein Complexes Guided by the Overall Rotational Diffusion Tensor. J. Am. Chem. Soc. 2007, 129, 7894−7902. (84) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L.; Schulten, K. Scalable molecular dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781− 1802. (85) Brooks, B. R.; Brooks, C. L.; MacKerell, A. D.; Nilsson, L.; Petrella, R. J.; Roux, B.; Won, Y.; Archontis, G.; Bartels, C.; Boresch, S.; et al. CHARMM: the biomolecular simulation program. J. Comput. Chem. 2009, 30, 1545−1614. (86) Berendsen, H. J.; van der Spoel, D.; van Drunen, R. GROMACS: a message-passing parallel molecular dynamics implementation. Comput. Phys. Commun. 1995, 91, 43−56. (87) Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 2015, 1-2, 19−25. (88) Malevanets, A.; Consta, S. Variation of droplet acidity during evaporation. J. Chem. Phys. 2013, 138, 184312. (89) Allen, M.; Tildesley, D. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (90) Verlet, L. Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 1967, 159, 98. (91) Andersen, H. C. Rattle: A “velocity version” of the shake algorithm for molecular dynamics calculations. J. Comput. Phys. 1983, 52, 24−34. (92) Nosé, S. A molecular dynamics method for simulations in the canonical ensemble. Mol. Phys. 1984, 52, 255−268. (93) Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 31, 1695. (94) Koopman, E. A.; Lowe, C. P. Advantages of a Lowe-Andersen thermostat in molecular dynamics simulations. J. Chem. Phys. 2006, 124, 204103. (95) Hutter, J. Car−Parrinello molecular dynamics. WIREs Comput. Mol. Sci. 2012, 2, 604−612. (96) Niklasson, A. M.; Tymczak, C.; Challacombe, M. Timereversible Born-Oppenheimer molecular dynamics. Phys. Rev. Lett. 2006, 97, 123001. (97) Soleilhac, A.; Dagany, X.; Dugourd, P.; Girod, M.; Antoine, R. Correlating droplet size with temperature changes in electrospray source by optical methods. Anal. Chem. 2015, 87, 8210−8217. (98) Gibson, S. C.; Feigerle, C. S.; Cook, K. D. Fluorometric measurement and modeling of droplet temperature changes in an electrospray plume. Anal. Chem. 2014, 86, 464−472. (99) Larriba, C.; Fernandez de la Mora, J. The Gas Phase Structure of Coulombically Stretched Polyethylene Glycol Ions. J. Phys. Chem. B 2012, 116, 593−598.

(100) Bogan, M. J.; Agnes, G. R. Poly (ethylene glycol) doubly and singly cationized by different alkali metal ions: Relative cation affinities and cation-dependent resolution in a quadrupole ion trap mass spectrometer. J. Am. Soc. Mass Spectrom. 2002, 13, 177−186. (101) Gidden, J.; Wyttenbach, T.; Jackson, A. T.; Scrivens, J. H.; Bowers, M. T. Gas-phase conformations of synthetic polymers: poly (ethylene glycol), poly (propylene glycol), and poly (tetramethylene glycol). J. Am. Chem. Soc. 2000, 122, 4692−4699. (102) Chung, J. K.; Consta, S. Release mechanisms of poly(ethylene glycol) macroions from aqueous charged nanodroplets. J. Phys. Chem. B 2012, 116, 5777−5785. (103) Jackson, J. D. Classical Electrodynamics, 3rd ed.; John Wiley & Sons: New York, 1998. (104) Luedtke, W. D.; Landman, U.; Chiu, Y.-H.; Levandier, D. J.; Dressler, R. A.; Sok, S.; Gordon, M. S. Nanojets, Electrospray, and Ion Field Evaporation: Molecular Dynamics Simulations and Laboratory Experiments. J. Phys. Chem. A 2008, 112, 9628−9649. (105) Cramer, T.; Zerbetto, F.; García, R. Molecular mechanism of water bridge buildup: Field-induced formation of nanoscale menisci. Langmuir 2008, 24, 6116−6120. (106) Cao, Q.; Li, L.; Huang, F.; Zuo, C. Ion-Specific Effects on the Elongation Dynamics of a Nanosized Water Droplet in Applied Electric Fields. Langmuir 2017, 33, 428−437. (107) Taylor, G. Disintegration of Water Drops in an Electric Field. Proc. R. Soc. London, Ser. A 1964, 280, 383−397. (108) Ramos, A.; Castellanos, A. Conical points in liquid-liquid interfaces subjected to electric fields. Phys. Lett. A 1994, 184, 268−272. (109) Richter, R.; Lange, A. Colloidal Magnetic Fluids; Springer, 2009; pp 1−91. (110) Nguyen, S.; Fenn, J. B. Gas-phase ions of solute species from charged droplets of solutions. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 1111−1117. (111) Peschke, M.; Blades, A.; Kebarle, P. Charged states of proteins. Reactions of doubly protonated alkyldiamines with nh3: Solvation or deprotonation. extension of two proton cases to multiply protonated globular proteins observed in the gas phase. J. Am. Chem. Soc. 2002, 124, 11519−11530. (112) Heck, A. J.; van den Heuvel, R. H. Investigation of intact protein complexes by mass spectrometry. Mass Spectrom. Rev. 2004, 23, 368−389. (113) Catalina, M. I.; van den Heuvel, R. H.; van Duijn, E.; Heck, A. J. Decharging of globular proteins and protein complexes in electrospray. Chem. - Eur. J. 2005, 11, 960−968. (114) Niu, W.; Chua, Y. A. A.; Zhang, W.; Huang, H.; Lu, X. Highly symmetric gold nanostars: crystallographic control and surfaceenhanced Raman scattering property. J. Am. Chem. Soc. 2015, 137, 10460−10463. (115) Khoury, C. G.; Vo-Dinh, T. Gold nanostars for surfaceenhanced Raman scattering: synthesis, characterization and optimization. J. Phys. Chem. C 2008, 112, 18849−18859. (116) Miszta, K.; De Graaf, J.; Bertoni, G.; Dorfs, D.; Brescia, R.; Marras, S.; Ceseracciu, L.; Cingolani, R.; Van Roij, R.; Dijkstra, M.; et al. Hierarchical self-assembly of suspended branched colloidal nanocrystals into superlattice structures. Nat. Mater. 2011, 10, 872− 876. (117) Almería, B.; Gomez, A. Electrospray synthesis of monodisperse polymer particles in a broad (60nm−2μm) diameter range: guiding principles and formulation recipes. J. Colloid Interface Sci. 2014, 417, 121−130. (118) Senftle, T. P.; Hong, S.; Islam, M. M.; Kylasa, S. B.; Zheng, Y.; Shin, Y. K.; Junkermeier, C.; Engel-Herbert, R.; Janik, M. J.; Aktulga, H. M.; et al. The ReaxFF reactive force-field: development, applications and future directions. npj Comput. Mater. 2016, 2, 15011. (119) Dinpajooh, M.; Matyushov, D. V. Dielectric constant of water in the interface. J. Chem. Phys. 2016, 145, 014504.

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