Molecular Trajectories Provide Signatures of Protein Clustering and

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Molecular trajectories provide signatures of protein clustering and crowding at the oil/water interface Aaron C. McUmber, Nicholas R. Larson, Theodore W. Randolph, and Daniel K. Schwartz Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b00984 • Publication Date (Web): 07 May 2015 Downloaded from http://pubs.acs.org on May 11, 2015

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Molecular trajectories provide signatures of protein clustering and crowding at the oil/water interface

Aaron C. McUmber, Nicholas R. Larson, Theodore W. Randolph, and Daniel K. Schwartz* Department of Chemical and Biological Engineering University of Colorado Boulder, Boulder, CO 80309

*To whom correspondence should be addressed: [email protected]

ACS Paragon Plus Environment

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Abstract Using high throughput single-molecule total internal reflection fluorescence microscopy (TIRFM), we have acquired molecular trajectories of bovine serum albumin (BSA) and hen eggwhite lysozyme during protein layer formation at the silicone oil-water interface. These trajectories were analyzed to determine the distribution of molecular diffusion coefficients, and for signatures of molecular crowding/caging, including subdiffusive motion and temporal anticorrelation of the instantaneous velocity vector. The evolution of these properties with aging time of the interface was compared with dynamic interfacial tension measurements. For both lysozyme and BSA, we observed an overall slowing of protein objects, the onset of both subdiffusive and anticorrelated motion (associated with crowding), and a decrease in the interfacial tension with aging time. For lysozyme, all of these phenomena occurred virtually simultaneously, consistent with a homogeneous model of layer formation that involves gradual crowding of weakly interacting proteins. For BSA, however, the slowing occurred first, followed by the signatures of crowding/caging, followed by a decrease in interfacial tension, consistent with a heterogeneous model of layer formation involving the formation of protein clusters. The application of micro-rheological methods to single molecule trajectories described here provides an unprecedented level of mechanistic interpretation of interfacial events that occurred over a wide range of interfacial protein coverage.

Keywords: Aggregation, interface, subdiffusion, caging, molecular confinement, 2D anomalous diffusion


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Introduction Protein aggregation at interfaces and the formation of interfacial protein layers represent important phenomena for several areas of biotechnology and biomaterials.1 For example, fouling of biosensing devices2 or filtration membranes,3 aggregation of protein molecules in therapeutic formulations,4 and undesirable immune responses to implanted devices5 have all been related to the formation of adsorbed protein layers. Aggregation of protein molecules at silicone oil-water interfaces specifically, has been the subject of increasing scrutiny within the biopharmaceutical industry.6–10 Silicone oil-water interfaces are now ubiquitous due to the popular packaging strategy of using prefilled glass syringes as storage and delivery devices, which require the use of silicone oil as a lubricant. Studies have indicated that an increased incidence of protein aggregation may be related to the presence of silicone oil-water interfaces.8,9,11–13 From a fundamental perspective, liquid-liquid interfaces, such as the silicone oil-water interface, represent an attractive system to study the mechanisms that lead to protein layer formation, in part because they exhibit excellent spatial homogeneity, which virtually eliminates confounding effects due to isolated surface defects (a.k.a. strong binding sites) inevitably found on solidliquid interfaces.14–16 The formation of protein layers at fluid interfaces is readily characterized by macroscopic phenomena that involve thermodynamic (e.g. interfacial tension) or dynamic/rheological (e.g. changes in interfacial mobility) properties. Historically, dynamic interfacial tensiometry (DIFT)17–20 has been the standard approach for studying interfacial adsorption at liquid-liquid interfaces, while interfacial rheology21–23 has been used to characterize well-developed protein layers that display measurable viscoelastic properties. Additional techniques such as fluorescence-activated cell sorting24 and front-face fluorescence spectroscopy have been applied


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to analysis of proteins adsorbed to liquid-liquid interfaces in high surface-area systems (e.g. emulsions).25,26 Interestingly, the correlation between the temporal evolution of thermodynamic and hydrodynamic phenomena is highly variable and poorly understood. For example, one can define “lag times” to provide an approximate description of the interfacial aging time required to measure a significant change in the interfacial tension (𝑡𝐼𝐹𝑇 ) or interfacial diffusivity (𝑡𝑑𝑖𝑓 ). Here we describe the behavior of lysozyme at silicone oil-water interfaces, where a reduction of interfacial tension follows quickly behind the reduction in interfacial diffusivity (𝑡𝐼𝐹𝑇 ≈ 2 𝑡𝑑𝑖𝑓 ), and the contrasting behavior of bovine serum albumin (BSA) at silicone oil-water interfaces, where interfacial mobility decreases long before the interfacial tension begins to drop (𝑡𝐼𝐹𝑇 > 10 𝑡𝑑𝑖𝑓 ).

While the physical interpretation of interfacial tension is complex for interfaces laden with proteins or colloidal particles,17,21,27,28 nevertheless, a significant reduction in interfacial tension is general related to large coverage of interfaces with surface-active molecules. For example, for Langmuir monolayers of poorly soluble fatty acids or phospholipids, which have been thoroughly characterized, a significant reduction of interfacial tension (e.g. by ~10%) generally requires a fractional surface coverage of 0.3-0.5.29–33 So intuitively, one can expect that a significant reduction of interfacial tension will be observed for an interface that is approaching its upper limit of surface coverage. In this context, the two lag time regimes described above correspond to situations where the mobility begins to decrease when the surface is already highly crowded (lysozyme) or when the interfacial protein coverage is still very sparse (BSA).

It has been proposed that interfacial “slowing down” may be caused by two distinct mechanisms,


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which can potentially act in concert.34 The so-called homogeneous (or two-dimensional) mechanism involves a reduction in molecular mobility that is primarily due to drag experienced by individual proteins due to collisions with other adsorbed proteins, i.e. interfacial crowding. On the other hand, a heterogeneous mechanism for interfacial slowing involves a reduction in mobility caused by increased viscous drag from the adjacent bulk phases; this is hypothetically due to the formation of interfacial clusters/aggregates that exhibit large hydrodynamic radii. It is reasonable to hypothesize that since homogeneous slowing can occur only under crowded interfacial conditions where the surface coverage is relatively high, homogeneous slowing should be correlated with the reduction of interfacial tension. However, heterogeneous slowing, which relies upon the formation of molecular clusters/aggregates, can potentially occur even under conditions of relatively low surface coverage.

While these are reasonable hypotheses, it is clear that macroscopic, ensemble-averaging measurements cannot distinguish directly between these mechanisms for interfacial protein layer formation. However, the recent application of single-molecule methods such as fluorescence correlation spectroscopy (FCS)35–37 and TIRF38,39 has directly demonstrated the ability to identify interfacial heterogeneities in the form of multiple molecular populations (e.g., based on oligomerization or conformational state).14,16,40–42 TIRF, in particular, explicitly separates distinct dynamic mechanisms and provides detailed information about interfacial mobility and adsorption kinetics, including the distribution of interfacial diffusion coefficients. In addition, TIRF measurements may be used to decouple net adsorption into individual adsorption and desorption events and to probe step-size distributions of molecular trajectories.14–16,41,43


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Donsmark and coworkers used FCS to show that the dynamic behavior of insulin35 and betalactoglobulin36 slowed significantly with aging time at the oil-water interface, and that the details of this slowing were highly dependent on the identity of the protein. Walder et al.40 applied a molecular tracking approach to study the slowing-down behavior of BSA at an oil-water interface. They found that the distribution of individual diffusion coefficients broadened significantly as the interface aged, consistent with a heterogeneous mechanism for layer formation. They supported this interpretation by comparing the experimental observation with the results of a population-balance model for protein cluster formation. These results provided support for the importance of protein-protein interactions, and cluster formation, as part of interfacial protein layer formation. However, the analysis of diffusion coefficient distributions represented a limited approach for several reasons. For example, these distributions are sensitive primarily to the very early stages of layer formation, precluding direct comparisons with the kinetics associated with interfacial tension reduction. Moreover, the distribution of individual diffusion coefficients need not necessarily broaden significantly, depending on the detailed mechanism of cluster formation, and importantly, these distributions fail to provide direct information about interfacial crowding.

To address these limitations, here we apply more sophisticated analysis tools, commonly applied in micro-rheological studies of colloidal systems,44 to the interfacial trajectories of individual protein objects. These molecular trajectories provide detailed information about the environment experienced by the molecular objects, including the presence of crowding or “caging” effects.44 Regular unconstrained Brownian motion is characterized by the expression 〈𝑟 2 (𝜏)〉 = 4𝐷𝜏, where the mean square displacement (MSD) exhibits a linear dependence on the time interval, 𝜏,


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over which it is measured. In general, anomalous diffusion can be described using an ad hoc power law expression law such that: =2dK𝜏α, where is the MSD, d is the dimensionality of the system (d=2 in the case of interfacial diffusion), K is the mobility coefficient, and α is the power law exponent. This equation corresponds to simple Brownian motion in the limit that α=1, in which case K corresponds to the Brownian diffusion coefficient D.37 Values of α1 are less commonly observed, for trajectories that are called superdiffusive. It is widely observed that diffusion in crowded environments deviates from traditional Brownian motion, becoming subdiffusive; this can be observed through careful analysis of molecular mean squared displacement versus time interval.37 Moreover, diffusion in structured and/or crowded environment can become history-dependent, or non-Markovian, which may result in temporal anti-correlation of the instantaneous velocity vector.37 For example, previous experimental and computational studies have connected temporal velocity anticorrelation to “caging” effects in glassy systems,45 motion in viscoelastic media46 (e.g. for the fractional Brownian motion model47) or dynamic heterogeneity.48 In each of these systems, anticorrelated velocity is directly related to highly crowded conditions, typically with volume fractions >0.2. Compared with colloidal systems which can be imaged with extraordinarily high time resolution and contrast, this type of analysis is challenging in the context of single-molecule tracking which intrinsically provides low signal/background data. However, by performing careful statistical analyses, we are able to directly identify clear signatures of the onset molecular crowding in the form of correlated subdiffusive trajectories and temporally anti-correlated velocities for lysozyme and BSA layer formation at the oil-water interface. Lysozyme and BSA have previously been shown


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to exhibit distinctly different rates of interfacial layer formation.22 For lysozyme, these signatures of crowding appear at aging times similar to those where both the interfacial mobility and interfacial tension begin to decrease, consistent with a homogeneous mechanism for layer formation. In contrast, for BSA the signatures of crowding/caging appear long after the interfacial mobility decreases, but before the reduction of interfacial tension, consistent with a heterogeneous mechanism (involving protein cluster formation).


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Materials & Methods Hen egg white lysozyme (Aldrich CAS 12650-88-3) was labeled with Alexa Fluor 555 succinimidyl ester using Molecular Probes microscale protein labeling kit (Invitrogen CAS A30007). The average labeling efficiency was found to be 3±1 fluorophores per protein using UV-visible spectroscopy at 280 and 555 nm (data not shown). Bovine serum albumin (BSA) conjugated with Alexa Fluor 555 (5 labels/molecule, as reported by the vendor) was purchased from Invitrogen (CAS A34786). All lysozyme and BSA (Aldrich CAS A2153) solutions were made using 1x PBS buffer (Gibco CAS 10010-23), pH 7.4 with 0.1 mg/ml sodium azide (Aldrich CAS 438456).

TIRFM experiments were performed using a Nikon Eclipse TI-93 outfitted with a custom through-the-objective TIRF illuminator used in conjunction with a 100x oil immersion objective. A cooled CCD camera (Photometrics Cascade 512B) operating at -80°C was used to capture a sequences of images with a typical acquisition time of 200 ms. A Cobolt Samba laser emitting at 532 nm was used as an excitation source; movies were continuously captured for short-time experiments and movies of 3 minute duration were captured at various time intervals for longer time-scale experiments.

For TIRFM experiments, glass coverslips (Fisher CAS 12-542-C) were cleaned using a cationic surfactant (Micro-90 International Products M9031-12), Millipore filtered water with a resistance of 18.2 MΩ-cm, and isopropanol (Aldrich W292907), and were then dried under a nitrogen stream. Silicone oil droplets with a viscosity of 350 cSt (Dow Corning 360 CAS 01472666) were added to the clean coverslips and stabilized using a nickel TEM grid, ensuring a


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stable planar interface between the silicone oil and buffer.40,49,50 A Teflon® ring was then placed in contact with the coverslip, surrounding the silicone oil-filled TEM grid, creating a well to contain a small volume of buffer. 100 μl of buffer containing either 7.0x10-2 nM of Alexa555labeled lysozyme or 1.5x10−3 nM of Alexa555-labeled BSA were then added to the well and allowed to reach steady state. Once stable, a sequence of images was captured, and then 100 μl of 140 nM of unlabeled protein, doped with either 7.0x10-2 nM of Alexa555-labeled lysozyme or 1.5x10−3 nM of Alexa555-labeled BSA, were added to the well, leaving a final concentration of 70 nM of unlabeled protein. Following addition of unlabeled protein, a series of 3-minute, timelapse TIRF movies was captured at periodic time intervals during the experiment. TIRF movies were analyzed using a custom-made molecule identification and tracking algorithm.51,52 Data from experiments involving only a very low concentration of labeled protein in the absence of unlabeled protein (i.e. low surface-density experiments) were analyzed to identify the surface residence times and diffusion coefficients for individual molecules and small, well-defined oligomers, as reported previously for BSA.40 Time-lapse data from experiments that included various concentrations of unlabeled protein (i.e. high surface-density experiments) were obtained in triplicate and analyzed by binning the movies into 60 s and 20 s time segments for lysozyme and BSA, respectively, and considering each time segment as one time point. Within each time bin approximately 500 – 1,000 identified objects were tracked and an effective diffusion coefficient was calculated for each individual object. The mean squared displacement versus time interval, 〈𝑟 2 (𝜏)〉, was calculated for each object, and fit using the expression 〈𝑟 2 (𝜏)〉 = 4𝐷𝜏. This allowed us to determine the distribution of diffusion coefficients and the mean diffusion coefficient, as a function of aging time. The mean effective diffusion coefficient was calculated by taking the arithmetic mean of diffusion coefficients for each molecule within


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binned time segments. Hydrodynamic radii were calculated from the diffusion coefficients found by applying the Stokes-Einstein equation for diffusion of a disc at the interface between two viscous liquids using the equation: D=3kbT⁄16R(ηoil + ηwater) where D, T, kb, R, and η represent the diffusion coefficient, temperature, Boltzmann constant, hydrodynamic radius, and viscosity, respectively.53 Relative mean diffusion coefficients were first calculated by dividing the mean diffusion coefficient of objects within a time bin by the diffusion coefficients for objects in the first time bin (t=0). Then the arithmetic mean was calculated for relative diffusion coefficients calculated from each triplicate measurement. Reported error bars were calculated as the standard deviation from the mean of the experimental triplicates.

To determine the anomalous power law exponent associated with diffusive motion, trajectories were accumulated as a function of aging time, and the mean squared displacement, 〈𝑟 2 (𝜏)〉, versus time interval was calculated for both BSA and lysozyme. In order to minimize effects from possible immobilized objects and short trajectories, MSD values were calculated for molecules that were present on the interface for greater than 10 frames (2 s) and that displayed diffusion coefficients within two standard deviations from the mean diffusion coefficient or that had diffusion coefficients greater than 0.001 μm2/s. For each time bin, all squared displacements associated with a given time interval were obtained, and averaged using equal weights. These data were fitted to the anomalous diffusion expression, =2dKα, where is the MSD, d is the dimensionality of the system (d=2 in the case of interfacial diffusion), K is the mobility coefficient, and α is the power law exponent that was used for subsequent analysis.

The velocity-velocity autocorrelation function, G(𝜏) = /, was also calculated,


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where v(t) represents the instantaneous velocity vector at time t. Similar to the MSD calculations, effects from possible immobilized objects and short trajectories were minimized by calculating values based on molecules that existed on the interface for greater than 10 frames (2 s) and displayed diffusion coefficients within two standard deviations from the mean diffusion coefficient or that had diffusion coefficients greater than 0.001 μm2/s. For each time bin, all velocity-velocity scalar products, v(t)v(t+𝜏), associated with a given time interval were obtained, and averaged using equal weights.

D-IFT measurements were performed using a custom-made pendant bubble flow cell apparatus. A droplet of silicone oil was initially injected from a stainless steel needle into buffer, remaining in contact with the needle. After the oil droplet relaxed, 10 ml of buffer containing either lysozyme or BSA were injected into the cell and a time-lapse movie of the pendant drop was acquired immediately after injection. The shape of the oil droplet was then analyzed with software developed by First Ten Angstroms® wherein the curvature of the bubble was used to calculate the surface tension using a modified Young-Laplace equation of an axisymmetric bubble known as the Bashforth-Adams equation.54 This analysis permitted the dynamic determination of interfacial tension as previously described.55 Relative interfacial tension was calculated by dividing the interfacial tension by the initial interfacial tension. Measurements were grouped into time bins, and each condition was repeated three times. Error bars indicate the standard deviation between replicates.


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Results & Discussion Adsorption rates for each protein were calculated from single-molecule measurements captured using TIRFM by examining a low concentration of fluorescently-labeled protein in PBS buffer. Under these conditions, steady state conditions were reached quickly and the adsorption rate constant was calculated by counting the number of adsorbed molecules with respect to the observation duration and area observed and normalizing by solution concentration. We note that this represents the absolute adsorption rate, as opposed to the net adsorption rate, and is uniquely measured using single molecule observations. The adsorption rate constants for BSA and lysozyme were 600±300 nm/s and 3000±1500 nm/s, respectively, where experiments were repeated three times, and uncertainties represent the standard deviation between replicates. Intuitively, an adsorption rate constant of 600 nm/s suggests that the number of protein molecules equivalent to those contained in a 600 nm thick slab of solution impinges on the interface each second. Under the pH conditions employed here, previous work has suggested that the silicone-oil interface exhibits an effective negative charge,56 whereas BSA and lysozyme are expected to exhibit net negative and positive charges, respectively, due to their respective isoelectric points.57,58 Therefore, BSA molecules in the bulk solution are expected to experience repulsive electrostatic interactions with the interface, whereas those of lysozyme molecules are attractive. The modest difference in the observed adsorption rates is likely due to these factors, despite the relatively high ionic strength of the PBS solution used. However, other effects, including hydrophobic exposure, can significantly influence the measured adsorption rate. Most importantly, these measured adsorption rates provide an important scaling parameter that will be used below to calculate a “dimensionless time” variable, permitting direct comparison of layer formation kinetics for BSA and lysozyme.


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Dynamic interfacial tension measurements were obtained as a function of interfacial aging time for BSA and lysozyme. As described above, interfacial tension provides approximate information about the extent to which the interface is covered by a protein layer. For example, a 10% reduction in the relative interfacial tension (𝛾/𝛾0 = 0.9 in Figure 1) is likely to correspond to a situation where the surface coverage has reached 30-50% of its maximal value.18–20 As seen in Figure 1, the dynamic interfacial tension for both proteins exhibits a characteristic initial lag time before dropping sharply. The behavior is slightly different for the two proteins, for example BSA exhibits a more significant initial downward drift during the induction phase and begins to saturate after the interfacial tension decreases to ~70% of its initial value. However, the salient features in Figure 1 involve the distinctive sharp decreases in interfacial tension, occurring at ~400s for BSA and ~1500s for lysozyme. The decrease in interfacial tension occurs distinctly earlier for BSA than for lysozyme.18–20

Figure 1: Temporal evolution of the relative interfacial tension for BSA (filled circles) and lysozyme (open diamonds) at a bulk concentration of 70 nM in PBS where time is on a logarithmic scale and the relative interfacial tension is defined as the instantaneous interfacial tension γ divided by the initial value, γ0. Error bars indicate the standard deviation between three replicate experiments.


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To account for differences in adsorption rate and molecular size in comparing these dynamic interfacial tension measurements, it is convenient to calculate a dimensionless time, Γ. Assuming that each protein molecule occupies an area corresponding to amol=πR2, where R is the solution-phase hydrodynamic radius (3.3 and 1.8 nm for BSA and lysozyme, respectively),59,60 this dimensionless time is defined using the equation

Γ=kads c amol t

where kads is the adsorption rate coefficient described above, c is the bulk protein concentration, and t is time. Intuitively, Γ represents the approximate fraction of the surface that would be covered by protein assuming that all absorbing molecules remain on the surface permanently in their three-dimensional conformation. In practice, Γ represents an upper limit on the surface coverage, since molecules often desorb from the interface. In the surface science community, this quantity would correspond to the dose of adsorbate molecules, and would be expressed in units of Langmuirs. Figure 2a shows the relative interfacial tension as a function of Γ. While the shapes of the data for BSA and lysozyme are somewhat different, it is interesting that, after adjusting for protein size and adsorption rate, the aging times at which the interfacial tensions drop sharply fall within a fairly narrow range (Γ=0.5 for BSA and Γ=0.8 for lysozyme). Importantly, the quantities measured using single-molecule tracking allow us to account for differences in the rate at which proteins appear at the interface and to express the kinetics of aging in terms of time intervals that can be directly compared, despite the significant differences in protein, size, charge, hydrophobicity, etc.


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Figure 2: Various properties of 70 nM BSA (filled circles) and 70 nM lysozyme (open diamonds) plotted versus the dimensionless time Γ, a value calculated by adjusting for protein adsorption rate, bulk concentration and molecular size. (a) Relative interfacial tension, (b) relative mean diffusion coefficient, (c) power law exponent, α, associated with the mean squared displacement vs. time, and (d) the first non-trivial value, 𝐺(𝜏 = 0.2𝑠), of the velocity-velocity autocorrelation function. Error bars from figures (a) and (b) represent the standard deviation between three replicate experiments.


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The most direct way to characterize the molecular motion is to measure the apparent diffusion coefficients, D, of the objects observed as a function of aging time. Figure 2b shows the relative mean diffusion coefficient as a function of aging time (normalized by the initial mean diffusion coefficient). For each replicate experiment, the values of D for individual trajectories were averaged (using equal weights) within each time bin, these averages were normalized by the initial mean diffusion coefficient for that replicate, and the overall average was obtained by averaging the relative mean diffusion coefficients calculated individually from three replicate experiments (using equal weights). For BSA, it is interesting to note that the mean diffusion coefficient decreases significantly by a dimensionless time Γ ~0.01, whereas the interfacial tension only begins to drop sharply at a dimensionless time Γ ~0.5. Thus, the lag times for mobility and interfacial tension differ by approximately two orders of magnitude. In fact, at a dimensionless time of Γ ~0.5, the average diffusion coefficient of the BSA layer decreases by an order of magnitude, while the interfacial tension decreases by only 10%. This is in contrast to the behavior of lysozyme, where the dimensionless lag times for mobility (Γ ~0.4) and interfacial tension (Γ ~0.8) differ by only a factor of two. As mentioned previously, this behavior is consistent with a scenario where slowing down is dominated by a heterogeneous mechanism of protein cluster formation for BSA (which can occur at low overall surface coverage) and by a homogeneous crowding mechanism for lysozyme (which occurs only at high surface coverage).


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Figure 3: Population distribution of relative diffusion coefficients observed for (a – c) lysozyme and (d – f) BSA. (a) and (d) depict data obtained at D⁄=1.0; (b) and (e) depict D⁄~0.4 ; (c) and (f) depict late time distributions at D⁄ less than or equal to 0.2.

In order to characterize the dynamic heterogeneity of the diffusing objects during interfacial aging, we examined the distributions of apparent relative diffusion coefficients (normalized by the initial mean diffusion coefficient) as a function of aging time. Figure 3 shows representative distributions, in the form of histograms, of the relative diffusion coefficients at various stages of interfacial aging. For short aging times, both lysozyme (Figure 3a) and BSA (Figure 3d) exhibit relatively narrow distributions of diffusion coefficients, with the BSA distribution being somewhat narrower. As the aging time increases, and the mean diffusion coefficient decreases, the peaks of the distributions for both proteins gradually shift to smaller values. For BSA (Figures 3e and 3f), the peak of the distribution clearly broadens, and appears to approach a flat


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distribution for the longest aging time. For lysozyme (Figures 3b and 3c), the main peak of the distribution maintains an approximately constant width, and a subtle tail is also observed to develop with aging time. Thus there is subtle evidence for the development of greater heterogeneity in the case of BSA than for lysozyme, which would be expected for the layer formation mechanisms hypothesized above. However, on the basis of these data alone, there is no question it would be difficult to make very strong mechanistic conclusions. In particular, our ability to observe the expected very broad distribution associated with heterogeneous layer formation is hampered by the fact that we cannot resolve very small values of the diffusion coefficient (these small values cluster in a resolution-limited peak). For lysozyme, where one might expect to see a well-defined peak whose peak moves to smaller values with aging time, it is inevitable that we will see a small population of fast-moving objects, due in part to short-lived tracking artifacts, and in part to molecules that may adsorb into a second layer on top of the main protein layer. Moreover, in general, it is not clear that cluster formation should always lead to a broad distribution of apparent diffusion coefficients, since some clustering mechanisms (which involve dynamic association and dissociation) can result in a distribution of clusters with a characteristic size that increases with time. Therefore, it became useful to perform more detailed types of trajectory analysis that provided direct signatures of molecular crowding.


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Figure 4: Mean squared displacement plotted vs. time interval for (a) BSA and (b) lysozyme at selected time bins as annotated in the legends. These time bins were chosen to represent aging times (early, middle, and late) at which the respective protein layers exhibited similar behavior.

The MSD versus time interval for both BSA and lysozyme, calculated from a typical experimental run, is shown in Figure 4. On the logarithmic axes of Figure 4, the evolution of the power law exponent is clearly visible as a change in slope with aging time. These data were fitted to the anomalous diffusion expression described above, and the power law exponents, α, from these fits were determined, and are shown in Figure 2c versus dimensionless time for both BSA and lysozyme. As expected for isolated proteins diffusing at a liquid-liquid interface, both BSA and lysozyme initially exhibit Brownian motion (α=1). As aging time and surface coverage increase, anomalous subdiffusive motion is observed for both protein systems, suggesting that obstacles within a crowded interface hinder molecules (or diffusing clusters) from exploring their


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environment to the extent that would occur in the absence of obstacles/crowding. Possible explanations for interfacial subdiffusion include surface crowding by an excess of molecules or confinement of the diffusing molecules by larger objects that create confined environments.44

The evolution of the subdiffusive behavior differs between the two protein systems in important and interesting ways. The decrease in α for BSA (indicating the onset of subdiffusion) appears at Γ~0.2, long after the interfacial mobility has slowed but slightly before interfacial tension begins to decrease (Figures 2 a–c). This observation further supports the hypothesized heterogeneous mechanism for the BSA slowing-down phenomenon. A heterogeneous model implies that initial slowing is due to the creation of protein clusters that are initially isolated (hence exhibiting Brownian diffusion). However, as the clusters become crowded enough to serve as obstacles, their trajectories would become subdiffusive. Because the clusters include some large aggregates that do not pack efficiently, the subdiffusive motion would be expected to occur at relatively low values of total surface coverage before the interfacial tension begins to decrease significantly. This effect would be even more pronounced for aggregates that are dendritic or fractal, as opposed to compact.23 For lysozyme, on the other hand, the power law exponent α begins to decrease at values of surface coverage (Γ~1) that are similar to those at which the mobility and interfacial tension also begin to decrease (Figures 2a-c). This is consistent with a homogenous model of layer formation since interfacial crowding of individual proteins simultaneously slows and obstructs diffusion, and decreases the interfacial tension.

Crowding or “caging” effects have been widely observed to influence the correlation of subsequent steps within diffusive trajectories. For example, in principle an unconfined Brownian


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trajectory exhibits no correlation whatsoever between subsequent steps. However, in real systems, displacements that are measured at very short time intervals generally exhibit some positive correlation, which decays over a characteristic relaxation times. Interestingly, in situations where trajectories are obstructed or confined (or in viscoelastic media), displacements measured over an appropriate range of time scales may exhibit anticorrelated behavior, i.e. a step is more likely to be in the opposite direction than the previous step.44–48 Although the low signal-to-background ratio associated with single-molecule measurements greatly limits the time resolution of our observations, we nevertheless decided to calculate velocity-velocity autocorrelation functions to see if crowding effects resulted in any measureable anticorrelation. In particular, we calculated the autocorrelation function, G(𝜏) = /, where v(t) represents the instantaneous velocity vector at time t.

Figure 5 plots G(𝜏) as a function of time interval for various aging times, for both BSA and lysozyme for a representative experimental run. The time resolution of the experiments is necessarily coarse, due to the need to acquire sufficient photon counts from individual fluorescent molecules. However, it is interesting to note that a clear empirical trend is observed in the overall shapes of G(𝜏) with aging time. As expected, for short aging times where diffusing objects are isolated and un-obstructed, both protein systems initially exhibit either an absence of autocorrelation or slight positive autocorrelation for 𝜏 > 0. However, as the interface ages, anticorrelation is observed for G(𝜏 = 0.2𝑠), i.e. the shortest measureable time interval. Figure 2d plots the evolution of G(𝜏 = 0.2𝑠) as a function of surface coverage, Γ. For time intervals of 0.4s or longer, no significant correlation, positive or negative, is observed. Similar behavior has


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recently been observed by Granick and coworkers for crowded colloidal systems,48 where anticorrelated motion was observed for time intervals of 𝜏 = 0.1𝑠 at sufficiently high volume fractions.

Figure 5: Velocity-velocity autocorrelation function vs. time interval for (a) BSA and (b) lysozyme at selected time bins depicted in the legends. The time bins for (a) BSA are solid line 𝛤 = 8𝑥10−4, dotted line 𝛤 = 4𝑥10−1 , dashed line 𝛤 = 7𝑥10−1 ; and for (b) lysozyme are solid line 𝛤 = 4𝑥10−4 , dotted line 𝛤 = 2, dashed line 𝛤 = 5.

Remarkably, there is essentially a perfect correlation, with respect to aging time, between the appearance of anticorrelated motion (Figure 2d) and the onset of subdiffusive motion (Figure 2c), despite the fact that these analyses are completely independent. As with the anomalous power law exponent described above, the appearance of anticorrelated motion coincided with the


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decrease in mobility and interfacial tension for lysozyme, again consistent with a homogeneous mechanism for surface layer formation. For BSA, like the evolution of the anomalous power law exponent, the onset of temporally anticorrelated motion occurred long after the decrease in average mobility, but slightly before the decrease in interfacial tension. By the same reasoning described previously, this is also consistent with a heterogeneous model of layer formation, assuming that the anticorrelated motion is a consequence of the caging of diffusing protein clusters by other vicinal clusters. It is interesting to consider the molecular-level mechanisms that could potentially lead to the distinctly different layer-formation mechanisms observed for BSA and lysozyme. The most likely considerations are electrostatic interactions, which could serve to stabilize proteins against interfacial aggregation, and hydrophobic interactions, which would tend to enhance clustering and aggregation as seen for BSA. Under the high ionic strength conditions associated with PBS buffer in the experiments performed here, the effective Debye length was only 0.56 nm, and electrostatic interactions were significantly reduced. Nevertheless, the absolute value of the zeta potential was greater for lysozyme than for BSA, which may have provided a modest stabilizing effect, reducing the propensity for lysozyme cluster formation compared to BSA.57,58 In addition, BSA exhibits greater hydrophobic exposure in its native state compared to lysozyme, 61,62

and BSA has also been shown to restructure on hydrophobic surfaces, while lysozyme

demonstrates minimal restructuring.63,64 Thus, it is reasonable to hypothesize that the greater exposure of hydrophobic residues for BSA, combined with the potential for electrostatic colloidal stabilization of lysozyme are responsible for the distinct mechanisms of interfacial layer formation.


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Conclusions Empirical observations suggest that different protein systems exhibit distinctive mechanisms of interfacial layer formation. While they can be modeled using undetermined parameters, it has been difficult to obtain direct information connecting interfacial structure to dynamic phenomena, particularly in the context of spatial and population heterogeneity. Previous observations, employing single molecule/particle tracking methods, suggested the importance of a heterogeneous mechanism for layer formation that involved the creation of interfacial protein clusters. However, that approach, based on distributions of individual diffusion coefficients, did not generally enable direct connections between behavior at short and long aging times. By employing trajectory analysis approaches traditionally applied to microrheological studies of colloidal systems, we showed that dynamic single molecule/particle analysis provided direct signatures of interfacial crowding, in addition to measuring the evolution of mobility. By comparing these dynamic signatures to macroscopic measurements of dynamic surface tension, we readily distinguished between a system where layer formation (and slowing down) was dominated by interfacial cluster formation (BSA) and one where layer formation was dominated by crowding of individual protein molecules (lysozyme). These mechanisms are, of course, not mutually exclusive. We believe that the methods can be applied generally, e.g. to understand how changing experimental conditions may alter mechanisms of interfacial layer formation.

Acknowledgements The authors gratefully acknowledge support from the National Science Foundation award #CBET-1133871.


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Table of Contents Graphic


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Molecular Trajectories Provide Signatures of Protein Clustering and

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