Resistive Pulse Sensing of Pre-Nucleation Activities during Single-Entity Lysozyme Crystallization on Single Nanopipettes

Abstract

The formation of cluster aggregates in a (super)saturated solution prior to protein nucleation is crucial to overcoming the thermodynamic energy barrier which enables further growth of single crystals. This process is important for single crystal growth, separation and energy conversion among other important applications. For structural determination of biomacromolecules, neutron crystallography holds unique advantages in resolving hydrogen/proton over other structure determination techniques but faces technical obstacles in requiring large high-quality single crystals and preferentially hydrogen-deuterium exchanges. Herein, we explore protein nucleation in heavy water (D₂O) via nanopore-based resistive pulse sensing, with lysozyme as prototype. By controlling localized supersaturation and phase transition at a nanopore through adjusting the potential waveform, a single protein crystal can be grown. Our focus is on understanding the translocation and/or transformation of protein aggregates through nanopores prior to the irreversible nucleation. As expected, higher protein concentrations tend to facilitate nucleation and growth of a single protein crystal with higher supersaturation, consistent with bulk experiments. At lower protein concentrations, individual current spikes are resolved as characteristic single-entity events in resistive pulse sensing. Those transient events are potential-dependent characterized by the peak amplitude, duration and area/charges. Statistical analysis reveals both translocation of protein oligomers and their transformation or further aggregation. This study represents the first step toward elucidating valuable insights into the dynamics of protein translocation and aggregation in heavy water and demonstrates the potential of using nanopores in the detection and characterization of dynamic phase transitions at single-event levels.

Graphical Abstract

1. Introduction

Resistive pulse sensing with protein or synthetic nanopores offers exciting capabilities in real-time detection of individual molecules/nanoparticles or events, generally speaking single entities.^1–9 A unique advantage is capturing dynamic and transient events that might be obscured by ensemble methods, so as to understand the heterogeneity of the system and to resolve rare events. One such challenge is nucleation that precedes crystallization,^10–12 for example in growing protein single crystals for structure determination. Nucleation is fundamentally significant in basic research and plays vital roles in various industries ranging from materials synthesis to pharmaceutical formulation and drug design. Crystallization of solutes starts with molecular assembly and the formation of thermodynamically stable embryos, a dynamic process in ensemble referred to as nucleation.^13–15 The formation of individual nuclei, however, are asynchronous as stochastic events in a bulk solution or interfacial region. Pre-nucleation clusters and dense liquid domains are among the intermediates that may facilitate the stable nuclei formation to overcome the energy barrier for successful nucleation and determining the rate of nucleation.^16–19 These asynchronous and stochastic/chaotic single entity events, together with the dynamic growth and dissolution of those transient ‘instable’ intermediates, impose fundamental limitations to ensemble-based, static ex-situ, or energy-intense and invasive methods such as X-ray scattering or electron microscopy methods.^20–24

Scheme 1 illustrates our strategy to control nucleation and subsequent crystal synthesis at the single-entity level using lysozyme and insulin in H₂O as prototypes previously reported.^{12, 25} The supersaturation is localized at the interface between a sample and a precipitant solution, spatially confined by the tip of a single nanopipette. The degree of supersaturation is governed by the exchange of matter between the two solutions, a process actively regulated by electrokinetic ion transport driven by an external potential waveform in addition to the diffusion governed by the concentration gradients of the chosen solutions. Precipitants inside the nanopipettes and lysozyme in the exterior solution will diffuse toward each other. Additionally, under an applied potential bias, lysozyme with positive charges will migrate toward or away from the nanotip under positive or negative bias respectively, similar for other electrolyte cations (in opposite direction for anions). Equipped with the rich literature on fundamental studies on the physicochemical properties of various nanopores and their sensing applications,^26–34 two independent current feedback mechanisms are identified to be associated with the nucleation process: a change in current amplitude and a reduction in noise. While true atomic resolution diffraction quality has been achieved by tuning the rates of nucleation and crystal growth, the physical origin of those captured higher ‘noise’ during the pre-nucleation stage remains to be determined.²⁵

Scheme 1.

Experimental setup and mass transport directions. A precipitant-loaded nanopipette is inserted into a microliter lysozyme solution droplet. The precipitants generally contain 2M NaCl with 2–10% polyethylene glycol (PEG). Lysozyme is positively charged at pH 4.8, either (super)saturated for crystal growth or undersaturated or pre-nucleation sensing. The potential bias is measured with two Ag/AgCl wires, one as working electrode (WE) in lysozyme solution against the reference/ground electrode (RE) inside the quartz capillary.

Neutron diffraction is uniquely advantageous in determining the positions of light atoms such as hydrogen in comparison to X-ray or electron beams, but limited by the relatively weak flux or signal (signal-to-noise, S/N).^{35, 36} Longer data-collection time is a necessity, and preferentially by synthesizing larger high quality crystals (typically at least 0.1 mm³) and replacing hydrogen by deuterium because deuterium has a larger coherent scattering cross-section than hydrogen.^37–40 Combining the controllable nucleation and crystal growth directly in D₂O could mitigate the uncertainties associated with H-D exchange after crystal synthesis as well as obtaining high quality large crystals to improve the efficacy of neutron crystallography. Herein, we report our first step in studying the pre-nucleation activities of prototype lysozyme in D₂O directly to understand the fundamentals and developing strategies to synthesize high quality protein crystals directly in D₂O.

2. Material and methods

2.1. Chemicals and tools

Hen egg white lysozyme (HEWL, ≥ 90%, Sigma-Aldrich), Deuterium Oxide (D₂O, 99.9% atom % D, Sigma- Aldrich) α,ω-dicarboxylic polyethylene glycol (COOH-PEG-COOH, M.W. 3.5 kDa, ≈96.8%, Advanced BioChemicals), Sodium Chloride (Crystalline, Fisher Chemical), Sodium Acetate anhydrous (Fused, Fisher Scientific), quartz capillaries (O.D. : 1.0 mm, I.D.: 0.70 mm, 7,5 cm length, QF100-70-7.5, Sutter Instrument Co.)

Nanopipette characterizations and coupled electroanalytical-optical setup have been previous reported.^41–44 Briefly, quartz nanopipettes were fabricated using a P-2000 laser puller (Sutter Ins.) under the following parameters: Heat: 700, Filament: 4, Velocity: 60, Delay: 150, Pull: 120. The optical images were taken with an Olympus BX51 microscope and a 40 X Olympus LumPlanFLN water immersion objective. The current-time data were collected using a Dagan Chem-Clamp amplifier and a Dagon 100 M head stage preamp at 100pts/s sampling rate. The potential was changed manually based on the feedback of current and real-time optical imaging. The brightfield images were analyzed using ImageJ software and the current-time data analysis was processed using OriginLab.

2.2. Solutions for resistive pulse sensing and crystallization

The D₂O solutions adopt the same parameter as those in our previous studies on lysozyme crystallization in H₂O. For crystallization, the HEWL sample contains 25 mg/mL of HEWL and 0.55M of NaCl in 0.1 M acetate buffer at pH 4.74. A 2M NaCl solution containing either 2 or 10% wt of α,ω-dicarboxylic polyethylene glycol (COOH-PEG-COOH, M.W. 3.5 kDa) serves as the precipitant solution. All solutions were centrifuged for at least 20 minutes at 4200 rpm to ensure no solid precipitates are optically seen under the microscope. For resistive pulse sensing, the HEWL concentration was lower, containing either 350 μM or 35 μM (2.5 mg/mL or 0.25 mg/mL).

2.3. Data analysis

Asymmetric Least Squares Smoothing is used for current-time baseline treatment. ALS is particularly useful for cases where baseline is not well-defined, drift is nonlinear, and signals are intrinsically low and/or without baseline separation. Four adjustable parameters are set based on control experiments: asymmetric factor, threshold, smoothing factor, and number of iterations. Details are provided in supporting information and further discussed in 3.2. Briefly, asymmetric factor ranges between 0 and 100%, with lower values (say 1 or 10%) defining a baseline floor for positive peak signals while higher values (say 90–99%) setting a ceiling baseline for negative signals. In other words, asymmetric factor sets an estimated baseline based on the weight percentage of the total data points. With an appropriate asymmetric factor, a Gaussian distribution due to random noise can be expected with the mean as baseline zero, i.e. about the same number of points above and below excluding the signals. For our data analysis, the asymmetric factor for negative peaks is either 0.99 or 0.90 and for positive peaks is either 0.01 or 0.1 unless defined otherwise. The threshold separates signal from noise. The threshold was set using 1.5 times the standard deviation of baseline divided by the tallest peak in the dataset. The smoothing factor controls the balance between retaining the peak shape and reduced noise fluctuations. For the smoothing factor, 5 or 7 was used for datasets with more/less obvious baselined drift. The number of Iterations allocates the computational expense for the algorithm to converge. The number of iterations was kept consistent at 10. Local maxima detection that searches for maxima in a moving window across the signal is used for peak search.

3. Results and Discussion

3.1. Overview of sequential phase transitions during lysozyme crystallization in D₂O and H₂O

Representative electrical current features during lysozyme crystallization in D₂O are provided side-by-side with those in H₂O in Fig. 1. Time lapse brightfield images capture a dark spot on the nanotip starting at about 6 minutes which further grows inside the nanopipette forming a larger dense liquid domain.²⁴ Thermodynamically, the driving force is the increase in supersaturation due to the efflux of precipitants from inside the nanopipette and the influx of the protein molecules, via diffusion and uniquely in NanoAC with migration controlled by the applied potential. If the exterior protein solution is supersaturated in metastable states, growth of individual crystals on the nanotip can be sustained which generally takes several hours to grow up to tens of microns depending on the supersaturation, as shown in the top right time lapse images observed in D₂O for the first time. These results are qualitatively consistent among different nanopipettes in the size ranges of tens up to sub-200 nm in diameter, as well as our earlier report in H₂O focusing on the controls of crystal quality.²⁵

Figure 1.

Controlled nucleation and crystal growth of lysozyme in D₂O (A-C) and in H₂O (D-F). Lysozyme concentration is about 3.5 mM in D₂O or H₂O. Representative brightfield images on the top show the formation and growth of the dense liquid domain (left series), and crystals grown (right series, about 8 hours from time zero) in D₂O. Current is driven by + 1.0 V bias. Panels A & D are 15-s zoom-ins of the current data in panels B & E respectively. The corresponding noise level in panels C & F is determined by 5-second moving standard deviation of the raw current data in B & E.

Evolution of the optically resolved phase transitions is associated with rich current features. Dense liquid domain formation induces drastic current decrease within the first few minutes. Time zero is when a positive bias potential is applied to further increase supersaturation of positively charged lysozyme. Noteworthily, diffusion alone, upon the insertion of nanopipette loaded with precipitant solution into the micro-liter sample droplet, is inadequate to induce protein nucleation because low lysozyme concentration is adopted herein to resolve transient pre-nucleation events. As the current arises primarily from the transport of electrolyte ions (NaCl) at much higher concentrations, the ca. five-fold current decrease suggests five-fold increase in viscosity of the dense liquid domain assuming other factors remain unaffected.⁴⁵ The current continues to decrease slightly over a period that varies significantly, attributed to the stochastic nature of individual molecular assembly events analyzed next. A relatively abrupt decrease in current amplitudes (panels B&E) combined with noise level (panels C&F), at around 470 mins in D₂O and 7 mins in H₂O, indicate successful nucleation which overcomes the energy barrier and enables further crystal growth. Lower protein concentration generally leads to longer waiting time for the irreversible nucleation and subsequent crystal growth. Limited by the heterogeneity of individual nanopipettes and the stochastic nature of single entity activities, the differences of nucleation kinetics in D₂O and H₂O environment cannot be resolved yet.

By scrutinizing the current features around nucleation, transient current spikes are revolved prior to nucleation denoted by red dots in A(i) and D(i) analyzed next. These transient individual events in ensemble account for the much higher noise level. As discussed in the following sessions, these transient spikes represent individual molecular assembly events as lysozyme molecules aggregate and interact locally in the dense liquid domain. The spikes can be interpreted as stochastic fluctuations in ionic transport caused by the dynamic, non-uniform aggregation of protein molecules. This aligns with Classical Nucleation Theory (CNT), which describes nucleation as a stochastic process involving the formation of unstable, small nuclei that either grow to critical size or dissolve back into the solution.⁴⁶ Those transient spikes disappear and show much lower baseline fluctuation in panels (ii), signaling irreversible transitions from more dynamic gel-like dense liquid into more rigid crystalline nuclei formation at the nanotip. Further growth of individual crystals on the nanotip is not associated with distinctive electrical or optical features.

3.2. Identification of translocation events

In Coulter Counter stochastic single entity sensing, the signal associated with the translocation of larger objects such as protein aggregates through the nanopore arises from the disturbance of the baseline current carried by smaller electrolyte ions. Shown in Fig. S1 & Table S1, under otherwise identical conditions, the current measured without protein maintains a stable featureless baseline with the standard deviation (SD) at about 0.04 nA which is used as noise level. Accordingly, any current fluctuations above 3×0.04=0.12 nA are determined as signals qualitatively. Fig. 2 illustrates the workflow of signal identification through asymmetric least square baseline subtraction. Correct baseline selection is critical because positive and negative current spikes can be resolved as shown in Figs. 2A and 2B, respectively. This is straightforward in the cases where adequate data points are collected, and/or the event frequency is low for example Fig. 2Ai. For high frequency consecutive events without baseline resolution such as those in Fig. 2Bi, Figs S2–S5 provide additional details on appropriate baseline establishment. Subtraction of the established baseline from the original current data effectively overcomes the inevitable baseline drift over longtime recording.

Figure 2.

Strategies for baseline treatment and peak identifications. (A) Positive Resistive Pulses driven by + 0.6 V bias; (B) Negative Resistive Pulses driven by + 0.9 V bias. Data collected from 350 μM lysozyme in 0.55 M NaCl in D2O, with 10% PEG and 2 M NaCl in D2O as precipitant. (i) Raw i-t trace (black) with baseline (red) determined through asymmetric least square smoothing. (ii) Baseline-subtracted current trace highlighting isolated resistive pulses. (iii) Identification of individual events, 5 local points (blue and red dots) and 10 local points (red dots only). Details in experimental section.

Several possibilities could cause the current spikes to be positive or negative. Given lysozyme is positively charged (PI>pH), both diffusion and migration would be in the direction toward inside the nanopipettes by diffusion and by migration under a positive bias. However, the segment of dense liquid confined further inside the conical nanopore is likely more restrictive to be the signal limiting region, as the region outside or near exterior interface would be more dilute. Assuming a particle of lysozyme oligomer remains unchanged while transporting through the dense liquid which oversimplifies the case discussed next, the signals toward and passing the signal-limiting region would display opposite features such as peak fronting or tailing shown in Figs. S6 & 2A, respectively.^47–49 In nanopore sensing, both positive and negative spikes have been observed where redox reactions enhance transport conductivity to generate positive peaks while temporary blockage of the pore causes negative peaks.⁵⁰ It’s also known that surface charge effects could produce biphasic pulses, increase in current before decreasing, due to the effects of higher ion conductivity produced by the surface charge and volume exclusion of charge carriers by the translocating particle.^47–49 The opposite effects of volume exclusion and surface charges of the lysozyme oligomers would surely play a role here. A more conclusive assignment of the peak polarity is hampered by the dynamic growth or dissolution of the dense liquid, which originates from and suggests the transient transformation of those oligomers or pre-nucleation clusters. The dynamic view is further supported by the occasional switches between positive and negative peaks during our measurements. Independent structural characterization of the dynamic dense liquid domain formed in the nanotip, about femto-to-picolitre, is unfortunately beyond our technical capability and the scope of this work.

To identify individual events for statistical analysis, effects of the local points between adjacent local maxima are compared in panels iii. Within one current trace, using a window of fewer local points usually identifies more transient and smaller events which otherwise appear as shoulder peaks, resulting in an increase in the number of events. This is evident from the additional peaks labelled by the blue dots. The integrated area of all the peaks is independent of whether the smaller shoulder peaks are resolved as separate events from the major peaks. The results are reasonable and supportive of the baseline treatment and signal identification, as the total area is associated with the total charges displaced by the translocation events regardless of the transformation of different oligomers. The analysis of multiple datasets with varied local points is summarized in Table S2. Fig. S7 provides additional examples of those additional or missing peaks. Overall, these examples demonstrate a robust parameter range to identify distinct events consistently which is optimized for different experimental data used in further analysis.

Measurement-wise, adopting undersaturated lysozyme solution and adjusting the applied potential to lower event frequency are generally favorable in achieving baseline resolutions for peak identification. The convenient controls in NanoAC via applied potential-time waveform also make the experiments highly effective over a broad range of solution conditions such as varied protein concentration (tens micromolar to millimolar) and precipitants (2–10 % PEG). Similarly, it also tolerates heterogeneity issues of individual nanopipette devices.

3.3. Classification of different translocation events

In the chemical space for tetragonal lysozyme crystal growth, dimers and octamers are identified as intermediate species prior to nucleation in ensemble systems, with octamers absent at lower lysozyme concentrations.^{20, 51} To corroborate, the current spikes are categorized statistically illustrated in Fig. 3. In a representative current-time trace (3A), the highest counts in histogram (3B) will center around zero after baseline subtraction (not shown), with 0.033 nA SD from the Gaussian distribution indicating random noise. This baseline noise is consistent with those results without lysozyme (0.04 nA, Fig. S1 & Table S1). Using 3×SD as threshold for qualitative analysis, any current spikes larger than 0.1 nA are deemed as signals. The high counts, below 0.1 nA but higher than 0.033 nA, indicate agitations from individual protein molecules on the electrolyte ion flux within the dense liquid that require further studies. Three Gaussian distributions fit the histogram (about 2000 peaks) well, though the first one at 0.26 nA is restricted to the right side due to the significant overlap with the low amplitude current counts (Table S3). The intermediate peaks (labeled by blue dots, 0.50 ± 0.07 nA) can arguably be assigned to either the 0.26 nA± 0.01 or the 0.93 ± 0.09 nA category, which would have conveniently matched the dimers and octamers characterized in the bulk. However, it is also possible that other oligomers have been formed and detected.

Figure 3.

Identification of different transport events. (A) Representative I-t traces after baseline subtraction. Current was measured through a nanopipette in 350 uM lysozyme, 10% PEG in D2O at 0.6 V with the original baseline current ca. 6 nA. Colored dots represent peaks identified and classified according to the fitting results in B. Dashed color lines denote the fitted peak centers in B. (B) Peak height histogram for the current in A, but over 200 s. Colored lines are single peaks resolved from Gaussian fitting and cumulative peaks, representatively. Full data in Fig. S1A and the fitted parameters from about 500 peaks in Table S3.

3.4. Controls on the event characteristics by the applied potential

Lysozyme oligomers are the building blocks for the growth of dense liquid and ultimately nucleation. While larger assemblies such as nanowires have been observed as precursors for nucleation,^{23, 24} the dynamics of the assembly processes, for example whether it involves the transformation from smaller into larger oligomers, remain elusive to the best of our knowledge, especially under operando crystal growth conditions. By adjusting the applied potential, the peak height, duration and area are tuned as analyzed in Fig. 4 and S8, where the lysozyme concentration in the sample droplet is about 100X and 10X more diluted from spontaneous nucleation. Interestingly, the event frequency is higher under 0.8 V than 0.9 V (Fig. S9), though the 0.9 V bias induces larger peaks in height and area, as well as longer duration. With dilute sample and under lower driving potentials, the signals at 0.7 V are less defined for quantitative comparison. The correlation plots in panel B clearly reveal two zones separating the 0.9 V data from the rest, with or without normalization (Fig. S10). Representative peaks at each potential are numbered and listed in the zone plots. Two outliers pointed out by the arrows show the effects of overlapping baseline: those peaks with a large FWHM can be a result of unresolved baseline, and/or inadequate sampling rate (resolution: 10 ms in FWHM; 0.033 nA in height). Since baseline is difficult to visualize in the 3 second time frame in Fig. 4, histograms and current traces before and after baseline treatment are provided in Fig. S11 analyzed consistently as explained in Fig. S3–S5. Positive peak signals larger than the Gaussian shaped baseline signal are clearly seen from 0.8 V and 0.9 V data, while those from 0.7 V do not have adequate S/N to be resolved as positive or negative peaks quantitatively and conclusively.

Figure 4.

Statistical analysis of current features at different potentials. Current was measured through a nanopipette in 35 μM lysozyme, 2% PEG in D2O at 0.7 V, 0.8 V and 0.9 V. (A) Current after baseline subtraction (black curves) and identified peaks (red dots). Dashed lines denote current zero. Peak 1–8 are highlighted to show the distribution of the peak parameters in Bi and Bii. Arrows point out the outliers, that is caused by uneven sampling rates or unresolved baseline. (B) Correlation plots of FWHM-height and peak area-height from individual peaks at varying potentials: 0.7 V-blue, 0.8 V-red, and 0.9 V-black. Each dot represents an individual peak. Correlation plots after potential- and current-normalization were in Fig. S10 (C) Corresponding histograms with a bin size of 0.05 nA in height, 10 ms in FWHM, and 0.005 nC in peak area, respectively. Black and colored lines are from Gaussian fittings. Fitting details in Table S3. (D) Statistical peak parameters from Gaussian fitting of the histograms in C. (E) Cartoon illustrating the formation of larger oligomers or clusters around the nanopore.

Two peak heights are resolved statistically at 0.9 V, while others fitted well with a single Gaussian distribution (panel C & Table S3). The low amplitude peak height scales with the potential (panel D). The high amplitude one appears isolated here, but aligns with those events in Fig. S8 with ten times higher lysozyme concentration. The peak duration (FWHM) is shorter at about 25 ms, together with a smaller area of about 0.01 nC under lower bias. Both increase by several folds (to 60–120 ms and 0.06 nC respectively) under higher bias (0.9V data) OR in higher bulk concentrations (Fig. S8). For the consecutive measurements using the same nanopipette, a lower event frequency at higher potentials is somewhat counterintuitive in the sensing of stable and intact objects. These results strongly suggest favored formation of larger oligomers around the tip region due to the localized high concentration. Further, two or more peak heights are detected in Fig. S8, with higher bias favoring larger peak heights, again suggesting a transformation of smaller into larger aggregates. While both dense liquid and particle translocations could change with the applied potential, the impacts of overall domain growth/dissolution are expected to be much slower relative to the transient translocation events and eliminated by baseline subtraction. Statistical analysis of these additional results further supports the transformation of individual smaller oligomers into larger ones as resolved in Fig. 3 and corroborates with ensemble results in literature qualitatively.

4. Conclusion

Stochastic single entity sensing using single nanopipettes is demonstrated as an effective toolbox to study the dynamic and asynchronous early-stage transformations during protein crystallization. The unique advantages over ensemble methods include the spatial resolution intrinsically confined at the nanopore tip, combined with the temporal resolution and in-situ electroanalytical controls. The formation of a dense liquid domain is unequivocally detected in both H₂O and D₂O environment and determined to have about five-fold increase in viscosity characterized by current decrease. Inevitable baseline drift/fluctuation in this highly challenging sample system is addressed by asymmetric least square smoothing which is expected to be applicable to other sensing systems facing similar challenges. Individual current spikes are analyzed statistically and reveal the transformation of smaller oligomers into larger complexes. The evert characteristics is qualitatively or semi-quantitatively correlated with the solution and measurement parameters. The results demonstrate enabling capabilities for detailed mechanistic studies and generalization to other materials, also point out the needs such as in-situ structural characterizations. In addition to the obvious needs in high temporal resolution and current sensitivity, temperature controls will be essential, especially when the fluctuation of room temperature is beyond several degrees, as these molecular assembly and phase transition processes are sensitive to temperature variations.

Supplementary Material

Additional results and discussion; experimental and data analysis details; Tables S1–S4; Figures S1–S9.

Highlights:

• lysozyme crystallization in D₂O at single entity resolution achieved

• single entity events resolved in dense liquid during pre-nucleation stage

• nanopore electrochemical sensing as promising toolbox for mechanistic insights on nucleation and phase transitions