Single-Molecule Mechanochemical pH Sensing Revealing the

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Single-molecule mechanochemical pH sensing reveals the proximity effect of hydroniums generated by an alkaline phosphatase Prakash Shrestha, Yunxi Cui, Jia Wei, Sagun Jonchhe, and Hanbin Mao Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b03478 • Publication Date (Web): 29 Dec 2017 Downloaded from http://pubs.acs.org on December 30, 2017

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Analytical Chemistry

Single-molecule mechanochemical pH sensing reveals the proximity effect of hydroniums generated by an alkaline phosphatase Prakash Shrestha1, Yunxi Cui#, Jia Wei1, Sagun Jonchhe1 and Hanbin Mao1* #

State Key Laboratory of Medicinal Chemical Biology, Nankai University, Tianjin, 300071, P R China Department of Chemistry & Biochemistry and School of Biomedical Sciences, Kent State University, Kent, Ohio 44240, United States 1

ABSTRACT: Due to the fast diffusion, small molecules such as hydronium ions (H3O+) are expected to be homogeneously distributed, even close to the site-of-origin. Given the importance of H3O+ in numerous processes, it is surprising that H3O+ concentration ([H3O+]) is yet to be profiled near its generation site with nanometer resolution. Here, we innovated a single-molecule method to probe [H3O+] in nanometer proximity of individual alkaline phosphatases. We designed a mechanophore with cytosine(C)-C mismatch pairs in a DNA hairpin. Binding of H3O+ to these C-C pairs changes mechanical properties, such as stability and transition distance, of the mechanophore. These changes are recorded in optical tweezers and analyzed in a multivariate fashion to reduce the stochastic noise of individual mechanophores. With this method, we found [H3O+] increases in the nanometer vicinity of an active alkaline phosphatase, which supports that the proximity effect is the cause for increased rates in cascade enzymatic reactions.

As a measure of solute density in a solution, concentration is inversely proportional to the average distance between two solute molecules. Due to the thermal motion of a molecule in solution, the distance between any two solute molecules varies constantly. Such a variation does not pose a problem for bulk reactions in which it is the average distance from zillions of molecules that determines the concentration effect. However, for molecules with limited copies as those found in small cellular compartments, the variation in concentration becomes significant, which leads to intermittent or localized biochemical reactions characteristic of many vital processes such as replication, transcription and translation1. To fully understand these processes, it is necessary to follow localized variation of reactant or product concentrations in real time. Due to the ensemble nature of conventional concentration measurements, however, the concentration variations in nano-space are often beyond experimental measurement. The lack of such a measurement has left many fundamental problems unresolved. For example, it has been observed that enzyme activities increase for cascade reactions catalyzed by different enzymes arranged in nanometer distance on a DNA scaffold2,3. It has been proposed that efficient supply of intermediate substrates from the upstream to the downstream reactions is achieved by two means. First, due to the close arrangement of the two enzymes on the nano-scaffold, the intermediates from

the upstream reaction are enriched near the surface of the downstream enzyme (the proximity effect). Second, the diffusion of the intermediates becomes slower in the twodimensional surface connecting the two enzymes. However, for small molecules that have fast diffusion coefficients such as hydronium ions (H3O+)4, it has been estimated that their concentrations are homogeneous in a solution milliseconds after their generation, even close to the place they are produced5. This suggests that proximity effect may play a significant role in the increased efficiency observed in specific cascade reactions located in a close range. This hypothesis can be tested by concentration measurements of small-molecules in the nanometer vicinity of their origin. Although miniaturized pH sensors have been demonstrated6-9, none of them is small enough to probe the pH in a nano-space. Fluorescence measurements can probe the pH in the nanospace10-12, however, their resolution is often diffractionlimited. This difficult task can be accomplished by singlemolecule methods6,13,14. Working as a molecular counter, single-molecule templates with nanometer sizes15 can record the time interval between the two arrivals of analyte molecules. Given the diffusion constant of the analyte, the time interval can be converted to the analyte concentration. To retrieve concentration information, which is an ensemble average property, a large set of single-molecule

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Figure 1. (A) Schematic of a single-molecule mechanochemical pH sensor, in which the mechanical property of a DNA hairpin is expected to vary with pH in an optical tweezers setup. The red arrow represents the application of force. Right panel depicts chemical process of cytosine-cytosine base pairing in the presence of a proton cation. (B) A typical force-extension curve at pH 5.5 depicting four sensing signals used in multivariate analysis. The red and black traces represent stretching and relaxing processes. (C) pH measurement using multivariate linear discriminate analysis (LDA) for the four sensing signals of extension hysteresis, unfolding force, refolding force, and refolding size.

events should be recorded to account for the stochastic noise in individual measurements. As a result, the temporal resolution is compromised. If, however, concentration can be evaluated by different observables simultaneously, stochastic noise can be reduced to obtain more accurate information within a shorter time frame, thereby improving the temporal response of singlemolecular measurements. Recording of different observables has been demonstrated in multivariate sensing such as electronic tongues and noses16,17. However, single molecules have been rarely served as templates for multivariate analyses.18 This can be ascribed to the weak signals inherent in individual molecules. In singlemolecule fluorescence techniques, for example, it is highly challenging to observe variables other than the fluorescent intensity since only a limited number of photons can be collected from each fluorophore before photo-bleaching occurs. In addition, fluorescence signals from surroundings can interfere with the data interpretation. Recently, we pioneered a new strategy, mechanochemical sensing19,20, to probe individual molecules in solution. This method uses a single-molecule mechanophore to transduce binding events into mechanical signals. Since the probing template is levitated between two optical traps, much of the mechanical noise from environment can be eliminated. Given that direct exposure to laser beams is not necessary, the photobleaching is also avoided. In this report, we created a new mechanophore to measure hydronium concentrations in localized space by monitoring either the tension or extension of a single-molecule pH sensing template. Using this template, we measured the concentration of hydronium ions in the vicinity of individual alkaline phosphatases during its enzymatic action of ATP hydrolysis. We found pH has been lowered with 0.4 units 10 nm away from the active alkaline phosphatase. This result supports that locally-increased concentration of the substrate is the cause for enhanced activity of cascade enzymatic reactions which are arranged in nanometer proximity.

EXPERIMENTAL SECTION Materials and Reagents. All DNA oligomers were purchased from Integrated DNA Technologies (www.idtdna.com) and purified by using denaturing polyacrylamide gel electrophoresis (PAGE). Streptavidin conjugated alkaline phosphatase was purchased from Vector Laboratories (www.vectorlabs.com). All chemicals including Tris-HCl, KCl and MgCl2 were purchased from either Fisher Scientific or Sigma with purities ˃99.0% and these were used without further purification. The antidigoxigenin and streptavidin coated polystyrene beads for optical tweezers experiments were purchased from Spherotech (Lake Forest, Illinois, USA). Unless specified otherwise, all enzymes were purchased from New England Biolabs (www.neb.com). Synthesis of the DNA constructs. The DNA constructs for single-molecule mechanochemical sensing (SMMS)19 were prepared as described in the previous report21. The sensing element was contained inside the DNA hairpin (see DNA sequences in Table S1) sandwiched between two long dsDNA handles22. Briefly, the digoxigenin labeled 2690 bp dsDNA handle was prepared by digesting pEGFP (Clontech, Mountain View, CA) plasmid with SacI (NEB) and EagI (NEB). After agarose gel purification of the handle, it was labeled at the 3′ end by digoxigenin using 18 µM Dig-dUTP (Roche, Indianapolis, IN) and terminal transferase (Fermentas, Glen Burnie, MD). The pure digoxygenin-labeled 2690 handle was extracted by ethanol precipitation. On the other hand, the biotin labeled 2028 bp dsDNA handle was prepared by amplifying a section of pBR322 plasmid template (New England Biolab, NEB) using PCR with 5' biotinylated primer 5'GCA TTA GGA AGC AGC CCA GTA GTA GG-3´(IDT, Coralville, IA). The PCR product was purified with PCR purification kit (Qiagen, Germantown, MD) and digested by XbaI restriction enzyme (NEB) for 8 hrs at 37°C. The digested 2028 bp handle was purified by agarose gel. To synthesize the mechanochemical pH sensor that contains 3 cytosine-cytosine mismatch pairs at the base of the hairpin stem (Figure S5), B1-3C was annealed with B5 while B3-


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Figure 2. Characterization of the single-molecule mechanochemical pH sensor. (A) Three pairs of cytosine-cytosine bases are separated by an A-T pair. (B) Typical force-extension curves observed at different pH. Blue arrowheads depict cooperative refolding transitions. X-axes are offset for clarity. (C) Left to right panels depict histograms of the change-in-contour-length during cooperative refolding (∆Lrefolding), extension hysteresis (∆x), and the difference between the unfolding and refolding forces (∆F), respectively, in the pH range 5.0–7.4.

3C was annealed with B4. They were ligated with the 2028 bp and 2690 bp dsDNA handles, respectively, by T7 DNA ligase (NEB) at 16°C for 16 hrs. The ligated products were separately purified on agarose gel. Then, these two ligated products were linked together by Cap4 oligo (Table S1) by using a 3-piece ligation carried out by T7 DNA ligase at 16 °C for 16 hrs (Figure S1). To prepare the other two mechanochemical pH sensors, B1-3C and B3-3C oligos were replaced by B1 and B3, respectively (see Table S1 for sequences). These were followed by the 3-piece ligations using Cap-5C (for 5 consecutive cytosine-cytosine mismatch pairs at the neck of the hairpin stem, see Figure S6) and Cap-3Cmix (for 3 cytosinecytosine mismatch pairs separated by an A:T pair close to the stem-loop interface of the hairpin, see Figure 2A), respectively, by the T7 DNA ligase at 16 °C for 16 hrs. To prepare the DNA construct to probe pH near alkaline phosphatase, the biotin labeled deoxythymine was introduced ~10 nm away from the hairpin sequence by using the templated ligation (Figure S2). For templated ligation, the DNA oligonucleotides AP template20, AP 12, AP 5, and AP 32 (see Table S1) were mixed in the ratio of 2:8:8:1 and ligated by T7 DNA ligase (NEB) at 16°C for 16 hrs. The ligated product was purified by native polyacrylamide gel electrophoresis. The incorporated biotin was confirmed by incubation of 1.0 µL of purified product with 1.0 µL (~1.0 mg/mL) of streptavidin conjugated alkaline phosphatase (company) for 1 hour before loading to the PAGE gel. Lane 2 showed a smear in bands, indicating the purified ligation product was bound to streptavidin conjugated alkaline phosphatase (Vector laboratories). Next, the purified ligation product was further ligated with the 2028 bp DNA handle by T7 DNA ligase (NEB) and purified by agarose gel

electrophoresis as described in section II (Figure S1). Similarly, the annealed B3 and B4 fragments (see Table S1) were ligated with the 2690 bp DNA handle and purified by agarose gel electrophoresis as described in section II. Finally, these two ligated handles were linked together by Cap-3Cmix (see Table S1) using 3-piece ligation carried out by T7 DNA ligase at 16°C for 16 hrs. Single molecule mechanochemical experiments in optical tweezers. Detailed description of optical tweezers instrument used for the single-molecule analysis has been reported elsewhere.23 To perform mechanochemical sensing experiment, the DNA construct was immobilized by incubating 1.5 µL of a diluted DNA construct (~1 ng/µL) with 1 µL of 0.1 % solution of anti-digoxigenin coated polystyrene beads (diameter: 2.10 µm) for about half hour at room temperature (25 ᵒC). The incubated samples were further diluted to 1 mL buffers with different pH. For buffers at pH 6.5, 7.0 and 7.4, 10 mM Tris-base was supplemented with 100 mM KCl; for buffers at pH 5.0, 5.5 and 6.0, 50 mM MES solution was supplemented with 100 mM KCl. Streptavidin-coated polystyrene beads (1 µL, diameter: 1.87µm) were dispersed into the same buffers (1 mL) as used for the anti-digoxigenin coated polystyrene beads. The bead-containing solutions were then injected into the microfluidic chamber. Two different types of beads were trapped inside two separate laser foci. By moving one of the trapped beads closer to another using a steerable mirror (Madcity Labs Inc., Madison, WI), individual DNA constructs were tethered between the two beads. Once a single DNA tether was confirmed between the two trapped beads with a 65 pN plateau, the Nano-MTA steerable mirror that controls the anti-Digcoated bead was moved away from the streptavidin-coated bead with a loading speed of ~5.5 pN/s. The DNA hairpin



of analytes22. We reasoned that with the incorporation of C:C pairs in a DNA hairpin, the mechanophore should become pH sensitive. Thus, at pH (e.g. 7.4) where C:C pairs are not protonated, the hairpin may refold slowly and less cooperative. At low pH (e.g. 5.5) where C:CH+ forms10,26-28, the refolding of hairpin is expected to be faster and more cooperative. Such a refolding behavior can be directly observed in laser tweezers in which a single-molecule template hosting the pH sensitive mechanophore is tethered between two optically trapped particles (Figure 1A). To construct a pH sensitive mechanophore, we used a hairpin with a 25-bp stem and a tetrathymine loop. Such a hairpin has shown rapid and reversible unfolding and refolding transitions (or ∆ 1 ……(1) mechanoescence) with a pronounced change-in-contour∆ length (∆L) of ~19 nm under a constant force29,30. where ∆e is the difference in extension between the In the first design, we introduced 3 adjacent cytosinestretching and relaxing curves at a particular force (F), kb cytosine mismatch pairs in the base of the hairpin stem is the Boltzmann constant, T is absolute temperature, P is (Figure S6, middle panel). Force ramping experiments the persistent length (50.9 ± 1.6nm)25 and S is the (see Experimental Section) were performed at two stretching modulus (1243 ± 63pN)25. physiologically relevant pH (5.5 and 7.4) to evaluate the mechanical unfolding and refolding of the modified RESULTS AND DISCUSSION hairpin mechanophore. We observed almost identical Development of a single-molecule mechanochemical unfolding and refolding patterns at these two pH’s pH sensor. Like a fluorescence-based pH sensor in which (compare histograms of the unfolding/refolding force and a fluorophore changes its photo-physical properties in the change-in-contour-length in Figure S6). In fact, response to hydronium ions, in mechanochemical sensing, transition features at pH 5.5 are almost identical with the a mechanophore changes its mechanical property in hairpin without C:C pairs, indicating that either the three presence of protons. DNA hairpins containing cytosine C:CH+ pairs are too weak or the insert position is not (C): C pairs have such a proton-responsive mechanical appropriate to induce different mechanical properties. To property. While the C:C pair dissociates in absence of generate significantly different signals in the pH range protons, it becomes stable as the hemiprotonated pair 5.5–7.4, in the second design, we placed five adjacent (C:CH+) (Figure 1A). Previously, DNA hairpins have cytosine-cytosine base pairs in the neck of the hairpin stem been demonstrated as mechanophores to report the binding (Figure S7). While the five C:C mismatch pairs are expected to respond to hydroniums more strongly, their placements in the hairpin neck are close to the transition state for the folding and unfolding of the hairpin, which is known to significantly vary the transition kinetics of the hairpin29 (Figure S7). However, singlemolecule mechanochemical experiments still showed that the unfolding and refolding trajectories of the hairpin were similar at both pH 5.5 and 7.4 with relatively big hysteresis between the two trajectories. As hysteresis area between the unfolding and refolding trajectories is inversely correlated with the refolding kinetics,31 the Figure 3. (A) Calibration curves for pH vs change-in-contour-length of cooperative refolding became slower at pH 5.5 refolding (∆Lrefolding) (i), extension hysteresis (∆x) (ii), and the difference between the for this hairpin compared to the unfolding and refolding forces (∆F) (iii). (B) The planar fitting of the two major LDA previous hairpin (Figure S6). This factors vs. pH. Inset represents the fitting plane from a particular viewpoint. (C) indicates that not all C:CH+ pairs Histograms of the measured pH for different buffers (pH 5.0 -7.4). The pH was were formed in the five C:C retrieved by the fitting equation obtained from the 3D calibration plot in B. Inset is the mismatch hairpin at this pH (see Fcorrelation plot of the actual pH vs measured pH. was unfolded when the tension inside the tether was gradually increased. Unfolding events were manifested by the sudden change in the end-to-end distance during the process. The F-X curve for each tether was recorded in a Labview 8 program (National Instruments Corp., Austin, TX), and data treatment was performed using Matlab (The MathWorks, Natick, MA) and Igor (WaveMetrics, OR, USA) programs. The unfolding and refolding forces were directly measured from the F-X curves while the changesin-contour length (∆L) due to unfolding or refolding transitions were calculated by the two data points flanking a rupture event by using an extensible worm-like chain (WLC) model (Equation (1)).24


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One solution to this issue is to collect independent observables during the folding/unfolding transition of the mechanophore, which is then followed by multivariate analysis. Such an approach is based on the unpredictable nature for stochastic transitions: it is extremely rare for stochastic transitions with the same trend to be observed from different but orthogonal perspectives. Single molecule multivariate analysis. After inspecting F-X curves at different pH, three variables were identified to vary with pH independently: the cooperative section of the change-in-contour-length for refolding (∆Lrefolding), the difference in the extension between unfolding and refolding transitions (∆x) (see Figures S3 and S4), and the difference between the unfolding and refolding forces (∆F) (see respective histograms in Figure 2C). For each variable, we plotted a calibration curve with pH (Figure 3A). All three variables show decent linear relationship with pH (R2 = 0.943 to 0.967). To determine a calibration function for pH that combines all three variables, we performed linear discriminant analysis (LDA)32. LDA is a multivariate statistical method that assigns each unknown to a specific group based on prior training of the known groups.33 The training generates a matrix function that projects unknown data to a new space in which known groups have been separated with maximal distance from each other. The assignment of the unknown is accomplished by the closest distance to a certain training group. In our case, the aforementioned three variables collected at six pH conditions (pH = 5.0, 5.5, 6.0, 6.5, 7.0, and 7.4) served as 6 training groups (see Supporting Information, section II.4). In the matrix function generated, we used two major factors (factor 1 and factor 2) that account for 97.8% of all the information provided by the three variables in the training groups. Using this matrix, each data point with three observables was then reduced to the two major factors (factor 1 and factor 2) in a 3dimensional space. Next, we constructed a 3D calibration plot using pH as the z axis and the factors 1 and 2 as the x and y axes, respectively, for each pH group (Figure 3B). A planar function, pH = 5.61 + 0.4958x + 0.01605y ……. (2) Figure 4. pH measurement in the vicinity of an alkaline phosphatase (AP). (A) provides a fitting (R2=0.995) Schematic of the pH variation due to the ATP hydrolysis catalyzed by the AP (not to superior to each pH calibration scale). (B) pH profile with (red) and without (black) ATP using the SMMA method. (C) using individual variables (R2 = Cooperative refolding ∆L was measured in 3 cycles that alternate in buffers (10 mM 0.967, 0.953, and 0.943 for Tris, pH 7.5) with (red) and without (black) 100 µM ATP. (D) Histograms of the ∆Lrefolding, ∆x, and ∆F, refolding ∆L and corresponding pH measured from the same molecule in buffer (black) respectively, see Figures 3A and and 100 µM ATP (red). The difference between the data points with and without ATP is 3B). statistically significant by Student’s t-test at 99.9% confidence level. To test the accuracy of this

X curves and force and ∆L histograms in Figure S7). To facilitate the formation of all C:CH+ pairs in the hairpin mechanophore, in the next design, we inserted a Watson-Crick A:T pair between the three C:C pairs. In addition, we added a Watson-G:C pair at the loop-stem interface (Figure 2A). These modifications are expected to bring together the two hairpin strands for the formation of desired C:CH+ pairs. During the force ramping experiments, the unfolding trajectories were similar at all pH’s (Figures 2B and S5). Significantly, the refolding trajectories displayed rather different features between pH 5.5 and 7.4. The refolding was faster and more cooperative at pH 5.5, as expected, while slower and less cooperative at pH 7.4. When we investigated this mechanophore in the pH range 5.0 – 7.4, we found the cooperative refolding transitions decreased while hysteresis regions between unfolding and refolding increased with pH (see black curves in Figures 2B, S3, and S4). This encouraging observation prompted us to fully characterize the pH response of this mechanophore. The minimal space in which this mechanophore can probe pH is governed by the size of the hairpin. The hairpin can be approximated by a column with 2 nm in diameter (width of the dsDNA stem) and 9.18 nm in height (0.34 nm/bp × 27 bp = 9.18 nm). This is equivalent to 2.9 × 10-23 liters, which, to the best of our knowledge, represents the smallest volume for pH measurement. As pH is probed by the mechanical transition of individual mechanophores, the stochastic nature of single-molecule transition adds noise to the pH measurement. To obtain pH accurately, multiple measurements should be carried out, which reduces the temporal resolution of the sensing.



single-molecule multivariable analysis, we prepared buffers with known pH and measured their pH using this single-molecular multivariate analysis (SMMA). As shown in Figure 3C, the measured and the actual pH values correlate rather well (R2=0.997, see Figure 3C), thereby confirming the accuracy of our SMMA approach. Although we used three variables here to perform the pH measurement, more independent variables can be used in the SMMA, which will provide more accurate pH measurement. For a balance of accuracy and better visualization, these variables can be reduced to two principle factors to construct a 3D calibration function as described in Figure 3B. Lowered pH at the nanometer vicinity of an active alkaline phosphatase. With the establishment of this SMMA method, we set out to probe the hydronium ion concentration in the vicinity of alkaline phosphatase, an enzyme that releases hydronium ions while catalyzing the ATP hydrolysis34. We constructed a DNA molecule in which the pH responsive mechanophore was placed 10 nm away from the alkaline phosphatase (see Figure 4A). As alkaline phosphatase is attached with streptavidin, it can be immobilized on the single-molecule template that contains a biotinylated thymine 12 bp and 14 nts (or 10 nm) away from the single-molecule pH sensor (see Figure S2 for the preparation the sensor construct). To ensure that the DNA templates were tethered to the trapped beads via the biotin at the end of the dsDNA handle, rather than that reserved for the attachment of the alkaline phosphatase close to the hairpin sensor, the length of the singlemolecule construct anchored between the two trapped beads was screened (Figure S9). Without ATP, the pH determined by the SMMA method (pH=7.4) matched with that of the buffer (pH=7.5) (Figure 4B). In the presence of 100 µM ATP, we found that pH significantly decreased to 7.0, which is consistent with the release of hydronium ions due to the phosphatasecatalyzed ATP hydrolysis34. As a multivariate approach, SMMA has increased accuracy at the expense of temporal resolution. Indeed, to collect three variables (∆Lrefolding, ∆x, and ∆F, see Figure 1B), the entire unfolding and refolding transitions of the hairpin sensor had to be recorded for ~ 3.4 sec. To improve temporal resolution, we measured the cooperative section of the ∆Lrefolding, which was recorded within 32 milliseconds. The measured ∆Lrefolding was then converted to pH by the calibration curve shown in Figure 3A (i). For molecules that cycled between buffers with and without 100 µM ATP, we again observed a decreased pH in each cycle (Figure 4C&D). In fact, transient pH as low as 5.0 was observed only in the ATP buffer (3.5 sigma). As controls, no difference in ∆Lrefolding (or pH) was observed when the AP containing DNA constructs were switched between two buffers without ATP, or when the constructs without AP were switched between the buffers with and without ATP (Figure S10).

CONCLUSIONS In summary, by using a new hairpin mechanophore responsive to hydronium ions, we innovated a multivariate single-molecule mechanochemical sensing to measure pH ~10 nm away from an active alkaline phosphatase. We found the concentration of hydronium ions increased by 0.4 pH units in the vicinity of the enzyme during its turnover of the ATP hydrolysis. We anticipate this multivariate mechanochemical sensor is generic for concentration measurement of different chemicals at the single-molecule level. As an example, the mismatch C:C pairs in the neck of the hairpin mechanophore can be replaced by DNA sequences such as split aptamers, which have demonstrated specific recognition for numerous chemicals35-37. Due to the fast diffusion constants of small molecules produced by enzymes, the concentrations of small molecules have been considered homogeneous even close to the enzymes5. Our results indicated that concentration fluctuation exists in the nanometer vicinity of an active enzyme, thereby supporting the hypothesis that proximity effect of the substrates generated from an upstream reaction leads to increased activity of a downstream enzyme in the nanometer distance.

ASSOCIATED CONTENT Supporting Information Synthesis of the DNA construct, Multivariate measurements, pH- responsive mechanochemical sensors, pH near alkaline phosphatases, Screening correct tethering, Analysis of the change-in-contour length. Table S1 and Figures S1-S10.

AUTHOR INFORMATION Corresponding author *E-mail: [email protected]

AUTHOR CONTRIBUTIONS H.M. and P.S. conceived the project. H.M. and P.S. designed the experiments. P.S. and J.W. performed the experiments and analyzed the data. Y.C. and S.J. contributed to multivariate analysis. H.M. and P.S. wrote the manuscript.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS HM is grateful to NSF CHE-1609504 for financial support.

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