Influence of Oligonucleotide Grafting Density on Surface-Mediated

Jun 21, 2019 - ... on the ACS Publications website at DOI: 10.1021/acsnano.9b02157. ... waiting time crawling diffusion coefficient distributions; fit...
1 downloads 0 Views 1MB Size
Download PDF
www.acsnano.org

Influence of Oligonucleotide Grafting Density on Surface-Mediated DNA Transport and Hybridization Jeremiah C. Traeger, Zachary Lamberty, and Daniel K. Schwartz*

Downloaded via BUFFALO STATE on July 23, 2019 at 12:10:13 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, United States S Supporting Information *

ABSTRACT: Adsorption of soluble DNA to surfaces decorated with complementary DNA plays an important role in many bionanotechnology applications, and previous studies have reported complex dependencies of the surface density of immobilized DNA on hybridization. While these effects have been speculatively ascribed to steric or electrostatic effects, the influence of surface-mediated molecular transport (i.e., intermittent “hopping diffusion”) has not been fully appreciated. Here, single-molecule tracking and Förster resonance energy transfer (FRET) were employed to characterize the mobility and the hybridization efficiency of adsorbed ssDNA oligonucleotides (“target”) at solid−liquid interfaces exhibiting surface-immobilized ssDNA (“probe”) over a wide range of surface grafting densities. Two distinct regimes were observed, with qualitatively different transport and hybridization behaviors. At dilute grafting density, only 1−3% of target molecules were observed to associate with probes (i.e., to hybridize). Adsorbing target molecules often searched unsuccessfully and “flew”, via desorption-mediated diffusion, to secondary locations before hybridizing. In contrast, at high probe grafting density, approximately 20% of target DNA hybridized to immobilized probes, and almost always in the vicinity of initial adsorption. Moreover, following a dehybridization event, target molecules rehybridized at high probe density, but rehybridization was infrequent in the dilute density regime. Interestingly, the intermittent interfacial transport of mobile target molecules was suppressed by the presence of immobilized probe DNA, presumably due to an increased probability of readsorption following each “hop”. Together, these findings suggested that many salient effects of grafting density on surface-mediated DNA hybridization can be directly related to the mechanisms of surface-mediated intermittent diffusion. KEYWORDS: single-molecule, nucleic acids, interfaces, transport, diffusion, biopolymers

S

requires the use of salt to screen Coulombic interactions. Experiments by Gong and Levicky indicated that higher probe DNA densities did not always lead to more dsDNA pairing;25 in fact, hybridization was strongly suppressed at high grafting density under some conditions. Similarly, theoretical work by Lei et al. found that DNA probes can be repelled at high DNA grafting density but also suggested that ssDNA bound in dense regions on the surface can be stabilized due to depletion forces within the dense brush.26 Other experiments support the notion that entropic forces are important at high grafting density and can affect the conformation of surface-immobilized hybridized DNA.27−29 While DNA−surface interactions are clearly important for the equilibrium competition between associated and denatured DNA on high grafting-density surfaces, the mechanisms by which these interactions influence elementary kinetic processes, such as on- and off-rates or molecular searching, remain

ystems that employ surface-immobilized ssDNA “probes” to bind with a complementary ssDNA “target” in solution are critical to a variety of technologies including DNA sequence detection,1−4 amplification,5−7 sequencing,8−10 and assays for mRNA10,−12 and protein13,14 detection. While the kinetics and thermodynamics of DNA binding/hybridization in solution have been thoroughly studied, the mechanisms for binding of DNA on a surface are not a simple function of solution formulation and thermodynamics. The presence of a solid−liquid interface introduces factors that may influence the dynamics and efficiency of hybridization, such as nonspecific adsorption to the surface,15−19 surface roughness,20 or molecular crowding,21,22 which may compete with the desired specific DNA− DNA interactions or influence the transport of targets on the surface, creating conditions where hybridization may be strongly coupled to the mechanisms of interfacial diffusion. The density of probes grafted to the surface has a strong and complex effect on surface-mediated hybridization phenomena. DNA is a negatively charged strong polyelectrolyte, so repulsive electrostatic interactions between DNA chains23,24 must be overcome in order for binding to occur; this often © 2019 American Chemical Society

Received: March 19, 2019 Accepted: June 21, 2019 Published: June 21, 2019 7850

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

Cite This: ACS Nano 2019, 13, 7850−7859

Article

ACS Nano

target transport, not only the underlying forces and interactions. Here, we investigate both the hybridization and the transport of ssDNA oligomers on surfaces functionalized with a wide range of surface grafting densities using singlemolecule total internal reflection fluorescence microscopy (SM-TIRFM) in combination with Förster resonance energy transfer (FRET). This approach permits the localization and tracking of individual molecules at the solid−liquid interface while simultaneously identifying associations between a mobile target DNA and an immobilized complementary probe. We observe the dynamic behavior of large molecular ensembles, permitting robust statistical insights into binding and diffusion kinetics that are not accessible using ensemble-averaging techniques that measure only the net effects of a macroscopic sample. Thus, we assess the effects of probe grafting density on transport and hybridization on a molecule-by-molecule basis. We have previously employed single-molecule FRET tracking methods to identify the mechanisms of hybridization kinetics and stability.31 Here, we probe the effects of molecular searching on hybridization and specifically address the ways in which changes in grafting density and CTRW transport can modify the effective DNA−DNA association dynamics. We find that hybridization efficiency and kinetics are influenced dramatically by the surface probe grafting density, with distinct low- and high-grafting density regimes identified. These regimes are characterized not only by qualitative differences in molecular searching and rehybridization, but also by inhibition of the transport of mobile target molecules apparently caused by interactions with immobilized probes.

unclear. Traditionally, the contributions of surface transport have been ignored, and the implicit assumption is often made that target DNA strands transition directly from bulk solution to a hybridized duplex.19,30 However, since recent research has shown that target DNA frequently adsorbs nonspecifically on DNA-modified surfaces,31 it is clearly important to include the dynamics of this nonspecifically adsorbed state when considering surface-mediated hybridization kinetics. Polymers near the solid−liquid interface exhibit anomalous diffusion, where adsorption to the surface initiates a period of low surface-bound mobility, followed by stochastic desorption and Brownian motion in the liquid phase, leading to successive surface encounters and ultimately readsorption, comprising bulk-mediated flights.32−34 This process results in nonGaussian two-dimensional surface diffusion that can be modeled as a generalized continuous time random walk (CTRW)35,36 process, where a given molecule successively adsorbs to the surface for random time intervals known as “waiting times”. Because these waiting times are characterized by low mobility, the overall CTRW diffusion is dominated by the bulk-mediated Lévy flights37,38 (due to the faster instantaneous diffusion in the liquid phase) that separate the waiting times. However, interactions with surface-bound species (such as catalytic sites or immobilized DNA) occur only during the slow-moving waiting times. Previous theoretical and experimental research has established that this form of anomalous diffusion, also known as “foraging”, can represent a more efficient search process compared to simple 2D Brownian motion,39−42 which is directly relevant for the system studied here, where encounters between a target and a probe are desired. As such, any factors that may change the properties of CTRW parameters, such as surface affinity, crowding, or liquid bulk properties, may interfere with effective surface-mediated hybridization. In the context of surface-mediated molecular transport, the effects of probe grafting density are expected to be complex and nuanced. For example, in a low-salt environment, one might expect that the large surface charge associated with a high-probe-density surface might prevent adsorption via electrostatic repulsion. However, with sufficient screening by counterions, a target in the near-surface environment could be stabilized by interactions with immobilized probe molecules, enhancing apparent surface interactions, thereby inhibiting bulk-mediated transport. Furthermore, targets that denature from an immobilized probe and re-enter an unbound state will have a higher likelihood of rehybridizing quickly on high grafting density surfaces compared to low grafting density surfaces due to shorter search distances. These considerations suggest that the grafting density of immobilized probe molecules may directly influence surface transport of mobile target, in turn affecting the efficiency of surface-mediated hybridization.21 Molecular crowding can cause subdiffusive two-dimensional transport of polymers,43−45 inhibiting interfacial exploration. Polymer crowding can also interfere with three-dimensional motion in the near-surface region,46−49 suggesting that bulk transport during flights may also be influenced by probe grafting density. Moreover, increased DNA−surface interactions can lead to long waiting times between flights, potentially leading to higher effective hybridization-rates and an increase in equilibrium hybridization efficiency. Therefore, to understand hybridization efficiency at the solid−liquid interface, it is important to consider the detailed mechanisms of CTRW dynamics and

RESULTS/DISCUSSION Frequency of Single and Multiple Hybridization Events. During the duration of a target DNA molecule’s trajectory near the surface, it may encounter an immobilized probe resulting in an associated (i.e., putatively hybridized) pair with a sufficient lifetime to be resolved. The fraction of trajectories that exhibited at least one identified FRET event was defined as the event fraction fe. Understandably, an increase in the probe grafting density, σg, resulted in an increase in fe (Figure 1a). Within the range of grafting densities studied, there appeared to be two distinct regimes based on fe, a low-density regime for σg < 104 μm−2, which exhibited fe in the approximate range 0.015−0.04, and a high-density regime for σg > 104 μm−2, which exhibited fe in the approximate range 0.12−0.2. Moreover, within the lifetime of a trajectory, in some cases multiple FRET transitions could be observed, representing hybridization, dehybridization, rehybridization, etc. Of the molecules that engaged in FRET, we defined the fraction that transitioned from low-FRET to high-FRET states multiple times as the rehybridization fraction f r. These rehybridization events are potentially important since they can extend the effective duration of target binding to a probe-laden surface. This rehybrization fraction followed a similar trend as the event fraction, where f r in the low-density regime was in the approximate range 0.015−0.022, and f r in the high-density regime was in the approximate range 0.027−0.041 (Figure 1b), again divided into two regimes by a grafting density of σg ≈ 104 μm−2. On the basis of these empirical observations, we treated the value of σg ≈ 104 μm−2 as an apparent threshold value dividing the low and high-grafting density regimes. 7851

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano

probes at similar rates. The fe and f r values for noncomplementary targets were similar to those of complementary targets at low grafting density samples, where hybridization and rehybridization events were both quite rare. At high grafting density, fe and f r increased for both complementary and noncomplementary targets relative to low-density surfaces, although the increase was significantly greater for complementary targets. Target Trajectories. The trajectories for adsorbed target oligonucleotides were found to exhibit intermittent CTRW dynamics, where molecules engaged in periods of slow, crawling diffusion (so-called “waiting times”, τw) with occasional longer steps (i.e., “flights”).32 Representative trajectories are shown in Figure 2, which shows simultaneous time series of x and y coordinates, and donor and acceptor trajectories. Taken together, these data provide coordinated information about intermittent mass transport and hybridization/dehybridization. For example, Trajectory 1 (Figure 2a−c) appears to depict a target that adsorbs nonspecifically to the surface and engages in a brief local search before successfully associating with a nearby probe. After ∼1.3 s, this target dehybridizes into a low-FRET state, engages in a bulk-mediated flight, searches locally (unsuccessfully), and then desorbs from the surface. Trajectory 2 (Figure 2d−f) appears to depict a target that nonspecifically adsorbs, searches locally, and associates with a probe. Trajectory 3 (Figure 2g−i) appears to depict a target molecule that nonspecifically adsorbs, searches locally, and then associates with a nearby probe; it subsequently dehybridizes, engages in a ∼400 nm flight, and successfully associates with another probe in a separate distinct FRET state.

Figure 1. (a) Event fraction fe as a function of surface grafting density, designating the fraction of targets that engaged in at least one FRET event. (b) Rehybridization fraction f r as a function of surface grafting density, representing the fraction of successful targets that engaged in more than one distinct FRET event.

To assess the effect of complementarity on fe and f r, control experiments were performed using mobile noncomplementary targets in bulk solution on two representative surfaces, in the low and high grafting density regimes, respectively (see Figure 1a,b). These noncomplementary targets, like the complementary targets, were 15 nucleotides in length and were expected to have similar transport properties and interact with surface

Figure 2. Representative spatial and FRET state trajectories. (a, d, g) Cartesian coordinates versus time. (b, e, h) Donor and acceptor emission intensities versus time. (c, f, i) 2D plots of the same trajectories in the x−y plane with color-coded positions indicating a low-FRET (blue) or high-FRET (red) state. 7852

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano Target Searching Behavior. To characterize the distribution of first-search distances (FSD), we measured the Euclidean distance between the position of each target’s initial appearance on the surface in a low-FRET state to the position at which it first entered a high-FRET state. Representative FSD distributions in the low- and high-grafting density regimes are shown in Figure 3a. As indicated by the prominent peak

grafting density (Figure S2), suggesting that the fundamental searching mechanisms remained constant as a function of surface grafting density. However, as indicated above, the fraction associated with the secondary population associated with longer search distances, f 2, decreased systematically with increased grafting density (Figure 3b). Specifically, the long search distance population, f 2, comprised ∼27% of the probability density function (PDF) at low grafting densities and decreased to only 6% at a high grafting density of σg = 3.3 × 103 μm−2. CTRW Dynamics. The intermittent dynamics of bulkmediated surface diffusion is conventionally described using the parameters associated with a CTRW model, that is, waiting times τw and flight lengths r. As in previous work, we segmented trajectories into waiting times and flights using a step-size threshold. A value of 0.2 μm was used to compile the statistics shown here; however, the major findings and systematic trends were not affected by modest changes in the choice of this threshold value. Consistent with previous observations of anomalous surface diffusion,33,50 the waitingtime distributions were heavy-tailed and adequately described by a power-law distribution (Figure 4a): Ψ(τw) ∝ τw−(α + 1)

(2)

To permit better visualization of the individual slopes, the probability density for the high-σg surface was offset in Figure 4a. Notably, α ≈ 1 for all values of σg (Figure 4b), which is

Figure 3. (a) Representative first-search distance PDFs at low (∼2.2 × 103 μm−2) and high (∼3.3 × 104 μm−2) σg. The solid lines correspond to mixed-log-normal function fits. (b) Fraction of the secondary log-normal population f 2 as a function of surface grafting density.

centered at ∼200 nm, a large fraction of successful targets associated with a probe within a distance of ∼400 nm from the initial adsorption position. Interestingly, the FSD distributions did not decay rapidly, instead exhibiting a broad tail under high grafting density conditions and a broad secondary peak at longer search distances (∼1 μm) for low grafting density surfaces. This suggested the presence of two searching populations, one that successfully located an immobilized target during its initial searching period, and a second population that initially searched unsuccessfully, executed a flight, and then identified a target molecule in a different search area. This secondary population systematically decreased in magnitude as the grafting density increased (Figure S1). To quantitatively characterize these populations, the probability density functions were fit to a log-normal mixture model, chosen due to the heavy tail in the short-search distance population, where i refers to either the population of short or long first-search distances: ij (ln x − μ )2 yz ij fi yz i z j z zz P(x) = ∑ jj z expjjjj− 2 zz j 2π σix zz j 2 σ i k { i k {

Figure 4. (a) Representative dimensionless waiting time probability densities Ψ(τw) at high and low grafting densities. The dashed line represents power-law decay for t−2. The high-σg function has been offset for visual clarity by multiplying the probability by a factor of 1/6. (b) Exponent α describing the power-law decay of waiting time distributions as a function of σg. (c) Representative dimensionless flight length probability densities Φ(r) at high and low grafting densities. The dashed line represents power-law decay for r−3. The high-σg function has been offset for visual clarity by multiplying the probability by a factor of 1/2. (d) Exponent β describing the power-law decay of the flight lengths as a function of σg. Error bars are 95% confidence intervals for fits.

(1)

Each mode of these mixed log-normal distributions featured a position parameter μi and a shape parameter σi, where each log-normal mode was weighted by its respective population fraction f i. We defined mode 1 to correspond to the shortrange search population while mode 2 referred to the longrange search population. The best-fit parameters μi and σi varied little and exhibited no discernible trend as a function of 7853

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano close to the upper limit for subdiffusive behavior where 0 < α < 1.51−53 This included a control sample without DNA on the surface as well as experiments with noncomplementary targets, indicating that the presence of complementary probes on the surface did not significantly impact waiting times. The flight length distributions of mobile target DNA molecules were also heavy-tailed and hence described by a power-law distribution (Figure 4c,d): ij β − 1 yzi rs y β Φ(r ) = jjj zzjj zz ∝ r −β j rs zzjk r z{ k {

(3)

To permit better visualization of the individual slopes, the probability density for the high-σg surface was offset in Figure 4c. In eq 3, β refers to the power-law exponent, while rs is a characteristic flight length. Here, the distributions decayed more rapidly with increasing probe DNA grafting density, that is, β increased from a value of ∼3 at low grafting density (or on a negative control surface with no immobilized probe DNA), to β = 3.4 at high grafting density, suggesting that the increased density of grafted DNA resulted in truncated flights. Control experiments with noncomplementary targets exhibited low values of β, regardless of grafting density. Crawling Diffusion During Waiting Times. Since searching for immobilized probe molecules occurred during waiting times, we calculated the average crawling diffusion coefficient Dcrawl for each distinct waiting period: Dcrawl =

σ2 4τw

Figure 5. (a) Complementary cumulative distributions P(Dcrawl) of Dcrawl on a low-grafting-density surface (σg = 6.6 × 103 μm−2). (b) Complementary cumulative distributions of Dcrawl on a highgrafting-density surface (σg = 3.3 × 104 μm−2). Black lines are biexponential mixture model fits. (c) Effective diffusion coefficient as a function of waiting time, error bars represent propagation of errors from confidence intervals in the fit parameters.

(4)

where σ is the variance of the trajectory during a waiting period of duration τw. The values of Dcrawl were heavily represented by very brief waiting events, where the variance was expected to be smallest and most obscured due to localization error. To characterize transport during the waiting time, Dcrawl was segregated by waiting-time duration, and separate complementary cumulative distributions of Dcrawl were constructed for each waiting-time (Figures 5a,b and S3). A distribution appearing as a straight line on a semilogarithmic plot was indicative of Gaussian diffusion. On low-graftingdensity surfaces, the distributions did not vary as a function of τw (Figure 5a), suggesting that the crawling diffusion was relatively Brownian. On high-grafting-density surfaces, however, the probability density functions decayed more rapidly as τw increased, suggesting that crawling motion during waiting periods at high grafting density was subdiffusive (Figure 5b), consistent with a more crowded and interacting environment. To quantify the crawling diffusion versus waiting time, the distributions described above were fitted to a biexponential model: 2

P(Dcrawl ) =

∑ fi e−( i

0.2 s waiting period, so it is likely that the slower diffusion coefficient was related to localization error. An effective diffusion coefficient was calculated by averaging the crawling diffusion coefficients weighted by their population fractions: = f1 D1 + f2 D2

(6)

This characterized the overall crawling diffusion as a function of waiting time (Table S2). was essentially independent of grafting density for short waiting times (where localization error dominated). While was constant with waiting time on low grafting density surfaces, it decreased systematically with waiting time for high grafting density surfaces (Figure 5c), quantitatively indicating subdiffusive crawling motion on high grafting density surfaces. Surface-Grafting Density Regimes. Measurements of multiple independent phenomena and parameters indicated a characteristic shift in behavior between low and high grafting density regimes, marked by a threshold value of σg ≈ 104 μm−2. At values of σg above this threshold, target DNA molecules exhibited distinctly higher probabilities of successful hybridization and rehybridization as well as slower characteristic diffusion compared to the behavior of target DNA on surfaces with lower σg. Interestingly, the transition appeared to be fairly abrupt as a function of grafting density, as opposed to a gradual systematic shift.

Dcrawl ) Di

(5)

Di is a characteristic diffusion coefficient and f i is the population fraction of a given diffusive mode (Table S1). Population 1 refers to the slower diffusive crawling mode, while population 2 refers to the faster diffusive crawling mode. D1, the slower diffusion coefficient ranged from ∼0.0004− 0.0015 μm2 s−1, while D2 was found to be in the range ∼0.0018−0.0037 μm2 s−1. For comparison, localization error caused by Gaussian noise with a width of 60 nm would result in an apparent diffusion coefficient of ∼0.0011 μm2 s−1 over a 7854

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano

secondary population at high grafting density reflects an increased probability of a successful first search because a target molecule is increasingly likely to adsorb very close to a probe molecule. Previous research by Kolomeisky found the ultimate success of a diffusive search is closely related to the initial distance between a particle and its destination,18,59,60 and surface-mediated DNA hybridization is similarly facilitated by the presence of direct pathways between adsorption sites and vicinal immobilized probes. Transport on a DNA-laden Surface. In the context of intermittent bulk-mediated surface diffusion, the distribution of flight lengths Φ(r) was affected by the grafting density of probe DNA; the power-law exponent associated with the distribution (eq 3) increased from β ≈ 3 ± 0.2 for low-density surfaces (σg < 104 μm−2) to β ≈ 3.44 ± 0.08 for high-density surface (σg > 104 μm−2). Similarly, the mean of the distribution was calculated from Φ(r):

To put the threshold grafting density into perspective, it is useful to compare it to the characteristic size of DNA molecules used in these experiments. Using the wormlike-chain model54,55 and the persistence length of ssDNA under the relevant experimental conditions, the end-to-end distance of the 15-base probe molecules was ∼6 nm, suggesting that steric interactions between neighboring probe molecules may be present for nearest-neighbor distances of 12 nm or less. Using a 2-dimensional hexagonal lattice model, this corresponds to a grafting density of σg = 1.6 × 104 μm−2, which is similar to our empirically determined threshold between low- and highdensity behavior. This suggests that physical overlap between immobilized probe molecules is a plausible hypothesis that may in part explain the transition from low to high grafting density hybridization behavior. Indeed, this concept has been suggested previously.27 However, it is likely that additional factors, including electrostatic interactions, may influence the particular range of grafting density at which the transition is observed. Hybridization and Rehybridization. The most dramatic effect of σg was on the event fraction fe, which is related to the fraction of adsorbing target molecules that undergo association/hybridization. As expected, an increase in probe grafting density resulted in an increase in fe for both complementary and noncomplementary targets. This increase was less significant for noncomplementary targets than for complementary targets, presumably because associations between noncomplementary DNA pairs were often very short-lived and therefore not resolved. Similarly, the fraction of molecules that rehybridized after a dehybridization event, f r, followed the same trend. Interestingly, the FRET lifetime, indicating the duration of hybridization/association events, had no systematic dependence on surface grafting density (Figure S4). At grafting densities above σg ≈ 104 μm−2, the event fraction reached an apparent maximum near fe ≈ 0.2 instead of continuing to increase with surface grafting density. This may be related to previous results by Levicky and co-workers suggesting that at certain salt concentrations, hybridization may be suppressed at high DNA surface grafting densities, presumably due to electrostatic repulsion.25 For the NaCl concentration in our experiments (∼0.137 M), they estimated that suppressed hybridization might occur around a surface grafting density of ∼4 × 104 μm−2, which is similar to the grafting density at which we observed a maximum of fe (i.e., 1.7−3.3 × 104 μm−2). The first search distance distributions provide further insight into the mechanisms of surface-mediated hybridization. While most hybridization events occurred within 0.4 μm of the adsorption location (with a peak at ∼0.2 μm), the probability density function of search distances did not decay monotonically but instead indicated the presence of a second population of searches that was characterized by a first-search distance of ∼0.8. These separate populations were signatures of spatially or temporally heterogeneous mechanisms in a molecular search process, conceptually similar to heterogeneous search mechanisms that have been investigated in diffusion-limited molecular kinetics. 56−58 This was consistent with the intermittent nature of bulk-mediated surface diffusion, where that the short-FSD population represents target molecules that encounter a probe within their initial waiting time, and the long-FSD population represents target molecules that fail to hybridize in their initial waiting time, and engage in a flight prior to a successful subsequent search. The decrease in the

r̅ =

β−1 rs β−2

(7)

The mean flight length r ̅ decreased from ∼0.42 μm for lowdensity surfaces to ∼0.34 μm for high-density surfaces. This suggested that the presence of complementary probe DNA grafted to the surface acted as an obstacle to targets diffusing near the surface during flights. A simplified theory of bulk-mediated diffusion predicts a Cauchy distribution of flight lengths,38,61 which scales as r−1 for short flight distances and r−3 asymptotically for long flight distances. The measured flight-length distributions were similar to this asymptotic limit, indicating that all steps identified as flights were in the tail end of this distribution. However, the measured exponent for high grafting density surfaces exceeded the theoretical limitation of r−3. Notably, the relevant theory models flights as unbiased three-dimensional Brownian walks between desorption and readsorption events to a perfectly planar surface but do not consider complications associated with surface roughness or biased motion. In their theoretical formulation, Bychuk and Oshaughnessy referred to a “surface capture range” from the surface, where within this range a particle has a stochastic probability of adsorbing to the surface.38 This suggests that the presence of immobilized probes, which extends away from the nominal surface, may increase the effective capture region. Furthermore, the adsorption kinetics of a target interacting with a surface probe may be higher relative to the adsorption kinetics of surface regions unoccupied by a probe, thereby increasing the effective sticking coefficient. Either of these effects could explain a faster decay of flight lengths than expected for a flat nonfunctionalized surface. To explore the effect of heterogeneous surface features on flight-length, we performed off-lattice Monte Carlo simulations of flights starting and ending at the surface (Figure S5), as described in the Supporting Information, to see if increasing probe grafting density could lead to a change in scaling behavior similar to our observations. The simulations incorporated a planar “capture region” of height h above the surface as well as superimposed hemispherical capture regions associated with grafted probe molecules. For simplicity, we considered the adsorption probability to be equal in both types of capture region. We controlled the spacing between these surface features as an analogy for the grafting density of DNA on the surface. The distributions of flight-lengths exhibited an approximate power-law decay for large flight distances that 7855

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano scaled with r−3 on surfaces with no features, consistent with theoretical predictions (Figure S6). With an increased density of surface features, however, the asymptotic behavior of the flight-length distribution was consistent with a more rapid power-law decay, indicating the truncation of long flights as observed in the experimental data. This suggests that the introduction of topographical features on a surface can act as an obstacle to particles diffusing in the near-surface bulk environment, leading to flight-length decay that is more rapid than traditional theoretical predictions of desorption-mediated diffusion at a planar interface. The presence of grafted probe DNA also hindered the crawling diffusion of target DNA during waiting periods. In particular, on low surface grafting density surfaces, the crawling diffusion was independent of the length of the waiting period, whereas on high surface grafting density surfaces the effective crawling diffusion systematically slowed as a function of the waiting period, indicating subdiffusive diffusion in the more crowded environment.

presence of a threshold value σg* for the high-grafting density regime suggests a surface grafting density that is ideal for measuring hybridization since the extent of hybridization did not increase beyond this value. Single-molecule tracking provides information about the coupling of surface transport and the presence of immobilized probes, providing insights regarding the role of anomalous transport in DNA hybridization at a solid−liquid interface.

METHODS/EXPERIMENTAL Materials. 11-Azidoundecyltrimethoxysilane (95% pure) was obtained from Gelest (Morrisville, PA). DBCO-PEG4-hydroxyl (95% pure) was obtained from Click Chemistry Tools (Scottsdale, AZ). n-Butylamine (99.5% pure) and anhydrous toluene (99.8% pure) were obtained from Sigma-Aldrich (Milwaukee, WI). The target molecule introduced from solution was oligonucleotide DNA from IDT (Coralville, IA) with the sequence 5′−ACA ACC AAC ACA CCA−3′ where the 5′ end was modified with a fluorescein dye via a C6 amino linker. The control target was also from IDT and contained the same modification, and had the sequence 5′−TTT TTT TTT TTT TTT−3′. The probe molecule covalently attached to the surface was oligonucleotide DNA obtained from Gene Link (Hawthorne, NY) and had the sequence 5′−TGG TGT GTT GGT TGT−3′, where the 5′ end was modified with a DBCO-TEG linker for click attachment to the surface, and the 3′ end was modified with a Quasar 670 via a C7-amino linker. All other chemicals were Optima grade from Fisher Scientific (Denver, CO). Aqueous solutions used water purified to 18 MΩ cm using a Millipore Milli-Q UV+ system. DNA bulk solutions were prepared by creating phosphate-buffered saline (PBS) solutions with 10−10 M DNA such that the target DNA was dilute enough to resolve single molecules in experiments. Surface Preparation and Characterization. DNA-functionalized surfaces were prepared using 2” fused silica wafers (Mark Optics) for microscopy experiments. The reflective surfaces required for ellipsometry and ATR-IR characterization were prepared using 2” silicon wafers (Sigma-Aldrich). Wafers were cleaned by immersion in a piranha solution (70% sulfuric acid, 30% hydrogen peroxide) for 1 h, followed by rinsing with copious amounts of Milli-Q deionized water and drying with ultrahigh purity nitrogen. Piranha solution is a strong oxidizer and highly corrosive, so safety measures were taken by wearing a thick labcoat and safety goggles. The surfaces were further cleaned afterward with UV-ozone for 30 min. An azide layer was deposited directly to the fused silica wafer surface via silanol chemistry. Specifically, the wafers were placed in a 200:3:1 by volume solution of anhydrous toluene (Sigma-Aldrich), 11-azido-undecyltrimethoxysilane (AUTMS, Gelest), and n-butylamine (Sigma-Aldrich) for 3 h at room temperature. After this reaction, the samples were rinsed with copious amounts of isopropanol. They were then placed in Milli-Q water and sonicated for 5 min. After a subsequent rinse with isopropanol, these were dried with nitrogen. The surfaces were then cured in an oven at 115 °C for an hour to evaporate any remaining water adsorbed to the monolayer to avoid hydrolysis of the silane monolayers. DNA and oligo(ethylene glycol) (OEG) were reacted to the surface through DBCO and azide click chemistry, which was used as a functionalization strategy due to the high efficiency and bioorthogonality of click chemistry.65 OEG was chosen to control DNA grafting density and as a surface blocking group due to its capacity to inhibit nonspecific binding of DNA molecules to the surface.66,67 Azide-modified wafers were exposed to DBCO-ssDNA and DBCO-PEG4 in PBS at various ratios of OEG/DNA, between 2000:1 and 25:1, including control surfaces functionalized only with OEG and no DNA. The total concentration of DNA and OEG reactants in the deposition solution was fixed at 0.2 mM. These reactions were performed for 1.5 h at room temperature. Afterward, modified wafers were rinsed with isopropanol and dried with nitrogen. Multiple methods were used to confirm the deposition of azidosilane SAMs on the silica surface as well as the subsequent deposition of OEG via azide click chemistry. After the wafers were removed from

CONCLUSIONS Single-molecule tracking of DNA oligonucleotides at the solid−liquid interface of a DNA-functionalized surface revealed a distinct change in molecular transport and hybridization efficiency between low grafting density and high-grafting density surfaces. An increase in probe grafting density resulted in an increase in the rate of association (and reassociation) between targets and probes, a decrease in the distance traveled by a target molecule between nonspecific adsorption and association, and truncated flight lengths during desorptionmediated diffusion. Interestingly, these properties changed abruptly at a threshold value of grafting density rather than gradually as a function of grafting density, suggesting the presence of a characteristic length scale dividing low and high grafting density regimes. The empirically measured threshold value for grafting density had a mean nearest-neighbor distance similar to the estimated end-to-end distance for two immobilized probes, suggesting that the threshold may correspond to a density where a target adsorbing on the surface is likely to be within reach of at least one probe. Since immobilized probe DNA molecules were effectively isolated even at the highest grafting density achieved here, we did not observe an increase in the duration of hybridization events. In hypothetical DNA brush systems with higher densities than explored here, targets may be able to effectively interact simultaneously with two immobilized probes or to engage in immediate rehybridization upon denaturation; this could potentially cause a dramatic shift of the target binding equilibrium. While such high grafting densities are not generally reported on silica, it is possible that they may be achievable on other surfaces such as gold.62−64 Since immobilized probes were observed to act as impediments to the mass transport of mobile target molecules (during both crawling and flying time intervals), the inhibition or facilitation of molecular searching appears to be an important mechanism for understanding surface-mediated hybridization and complements more traditional considerations such as electrostatic and steric repulsion. The transport limitations described here may alter macroscopic measurements in ways that are practically important. For example, transport-limited surface hybridization may affect the kinetics of hybridization signals measured in a sensing system and should be considered in sensor design. Importantly, the 7856

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano

relative surface coverage of two homologous surface-reactive compounds was equal to their relative mole fractions in solution.71 However, even if the absolute rate constants are slightly different, σg represents an effective DNA surface grafting density that is proportional to the true grafting density on the surface and can be employed to illustrate changes in transport behavior of target DNA as a function of the density of probes grafted to the surface. TIRF Microscopy. Prior to imaging, a flow cell was cleaned using subsequent rinses of Micro-90 detergent solution, Milli-Q water, and isopropanol before drying with nitrogen. Wafers were placed in the flow cell and mounted on a custom-built prism-based TIRF microscope (Nikon TE-2000 base, 60× water-immersion objective) and exposed to DNA solution. A 491 DPSS laser was used as an excitation source, incident through a hemispherical prism in contact with the wafer, creating a TIRF field with a decay length of ∼100 nm. The laser power was set at 35 mW, which allowed for continuous movie-length observations at a low enough power to minimize photobleaching on the time scales of FRET events31 while still providing sufficiently strong fluorescent emission to permit SM localization in the presence of background noise. Molecular diffusion in bulk solution was too rapid to be resolved, so all observed objects were assumed to be adsorbed to the surface. Six to ten movies per sample were captured with a frame acquisition time of 100 ms. The duration of each movie was 30 s such that each movie contained 300 frames. This allowed for the collection of statistically large numbers of molecular trajectories (∼50 000− 300 000 objects per experiment). An Optosplit II beam splitter (Cairn Research, Kent) was used to separate light from donor and acceptor fluorophores via a 610 nm dichroic mirror. The light from the donor and acceptor channels were filtered through 529 ± 20 nm and 685 ± 40 nm cleanup filters, respectively (Semrock, Rochester NY). The two channels were captured with a Photometrics EMCCD camera cooled to −92 °C using thermoelectric Peltier elements. DNA oligomers were resolved as diffraction-limited objects in each channel, revealing the locations of targets and FRET events. Image Processing. The two channels of each movie were aligned, and each object was localized using methods and algorithms described previously.31 Objects that appeared within five pixels of each other in consecutive frames were identified as the same object. To account for positional uncertainties between channels, objects that appeared within 2 pixels of each other in separate channels of the same frame were identified as the same object undergoing FRET. The positions of objects in the same channel were identified by the position of the object with the greatest signal-to-noise ratio. Single-pixel objects and trajectories that lasted a single frame were discarded from the analysis, due to inability to distinguish these objects from noise. For all experiments, the donor and acceptor intensity of each object in each frame were plotted as a heat map (Figure S9). These data revealed two distinct populations: a low-FRET population (“nonassociated”) corresponding to objects with high donor intensity and low acceptor intensity, and a high-FRET (“associated”) population corresponding to objects with high acceptor intensity and low donor intensity. There was no intermediate population in any experiment. To assign objects to either a high-FRET state or a low-FRET state within a frame, we created an algorithm that divided the two populations using a linear boundary on the heat map, where the dividing line minimized the integrated values of the heat map between states. To prevent the algorithm from anomalously assigning a molecule to the wrong state because of fluctuations due to noise or photoblinking, both the donor and acceptor intensities were required to cross the threshold line by more than their respective uncertainties for a state change to be assigned.

the toluene deposition solution and annealed in an oven, video goniometry was used to measure the contact angle of water droplets, which exhibited a contact angle of 74 ± 4° using five droplet measurements, consistent with a previously reported value of 77°,68 contrasting with total wetting on a clean silica surface. Upon click chemistry deposition with pure OEG, the water contact angle was 38 ± 4°, measured using five water droplets, consistent with the expected increase in hydrophilicity associated with the OEG functionality. Attenuated total reflection infrared (ATR-IR) spectroscopy was also used to characterize chemical deposition on the surface of silicon wafers. Measurements were performed using a Thermo Scientific Nicolet 6700 FT-IR spectrometer, with a Harrick VariGATR attachment to measure attenuated IR spectra. Background spectra were obtained from a piranha-treated silicon wafer. The spectra of azido-silane modified wafers exhibited a peak at 2098 cm−1, which indicated successful azide deposition69 (Figure S7). Wafers that underwent increasing click-chemistry reaction times (15−60 min) with an OEG monolayer exhibited a gradual loss of the azide peak at 2098 cm−1 consistent with the progression of the click reaction. The simultaneous appearance of a peak at 1653 cm−1 suggested an amide carbonyl stretch, which indicated that the OEG had reacted onto the surface. A variable angle spectroscopic ellipsometer (V-Vase, J.A. Woolam, Lincoln, NE, USA) was used to further characterize the thickness of the azide-silane layer on silicon wafers. Ellipsometry was performed by reflecting polarized light from a surface film at a defined incident angle and measuring the change in amplitude Ψ and phase Δ of the reflected light. These were measured using 400−900 nm light reflected at angles between 60° and 80°. These changes in phase and amplitude were fitted using an isotropic three-interface optical model consisting of air, azido-undecyltrimethoxysilane, native silicon dioxide, and silicon. This measurement gave an azide monolayer thickness of 0.94 ± 0.2 nm. Ellipsometry measurements on the model silicon surface after click deposition of the OEG monolayer indicated the presence of an additional OEG layer with a thickness of 1.2 ± 0.2 nm, consistent with our estimated length of DBCO-OEG4. We estimated the surface grafting density of OEG on the surface using the expression:70

σOEG =

ρdry hdry NA Mw

(8)

Where ρdry is the mass density of OEG, hdry is the dry thickness of the OEG monolayer, NA is Avogadro’s number, and MW is the molar mass of the OEG molecules. Using the thickness measured using ellipsometry, we estimated the surface grafting density of OEG to be 1.66 ± 0.23 × 106 μm−2. When depositing DBCO−DNA on the wafer surface, we altered the grafting density of DNA on the surface by controlling the molar OEG to DNA ratio in the aqueous deposition solution. Indeed, increasing the proportion of DNA in deposition solution led to distinctive changes in transport behaviors of oligomer targets on the surface and an increase in hybridization events as measured by FRET. Since the DNA was fluorescently labeled (using Quasar-670), the total fluorescence of a given microscope region of interest (ROI) when directly illuminated by a 640 nm laser was proportional to the DNA grafting density. Notably, using quantitative fluorescence microscopy, we found that the ROI fluorescence intensity was directly proportional to the DNA/OEG ratio in solution, suggesting that the grafting density was also proportional to the ratio of dissolved DNA to OEG in deposition solution (Figure S8). On the basis of these observations, we therefore calculated an effective grafting density σg to be proportional to this ratio in deposition solution: σg = σOEG

[DNA ] [DNA ] ≈ σOEG [OEG] + [DNA ] [OEG]

ASSOCIATED CONTENT

S Supporting Information *

(9)

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.9b02157. FSD probability density functions; fit parameters for FSD functions; waiting time crawling diffusion coef-

Under the scenario where the surface reaction rate constants of DBCO−DNA and DBCO−OEG are equivalent (a plausible approximation for the highly efficient click chemistry), σg represents the true DNA grafting density. In fact, previous work found that the 7857

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano ficient distributions; fit values for crawling diffusion coefficients; effective diffusion coefficient values; association lifetime distributions; simulation methods and schematic; simulation flight probability density functions and fitted values; ATR-IR spectra of silane chemistry; ROI intensity vs [DNA]/[OEG] in deposition solution; fluorescence intensity heat map (PDF)

Microbalance Sensors by Aptamer-Based Rolling Circle Amplification and Nanoparticle Signal Enhancement. Chem. Commun. 2014, 50, 1481−1484. (14) Teh, H. F.; Peh, W. Y. X.; Su, X.; Thomsen, J. S. Characterization of Protein-DNA Interactions Using Surface Plasmon Resonance Spectroscopy with Various Assay Schemes. Biochemistry 2007, 46, 2127−2135. (15) Chan, V.; Graves, D. J.; Fortina, P.; Mckenzie, S. E. Adsorption and Surface Diffusion of DNA Oligonucleotides at Liquid/Solid Interfaces. Langmuir 1997, 28, 320−329. (16) Elder, R. M.; Jayaraman, A. Structure and Thermodynamics of ssDNA Oligomers near Hydrophobic and Hydrophilic Surfaces. Soft Matter 2013, 9, 11521−11533. (17) Chan, V.; McKenzie, S. E.; Surrey, S.; Fortina, P.; Graves, D. J. Effect of Hydrophobicity and Electrostatics on Adsorption and Surface Diffusion of DNA Oligonucleotides at Liquid/Solid Interfaces. J. Colloid Interface Sci. 1998, 203, 197−207. (18) Esadze, A.; Kemme, C. A.; Kolomeisky, A. B.; Iwahara, J. Positive and Negative Impacts of Nonspecific Sites During Target Location by a Sequence-Specific DNA-Binding Protein: Origin of the Optimal Search at Physiological Ionic Strength. Nucleic Acids Res. 2014, 42, 7039−7046. (19) Sedighi, A.; Li, P. C. H.; Pekcevik, I. C.; Gates, B. D. A Proposed Mechanism of the Influence of Gold Nanoparticles on DNA Hybridization. ACS Nano 2014, 8, 6765−6777. (20) Wang, D.; He, C.; Stoykovich, M. P.; Schwartz, D. K.; Al, W. E. T. Nanoscale Topography Influences Polymer Surface Diffusion. ACS Nano 2015, 9, 1656−1664. (21) Zaid, I. M.; Lomholt, M. A.; Metzler, R. How Subdiffusion Changes the Kinetics of Binding to a Surface. Biophys. J. 2009, 97, 710−721. (22) Guigas, G.; Weiss, M. Sampling the Cell with Anomalous Diffusion - The Discovery of Slowness. Biophys. J. 2008, 94, 90−94. (23) Rau, D. C.; Lee, B.; Parsegian, V. A. Measurement of the Repulsive Force Between Polyelectrolyte Molecules in Ionic Solution: Hydration Forces Between Parallel DNA Double Helices. Proc. Natl. Acad. Sci. U. S. A. 1984, 81, 2621−2625. (24) Podgornik, R.; Rau, D. C.; Parsegian, V. A. The Action of Interhelical Forces on the Organization of DNA Double Helices: Fluctuation-Enhanced Decay of Electrostatic Double-Layer and Hydration Forces. Macromolecules 1989, 22, 1780−1786. (25) Gong, P.; Levicky, R. DNA Surface Hybridization Regimes. Proc. Natl. Acad. Sci. U. S. A. 2008, 105, 5301−5306. (26) Lei, Q. L.; Ren, C. L.; Su, X. H.; Ma, Y. Q. Crowding-Induced Cooperativity in DNA Surface Hybridization. Sci. Rep. 2015, 5, 1−7. (27) Watkins, H. M.; Simon, A. J.; Ricci, F.; Plaxco, K. W. Effects of Crowding on the Stability of a Surface-Tethered Biopolymer: An Experimental Study of Folding in a Highly Crowded Regime. J. Am. Chem. Soc. 2014, 136, 8923−8927. (28) Bracha, D.; Karzbrun, E.; Shemer, G.; Pincus, P. A.; Bar-Ziv, R. H. Entropy-Driven Collective Interactions in DNA Brushes on a Biochip. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 4534−4538. (29) Johnson-Buck, A.; Nangreave, J.; Jiang, S.; Yan, H.; Walter, N. G. Multifactorial Modulation of Binding and Dissociation Kinetics on Two-Dimensional DNA Nanostructures. Nano Lett. 2013, 13, 2754− 2759. (30) Nelson, E. M.; Rothberg, L. J. Kinetics and Mechanism of Single-Stranded DNA Adsorption onto Citrate-Stabilized Gold Nanoparticles in Colloidal Solution. Langmuir 2011, 27, 1770−1777. (31) Traeger, J. C.; Schwartz, D. K. Surface-Mediated DNA Hybridization: Effects of DNA Conformation, Surface Chemistry, and Electrostatics. Langmuir 2017, 33, 12651−12659. (32) Yu, C.; Guan, J.; Chen, K.; Bae, S. C.; Granick, S. SingleMolecule Observation of Long Jumps in Polymer Adsorption. ACS Nano 2013, 7, 9735−9742. (33) Skaug, M. J.; Mabry, J. N.; Schwartz, D. K. Single-Molecule Tracking of Polymer Surface Diffusion. J. Am. Chem. Soc. 2014, 136, 1327−1332.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. ORCID

Jeremiah C. Traeger: 0000-0002-1812-9131 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The authors acknowledge support from the Soft Materials Research Center (NSF-MRSEC DMR 1420736). REFERENCES (1) Li, Y.; Zhao, Q.; Wang, Y.; Man, T.; Zhou, L.; Fang, X.; Pei, H.; Chi, L.; Liu, J. Ultrasensitive Signal-On Detection of Nucleic Acids with Surface-Enhanced Raman Scattering and Exonuclease IIIAssisted Probe Amplification. Anal. Chem. 2016, 88, 11684−11690. (2) Papadopoulou, E.; Gale, N.; Thompson, J. F.; Fleming, T. A.; Brown, T.; Bartlett, P. N. Specifically Horizontally Tethered DNA Probes on Au Surfaces Allow Labelled and Label-Free DNA Detection Using SERS and Electrochemically Driven Melting. Chem. Sci. 2016, 7, 386−393. (3) Mou, X. B.; Ali, Z.; Li, B.; Li, T. T.; Yi, H.; Dong, H. M.; He, N. Y.; Deng, Y.; Zeng, X. Multiple Genotyping Based on Multiplex PCR and Microarray. Chin. Chem. Lett. 2016, 27, 1661−1665. (4) Johnson-Buck, A.; Walter, N. G. Discovering Anomalous Hybridization Kinetics on DNA Nanostructures Using SingleMolecule Fluorescence Microscopy. Methods 2014, 67, 177−184. (5) Bossler, A.; Van Deerlin, V. Conventional and Real-Time Polymerase Chain Reaction. In Cell and Tissue Based Molecular Pathology; Tubbs, R. R., Stoler, M. H., Eds.; Elsevier Inc.: Philadelphia, 2009; pp 33−49. (6) Isola, N. R.; Stokes, D. L.; Vo-Dinh, T. Surface-Enhanced Raman Gene Probe for HIV Detection. Anal. Chem. 1998, 70, 1352−1356. (7) Jiang, X.; Shao, N.; Jing, W.; Tao, S.; Liu, S.; Sui, G. Microfluidic Chip Integrating High Throughput Continuous-Flow PCR and DNA Hybridization for Bacteria Analysis. Talanta 2014, 122, 246−250. (8) Liu, L.; Li, Y.; Li, S.; Hu, N.; He, Y.; Pong, R.; Lin, D.; Lu, L.; Law, M. Comparison of Next-Generation Sequencing Systems. J. Biomed. Biotechnol. 2012, 2012, 1−11. (9) Drmanac, R.; Pant, K. P.; Baccash, J.; Borcherding, A. P.; Brownley, A.; Cedeno, R.; Chen, L.; Chernikoff, D.; Cheung, A.; Chirita, R.; Curson, B.; Ebert, J. C.; Hacker, C. R.; Hartlage, R.; Hauser, B.; Huang, S.; Jiang, Y.; Karpinchyk, V.; Koenig, M.; Kong, C.; et al. Human Genome Sequencing Using Unchained Base Reads on Self-Assembling DNA Nanoarrays. Science 2010, 327, 78−81. (10) Metzker, M. L. Sequencing Technologies - The Next Generation. Nat. Rev. Genet. 2010, 11, 31−46. (11) Wang, Q.; Liu, R.; Yang, X.; Wang, K.; Zhu, J.; He, L.; Li, Q. Surface Plasmon Resonance Biosensor for Enzyme-Free Amplified MicroRNA Detection Based on Gold Nanoparticles and DNA Supersandwich. Sens. Actuators, B 2016, 223, 613−620. (12) Miao, P.; Wang, B.; Meng, F.; Yin, J.; Tang, Y. Ultrasensitive Detection of MicroRNA through Rolling Circle Amplification on a DNA Tetrahedron Decorated Electrode. Bioconjugate Chem. 2015, 26, 602−607. (13) He, P.; Liu, L.; Qiao, W.; Zhang, S. Ultrasensitive Detection of Thrombin Using Surface Plasmon Resonance and Quartz Crystal 7858

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859

Article

ACS Nano (34) Giri, D.; Ashraf, K. M.; Collinson, M. M.; Higgins, D. A. SingleMolecule Perspective on Mass Transport in Condensed Water Layers over Gradient Self-Assembled Monolayers. J. Phys. Chem. C 2015, 119, 9418−9428. (35) Metzler, R.; Klafter, J. The Random Walk’s Guide to Anomalous Diffusion: A Fractional Dynamics approach. Phys. Rep. 2000, 339, 1−77. (36) Weigel, A. V.; Simon, B.; Tamkun, M. M.; Krapf, D. Ergodic and Nonergodic Processes Coexist in the Plasma Membrane as Observed by Single-Molecule Tracking. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 6438−6443. (37) Skaug, M. J.; Mabry, J.; Schwartz, D. K. Intermittent Molecular Hopping at the Solid-Liquid Interface. Phys. Rev. Lett. 2013, 110, 1−5. (38) Bychuk, O.; O'Shaughnessy, B. Anomalous Diffusion of Surface-Active Species at Liquid-Fluid and Liquid-Solid Interfaces. J. Phys. II 1994, 4, 1135−1156. (39) Viswanathan, G. M.; Buldyrev, S. V.; Havlin, S.; da Luz, M. G. E.; Raposo, E. P.; Eugene, S. H. Optimizing the Success of Random Searches. Nature 1999, 401, 911−914. (40) Bartumeus, F.; Da Luz, M. G. E.; Viswanathan, G. M.; Catalan, J. Animal Search Strategies: A Quantitative Random-Walk Analysis. Ecology 2005, 1, 3078−3087. (41) Salimi, H. Stochastic Fractal Search: A Powerful Metaheuristic Algorithm. Knowl-Based Syst. 2015, 75, 1−18. (42) Benichou, O.; Grebenkov, D. S.; Hillairet, L.; Phun, L.; Voituriez, R.; Zinsmeister, M. Mean Exit Time for Surface-Mediated Diffusion: Spectral Analysis and Asymptotic Behaviors. Anal. Math. Phys. 2015, 5, 321−362. (43) Morrin, G. T.; Schwartz, D. K. Three Regimes of Polymer Surface Dynamics under Crowded Conditions. Macromolecules 2018, 51, 1207−1214. (44) Horton, M. R.; Höfling, F.; Rädler, J. O.; Franosch, T. Development of Anomalous Diffusion among Crowding Proteins. Soft Matter 2010, 6, 2648−2656. (45) Yu, C.; Granick, S. Revisiting Polymer Surface Diffusion in the Extreme Case of Strong Adsorption. Langmuir 2014, 30, 14538− 14544. (46) Shakya, A.; King, J. T. Non-Fickian Molecular Transport in Protein-DNA Droplets. ACS Macro Lett. 2018, 7, 1220−1225. (47) King, J. T.; Yu, C.; Wilson, W. L.; Granick, S. Super-Resolution Study of Polymer Mobility Fluctuations Near C*. ACS Nano 2014, 8, 8802−8809. (48) Shakya, A.; King, J. T. DNA Local-Flexibility-Dependent Assembly of Phase-Separated Liquid Droplets. Biophys. J. 2018, 115, 1840−1847. (49) Guan, J.; Chen, K.; Jee, A. Y.; Granick, S. DNA Molecules Deviate from Shortest Trajectory when Driven through Hydrogel. J. Chem. Phys. 2018, 149, 1−6. (50) De Nigris, S.; Carletti, T.; Lambiotte, R. Onset of Anomalous Diffusion from Local Motion Rules. Phys. Rev. E 2017, 95, 1−8. (51) Metzler, R.; Jeon, J. H.; Cherstvy, A. G.; Barkai, E. Anomalous Diffusion Models and their Properties: Non-Stationarity, NonErgodicity, and Egeing at the Centenary of Single Particle Tracking. Phys. Chem. Chem. Phys. 2014, 16, 24128−24164. (52) Krapf, D. Mechanism Underlying Anomalous Diffusion in the Plasma Membrane. Curr. Top. Membr. 2015, 75, 167−207. (53) Xu, Q.; Feng, L.; Sha, R.; Seeman, N. C.; Chaikin, P. M. Subdiffusion of a Sticky Particle on a Surface. Phys. Rev. Lett. 2011, 106, 1−4. (54) Murphy, M. C.; Rasnik, I.; Cheng, W.; Lohman, T. M.; Ha, T. Probing Single-Stranded DNA Conformational Flexibility Using Fluorescence Spectroscopy. Biophys. J. 2004, 86, 2530−2537. (55) Yamakawa, H.; Takenao, Y. Equilibrium Properties. In Helical Wormlike Chains in Polymer Solutions; Yamakawa, H., Takenao, Y., Eds.; Springer-Verlag Berlin Heidelberg: Berlin, 2016; pp 129−191. (56) Godec, A.; Metzler, R. Universal Proximity Effect in Target Search Kinetics in the Few-Encounter Limit. Phys. Rev. X 2016, 6, 1− 11.

(57) Lanoiselée, Y.; Moutal, N.; Grebenkov, D. S. Diffusion-Limited Reactions in Dynamic Heterogeneous Media. Nat. Commun. 2018, 9, 1−16. (58) Grebenkov, D. S.; Metzler, R.; Oshanin, G. Strong Defocusing of Molecular Reaction Times Results from an Interplay of Geometry and Reaction Control. Commun. Chem. 2018, 1, 1−12. (59) Shin, J.; Kolomeisky, A. B. Surface-Assisted Dynamic Search Processes. J. Phys. Chem. B 2018, 122, 2243−2250. (60) Shvets, A. A.; Kochugaeva, M. P.; Kolomeisky, A. B. Mechanisms of Protein Search for Targets on DNA: Theoretical Insights. Molecules 2018, 23, 1−18. (61) Metzler, R.; Chechkin, A. V.; Klafter, J. Levy Statistics and Anomalous Transport: Levy Flights and Subdiffusion. In Encyclopedia of Complexity and Systems Science; Meyers, R. A., Ed.; Springer-Verlag New York: New York, 2009; pp 5218−5239. (62) Zhu, D.; Song, P.; Shen, J.; Su, S.; Chao, J.; Aldalbahi, A.; Zhou, Z.; Song, S.; Fan, C.; Zuo, X.; Tian, Y.; Wang, L.; Pei, H. PolyAMediated DNA Assembly on Gold Nanoparticles for Thermodynamically Favorable and Rapid Hybridization Analysis. Anal. Chem. 2016, 88, 4949−4954. (63) Peterson, A. W.; Heaton, R. J.; Georgiadis, R. M. The Effect of Surface Probe Density on DNA Hybridization. Nucleic Acids Res. 2001, 29, 5163−5168. (64) Castelino, K.; Kannan, B.; Majumdar, A. Characterization of Grafting Density and Binding Efficiency of DNA and Proteins on Gold Surfaces. Langmuir 2005, 21, 1956−1961. (65) Best, M. D. Click Chemistry and Bioorthogonal Reactions: Unprecedented Selectivity in the Labeling of Biological Molecules. Biochemistry 2009, 48, 6571−6584. (66) Lee, C.-Y.; Gamble, L. J.; Grainger, D. W.; Castner, D. G. Mixed DNA/Oligo (Ethylene Glycol) Functionalized Gold Surfaces Improve DNA Hybridization in Complex Media. Biointerphases 2006, 1, 82−92. (67) Szleifer, I.; Hager, R.; Howorka, S.; Ren, C.; Schlapak, R. Molecular and Thermodynamic Factors Explain the Passivation Properties of Poly(Ethylene Glycol)-Coated Substrate Surfaces against Fluorophore-Labeled DNA Oligonucleotides. Langmuir 2015, 31, 11491−11501. (68) Collman, J. P.; Devaraj, N. K.; Eberspacher, T. P. A.; Chidsey, C. E. D. Mixed Azide-Terminates Monolayers: A Platform for Modifying Electrode Surfaces. Langmuir 2006, 22, 2457−2464. (69) Davidson, G. 5: Vibrational Spectra of Some Co-Ordinated Ligands. In Spectroscopic Properties of Inorganic and Organometallic Compounds; Davidson, G., Ed.; The Royal Society of Chemistry: Cambridge, 2000; Vol. 33, pp 306−372. (70) Sofia, S. J.; Premnath, V.; Merrill, E. W. Poly(Ethylene Oxide) Grafted to Silicon Surfaces: Grafting Density and Protein Adsorption. Macromolecules 1998, 31, 5059−5070. (71) Noonan, P. S.; Shavit, A.; Acharya, B. R.; Schwartz, D. K. Mixed Alkylsilane Functionalized Surfaces for Simultaneous Wetting and Homeotropic Anchoring of Liquid Crystals. ACS Appl. Mater. Interfaces 2011, 3, 4374−4380.

7859

DOI: 10.1021/acsnano.9b02157 ACS Nano 2019, 13, 7850−7859