Kinetic Mechanisms in Morpholino-DNA Surface Hybridization

Abstract

Morpholinos (MOs) are DNA analogues whose uncharged nature can bring fundamental advantages to surface hybridization technologies such as DNA microarrays, by using MOs as the immobilized, or “probe”, species. Advancement of MO-based diagnostics, however, is challenged by limited understanding of the surface organization of MO molecules and of how this organization impacts hybridization kinetics and thermodynamics. The present study focuses on hybridization kinetics between monolayers of MO probes and DNA targets as a function of the instantaneous extent of hybridization (i.e. duplex coverage), total probe coverage, and ionic strength. Intriguingly, these experiments reveal distinct kinetic stages, none of which are consistent with Langmuir kinetics. The initial stage, in which duplex coverage remains relatively sparse, indicates confluence of two effects: blockage of target access to unhybridized probes by previously formed duplexes, and deactivation of the solid support due to consumption of probe molecules. This interpretation is consistent with a surface organization in which unhybridized MO probes localize near the solid support, underneath a layer of MO-DNA duplexes. As duplex coverage builds, provided saturation is not reached first, the initial stage can transition to an unusual regime characterized by near independence of hybridization rate on duplex coverage, followed by a prolonged approach to equilibrium. The possible origins of these more complex latter behaviors are discussed. Comparison with published data for DNA and peptide nucleic acid (PNA) probes is carried out to look for universal trends in kinetics. This comparison reveals qualitative similarities when comparable surface organization of probes is expected. In addition, MO monolayers are found capable of a broad range of reactivities that span reported values for PNA and DNA probes.

1. Introduction

Morpholinos (MOs), a class of uncharged DNA mimics,¹ are capturing increasing interest for diagnostic applications ^2-7 in addition to more established uses in gene knockdown.^1,8 Because thermodynamics of MO-DNA interactions are different from those between two DNA strands,^8-9 under suitable conditions MOs can favor formation of signal producing MO-DNA associations over competing interactions between sample nucleic acid sequences.⁸ In addition, MOs’ lack of charge makes them especially useful for electrostatic transduction; indeed, the assays reported to date have in one way or another relied on electrostatics.^2-7 These assays have been performed on solid supports on which immobilized MO “probes” react with analyte “targets” from solution. A key motivation for use of solid supports is their capacity for high-throughput multiplexing.¹⁰

Hybridization on solid supports is considerably more complex than in solution because of additional interactions that arise from the support and from the high concentration of probe molecules. Experience with the corresponding DNA-DNA reaction shows that hybridizations on solid supports manifest rich phenomenology thermodynamically^11-25 and kinetically.^15-16,26-30 At the surface new variables emerge, including probe density^{11,13-14,18-19,21,23,25,28,31-37} and surface potential,^12,30,38 that can strongly impact hybridization. Surface hybridization of even short oligomeric strands can proceed in multiple stages suggestive of sequential molecular rearrangements,^26-28,30 with origins of this intriguing behavior still not well understood.^27,29 These complex characteristics limit predictive modeling, interfere with accurate interpretation of diagnostic results, and motivate basic research to connect organization of the surface with kinetic barriers and thermodynamic functions. The present study addresses key facets of this relationship for kinetics of hybridization between MO monolayers and comparably sized, complementary DNA targets.

Our analysis is based on real-time electrochemical quantification of unhybridized and hybridized surface sites that is used to directly correlate the instantaneous surface state with reaction rates. When applied to early stage hybridization, this analysis reveals important corrections analogous to those in sequential adsorption processes where previously bound molecules pose a barrier to later arrivals.^39-40 Incorporation of these corrections in a kinetic model together with description of the surface molecular packing leads to close agreement between experiment and model calculations. In comparison, the classic Langmuir model introduced in 1918 for gas adsorption,⁴¹ and often used to interpret kinetics of surface hybridization reactions,^42-48 produces equally good fits but only if certain physical constraints are relaxed, ultimately underscoring oversimplifications in its underlying assumptions. At higher duplex coverages MO-DNA surface hybridization exhibits additional, qualitatively different kinetic regimes. Possible origins of this more intricate behavior are discussed, and a comparison is carried out to available kinetic data for DNA and peptide nucleic acid probes in search for elements of universal behavior across different probe types.

2. Materials and Methods

2.1. Materials

The morpholino probe sequence PM1 (Table 1) was taken from the retinoblastoma RB1 marker and was purchased from Gene Tools LLC (Philomath, OR). The 20mer probes were modified with a C3 disulfide at the 3’ end to allow for surface attachment to gold electrodes, and with a primary amine at the 5’ end to provide a bioconjugation site for ferrocenylformylglycine-NHS ester (FcFG-NHS), which served as an electroactive tag.⁴⁹ Complementary 18mer DNA targets TD1 and noncomplementary 18mer DNA controls TP53 (Table 1) were purchased from Integrated DNA Technologies (Coralville, Iowa). Both oligonucleotides contained a C6 disulfide for conjugation to N-(2-ferrocene-ethyl) maleimide (FEM), with labeling performed as previously described.¹⁸ The labeling protocol for FcFG-NHS was the same as that for the NHS ester of ferrocene carboxylic acid (FcCA-NHS) in reference 9. FcFG-NHS was used instead of FcCA-NHS because its longer linker arm increases labeling yields.⁴⁹ All ferrocene modified MO and DNA molecules were purified by HPLC prior to use. Figure S1 in the Supporting Information depicts structures of the modified MO and DNA oligomers.

Table 1.

Morpholino and DNA Sequences.

Sequence	Abbreviation	Comments
5' NH2-TTT TAA ATT CTG CAA GTG AT-CO(CH2)3SS(CH2)3CONH2 3'	PM1	MO probe
5' HO(CH2)6SS(CH2)6-ATC ACT TGC AGA ATT TAA 3'	TD1	complementary DNA target to PM1a
5' GAG GTT CAT GTT TGT GCC-(CH2)3SS(CH2)3OH 3'	TP53	non-complementary DNA control

^aTD1 is complementary to the first 18 bases at the 3’ end of the PM1 probe.

2.2. Preparation of Morpholino Monolayers

A 3 mm diameter, polycrystalline gold rotating disk electrode (RDE) served as the solid support. Prior to preparation of a probe layer the electrode was mechanically polished with a 1 μm diamond suspension (Bioanalytical Systems, West Lafayette, IN), rinsed with methanol and deionized water (18.2 MΩ cm resistivity), and electrochemically cleaned in 0.5 mol L^-1 sulfuric acid with potentiodynamic cycling.² After a deionized water rinse, the roughness factor r_f(r_f = actual area/geometric area; r_f ≥ 1) of the cleaned electrode was measured from the double-layer capacitance using previously described methods.^50-51 Values of r_f ranged from 1.41 to 1.88, with an average of 1.50 ± 0.16.

FcFG-labeled PM1 morpholinos were dissolved in deionized water to a concentration of 1.0, 2.0 or 4.0 μmol L^-1. 15 μL of the morpholino solution was deposited on freshly polished RDE electrodes for 30 min, followed by a deionized water rinse and immersion in 1 mmol L^-1 blocking solution of 6-mercapto-1-hexanol (MCH; 97% purity) in deionized water for 2 h. The MCH passivation minimizes nonspecific adsorption of DNA targets and disrupts nonspecific contacts between MO probes and the electrode.² The change from mercaptopropanol as the passivant, used previously,^2,9 to MCH was motivated by improved stability of the thicker MCH monolayers to repeated potential scanning with cyclic voltammetry (CV) used for real-time monitoring of kinetics. This change also resulted in decreased hybridization yields, attributed to increased steric penalties from MCH interfering with base-pair formation at the one or two positions closest to the solid support, similar to observations for DNA probe films.¹⁶ After a final rinse with deionized water, MO-modified electrodes were mounted on the RDE rotator and immersed in hybridization buffer containing 25 nmol L^-1 target. The buffer was deoxygenated for at least 5 min prior to insertion of the RDE by nitrogen bubbling, and a nitrogen blanket was kept above the solution during measurements. To minimize possibility of contamination, electrodes were kept wetted by a droplet of the most recently applied solution during transfer steps.

2.3. Hybridization Measurements

Measurements were performed on an RDE rotator (Bioanalytical Systems, West Lafayette, IN) connected to a CHI660C electrochemical workstation (CH Instruments, Austin, TX). The sample cell contained the MO-modified and MCH-passivated 3 mm gold working electrode, a platinum wire counter electrode, and an Ag/AgCl/3 mol L^-1 KCl reference electrode. All potentials are reported relative to this reference. Hybridizations were performed using 25 nmol L^-1 FEM-labeled targets in pH 7.0 sodium phosphate at a concentration C_B of buffer phosphate groups of 0.01, 0.05, 0.1 or 0.5 mol L^-1. No other salt or buffer ingredients were present. Reverse, or dehybridization, reactions were performed by switching a hybridized probe layer into a target-free buffer of the same ionic strength. The RDE rotational speed was 1500 rpm.

The instantaneous target coverage S_D was determined from the total charge required to switch the oxidation state of the targets’ FEM tags. This charge was measured with CV and was converted to molecular coverage following previously reported methods.² CV measurements were taken every 5 min at a scan rate of 5 V s^-1. Briefly, S_D follows from S_D = Q_FEM/(eA_gr_f) where Q_FEM is total charge from conversion of the FEM oxidation state, e is elementary charge, and A_gr_f is total electrode area given by product of the geometric area A_g and roughness factor r_f. The total probe coverage S₀ was similarly derived from redox switching of the probe FcFG tags. Here, S₀ = S_D + S_P where S_P is coverage of unhybridized probes. Figure S2 in the Supporting Information shows a sample CV trace together with a computer generated fit used to determine Q_FEM and Q_FcFG.

Control experiments confirmed that (1) the sampling frequency of one CV scan every 5 min was sufficiently low to avoid biasing of hybridization kinetics, and (2) the scan rate of 5 V s^-1 was sufficiently slow to avoid signal attenuation due to electron transfer limitations. The first concern was addressed through measurements in which sampling times were varied from 10 s to 600 s as hybridization progressed, and noting that for times of 2 min or longer there were no discernible changes in hybridization rates. The second issue was addressed by calculating probe coverages from CV voltammograms measured at sweep rates from 0.1 to 2000 V s^-1 and noting that calculated coverages stabilized for 10 V s^-1 and lower, Fig. 1A. The need for slower sweep rates, compared to our earlier study which used 20 V s^-1,⁹ is attributed to a higher charge transfer barrier presented by the thicker MCH as opposed to mercaptopropanol passivation. When CV data were not being collected the working electrode was held at 0 V.

Figure 1.

Examples of experimental controls. (A) Effect of CV scan rate on calculated coverages, for three different samples. (B) Effect of RDE rotational speed on hybridization under conditions of low reaction resistance, thus emphasizing mass transfer limitations (conditions: S₀ = 1.24 ± 0.07 × 10¹² cm^-2; C_B = 0.5 mol L^-1; target concentration = 25 nmol L^-1). (C) CV traces after 5 h under 25 nmol L^-1 noncomplementry TP53 target in 0.1 mol L^-1 buffer at the indicated probe coverages. The large peak close to 0.5 V corresponds to FcFG signal from PM1 probes. The FEM TP53 signal, if present, would lie between 0.25 and 0.3 V.

2.4. Other Controls

Hybridization kinetics were analyzed under the assumption that mass transport resistance associated with delivery of targets to the probe layer was negligible. The significance of mass transport can be assessed using the Damköhler number Da = k_FS₀/k_M, where k_F is the forward hybridization rate constant and k_M is the mass transport coefficient.^28,52 For Da ≪ 1 reaction kinetics are slower than mass transport and therefore represent the dominant rate resistance; in this limit, mass transfer limitations can be neglected. To check consistency with this approximation Da was estimated for experimentally derived k_F values as described in section S3, Supporting Information. Depending on S₀ and ionic strength, Da was found to range from 0.0035 to 0.18; therefore, kinetic limitations rather than mass transport were dominant. The highest value of 0.18 applied to lowest probe coverage S₀ and highest buffer concentration C_B, when hybridization rates were observed to be fastest. Even for these conditions, however, mass transport was not significant at the RDE rotational speed used, ω = 1500 rpm, since doubling ω had little if any effect (Fig. 1B). Accordingly, data were interpreted purely from a reaction kinetic perspective, under assumption of negligible mass transport resistance.

Controls for nonspecific adsorption of targets used the TP53 sequence (Table 1) labeled with the FEM tag. Experiments were performed at high and low probe coverages, and various buffer concentrations. These measurements showed that nonspecific target adsorption was below quantification, Fig. 1C. Therefore, nonspecific adsorption was treated as negligible and target signals were fully attributed to duplexes formed through sequence specific base pairing.

3. Results and Discussion

3.1. General Observations

Kinetic traces, consisting of the duplex coverage S_D as a function of time, were determined for four sodium phosphate buffer concentrations C_B (0.01, 0.05, 0.1 and 0.5 mol L^-1), with no other salt present, and three probe coverages S₀ (~ 1.5 × 10¹², ~ 3.5 × 10¹² and ~ 6 × 10¹² cm^-2). Table 2 summarizes these conditions, with remaining entries discussed below. Hybridization was followed for 2 h, with a few runs performed for longer times. Figs. 2A-C show examples of data collected at the three coverages and at C_B = 0.1 mol L^-1. All coverages exhibit a gradual decrease in hybridization rate r = dS_D/dt over the initial hour, with the lowest coverage (Fig. 2A) approaching saturation within this time. After this initial or “stage I” regime, the behavior often transitioned to an approximately linear increase in S_D with time. During this second stage r was nearly constant, as indicated by the dashed lines in Figs. 2A-C. That consumption of the probe reagent was not accompanied by slowing of the reaction is suggestive of an “autocatalytic” effect. Our inspection of published hybridization traces reveals that such behavior can also arise in hybridization to PNA probes (especially at lower ionic strengths)^53-54 and, at times, to DNA probes,^26,55 as well as in protein adsorption.⁵⁶ At even longer times, stage III in Fig. 2D, the hybridization rate again starts to decrease with S_D in a protracted approach to equilibrium. Similar overall trends were observed when hybridization was carried out at C_B of 0.01 and 0.5 mol L^-1 at the high probe coverage, for which longer runs were also performed. This evidence indicates that distinct kinetic mechanisms can become operative at different time points during MO-DNA surface hybridization.

Table 2.

Experimental Conditions and Derived Model Parameters.^a

S0 (1012 cm-2)	CB (mol L-1)	kF (103 L mol-1 s-1)b	ZE (nm2)b
1.20	0.010	15 ± 1	190 ± 3
3.5	0.010	1.4 ± 0.1	300 ± 8
6.1	0.010	0.86 ± 0.01	440 ± 9
1.8	0.050	18 ± 1	120 ± 2
4.0	0.050	2.8 ± 0.1	120 ± 3
6.2	0.050	4.0 ± 0.1	140 ± 2
1.4	0.10	100 ± 5	73 ± 1
3.8	0.10	14 ± 1	72 ± 1
6.6	0.10	6.6 ± 0.2	69 ± 1
1.4	0.50	320 ± 20	51 ± 1
3.0	0.50	27 ± 1	50 ± 1
6.4	0.50	27 ± 1	32 ± 1

^ak_F and Z_E are defined in equation 6. The listed values are from fits to the first hour of hybridization.

^bUncertainties represent standard error from fitting of equation 6 to data.

Figure 2.

(A)-(C) Hybridization kinetics for C_B = 0.1 mol L^-1 at three probe coverages S₀. (D) Long-term kinetic data for the experiment in part (C). The trace can be divided into distinct regimes as discussed in the text. In all cases, red lines serve as visual guides to help judge linearity of S_D with time.

Fig. 3 illustrates that dehybridization, following placement of samples under target-free buffer, was very slow. This is indicated by stability of the target peak appearing at ~ 0.27 V, and was true for all conditions of S₀ and C_B tested. The lack of dehybridization was an important constraint in the following kinetic analysis.

Figure 3.

CVs illustrating lack of dehybridization after 6 h under a target-free buffer, following a 14 h hybridization run (S₀ = 6.6 × 10¹² cm^-2, C_B = 0.1 mol L^-1). The peak around 0.27 V corresponds to the target FEM tags, while that around 0.47 V corresponds to the probe FcFG tags.

3.2. Stage I: Langmuir Analysis

Langmuir kinetics⁴¹ have modeled both DNA-DNA ^42-48,57 and PNA-DNA^45,53-54,58 surface hybridization, and provide an appropriate starting point for considering the corresponding MO-DNA process. In the irreversible Langmuir model, the forward rate r_F of hybridization between targets T and probes P to form duplexes D, P + T → D, is proportional to frequency of P-T collisions given by product of the solution target concentration C_T,B and the surface coverage of available probes S_P,

$$\frac{d{S}_D}{dt}=r_{\mathrm{F}}=k_{\mathrm{F}}{C}_{\mathrm{T},\mathrm{B}}{S}_{\mathrm{P}}=k_{\mathrm{F}}{C}_{\mathrm{T},\mathrm{B}}\left(S_0\text{-}{S}_{\mathrm{D}}\right)$$ (1)

with k_F the forward rate constant. For reversible reactions, P + T ↔ D, a reverse rate r_R is added to represent dehybridization; thus

$$\frac{d{S}_D}{dt}=r_{\mathrm{F}}-r_{\mathrm{R}}=k_{\mathrm{F}}{C}_{\mathrm{T},\mathrm{B}}\left(S_0\text{-}{S}_{\mathrm{D}}\right)-k_{\mathrm{R}}{S}_{\mathrm{D}}$$ (2)

with k_R the reverse rate constant. k_F and k_R are expected to depend on all parameters that affect molecular interactions at the surface including total probe coverage, surface potential, buffer composition, temperature, strand sequences, and the extent of hybridization. Although the extent of hybridization varies with time the Langmuir model assumes that binding sites do not interact; this implies that k_F and k_R are independent of the state of surrounding sites and thus independent of S_D. Recalling that mass transport resistances were negligible (section 2.4), the time-integrated analytical forms of equations 1 and 2 were used to directly fit stage I data during the first 60 min of hybridization.

Fig. 4 illustrates Langmuir fits for S₀ = 1.2 × 10¹² cm^-2 and C_B = 0.01 mol L^-1. Assumption of irreversible kinetics according to equation 1, with k_F and S₀ treated as adjustable, led to good agreement as shown by the black line in Fig. 4; however, the derived S_0Fit = 4.8 × 10¹¹ cm^-2 was significantly off the actual coverage S₀ = 1.2 × 10¹² cm^-2. If, instead, S_0Fit was set equal to S₀ and only k_F was allowed to vary the agreement was poor, Fig. 4 red line. Assumption of reversible kinetics as per equation 2 with the constraint S_0Fit = S₀ and k_F and k_R as floating parameters recovered good agreement, Fig. 4 green points. This fit, however, was again not physically meaningful because the derived k_R predicted significant dehybridization where little was observed experimentally. In summary, although Langmuir kinetics could produce numerically excellent fits, this was only possible by violating constraints on dehybridization rates or probe coverage. Therefore, an alternate kinetic model was sought that could simultaneously account for all experimental information.

Figure 4.

Comparison of fits based on Langmuir kinetics for S₀ = 1.2 × 10¹² cm^-2 and C_B = 0.01 mol L^-1. Black points (●): experimental data. Black line (): irreversible kinetics, equation 1, with k_F and S_0Fit as fit parameters (k_F = 3.2 × 10⁴ L moL^-1 s^-1, S_0Fit = 4.8 × 10¹¹ cm^-2, R² = 0.992). Red line (): irreversible kinetics, equation 1, with k_F variable and S_0Fit constrained to S_0Fit = S₀ = 1.2 ×10 cm^-2 (k_F = 6.8 × 10³ L moL^-1 s^-1, R² = 0.82). Green points (): reversible kinetics, equation 2, with k_F and k_R variable and S_0Fit constrained to 1.2 × 10¹² cm^-2 (k_F = 1.3 × 10⁴ L moL^-1 s^-1, k_R = 4.8 × 10^-4 s^-1, R² = 0.99).

3.3. Stage I: An Experimentally-Derived Kinetic Mechanism

Rather than assume a particular kinetic model, one can ask what model features are suggested by experimental data. The reaction rate is taken to follow

$$\frac{d{S}_D}{dt}=k_{\mathrm{F}}g\left(S_{\mathrm{D}}\right)C_{\mathrm{T},\mathrm{B}}(S_0-S_{\mathrm{D}})$$ (3)

where dehybridization has been neglected because of the very slow off rates. Equation 3 abandons the assumption of site independence and recognizes that changes in layer structure with hybridization may alter reactivity of the probe layer. The impact of these changes is captured in the effective rate constant k_F g(S_D), where S_D parametrizes the extent of hybridization and through the unknown function g alters the site reactivity. k_F now represents an “intrinsic” rate constant at the onset of hybridization, when S_D = 0 and g = 1. The dependence of g on S_D follows directly from equation 3

$$k_{F}g\left(S_D\right)=\frac{1}{C_{T,B}(S_0-S_D)}\frac{d{S}_D}{dt}$$ (4)

with all terms on the right accessible from experiment. Because calculation of dS_D/dt required differentiation, to minimize introduction of numerical noise the data were first fit to an analytic function which was then differentiated. A Lorentz type function was selected because it closely captured experimental S_D(t) traces over the first hour and yet was unrelated to any expected form of the response. Examples of Lorentz fits at the four limits of probe coverage and ionic strength are shown in Fig. S3 in the Supporting Information. Figs. 5A-D show the derived dependence of k_F g on S_D as calculated from equation 4.

Figure 5.

(A)-(D). Experimentally-derived dependence of k_F g(S_D) on S_D according to equation 4, for combinations of S₀ and C_B indicated at top. Points (●): data. Lines (): linear approximations. (E)-(H). Corresponding model fits. Points (●): data. Lines (): fits based on equation 6.

The results in Figs. 5A-D suggest an approximately linear decrease of the effective rate constant k_F g(S_D) with S_D. Therefore, stage I data were reanalyzed using g = 1 – Z_ES_D, corresponding to

$$\frac{d{S}_D}{dt}=k_{\mathrm{F}}\left(1\text{-}{Z}_{\mathrm{E}}{S}_{\mathrm{D}}\right)C_{\mathrm{T},\mathrm{B}}\left(S_0\text{-}{S}_{\mathrm{D}}\right)$$ (5)

and the time-integrated form

$$S_D=k_F{S}_0\frac{1-\exp \left[C_{T,B}{k}_{F}t(1-Z_E{S}_0)\right]}{k_F{Z}_E{S}_0-k_F\exp \left[C_{T,B}{k}_{F}t(1-Z_E{S}_0)\right]}$$ (6)

Equation 6 has two parameters, k_F and Z_E, whose optimized values are compiled for all conditions in Table 2. Examples of fits are shown in Figs. 5E-H; these fits satisfy constraints of negligible off-rates as well as pinning of S₀ at the experimental value, which could not be simultaneously met by Langmuir kinetics. Fits were also performed to just the first 30 minutes of hybridization to check whether the 60 min analysis was biased by overlap with stage II; the 30 min and 60 min analyses yielded results that were identical within fitting uncertainties.

The good fit quality of equation 6 shows that a linear dependence of g on S_D successfully accounts for all experimental observations, but does not clarify physical origins of this dependence. In contrast to DNA probes, unhybridized MO probes are expected to exist in a desolvated state due to their lower solubility, as schematically depicted in Fig. 6A.⁹ A desolvated organization of MO probes, of the same sequence as in this study, was previously deduced from electrochemical measurements of the interfacial capacitance of such films.^2-3 MO-DNA duplexes are expected to be more soluble because of their DNA charge, and in a mixed layer should therefore segregate toward the solution, Fig. 6B.^3,9 The resultant stratification, in which duplexes protrude away from the surface, is expected to hinder hybridization because targets must first pass across the duplex layer before encountering an unhybridized probe. The dependence of g on the duplex coverage S_D presumably accounts for corrections due to this barrier.

Figure 6.

Schematic of (A) unhybridized and (B) partially hybridized MO layers. In (B), a stratified organization exists due to formation of more soluble MO-DNA duplexes that extend above the underlayer of less soluble, unhybridized probes.

The linear dependence of g on S_D indicates that each duplex contributes to the hybridization barrier independently; that is, corrections nonlinear in S_D, which would be expected once interactions between duplexes set in, are not yet significant. In this “linear” regime the parameter Z_E can be interpreted as an exclusion zone associated with a single duplex, with Z_ES_D then the surface fraction inaccessible to targets due to occlusion by duplexes. The form of this correction, although derived directly from experiment, is consistent with theoretical expectations. For example, it is analogous to the first order adjustment in the accessible surface fraction encountered in sequential adsorption processes (e.g. equation 18 in reference 39).

Z_E is expected to depend on ionic strength since both duplexes and targets are charged; therefore, the duplex-target interaction will have an electrostatic component. In contrast, it is not expected to depend strongly on coverage of unhybridized probes since there is no apparent mechanism through which the probes, collapsed on the solid support, could significantly influence the duplex-target interaction. Inspection of the Z_E values in Table 2 largely confirms these expectations. The increased scatter at the lowest ionic strength of 0.01 mol L^-1 is attributed to uncertainties in quantifying the rather small duplex coverages in this limit.

If the interpretation of Z_E as the area around a duplex from which targets are excluded is correct, it should be possible to relate it to the duplex and target molecular dimensions. As illustrated by the shaded region in Fig. 7B, this area depends on the duplex width D and length H (Fig. 7A), and the target radius R_T. If a duplex is on average tilted by an angle θ_AVG to the surface normal then, based purely on geometric considerations, the center of mass of a target coil would be excluded from an area Z_E,CAL ≈ (D + 2R_T)(Hsinθ_AVG + 2R_T),⁵⁹ assuming Hsinθ_AVG ≫ Dcosθ_AVG in Fig. 7A. The exclusion zone must in addition have an electrostatic component, the form of which is not known. However, since electrostatic interactions are exponentially screened over lengthscales comparable to the Debye length r_D, any additional separation imposed by electrostatics should be at most a few r_D. If m is the number of Debye lengths defining the target-duplex separation permitted by electrostatics, then the approximation for Z_E,CAL becomes

$$Z_{\mathrm{E},\mathrm{CAL}}\approx (D+2R_{\mathrm{T}}+2m{r}_{\mathrm{D}})(H\sin {\theta }_{\mathrm{AVG}}+2R_{\mathrm{T}}+2m{r}_{\mathrm{D}})$$ (7)

Figure 7.

(A). Definition of duplex width D, length H, and average tilt angle θ_AVG. (B). The shaded region approximates the area excluded by a duplex to the center of mass of a target coil, where R_T is the target radius. The picture assumes m = 0 in eqn. 7.

For comparing experimental Z_E values with those calculated from equation 7, and in the absence of structural information on MO-DNA duplexes,⁶⁰ molecular dimensions were assumed to correspond to those of B-form DNA with D = 2 nm and H = 5.8 nm. Moreover, duplexes were assumed to behave as freely-hinged rods subject only to impenetrability of the solid support; in this case a uniformly distributed θ_AVG evaluates to 57°. The assumption of freely-hinged orientation rests on absence of significant duplex-duplex interactions, consistent with early stage hybridization, as well as unimportance of duplex-surface interactions. Hydrodynamic alignment of duplexes due to the RDE shear flow was also neglected. This last assumption can be checked through the dimensionless ratio γ/D_ROT where γ is the local shear rate and D_ROT is the duplex rotational diffusion coefficient.^61-62 For our conditions γ/D_ROT is less than 1 × 10^-3 (section S5, Supporting Information); in this limit hydrodynamic alignment is not significant. The last input, R_T, was taken equal to the target radius of gyration R_g = (l_PL_C/3)^1/2 where L_C = N_T l_N is the contour length, N_T = 18 is the number of nucleotides per target, l_N = 0.43 nm is the length per nucleotide,⁶³ and l_P = c₀ + c₁/C_Na,B^1/2 is the persistence length of single-stranded DNA with c₀ and c₁ taken from reference 64 and C_Na,B the solution cation concentration.

Fig. 8 compares experimental Z_E to Z_E,CAL estimated from equation 7. For m = 0 (open circles, Fig. 8) the ratio Z_E/Z_E,CAL clusters around 2, a reasonable agreement given the approximate treatment; however, Z_E/Z_E,CAL tends to decrease with ionic strength suggesting that setting m = 0 underestimates the role of electrostatics. For m = 0, electrostatics enter solely through the target persistence length l_P. Setting m = 2 (filled circles, Fig. 8) has the simultaneous effect of nearly eliminating variation of Z_E/Z_E,CAL with ionic strength and of bringing predicted values close to experimental ones, so that Z_E/Z_E,CAL ≈ 1. These improvements are consistent with importance of electrostatics in the duplex-target interaction.

Figure 8.

Ratio of measured (Z_E) to estimated (Z_E,CAL) exclusion areas, for the twelve experimental conditions listed in Table 2. Open circles (○): Z_E,CAL based on steric exclusion only; m = 0 in equation 7. Filled circles (●): Z_E,CAL based on combination of steric and electrostatic exclusion; m = 2 in equation 7. The experiments are listed by ionic strength, as indicated at top of the plot.

The second model parameter, k_F, represents the intrinsic reactivity of the probe layer in the limit S_D = 0. From Table 2, a roughly tenfold decrease in k_F occurs as probe coverage increases from ~ 1.5 × 10¹² cm^-2 to ~ 3.5 × 10¹² cm^-2. This decrease in k_F is attributed to increased stabilization of probes by probe-probe associations at higher S₀, since such aggregation presents an activation barrier to hybridization. The data in Table 2 moreover suggest this effect plateaus at higher coverages, perhaps because of diminished impact of coverage changes once the films become nearly continuous around S₀ ~ 5 × 10¹² cm^-2.³ A practical consequence of these observations is that faster response times should result if probe coverages are kept low.

Interestingly, k_F decreased approximately 20-fold when C_B was lowered from 0.5 to 0.01 mol L^-1, Table 2. This trend could in principle arise from charge on the solid support that is repulsive to the DNA target molecules. Although unhybridized MO probes are not charged, negative charge could reside on the metal electrode itself and increasingly oppose hybridization as ionic strength is lowered. Such an explanation, however, is inconsistent with MCH-passivated electrodes typically exhibiting negative potentials of zero charge (pzc),^65-66 what implies MCH supports to have a positive charge at the 0 V used for hybridization. Our own measurements, based on minimum in interfacial capacitance,⁶⁷ confirmed that pzc is negative for MCH-passivated electrodes bearing unhybridized MO probes under pH 7.0 sodium phosphate, with pzc falling between -0.1 and -0.2 V.⁶⁸ Therefore, some other, as yet unidentified effect is believed responsible for the dependence of k_F on C_B. One such possibility arises from C_B-induced changes in target conformation. Kinetics of duplex formation might be favored, for example, by more compact target conformations, realized at higher C_B, that locally concentrate nucleotides to accelerate formation of stably base-paired MO-DNA nuclei.

In summary, the forward rate for stage I kinetics is found to obey

$$r_{\mathrm{F}}=k_{\mathrm{F}}\left(1\text{-}{Z}_{\mathrm{E}}{S}_{\mathrm{D}}\right)\left(S_0\text{-}{S}_{\mathrm{D}}\right)C_{\mathrm{T},\mathrm{B}}$$ (8)

Here, k_F represents intrinsic reactivity of the functionalized support, in the S_D = 0 limit, and depends on all parameters that affect the interaction of a target with the unhybridized probe film. The factor (1-Z_ES_D) accounts for steric and electrostatic occlusion of target access to unhybridized probes due to protrusion of previously formed duplexes normal to the support. Third, the conventional term (S₀-S_D) enforces the upper limit S_D = S₀ and accounts for deactivation of the support due to consumption of probe segments by hybridization, what leaves fewer MO segments per area to nucleate duplex formation.⁶⁹ The last factor, C_T,B, is the usual impact of solution concentration on the frequency of hybridization attempts.

3.4. Comments on Later Kinetic Stages

The transitions to stage II and III behavior are not yet fully understood. Since during stage I interactions between duplexes are weak, one possible explanation for the stage I/II transition is that it coincides with onset of duplex-duplex interactions. Such interactions could cause duplexes to align, decreasing Z_E and thereby facilitating access to unhybridized probes. By offsetting deactivation of the solid support due to consumption of probes, the alignment could contribute to the near constancy in rate of hybridization observed during stage II. Interestingly, in protein adsorption, stage II like behavior has been attributed to conformational changes in which the occupied area per protein decreases as coverage increases;⁵⁶ this is analogous to the duplex reorientation mechanism proposed here.

Once duplexes become significantly aligned, the hybridization rate would be expected to again decrease with S_D as indeed observed in stage III. If this interpretation is correct, then according to Fig. 2D a modest increase in S_D during stage II (e.g. by about 20% from 1.6 × 10¹² to 1.9 × 10¹² cm^-2 in Fig. 2D) should trigger significant alignment. These coverages correspond to inter duplex distances of 7 to 8 nm and are thus well within contact range, as would be required. Also, as recently discussed,⁹ in this last stage approach to equilibrium is expected to become especially hindered once dimensions of the voids between duplexes fall below those of average target conformations, thereby forcing targets to adopt significantly distorted, and hence rarer, conformations in order to reach an unhybridized probe. These more complex kinetic behaviors can be avoided by restricting duplex coverages to remain in stage I (e.g. by keeping the total probe coverage S₀ modest), what should simplify analysis of surface hybridization data based on MO probes.

3.5. Comparison of MO-DNA, DNA-DNA, and PNA-DNA Surface Hybridization Kinetics

Direct comparison of different probe systems at present is challenged by variations in surface chemistry, experimental conditions, and data interpretation methods between studies. Even for the most investigated scenario, that of DNA-DNA surface hybridization, some studies find Langmuir kinetics a reasonable approximation^42-48,57,70 while others find richer behavior with multiple stages or timescales,^15-16,26-30 reminiscent of the multiple stages in MO-DNA hybridization. Based on studies with model oligonucleotide systems, behavior closer to Langmuir kinetics appears to result when DNA probe lengths are kept below 20mers ^42-45,47-48 and the probes are not too close together.¹⁵

When more intricate behavior with multiple stages is observed, it may not necessarily reflect correspondence of underlying mechanisms and, indeed, we are not aware of our explanations for MO probe systems being applied in situations when DNA probes are used.^27,30 However, kinetic mechanisms for the two cases should become similar if a DNA probe layer stratifies into an underlayer of unhybridized probes and an overlayer of DNA-DNA duplexes. This situation could arise, for example, from adsorption of the unhybridized probes to the support, thereby producing similarity in layer organization and hybridization mechanisms to the MO system. In one study³⁴ where DNA probes adsorbed to the solid support predictions of Langmuir kinetics were especially far from experimental observations and the hybridization trace (Fig. 3 in reference 34) exhibited similarity to Fig. 2D.

Most studies of surface hybridization to PNA probes have employed shorter assay times, 10 minutes or less,^45,53,58,71 precluding comparison with long term trends. When times of up to 2 h were considered deviations from Langmuir kinetics became apparent that bear resemblance to regime I/II behavior, especially at lower ionic strengths (e.g. Fig. 2 in reference 54, Fig. 5 in reference 53). Like MOs, PNAs are uncharged and even less soluble;⁸ therefore, it seems plausible that surface organization of PNA probes may be similar to that of MO probes, with unhybridized PNA near the solid support. Similarity in kinetic mechanisms would then be expected as, in order to hybridize, targets would have to again traverse the barrier presented by the duplex layer. This expectation could be further examined by testing PNA probes over a similar range of conditions as for MO probes.

Fig. 9 compiles literature values of rate constants k_F for the three probe systems. All of the data are for oligomer-sized, 10mer to 30mer, probes hybridizing to fully complementary, comparable length DNA targets under noncompetitive conditions (i.e. no other target sequences are present). On the right side of the plot the rates approach 10⁶ L moL^-1 s^-1. This limit can be compared to solution rates which, for hybridization of DNA oligonucleotides, fall between 10⁵ to 10⁷ L moL^-1 s^-1.⁷² The upper k_F limit, therefore, appears to approach solution values. While both DNA and MO probes demonstrate reactivities close to this limit, such performance is only realized under favorable conditions. As discussed in section 3.3 and Table 2, MO probes hybridized fastest at low coverages and high ionic strengths. Probe coverage is also crucial for kinetics of DNA-DNA surface hybridization;³² indeed, two of the fastest rates in Fig. 9 were for probe coverages below 1 × 10¹² cm^-2.^46,55

Figure 9.

Compilation of forward rate constants k_F for noncompetitive surface hybridization of complementary DNA targets to DNA, PNA, and MO probes. Numbers next to each entry cite the original study.

Interestingly, DNA probes generally do not yield k_F values less than 10⁴ L moL^-1 s^-1, with the one exception the study by Sekar et al.⁷³ In contrast, MO and PNA probes exhibit values down to ~ 10³ L moL^-1 s^-1. As discussed in section 3.3, the slow limit for MO probes arises under high coverages at which these probes are expected to aggregate, thus creating an activation barrier to hybridization. Keeping probe coverages modest can avoid this slowdown. However, it is important to recognize that the postulated benefits of reduced probe coverage are based on results from noncompetitive hybridization, and may not directly extrapolate to multiplexed hybridization as practiced in microarrays. Multiplexed experiments must also contend with cross-reactions in which partly matched targets occupy the probes and interfere with binding of the perfect match;^74-76 these cross reactions, whose impact depends on rates of dehybridization of the partial matches, may be a more significant kinetic obstacle to buildup of the sequence-specific signal than probe-probe interactions. Temperature, not considered as a variable in the present study, also becomes critical to optimization of multiplexed assays.⁷⁷

4. Conclusions

Hybridization between oligomer morpholino (MO) probes and complementary DNA targets exhibits a rich kinetic behavior that, in general, defies explanation by a single mechanism. The intrinsic reactivity of the unhybridized probe layer depends both on probe coverage and ionic strength, with fastest kinetics observed at low probe coverages and high ionic strengths. The dependence on probe coverage is attributed to lessened association between probes at low coverages; that on ionic strength is not yet understood. As hybridization proceeds, distinct kinetic stages appear and the rate of hybridization exhibits dependency on the extent of hybridization not captured by classical Langmuir kinetics. These observations are consistent with an interfacial organization in which unhybridized probes segregate near the solid support, while hybridized duplexes segregate to the solution side. The resultant stratification subjects later-arriving targets to a barrier imposed by the growing duplex layer. During the first stage of hybridization, duplexes contribute independently to this barrier through exclusion of targets from a zone around each duplex. At higher duplex coverages, an unusual regime can arise in which the hybridization rate becomes nearly independent of the extent of hybridization, followed by a third stage in which the rate again decreases with duplex coverage. One possible explanation for the second stage is that it reflects onset of duplex-duplex interactions that, temporarily, can be relaxed by duplex alignment to maintain the hybridization rate approximately constant; once this degree of freedom is exhausted further hybridization becomes more and more kinetically attenuated as the duplex layer continues to fill in.

Comparison with literature data reveals that MO probes exhibit reactivities that span the full range observed with DNA and PNA probes, and that approach solution rates under favorable conditions. These comparisons are also supportive of the notion that different probe types exhibit comparable kinetic mechanisms if their interfacial organization is similar; however, available data sets are limited and more systematic studies, across multiple probe types and under similar conditions, are needed to fully explore this issue.