Kinetic Microscale Thermophoresis for Simultaneous Measurement of Binding Affinity and Kinetics

Abstract Microscale thermophoresis (MST) is a versatile technique to measure binding affinities of binder–ligand systems, based on the directional movement of molecules in a temperature gradient. We extended MST to measure binding kinetics as well as binding affinity in a single experiment by increasing the thermal dissipation of the sample. The kinetic relaxation fingerprints were derived from the fluorescence changes during thermodynamic re‐equilibration of the sample after local heating. Using this method, we measured DNA hybridization on‐rates and off‐rates in the range 104–106  m −1 s−1 and 10−4–10−1 s−1, respectively. We observed the expected exponential dependence of the DNA hybridization off‐rates on salt concentration, strand length and inverse temperature. The measured on‐rates showed a linear dependence on salt concentration and weak dependence on strand length and temperature. For biomolecular interactions with large enthalpic contributions, the kinetic MST technique offers a robust, cost‐effective and immobilization‐free determination of kinetic rates and binding affinity simultaneously, even in crowded solutions.


Introduction
Thed issociation constant K d = k off /k on characterizes the binding affinity of ab inder-ligand system and has been extensively studied in many research fields. [1][2][3][4] K d is usually determined by the analysis of equilibrated states of binderligand systems.O nt he other hand, the determination of the underlying kinetic association and dissociation rates k on (onrate) and k off (off-rate) usually requires the time-resolved measurement of the transition of the system from an onequilibrium state towards equilibrium. [5] Then ecessary deflection from equilibrium can be introduced to the system either by rapid mixing of the reactants [6] or by rapid temperature jumps. [7] During this transition, the change in concentration of bound and unbound molecules is governed by the kinetic rates. [8] Thek inetic rates provide am ore thorough understanding of the binding process,because they characterize the binding (on-rate dependent), the dissociation (off-rate dependent) of the complex and the timescales of the binding process,aswell as its stability.However,due to the difficulty of their measurement, kinetic rates have not received as much attention as the dissociation constant. [8,9] Themeasurement of kinetics by rapid mixing of reactants often requires immobilization of one of the reactants.The free ligand is then added to the mixture containing the immobilized binder for adefined period and the subsequent binding is recorded, for example,b ys urface-plasmon resonance measurements (SPR), [10] nanotube biosensors [9] and biolayer interferometry (BLI). [11] SPR and BLI offer label-free detection and real-time data acquisition and are independent of temperature-related characteristics.I mmobilization-based methods that apply electric potentials to expose the ligand and the binder are useful for studying systems such as aptamer-analyte complexes. [12] However,i mmobilization might alter the chemical and physical properties of biomolecules [13] leading to modified binding properties or even loss of binding in extreme cases, [14] for example,t he binding site could be inaccessible due to random orientation of the molecule attached to the surface. [15] It was reported for SPR that the binding affinity could be overestimated due to underestimated off-rates. [1,16] To conclude,the immobilization techniques are suitable for studies of interactions near or on surfaces,b ut not ideal for studying in-solution interactions.
Many physiological interactions take place in crowded solutions.E xperimental methods which allow determination of kinetic rates under such conditions and without immobilization include fluorescence anisotropy (FA), [17] fluorescence correlation spectroscopy (FCS), [18] Fçrster Resonance Tr ansfer (FRET) [19] and fluorescence quenching (coupled to stopped-flow technique) [6] among others. [20] Even though all these are excellent options for determining the kinetic rates, they often suffer from prohibitive costs,t ime-consuming sample preparation steps and extensive data analysis.
Here,w ep resent an ovel method called "kinetic microscale thermophoresis" (KMST) to experimentally determine kinetic reaction rates in bulk solution, in an all-optical way that only requires minimal preparation steps.K MST is an extension of the well-established and widely used microscale thermophoresis (MST) method. [1,[21][22][23][24][25][26][27] MST uses bindingdependent intensity change of fluorescently labeled molecules in am icroscopic temperature gradient to measure the binding affinity.M ST can also detect minute changes in conformation, charge,a nd size upon binding or enzymatic activity. [1] MST has been successfully used in the past to determine affinities in complex solutions. [21] TheK MST technique offers measurement of binding kinetics together with binding affinity in as ingle experimental run. This is achieved by increasing the thermal dissipation of the samples (Figure 1), making the MST setup capable of temperature jumps.A nalysis of the temperature-dependent features, including the bleaching,diffusion, thermophoretic and kinetic contribution to the fluorescence intensity ( Figure 1a nd Figure 2), allows for the determination of not only the binding affinity but also the kinetic rates in as ingle experiment ( Figure 3). We measured the relaxation constants in the range of 0.01-0.5 s À1 ,allowing measurements of k on values between 10 4 and 10 6 m À1 s À1 and k off between 10 À4 and 0.1 s À1 .Although these ranges do not cover the entire spectra of biomolecular on-rates (10 3 -10 9 m À1 s À1 )a nd off-rates (10 À5 -1 s À1 ), [28] the method provides al arge enough interval to study many biomolecular systems.T odemonstrate the effectiveness of the method, we systematically measured the kinetic hybridization rates of fully complementary DNAstrands between 10 bp and 16 bp in varying salt concentrations (Figures 4and 5). Theoffrates showed exponential dependence on strand length, temperature and salt concentration. Theo n-rates showed weak dependence on strand length and temperature and linear dependence on salt concentration. Moreover,a n analysis of the temperature dependence of the kinetic rates shed light on the hybridization mechanism of DNAa nd summarized the determinants of DNAbinding.Our results on DNAh ybridization show that KMST is ap romising method to measure reaction kinetics without immobilization, with fluorescent labeling of only one binding partner and in crowded solutions ( Figure 6).

Binding Kinetics from Kinetic Microscale Thermophoresis
We extended the conventional MST setup (Nanotemper Monolith NT.115 Pico )t ok inetic MST by placing the samplecontaining capillary on asilicon wafer and immersing it in oil ( Figure 1). Thef luorescence excitation/detection unit of the NT.115 Pico measured the fluorescence intensity change over time at acertain spot of the sample (Figure 1b). An infrared (IR) laser with an emission wavelength of 1480 nm was focused on the center of the capillary to create atemperature gradient within the capillary for ad efined time period. The strong thermal coupling provided quick formation and reduction of the temperature gradient in less than 250 ms (SI- Figure 1). Averaged over the volume,t he temperature gradient spanned about 10 Ka nd led to convection and thermophoretic movement of the binder and the ligand [1] (SI-1).
Thebinding affinity K d and the kinetic parameters k on and k off were obtained from the fluorescence intensity measurements of adilution series with aconstant amount of (labeled) binder B * tot = 2nm and increasing concentration of the ligand L tot .E ach measurement could be divided in three successive phases ( Figure 2). In the pre heat phase,t he reaction system was at (thermal) equilibrium and the fluorescence intensity was only governed by the binding-dependent photobleaching rates k bleach of the sample.The K d and the binding curve were determined by plotting k bleach over L tot and fitting the data to Equation (1(SI)) [24] (Figure 3a and SI-2). In the successive heat phase,t he sample was heated by the IR laser for 40 seconds,l eading to dissociation of the complex and rapid decrease in fluorescence due to the temperature dependence of the dye. [26] In this phase,t he fluorescence intensity of the system was governed by thermophoretic movement, convection, bleaching and kinetics,thus not reliable enough to derive the kinetic fingerprint (SI-3). When the IR laser was switched off,the system returned to thermal equilibrium within 250 ms. Subsequently,dissociated binder and ligand re-associated and the kinetic fingerprint could be derived in this so-called post heat phase by dissecting kinetics from the bleaching and diffusion contributions to the fluorescence.The bleaching and diffusion contributions were elucidated from pre heat phase and the zero-ligand sample (L tot ¼0 m and B tot * ¼2nm)inthe post heat phase,r espectively.T hen, the fluorescence intensities of the post heat phase were corrected for bleaching and diffusion for each ligand concentration and exponential kinetic relaxation / exp Àt=t kinetic ðÞ was fitted using Equation (7(SI)) ( Figure 3b and SI-4). Ther esulting inverse kinetic relaxation constants t À1 kinetic were plotted against the total ligand concentration and fitted according to Equation (2 (SI)) to derive k on (Figure 3c), which was then used to calculate k off = K d k on .
To confirm the experimental results,w ep erformed finite element simulations using COMSOL Multiphysics,w hich captured the relevant interactions between heating, laminar flow,bleaching and reaction kinetics of diluted species in the KMST benefits from the advantages of the widely used MST technique: [1,[21][22][23][24]26] reliable and reproducible data acquisition, low cost and low sample consumption. Importantly, both methods rely on labeling of only one of the reactants (instead of both) which is less expensive,f acilitates sample preparation and ultimately minimizes label-related interferences in the binding process.K MST additionally offers determination of the kinetic rates along with the binding affinity in asingle dilution series.Avolume of less than 5 mL and around nm concentrations of labeled binder and down to mm concentrations of ligand substantially decrease the cost of the measurement. [1] Thea dditional features of KMST:t he dilution series,t he capillary filling, the placement of the capillaries on the silicon plate and immersion in oil do not require high-precision handling.The subsequent data analysis is based on fundamental rate equations rather than complex theoretical models and is robust against uncertainties of individual capillaries.Moreover,due to its ease of use and fast preparation, KMST can also be used for high-throughput K d and kinetic rates determination.
Thek inetic fingerprint deduction from KMST relies on ac onformational change upon binding in the ligand-binder system. This leads to different absolute fluorescence levels (bound vs.unbound state) which were sufficient to detect the kinetic rates.I nt he probed system, the Cy5-label was attached at the 5'-end of asingle strand DNA16mer (binder). Complementary ssDNAs trands of different lengths were used as the ligand. Our control measurements with amodified Figure 2. Fluorescenceintensity unravels kinetics. In the pre heat phase, the fluorophore bleached due to LED illumination. The bleaching rate was higher for the bound complex (light blue). When the IR laser was switched on, the fluorescence quickly changed upon the temperature jump within 250 ms. In the subsequent heat phase, fluorescence was governed by unbinding kinetics, bleaching,c onvection and thermophoresis. When the laser was switched off, the sample quickly returned to ambient temperature. In this so-called post heat phase, fluorescence was governed by bleaching, diffusion and kinetic relaxation from the unbound state towards the bound state. Fluorescence intensities are shown for 0 mm and 2.5 mm of 12mer DNA strands (dark and light blue) at 19 8 8Cwith 2nm complementary labeled binder strand and COMSOLs imulations(yellow), respectively. kinetic were plotted over L tot to fit the onrate accordingtoEquation (2(SI)). The data is shown for af ully complementary 12mer in 0.1 PBS at 16 8 8C, resulting in k on = 2.2 10 4 m À1 s À1 and k off = 2.4 10 À4 s À1 . location of the fluorescent label that was more distant to the binding area resulted in similar affinities and kinetic rates (SI-6). We conclude that the change of the electronic configuration of the fluorophore due to ad istant binding was sufficient to detect binding, thus kinetics.W eused simulation data to test the applicability of the method to systems with significant size difference between the reactants (SI-7). The results suggest that the analysis is robust to reactants with significantly different sizes and the effects can be corrected by numeric simulations.T he effects are minimized if the larger reactant is labeled.
We discuss four conditions which contribute to optimal experimental rate determination (SI-8). First, for reliable fluorescence detection B tot * >1nm is optimal, allowing robust analysis of binding affinities K d >1nm.S econd, the kinetic and temperature jump-related components of the fluorescence had to be clearly separable in time,a llowing for the study of systems with t kinetic >1s .T hird, since the measurements rely on temperature-dependent (un)binding,the binder-ligand system needs to have as ignificant enthalpic contribution. Fourth, similar to every technique that relies on fluorescence imaging, [5,29,30] the quantum yield of the fluorescence label has to depend on binding for deriving the kinetic fingerprint from the fluorescence intensity.
Ther ange of measurable on-rates and off-rates with KMST was comparable with that of label-free methods,f or example,t he measurable ranges by SPR [31,32] are 10 3 m À1 s À1 -10 8 m À1 s À1 for k on and 10 À6 s À1 -1 s À1 for k off .H owever,t he limitations for measuring high on-rates with KMST and SPR differ:while SPR is limited by mass transport [33] and requires molecules with large molecular mass,KMST is limited by the speed of the temperature jump and small K d <1nm in combination with fast kinetics. [34] With KMST,k inetic rates can be measured over awide range of salt concentrations and in crowded solutions without significant loss of accuracy (see below). In contrast, with decreasing ionic strength the nonspecific electrostatic binding increases and changes the sensor response in surface-based kinetic measurement methods. [35] Thekinetic rates for DNAhybridization vary significantly (up to several orders of magnitude) between different studies in the literature including ours. [7,9,34,[36][37][38][39] This most probably originates from the fact that the kinetic rates strongly depend on the system parameters,f or example,b uffer, immobilization, fluorophore,t emperature and other boundary conditions which vary remarkably among different studies.

DNA Hybridization Kinetics
We measured hybridization kinetics of complementary DNAs trands of different lengths with KMST under varying ionic strength and temperature conditions (SI-9 and SI-10). We also tried to get kinetic measurements of the same samples by using Eva Green intercalation dye in temperature jump experiments with athermocycler (SI-10). Although such measurements were successful for kinetic FRET measurements, [40] the intercalating dye was unfortunately not suitable for kinetics measurements of the short DNAs trands in our hands.T he KMST-measured on-rates showed weak to no dependence on strand length and increased linearly with salt concentration by ð1:9 AE 0:2Þ Â 10 6 M À1 s À1 ÂPBS (Figure 4a,b). On the other hand, the measured off-rates showed exponential dependence on strand length (characteristic length 0.81 bp) and salt concentration (characteristic concentration 0.19xPBS,F igure 4c,d). This correlation was reflected in the relationship of the dissociation constant K d ,with strand length (characteristic length 0.72 bp) and salt concentration K d / e Àc PBS =c PBS (Figure 4e,f). Direct comparison of the absolute values of the measured rates with other studies is

Angewandte Chemie
Research Articles difficult due to varying parameters between the systems. Instead, we compare the measured values in terms of order of magnitude,their dependence on the salt concentration, strand length and temperature.
Our results suggest DNAh ybridization on-rates at low salt concentrations to be in the range of 10 4 -10 5 m À1 s À1 .T he on-rates linearly increase with salt concentration up to 10 6 m À1 s À1 for 0.75 PBS (Figure 4b), as reported earlier. [41] At high salt concentrations (1 PBS), SPR experiments measured on-rates of 10 4 m À1 s À1 , [36] an order of magnitude smaller than our measurement. FRET measurements for 9mers reported on-rates in the low range of 10 6 m À1 s À1 (in 50 mm HEPES), [37] similar to our findings.M easurements with TOOL reported on-rates in the order of 10 6 -10 7 m À1 s À1 for 12mer and 16mer complementary DNAs trands, [38] an order of magnitude larger than our results.A tl ow salt concentrations (< 0.1 PBS), FRET measurements reported for 10mers on-rates of 10 4 m À1 s À1 (in 3mm PB buffer), [19] which were also reported with quartz crystal microbalance of immobilized 10mers (in 10 mm TRIS,0 .1 m NaCl), [39] and are similar to our results.Multi-channel graphene biosensors reported on-rates of 10 5 m À1 s À1 for immobilized target strands, [9] which is an order of magnitude higher than our findings.
We observed on-rates to be independent of the strand length (Figure 4a), as previously reported. [7] However,l iterature also reports the opposite: [19,38,39] Bielec et al. argue that the higher total charge of the longer strands pose ah igher energetic barrier for hybridization, especially for low ionic salt environments. [19] We tested astrand length difference of 6 up to atotal length of 16 bases;these values may be too low to observe strand-dependent on-rates.Because Okahata et al. [39] used immobilized probes,d irect comparison is unfortunately limited.
Literature reported both smaller and larger off-rates of DNAh ybridization at low and high ionic strengths than our results.A tl ow salt concentrations (< 0.1 PBS), FRET measurements of Bielec et al. [19] reported off-rates two orders of magnitude smaller than ours.Morrison et al. [7] found higher off-rates at much higher salt concentrations of 10 PBS in temperature jump experiments with FRET pairs.T awa et al. [36] measured smaller off-rates for longer strands at higher salt concentrations.Our measured off-rates showed an exponential decrease with salt concentration (Figure 4d), which was also reported by Okahata et al. [39] and qualitatively supported by Braunlin et al. [41] Similarly,t he exponential decrease of the off-rates with strand length (Figure 4c)i si n agreement with other studies. [7,34,39,42]

DNA Hybridization Thermodynamics
Themeasurements of the binding affinity and the kinetic rates at various temperatures allowed us to perform at hermodynamic analysis.T he Va n tH off plot was calculated by Equation (1) using the standard enthalpy DH 0 and standard entropy DS 0 ,w hich were fitted to K d values of Figure 5e,f under K 0 d ¼1 m standard conditions at 295 K, see Table 1(R = 1.987 cal K À1 mol À1 is the gas constant). TDS 0 and the Gibbs free energy DG 0 = DH 0 ÀTDS 0 were calculated. Increasing temperature destabilized the bound state and increased K d . Then egative slope and positive intercept of the Va n tHoff fits yielded for DH 0 < 0a nd DS 0 < 0.
TheV antHoff plots suggest DH 0 to be in the range of about À60 to À80 kcal mol À1 and DS 0 between À170 and À270 cal K À1 mol À1 ,w hich were also reported by surfacetethered FRET measurements [37] and are slightly above the values reported for 8mers by NMR. [41] Additional melting curve measurements of the 12mer strands and associated Va n tHoff analysis showed similar K d dependence on inverse temperature and similar DH 0 (SI-11). At room temperature, enthalpic and entropic contributions nearly cancel each other resulting in small negative DG 0 ,s upporting that DNA hybridization is as pontaneous process: [37,43] the hydrogen bond formation and base stacking lead to release of heat and decrease in entropy due to reduced conformational flexibility in the bound state. [44,45] Increased ionic strength increased both DH 0 and DS 0 .However, DH 0 increased more than TDS 0 , resulting in ahigher net negative DG 0 ,thus favoring binding. Thes ignificance of DG 0 is limited due to large propagating uncertainties,s ee SI-11. With increasing strand length, the increase in DH 0 and DS 0 resulted in ad ecrease of DG 0 ,t hus favoring the hybridized state,similarly reported before. [37] Them easured temperature dependence of the on-rates and off-rates allowed us to determine the Arrhenius activation energies E A,on and E A,off (Figure 4g,h)t hrough k ¼ Aexp ÀE A =RT ðÞ ,w here A is the pre-exponential factor and k is either the on-or off-rate (SI-12). TheArrhenius plots are shown in Figure 5a-d. Theo n-rates showed no or slight increase with temperature (Figure 5a,b), resulting in small positive E A,on .T he temperature dependence of on-rates of DNAh ybridization is still am atter of open debate.F or T < T melt ,l iterature reports increasing, [7] decreasing [34] and also non-monotonic [39,46] behavior. Our findings suggest that E A slightly above or below zero cannot be used to rule out either of the hypotheses. E A,on showed no significant dependence on strand length or salt concentration (Figure 4g,h). Theo ffrates showed the expected exponential dependence on inverse temperature [7,34,39,42] (Figure 5c,d). Them easured E A,off became smaller with increasing strand length and salt concentration (Figure 4g,h). This is consistent with the view that the electrostatic repulsion between the negative chains of the DNAs trands decreases at high salt concentrations, stabilizing the hybridized state. [39] Similar behavior was observed for DNAh airpins. [47] Thei dentification of the Arrhenius activation energies with the thermodynamic quantities of the Eyring-Polanyi equation (E A,on DH°o n and E A,off DH°o ff )a llowed ac onnection of kinetic quantities with thermodynamic quantities. [37,43] Thet hermodynamic enthalpy and entropy landscapes of free,t ransition, and bound state could be determined (SI-12). However, due to conceptual difficulties, [48] the interpretation of the resulting DH°and DS°is limited.

DNA Hybridization Kinetics in Crowded Solutions
Like most physiological processes,D NA hybridization takes place in crowded environment. However,m easurements in complex solutions are typically experimentally more challenging.T os imulate crowded environment, we used polyethylene glycol (PEG) 8000, which was used in earlier studies to simulate molecular crowding. [38,49] As shown in Figure 6, the on-rate, off-rate and K d did not show ac lear relationship between PEG concentration and hybridization rates (SI-13). Our results agree with other measurements by FRET [38,50] that showed weak or no dependence of the DNA hybridization time constants on crowding agent concentrations. These results indicate that KMST,l ike other methods, [38,49,50] is av ersatile technique which is able to measure kinetic reaction rates and binding affinity at different ionic strengths and in crowded environments.

Conclusion
Herein, we have shown that combining MST with the temperature jump technique provides an ovel method to determine the kinetic rates along with binding affinities in [a] DG 0 and TDS 0 were calculated.
[b] The error was calculated by Gaussianerror propagation. All values refer to standard temperature 298 K. as ingle experiment. As imple hardware modification of aconventional MST setup to increase the thermal dissipation of the sample is sufficient to deduce kinetic relaxation from the fluorescence intensities.W es ystematically investigated the dependence of kinetic parameters of DNAh ybridization on strand length, temperature and ionic strength. We found an exponential dependence of the off-rate on strand length, salt and inverse temperature.W ea lso showed no or weak dependence of the on-rate on temperature and strand length and alinear dependence on salt concentration. These results did not only show the power of the kinetic MST as amethod but also shed light on the hybridization mechanism of DNA. Unlike several other methods,l abeling of only one of the reactants is sufficient, reducing the cost and time required as well as the label-related interferences to the binding.T he setup is very easy to use,r obust and provides reliable and reproducible results.W hile the binding reaction of interest must have as ufficient enthalpic contribution, no artifactinducing processes,such as immobilization, are required. We believe that KMST could be of great interest to ab road audience and could offer new opportunities in biological and medical sciences.