Microfluidics and the quantification of biomolecular interactions

Microfluidic systems under laminar flow conditions provide in-solution information about species size and binding affinities at very modest sample costs. Flow-induced dispersion analysis directly measures the spread of the analyte profile using Taylor dispersion analysis, whereas microfluidic diffusional sizing quantifies the transfer of analyte from one phase to another. Species of sizes between 0.5 and 1000 nm can be analyzed, and different populations resolved. Both techniques also allow analysis in complex media and medium throughput analysis. These properties make them valuable complements to existing approaches to measure biomolecular interactions.


Introduction
In biology and biophysics, in-solution analysis of noncovalent interactions is of vital importance for complete system understanding.Examples include complex signaling pathways, drug target binding, oligomerization, and aggregation of pathogenic proteins.Many ligand binding technologies rely on surface bound species (Biolayer Interferometry, Surface Plasmon Resonance), relative changes in optical signals (microscale thermophoresis, fluorescence polarization), changes in electrophoretic mobilities (Affinity Capillary Electrophoresis), thermal readout (Isothermal Titration Calorimetry) or resistance to multiple washing steps (Enzyme-Linked Immunosorbent Assays).However, simultaneous information on the integrity of the starting material (e.g.lack of degradation) and structural changes require a structural readout missing from most ligand binding technologies.Microfluidic systems have emerged as an attractive alternative, giving lowresolution structural information (hydrodynamic radius R h ) in solution using laminar flow conditions.Other advantages include the possibility for parallel processes and integrating multiple advanced steps in one operation [1,2].

Taylor dispersion analysis
By definition, laminar flow systems have Reynolds number <2000 (i.e.viscosity h dominates over inertia and the fluids move in a sheet-like fashion without turbulence).Combined with solution phase properties (viscosity and temperature), diffusivity can be converted into R h [3e5], informing on protein and particle size [6], complex formation [7e11] and structural integrity (degree of unfolding) [12].In practice, the requirement for laminar flow is met in almost all microfluidic systems in the 10e100 mm range.Mass transport in microfluidic systems combines diffusion with convective transport (hydrodynamic flow and electrodriven transport).This is encapsulated in the Peclet number Pe (Eq.( 1)): where u is the linear flow velocity, l is a characteristic length (for example the channel width/radius), and D is the diffusion coefficient.For Pe < 1 diffusion dominates over convection and vice versa for Pe > 1.The Peclet number can be used to select the most optimal conditions for quantitative Taylor dispersion analysis (TDA) (Figure 1a).
The simplest and most widely used microfluidic system is a straight channel, e.g.fused silica capillaries, produced at high accuracy and used extensively in capillary electrophoresis (CE).In 1953, Taylor [13] showed theoretically (and verified experimentally) that a pulse of sample injected in a laminar flow under certain conditions is dispersed in the axial direction according to a modified Fick's 2 nd Law of Diffusion, providing a direct measure of diffusivities.In TDA, D is obtained from fitting the signal profile (originally obtained from elution profiles monitored by an external cell, later an internal detection window in the sub-mm-to-mm size range, more recently based on confocal focusing of LED light into the capillary) to a theoretical signal shape.
Conditions appropriate for TDA depend on diffusivity, flow rate, and capillary dimensions [14] although Taylorgrams outside ideal conditions have also been analyzed [15].Importantly, TDA is a 'first principle' technology giving precise values based on closed form solutions of basic mass transport equations.Diffusivities are easily converted into hydrodynamic radii: Despite its apparent simplicity, use of Eq. ( 2) requires accurate temperature control and determination of viscosity, which can be significantly different from that of pure water at high concentrations of salts, lipids, or in complex media.An advantage of a pressure-driven flow in a straight channel is that the peak appearance time is directly proportional to sample viscosity.Thus all necessary parameters are obtained in a single experiment.Particles between 0.5 and 1000 nm in diameter have been analyzed using TDA [16] (Figure 1a).Quantifiable particle size is limited by large particles' slow diffusion rates and by hydrodynamic chromatography effects when the particles approach the size range of the capillary [16].mm sized particles, e.g.large protein aggregates, can qualitatively be detected in Taylorgrams as 'spikes' d one spike corresponding to one particle.At the lower end of the size range, TDA has been used to measure complexation of small molecules in cyclodextrins [7,13] and the diffusivities of small molecules in different solvents [17], in both cases monitoring indicator dispersion by UVeVis absorption.Unlike dynamic light scattering, TDA measures a weight-averaged R h , making it much less sensitive to aggregates and particle impurities than DLS.Routinely up to 3 species of different sizes can now be resolved in mixtures from a Taylorgram (allowing us to account for unreacted dye molecules) and more sophisticated data analysis may result in an even higher number of species [18].As an estimator of size distributions, TDA has found use in a range of areas, including the polydispersity of inorganic nanoparticles <10 nm in size [19], degradation of biopolymers like dendrigrafted poly-lysine [20] and partitioning of peptides between water and droplets in drug delivery systems [21].Here dispersion signals can be analyzed in different ways (multiple Gaussian peaks, cumulant analysis or constrained regularized linear inversion approaches) to obtain more robust polydispersity estimates.

Flow-induced dispersion analysis
A major advantage of TDA and microfluidics in general is the very modest sample volume.Sizing a single species requires w10e50 nL (not including sample volume required for preparation/filling of vial/96 well plates).
The high surface to volume ratio may cause adsorption, leading to 'tailing' non-symmetric peaks.Tailing is usually circumvented with hydrophilic surfacepassivating reagents and can be excluded from analysis by selecting the first non-tailing part of the peak.The small sample volumes and short optical pathlength typically lead to mM detection limits based on absorption, but fluorescence tagging pushes this to < nM and just as importantly allows non-covalent interactions and molecular size to be determined in complex sample matrixes, e.g.plasma/serum or fermentation media [8,11].
Flow-induced dispersion analysis (FIDA) combines TDA and fluorescence detection in straight fused silica capillaries to measure the change in apparent R h of a fluorescent ligand (indicator) as it interacts with its target (analyte) (Figure 1b).Measurements at different [analyte] at constant [indicator] result in a binding curve from which the dissociation constant K d and R h of indicator and complex are obtained.FIDA can be performed in three ways (Figure 1c): Premix: analyte and indicator are premixed and equilibrated.Free analyte is injected in the capillary before and after injecting the premix sample, providing a constant analyte concentration in the dispersion zone and maintaining binding equilibrium during the run.This is the most common use of FIDA.Capillary mix: indicator is injected into a stream of analyte and binding takes place during the run.With fast binding kinetics, premix and capillary mix give similar results while reduced affinity in capillary mix reflects slow binding kinetics.The capillary mix approach is well-suited for screening ligand binding as only very limited sample preparation is needed.Capillary dissociation: a premixed sample of the indicator and analyte is injected into a stream of assay buffer.The sample dispersion driven by diffusion causes local sample dilution, driving complex dissociation.With slow dissociation, R h will be similar to the premix run, while fast dissociation will reduce R h .All three variants of the FIDA protocol can be carried out on the same samples, giving in-solution ligand and complex size, binding affinity and binding timescale in a single set of experiments [22].
Dedicated commercial equipment for TDA and FIDA (Fida 1 by Fidabio) allows relatively straight-forward automation based on well-established protocols for making and using fused silica capillaries.A single experiment takes 3e5 min (including washing and cleaning) allowing about 4 x 96 samples to be measured per day in walk away automation mode.Over the last decade, FIDA has been applied to a range of different in-solution proteineprotein interaction analyses (Figure 2).Examples include protein oligomerization (insulin self-association monitored by UV absorption [23]) and complexation between trimeric TNF-a (T) and the antibody Adalimumab (Ad) [22], in which it was possible to model the interaction taking into account 6 different species (T, Ad, T:Ad, T:Ad 2 , T 2 :Ad and (T:Ad) 2 ) with labeled TNF-a.Prior labeling of the indicator allows us to measure concentrations and affinities in complex media, e.g.antialbumin antibodies in plasma (with Atto488A-labeled albumin) [9], antidouble strand DNA antibodies from Lupus Erythematosus patient plasma [8], or various monoclonal antibodies in a fermentation broth with a labeled anti-IgG affibody [11].Importantly, the dynamic range of the binding assay can be tailored to the reaction conditions by adjusting the (fixed) indicator concentration.Binding of amphipathic proteins such as a-synuclein to phospholipid vesicles is also possible to be measured, providing binding affinities along with proteinevesicle complex sizes [24].

Microfluidic diffusional sizing techniques
Besides TDA/FIDA, other diffusion-based approaches to quantify the sizes and interactions of biomolecules in solution based on laminar flow have recently been developed and commercialized.Time evolution of a well-defined concentration field is measured in custommade microfluidic devices, providing information about particle size distribution.The simplest microfluidic diffusional sizing (MDS [25]) devices are usually based on coflow designs, where the analyte is injected as a continuous flow side by side with an auxiliary fluid, e.g.pure buffer, and the diffusion of the analyte molecules into the buffer stream is followed over time (Figure 3).This process is conceptually simple and (similar to TDA/FIDA) can be realized without valves and pumping systems.In MDS devices, diffusion is only observed perpendicular to the direction of flow, due to the absence of a concentration gradient along the flow direction.Two types of geometry are employed.Two- ) is observed which correlates with the formation of higher order complexes (from [22] with permission).(c) Binding between a fluorescently labeled affibody and an antibody (rituximab) in 0.3 and 5% fermentation media.Insert: overlay of the signal corresponding to the affibody alone and in the presence of 2000 nM rituximab.From [11] with permission.(d) Change in hydrodynamic radius of maltose-binding protein upon complexation with the small sugar molecule maltose (application note available from Fidabio).
phase geometry (Figure 3a) has one analyte and one buffer stream [26,27].In three-phase geometry (Figure 3b), a flow-focused analyte stream is in contact with buffer streams on both sides [25].In both cases, differently sized species can be individually resolved if the concentration profile is analyzed at various points along the channel, corresponding to different diffusion times [25].A commercialized version (Fluidity One by Fluidic Analytics) uses two-phase geometry.The diffusional analysis is performed in a binary manner, i.e. the relative amounts of analyte that exit the left and right outlets are quantified for a well-defined imposed flow rate, corresponding to a diffusion time [27].This analysis, simpler than the recording and analysis of the full spatial concentration profile, only yields an average R h for mixtures of differently sized species.MDS enables the analysis and quantification of proteineprotein interactions even in complex biological fluids, and this feature has been used to quantify antibody binding affinity to the SARS-CoV-2 spike protein receptor binding domain in patient samples [28].Dilution and consequent shifts in binding equilibria can typically be avoided since the molecules are only under out of equilibrium conditions for a few seconds or less on chip.
Other MDS applications include protein and peptide binding to lipid vesicles [29,30], interactions with membrane proteins [31], chaperone binding to protein aggregates [32] and affinity/stoichiometry profiling of therapeutic antibodies [33] (see examples provided in Figure 4).
To avoid labeling artifacts, it is possible to use external fluorescent labels or latent fluorophores that become fluorescent only once they have reacted with the biomolecule under study [27], i.e. after the sample stream has exited at the outlet.This approach can also quantify the protein concentration after appropriate calibration.Both concentration and average size in the supernatant of an amyloid fibril formation reaction have been monitored in this way [34].Nevertheless, extrinsic prelabeling remains orders of magnitude higher in sensitivity.
MDS is highly versatile and if custom designed microfluidic chips are used, flow rate and channel lengths and widths can be adapted to the particular size range under study [30,32].Yet current commercially available MDS instruments are limited to ca. 0.5e20 nm particle size.Although this size range covers most protein monomers and smaller complexes, it is unable to characterize larger complexes, aggregates, as well as liposomes.
The fact that these types of measurements rely entirely on molecular diffusion presents a fundamental limit on the sizing resolution, and species with very similar hydrodynamic radius cannot be resolved.Addressing a  wide dynamic range in size requires the ability to control the flow rate accurately over a wide range.This translates into a precise pressure control.Analysis time t can be reduced by reducing the required diffusion length (L) which scales with t 1 / 2 .However, reducing flow channel dimensions leads to lower sensitivity of detection.For practical purposes it is most advantageous to use 50e100 mm channel dimensions as found in FIDA.
Application of an external electric field (electrophoresis) can aid species resolution if they differ in electrophoretic mobility.In the type of capillary setup used in FIDA, the electric field can be applied along the direction of flow in CE.Indeed, early experimental demonstrations of sizing by Taylor dispersion were based on CE-equipment [3], and TDA of mixtures can be realized by application of an electric field [35,36].TDA can also be combined with affinity CE, providing both size, separation and affinity constants [37].MDS, on the other hand, allows electrodes to be added such that an electric field can be applied perpendicular to the direction of flow.This geometry opens for microfluidic free-flow electrophoresis, a method that can also resolve binding events that do not lead to a significant change in hydrodynamic radius but affect the electrophoretic mobility, e.g.metal ion binding [38].

Perspectives
Both TDA/FIDA and MDS approaches represent versatile and sample-economic microfluidic approaches to measure molecular interactions in solution under a wide variety of conditions and with the potential for automation.There is no restriction on the type of molecules to be analyzed as long as they can be fluorescently labeled.FIDA has a larger size range and allows even very large, nondiffusing particles to be counted.Both FIDA and MDS allow an easier integration of additional separation modules, such as electrophoresis.Future challenges will be to develop options for better quantitative kinetic resolution, expand size ranges, and exploit and extend temperature ranges and gradients to expand thermodynamic analyses of interactions etc. Common to both technologies is the unique link between structure (R h ) and affinity (K d ) which has the potential of advancing structural understanding of molecular interactions under in vivo-like conditions, aided by the growing ability to reliably estimate R h of complexes from individual components [39].Combined knowledge of R h and K d is an important supplement to structural methods such as xray crystallography, cryogenic electron microscopy (cryoEM), and NMR, all of which require pure sample solutions, have a lower sample throughput or demand large amounts of sample material.