Microfluidic Diffusion Analysis of the Size Distribution and

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Bioengineering

Microfluidic diffusion analysis of the size distribution and microrheological properties of antibody solutions at high concentrations Marie R.G. Kopp, Alessia Villois, Umberto Capasso Palmiero, and Paolo Arosio Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00666 • Publication Date (Web): 30 Apr 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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Industrial & Engineering Chemistry Research

Microfluidic diffusion analysis of the size distribution and micro-rheological properties of antibody solutions at high concentrations

Marie R.G. Kopp, Alessia Villois, Umberto Capasso Palmiero, Paolo Arosio*

Department of Chemistry and Applied Biosciences, Institute for Chemical and Bioengineering, Swiss Federal Institute of Technology, Zurich, 8093, Switzerland

* to whom correspondence should be addressed: [email protected]

Abstract The size distribution and rheological properties of dispersions of biological colloids are relevant quality attributes for a variety of industrial applications, including pharmaceutical, food and cosmetic products. For instance, the biophysical properties of monoclonal antibodies and therapeutic proteins, which represent an important class of drugs in the pharmaceutical market, are important for their safety and efficacy. In this work, we apply a microfluidic diffusion platform to analyze protein sizes and interactions in high concentration antibody solutions directly in the liquid state with minimal perturbation of the sample. We show that this method provides size distributions in a size range scaling from a few angstroms to hundreds of nanometers. The detection sensitivity of the technique is independent of the particle size and the method provides number-average distributions, enabling the simultaneous detection of both monomeric species and soluble aggregates. We further show that the same platform can be applied to measure viscosity-scaling effects in crowded environments by probing the Brownian motion of several tracers with different sizes. Such tracers experience a shift from the micro-viscosity to the macro-viscosity of the sample at a critical probe size that is equal to the characteristic dimension of the main components of the dispersions. The technique simultaneously provides quantitative measurement of the micro-rheological properties and the macro-viscosity of the sample, as well as information on the characteristic size of the components of the solution. Overall, these methods represent attractive tools in the context of the analysis of sizes and interactions of proteins in both diluted and high concentration solutions during development, manufacturing and formulation.

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Introduction Bio-based formulations and materials are ubiquitously encountered in several industrial areas, such as the pharmaceutical, food, agricultural, and cosmetic sectors. The size distribution and the rheological properties of these products represent essential quality attributes. Many successful methods have been developed to measure these two fundamental properties, as discussed for instance in [1-11] and in [12-21] . Yet, under certain conditions, the characterization of these properties could still exhibit challenges. Potential limitations include low throughput, limited amounts of sample available, sample perturbation during the analysis and narrow dynamic range of the sizes that can be probed by an individual technique. A conventional strategy to size macromolecules and colloids consists in exploiting their stochastic Brownian motion. The size can be evaluated from the measurement of the diffusion coefficient based on the Stokes-Einstein equation D=kT/6πηRh, where η is the viscosity of the solution, k is the Boltzmann constant, T the temperature and Rh the hydrodynamic radius of the species. This approach is applied for instance in dynamic light scattering (DLS), nuclear magnetic resonance (NMR) spectroscopy, fluorescence correlation spectroscopy (FCS) [22-24] and Taylor dispersion analysis (TDA) [25, 26]. However, these methods face challenges in the investigation of heterogeneous mixtures, since the average signal has to be deconvoluted into the contribution of the individual species. Moreover, light scattering methods are biased towards larger sizes due to the strong dependence of the particle size on the scattered intensity. These limitations compromise the study of the size distributions of heterogeneous mixtures. Size exclusion chromatography coupled with light scattering (SEC-LS) is currently the state of the art technology for the analysis of multi-component samples. [8, 27, 28] However, interactions with the stationary phase and the dilution of the sample during the analysis may induce artifacts, in particular when protein solutions at high concentrations are considered. Moreover, this technique has limitations in analyzing the size range between 100 and 600 nanometers, which currently exhibits several challenges for conventional biophysical approaches. [1] Alternative methods are based on field flow fractionation (FFF) techniques, which rely on the application of a separation field perpendicular to the direction of the flow. [29] These approaches enable the analysis of polydisperse mixtures, although under certain conditions interactions of the analyte with the surface of the membrane can induce low mass recoveries and clogs. A powerful method that addresses the limitations of SEC-LS


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and FFF is single particle analysis, in which the size distribution is constructed by tracking the Brownian motion of individual particles. [30] An attractive alternative approach has been recently developed based on microfluidic diffusion sizing platforms, in which the diffusion motion of the colloidal dispersion is monitored in a microfluidic channel under laminar flow. [31-36] In particular, a strategy has been developed to measure diffusion profiles at multiple diffusion times and diffusion positions. [37] This large amount of experimental data enables the robust measurement of the size distribution of heterogeneous mixtures. Under some conditions, this method, which has been extensively validated in [30], allows to outperform DLS and detect individual species in polydisperse mixtures. Here, we show the potential of this technique for the analysis of size distributions of soluble antibodies and antibody aggregates at high protein concentrations (150 mg/mL). The measurements are performed with limited sample dilution and in a time scale of minutes, with minimal interactions with the stationary phase. The technique provides size distributions in the range of hundreds of nanometers, which are particularly challenging to evaluate with conventional methods. Moreover, the detection sensitivity is independent of the size of the discrete components, and the technique measures a number-average size, in contrast with light scattering methods that provide an intensity-based average value. We further demonstrate that the same platform can be applied to measure microrheology [38-40], which provides relevant information on the structure and the viscoelastic properties of complex soft materials in both fundamental systems and practical applications. In particular, here we access both micro- and macro-viscosity by probing the Brownian motion of fluorescent tracers with increasing sizes introduced in the dispersion of bio-colloids of interest. Such tracers experience a shift from the microviscosity to the macro-viscosity of the sample at a critical probe size that is equal to the characteristic dimension of the main components of the dispersions. [41, 42] This principle can be applied with other methods such as fluorescence correlation spectroscopy [22-24] and image correlation spectroscopy (RICS) [43, 44], which measure diffusion coefficients by tracking the local fluctuations of fluorescence intensity. [2] Here we implement this concept on a simpler experimental set-up, covering a broad range of tracer sizes, scaling from a few angstroms to hundreds of nanometers, on a standard epi-fluorescence microscope with a sample consumption of a few microliters. We show how this technique simultaneously provides quantitative



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measurements of the micro and macro-viscosity of the sample as well as information on the characteristic size of the components in the complex medium.

Materials and Methods Materials The commercial antibody solution Gammanorm was purchased from Octapharma AG (Switzerland). A second model immunoglobulin (IgG2) of industrial origin was stored as a 45 mg/mL solution in 25 mM sodium phosphate (Acros Organics, Belgium) at pH 6.0 with 100 mM NaCl (Fisher Scientific, UK) at 4 °C. In the following, the commercial antibody and the IgG2 will be referred to as IgG I an IgG II, respectively. Glycerol,

4’4

azobis(cyanovaleric

(phenylcarbonothioylthio)-pentanoic

acid)

acid

(CPA,

(ACVA,

98 %),

4-cyano-4-

>97 %),

2-methacryloyloxyethyl

phosphorylcholine (MPC, 97 %), sulfopropyl methacrylate potassium salt (SPMAK, 98 %) and all other salts were supplied by Sigma-Aldrich (Switzerland). DMSO was purchased from Fluka Analyticals (St Louis, USA). Red fluorescent silica nanoparticles with a radius of 5 nm and green fluorescent polymethacrylate particles with a radius of 13 nm were purchased from Micromod Partikeltechnologie GmbH (Germany). Polystyrene nanoparticles labeled with Firefli fluorescent green dye with radii of 24 nm, 50 nm and 100 nm were purchased from Thermo Scientific (Germany).

Synthesis of zwitterionic fluorescent tracers Two fluorescent hydrophilic oligomers with 10 and 20 2-methacryloyloxyethyl phosphorylcholine (MPC) units were synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization of MPC, sulfopropyl methacrylate potassium salt (SPMAK) and of a Rhodamine B methacrylate (HEMA-RhB) using 4-cyano-4(phenylcarbonothioylthio)-pentanoic

acid

(CPA)

as

RAFT

agent

and

4’4

azobis(cyanovaleric acid) (ACVA) as initiator. HEMA-RhB was synthesized according to a previously published protocol. [45] Briefly, we synthesized MPC-based oligomers with 20 units (20MPC) by dissolving 0.30 g of MPC, 30 mg of HEMA-RhB, 12 mg of SPMAK, 14 mg of CPA, and 5 mg of ACVA in 3 ml of a 50/50 vol.% mixture of ethanol/ 3 mM acetic buffer. The solution was poured in a septa-sealed flask, purged with nitrogen for 5 min and left to react overnight at 65 °C under stirring. The oligomer was then dialyzed against deionized water for one week with a SpectraPor® RC membrane (MWCO 1 kDa) ACS Paragon Plus Environment

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in order to remove the unreacted monomers. An aliquot of the reaction mixture was withdrawn before purification, dried under air, and dissolved in D2O to evaluate MPC conversion (XMPC) via near magnetic resonance (1H-NMR, 400 MHz). [46] (XMPC > 95 % for both 10 and 20 MPC oligomers). For MPC-based oligomers with 10 units (10MPC) The MPC to CPA ratio was varied from 20 to 10, while the HEMA-RhB to CPA and SPMAK to CPA ratios were kept constant and equal to 1. CPA to ACVA molar ratio was set equal to 1/3.

Sample preparation and labeling For the sizing experiments, the commercial antibody solution Gammanorm (IgG I) was dialyzed in a 100 mM carbonate buffer at pH 10.7 and labeled with phthalaldehyde (OPA) using an already established protocol. [34] In brief, a stock solution of 60 mM OPA and 90 mM β-mercaptoethanol (BME) was prepared in the 100 mM carbonate buffer at pH 10.7. The stock was then mixed with the protein solution to reach a 20-fold molar excess of OPA. Since the excess free OPA is latent, no purification step is required after the labelling reaction, and the labelled protein solution was measured immediately after mixing. For the rheological experiments, the commercial solution was used without any modification. IgG II antibodies were labeled with the ATTO 488 dye according to the protocol described by the manufacturer (ATTO-TEC GmbH, Germany). In brief, the antibody stock solution was diluted to 7.5 mg/mL in a 1:21 v/v 200 mM sodium bicarbonate NaHCO3 at pH 9.0 and phosphate buffered saline at pH 7.4. A 2-fold molar excess of ATTO 488 dye was then added to the antibody solution under gentle shaking. The labelling reaction mix was gently stirred for 1 hour before removing the excess free dye by performing several washing steps in 30’000 MWCO spin filter unit (Vivaspin 500 PES, Sartorius, Switzerland). Aggregates of the labeled IgG II were generated by incubating a 1 mg/mL antibody solution with 25 mM citric acid and 150 mM Na2SO4 at pH 3.0 at 50 °C for 1.5 hours. Bovine Serum Albumin (BSA, Sigma Life Science, Germany) solutions were prepared by dissolving the lyophilized powder in 100 mM carbonate buffer at pH 10.7 in the absence and presence of 20 % v/v DMSO.

Fabrication and operation of the microfluidic diffusion device Master wafers were fabricated in house by spin-coating SU-8 photoresists (Microchem,



USA) on a silicon wafer and exposing selected regions to UV light. Standard softlithography was used to replicate the channels by casting polydimethylsiloxane (PDMS) (Silicone elastomer 184, Sylgard 184 kit, Dow Corning, USA) mixed with carbon powder (Sigma Aldrich, Switzerland) on the master wafer, curing it at 70 °C for 2 hours, peeling it off, and bonding it to a glass slide after plasma activation (ZEPTO plasma cleaner, Diener Electronics, Germany). The channels had a height of 30 μm, and widths of 40 μm in the hydrodynamic resistors at the inlets, 3000 μm in the nozzle region, and 300 μm in the detection regions. The flow in the channel was imposed through the application of a negative pressure using a syringe pump (Cetoni neMESYS, Cetoni GmbH, Germany). The flowrate was tuned for each experiment depending on the sizes of the analyte species in order to obtain information on the diffusion time scales of the smallest and the biggest species. A single measurement typically required 10 μL of sample. For micro-rheology experiments, the analyte was present in both the buffer and the analyte inlets, while the tracer particles were introduced only in the analyte inlet. Images were collected at 12 different points along the channel at downstream distances between 10 and 100 mm. Images were acquired on a Ti2-U inverted microscope (Nikon, Switzerland) equipped with a LED light source (Omicron Laserage Laserprodukte GmbH, Germany) and a camera (Zyla sCMOS 4.2P-CL10, Andor, UK). The different fluorophores were detected with the following filter cubes (AHF Analysentechnik AG, Germany) by applying the following excitation/emission wavelengths: the DAPI UC BP filter set (352-402 nm/417477 nm) for the OPA labeled proteins, the CFP ET filter set (426-446 nm/460-500 nm) for the green Firefli stained particles, and the Cy5 ET filter set (635-655 nm/665715 nm) for the rhodamine, the small oligomer tracers and the red silica particles.

Analysis of the diffusion profiles The experimental diffusion profiles were analyzed following the approach described in [37, 47, 48]. In brief, we simulated a library of diffusion profiles corresponding to a series of objects with defined diffusion coefficients by solving the diffusion advection equation with the boundary conditions related to the geometry of the device. [47] The concentration profiles of the analytes were extracted from the acquired images by integrating the signal over the height of the channel. The concentration profiles were fitted by a linear combination of the simulated profiles taken from the library using a basin hopping algorithm (scipy package) with 2500 random displacements, [49] by minimizing:


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,

, − ,

(1)

where P(t,y) is the integrated concentration profile at position y corresponding to the diffusion time t; ci is the probability coefficient for a given standard particle i, and Bri is the simulated concentration profile for the standard particle of size ri. The distribution of coefficients ci was constrained to the sum of two Gaussian size distributions, based on the following equation: [50]

& − &"

& − & 1 − − = , + exp − + exp − 2!" 2! 2! √2 !"

(2)

where δi,0 is the Kronecker delta function, accounting for extra diffusion at the nozzle before position 0, and r1, σ1 and r2, σ2 are the average radius and standard deviation of the two Gaussian components. The quality of the fit was estimated from the reduced χ2 coefficient, which was calculated according to Eq. 3: [47]

) =

1 +,,- − ,,.// 0 ∑ !1234

(3)

−5−1

where xi, data and xi, fit represent the values of the experimental and simulated diffusion profiles at pixel i, σnoise is the standard deviation of the signal (sampled in the 30 first pixels of the initial profile), n is the total number of pixels in one diffusion profile and l is the number of fit parameters.

Dynamic Light Scattering Dynamic Light Scattering (DLS) measurements were performed on a Zetasizer instrument (Malvern, UK), working in backscattering mode at 173 ° with a laser source of 633 nm. Before incubation, the solutions were filtered with Anotop 10 syringe filters (Whatman, GE Healthcare Life Sciences, UK) with a 20 nm cut-off.

Size Exclusion chromatography with inline Dynamic Light Scattering (SEC-DLS) Size exclusion chromatography was performed using an Agilent 1100 series HPLC unit (Santa Clara, CA, USA), consisting of a quaternary pump, an autosampler, a column thermostat and a UV detector, which was further connected to a multi-angle light scattering instrument (Dawn-Heleos II, Wyatt, Santa Barbara, CA, USA). Separation was achieved on a Superdex 200 10/300 GL, 10x300 mm size exclusion column operating at a flow rate of 0.75 mL/min. 100 μg of the BSA and of the IgG II aggregates were injected ACS Paragon Plus Environment


directly after incubation using as running buffer 200 mM L-Arginine (Sigma Life Science, USA), 100 mM sodium phosphate (Sigma Aldrich, Germany) at pH 6.5. The amounts of residual monomer and aggregates were estimated by quantifying the area under their respective peaks in the collected chromatograms at 280 nm using the Agilent ChemStation software (Santa Clara, CA, USA). The dynamic light scattering signal was recorded with an in-line detector (Dawn Heleos II, Wyatt, Santa Barbara, CA, USA) and analyzed using the Astra 6.0 software (Wyatt, Santa Barbara, CA, USA) to obtain the hydrodynamic radius of the separated species.

Results and Discussion Principle of the technique We measured diffusion profiles under laminar flow following the strategy described in [37]. The scheme of the device is shown in Fig. 1A. The fluorescent sample stream was flow-focused in the middle of a microfluidic channel between two streams of an auxiliary fluid (nozzle region in Fig. 1A). From this well-defined initial region, the sample diffused perpendicularly to the direction of the flow while travelling along the channel. After equilibrating the flow for few minutes, diffusion profiles were measured by epifluorescence at 12 different positions along the channel, corresponding to well-defined diffusion times. We note that this approach is not restricted to detection by external fluorescence and can be applied also with alternative detection methods, such as protein UV absorption [51] and protein intrinsic fluorescence. [52, 53] The analysis of unlabeled samples is beneficial to avoid potential artifacts induced by the presence of the fluorophore, as well as to save the time and effort required by the labeling reactions. The shape of the concentration profiles contains information about the distribution of the diffusion coefficients of the discrete species. The individual contribution of each species was obtained by fitting the experimental diffusion profiles with a combination of simulated profiles. The corresponding hydrodynamic radii were then estimated based on the Stokes-Einstein equation D=kT/6πηRh (Fig. 1B). It was shown that this approach allows to resolve distinct components differing of a factor of about 3 in size. [37] To be able to evaluate aggregate distributions, in this work we fitted the experimental data by considering two populations of species with a Gaussian distribution. [50] This approach allows to get key information about the size ACS Paragon Plus Environment

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distribution, such as the polydispersity, the average sizes and the presence of bimodality, with a limited number of fitting parameters. We applied the same platform to measure the viscosity of solutions at zero shear by evaluating the diffusion coefficient of standard fluorescent tracer particles (Fig. 1C). In this modality, the analyte solution was introduced in the system in both inlets, while the standard tracers were injected only in the sample inlet. Depending on the relative size of the tracer and the main components of the sample mixtures, the tracers could sample the micro-viscosity or the macro-viscosity of the solution (Fig. 1C).

Sizing of antibodies in concentrated solutions We first measured a solution of IgG I in 100 mM carbonate buffer at pH 10.7 in a concentration range scaling from 1 mg/mL to 150 mg/mL. The measured diffusion profiles and corresponding fittings at the lowest and highest protein concentration are shown in Fig. 2A-B. For each protein concentration, the resulting size distributions exhibited a single peak, as illustrated by the representative distribution acquired at 150 mg/mL shown in Fig. 2C. The average hydrodynamic radius measured by the diffusion device was 8.3±1.1 nm, well in agreement with the value of 8.6 nm evaluated by DLS in 1 mg/mL protein solution (Fig. 2D). Interestingly, measurements at different protein concentrations provided the same hydrodynamic radius within the experimental error (Fig. 2D). Indeed, the deviation in the hydrodynamic radius measured at different protein concentrations was lower than 15 %, which is the average deviation for different repeats of the same sample. [37] Moreover, the quality of the fit, quantified by the χ2 value (see Materials and Methods), did not decrease with increasing protein concentrations (Fig. S1A). This interesting result indicates that this specific molecule under these conditions does not exhibit strong self-interactions, and the diffusion coefficient is independent of the protein concentration. We verified the ability of the method to detect the presence of protein-protein interactions by measuring the diffusion coefficient of bovine serum albumin (BSA) at concentrations ranging from 1 mg/mL to 100 mg/mL (Fig. 3). This protein is known to self-interact and form oligomers. Indeed, an increase of the hydrodynamic radius from 3.5 nm to about 6 nm was observed when increasing the protein concentration. The quality of the fit was independent of the protein concentration, except for the largest concentration (Fig. 1B). The value of 3.5 nm measured at 1 g/L was identical to the size



of BSA monomer measured by inline DLS after fractionating the oligomer population at low protein concentration on a size exclusion column (Fig. S2). We further confirmed these results by analyzing BSA solutions in which intermolecular interactions were eliminated by adding 20% v/v DMSO. Under these conditions, we expected to observe a constant hydrodynamic radius at different protein concentrations equal to the size of monomeric BSA. Indeed, a radius of 3.5±0.3 nm (Fig. 3B) was obtained independently of the protein concentration and consistent with the size of monomeric BSA evaluated by SEC coupled with inline DLS. The quality of the fit was excellent at every protein concentration (Fig. S1B). These findings demonstrate that the microfluidic diffusion sizing platform can detect the presence of strong self-interactions by monitoring the dependence of the diffusion coefficient on the protein concentration, although these interactions cannot be quantified with the current configuration of the approach. In cases where the measured average radius is independent of the protein concentration, this value can be considered equal to the size of the monomeric protein in concentrated solutions. In both the absence and presence of interactions, the measured size represents a reference to constrain the method when looking at the potential presence of aggregates. We finally note that we often observed the presence of a smaller peak at around 0.2 nm in the size distribution. This artifact, which does not affect the analysis, may arise from the fact that diffusion already occurs inside the nozzle, and the initially measured distribution is therefore slightly broader than the simulated initial hat function. [37]

Sizing of antibody aggregates We generated a population of aggregates of IgG II conjugated with a fluorophore by incubating a solution of 1 mg/mL IgG II at 50 °C for 1.5 hours. We then analyzed this mixture with the microfluidic diffusion sizing device, and we compared the size distributions with the results obtained by dynamic light scattering. At time zero, the size distributions measured by DLS and by the microfluidic device were consistent and showed the presence of single monomeric species (Fig. 4A). After incubation for 1.5 hours, the peaks in the size distribution shifted towards larger sizes, indicating the presence of aggregates. Although both techniques detected the presence of aggregation, the shape of the distributions acquired with the two different methods differed significantly (Fig. 4B-C). In particular, dynamic light scattering showed a single broad population centered at around 100 nm (Fig. 4C). By contrast, the size distribution


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measured by the microfluidic diffusion method was bimodal: in addition to a population of aggregates of size around 100 nm, consistent with the population detected by DLS, the distribution exhibited a second peak with size of about 10 nm, corresponding to a mixture of monomers, oligomers of few units and fragments (Fig. 4B). The presence of the bimodality was confirmed by independent replicate measurements (Fig. S3) and cross-validated by SEC analysis (Fig. 3D). Indeed, the SEC chromatogram showed the presence of a peak eluting at 16 minutes, corresponding to monomers, and additional peaks at earlier residence times, corresponding to aggregates. The relative amount of monomer and fragments measured by SEC and microfluidic device was 15 % and 19 %, respectively. Therefore, the results acquired with the two techniques agreed not only qualitatively but also quantitatively. We note that a similar bimodal size distribution has been reported in the literature for another IgG system at low pH [54]. These results demonstrate the ability of the microfluidic diffusion device to measure heterogeneous size distributions, providing relevant information for mechanistic studies.

Microfluidic diffusion for probing the micro-rheology of antibody solutions After showing the potential of the approach in characterizing size distributions in the submicron range, we applied the microfluidic diffusion platform for the analysis of the micro-rheological properties of an IgG solution at high concentration. We selected a series of standard fluorescent tracers spanning a broad range of radii, from 0.4 nm to 100 nm. In particular, we considered a fluorescent small molecule (rhodamine B), highly charged polymeric oligomers with a radius of a few nanometers, and fluorescent nanoparticles (NPs) with radii between 5 nm and 100 nm. The polymeric oligomers have been designed to carry a high number of opposite charges to minimize interactions with the interfaces of the microfluidic chip. We measured the size distribution of these tracers with the diffusion method described in the paragraph above. The results are shown in Fig. 5. For all nanoparticles and for rhodamine B, the measured radii were consistent with the values reported by the manufacturer and by the literature [28], respectively. We started the analysis by measuring the viscosity of an aqueous solution with 23 %wt glycerol (Fig. 6A). The viscosity was quantified from the apparent hydrodynamic radius of the tracers, Rapp, which was evaluated from the measured diffusion coefficient assuming a bulk viscosity of 1 cP. The ratio Rapp/Rreal, where Rreal



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represents the hydrodynamic radius of the tracers measured in solution (Fig. 5), directly provided the viscosity that was sampled by the tracer. The values of this ratio as a function of the size of the tracers are shown in Fig. S4. Since the glycerol molecule has a characteristic radius of about 0.3 nm [55] and our smallest tracer has a radius of 0.4 nm, each tracer from our set was expected to experience the macro-viscosity of the solution. Indeed, the measured viscosity was independent of the size of the tracer (Fig. 6A) and consistent with the value reported in the literature. [56] We next analyzed a commercial solution of antibodies at 165 mg/mL (Fig. 6B). This molecule has a hydrodynamic radius of 8.3 nm, as measured previously in the sizing experiments (Fig. 2C). In this case, we observed different viscosity values as a function of the size of the tracer. Tracers that were smaller than the antibody molecules experienced a viscosity similar to that of water, while tracers larger than antibodies probed the macro-viscosity of the solution. The transition occurred for tracers with a radius between 12.5 nm and 25 nm, that is with a size close to the characteristic size of the antibody. The measured macro-viscosity was in agreement with the value obtained by bulk dynamic light scattering technique (Fig. 6B), indicating the absence of interactions between the tracers and the antibody molecules. The transition from micro-viscosity to macro-viscosity can be described by the following equation: [41]

@A C > =

Microfluidic Diffusion Analysis of the Size Distribution and

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