Microfluidic Diffusion Viscometer for Rapid Analysis of Complex

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A microfluidic diffusion viscometer for rapid analysis of complex solutions Paolo Arosio, Kevin Hu, Francesco Antonio Aprile, Thomas Müller, and Tuomas P.J. Knowles Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.5b02930 • Publication Date (Web): 04 Mar 2016 Downloaded from http://pubs.acs.org on March 5, 2016

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Analytical Chemistry

A microfluidic diffusion viscometer for rapid analysis of complex solutions Paolo Arosio#*, Kevin Hu#, Francesco A. Aprile#, Thomas Müller#¶ and Tuomas P.J. Knowles#* #University

of Cambridge, Chemistry Department, Lensfield road, Cambridge, UK ¶Fluidic Analytics Ltd, Cambridge, UK email to: [email protected], [email protected] Phone: +441223763845

Note: current address of Paolo Arosio is: ETH Zurich, Department of Chemistry and Applied Biosciences, Vladimir-Prelog-Weg 1, 8093 Zurich, CH

ACS Paragon Plus Environment

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Abstract The viscosity of complex solutions is a physical property of central relevance for a large number of applications in material, biological and biotechnological sciences. Here we demonstrate a microfluidic technology to measure the viscosity of solutions by following the advection and diffusion of tracer particles under steady-state flow. We validate our method with standard water-glycerol mixtures, and then we apply this microfluidic diffusion viscometer to measure the viscosity of protein solutions at high concentrations as well as of a crude cell lysate. Our approach exhibits a series of attractive features, including analysis time on the order of seconds and the consumption of a few μL of sample, as well as the possibility to readily integrate the microfluidic viscometer in other instrument platforms or modular microfluidic devices. These characteristics make microfluidic diffusion viscometry an attractive approach in automated processes in biotechnology and health-care sciences where fast measurements with limited amount of sample consumption are required.


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Introduction The measurement of the viscosity of complex solutions is a ubiquitous problem in a large variety of fundamental and applied sciences. Examples include systems ranging from the pharmaceutical to the food industry, in particular in cases where manufacturing steps require the application of flow.1 In addition, the measurement of viscosity of macromolecules in solution is a convenient probe of molecular properties such as size and shape,2,3 as well as of intermolecular interactions.4,5 Concentric and cone-and-plate bulk viscometers represent examples of standard methods that are routinely applied to measure viscosities of solutions.6 However, these conventional approaches often require a large amount of material and time-consuming sample handling steps, while in many fundamental and applied studies it is desirable to measure the viscosity via high-throughput techniques that consume small quantities of sample. To address these needs, a large variety of micro-rheological approaches have been developed in the last decades.3,7-10 One of the most common strategies consists in probing the viscosity of the solution by following the diffusion motion of tracer particles of known size. This objective can be achieved by monitoring single particle motion by video-microscopy,11,12 or by recording fluctuations in the average light scattering13-17 or fluorescence signal18 of the tracer particles. In this approach, the viscosity of the medium is quantified from the measured value of the apparent diffusion coefficient of the probe particle by applying the StokesEinstein relation. In diffusion wave spectroscopy (DWS) and single particle tracking, analysis using a generalized Langevin equation of motion can be applied to correlate the time evolution of the measured mean square displacement with the storage and loss moduli of the sample.7,12,13 These micro-rheology techniques represent attractive methods to measure the viscosity of complex solutions. Under certain conditions they may, however, have limitations. For example, the application of conventional dynamic light scattering techniques becomes challenging when the solution contains aggregates of comparable size of the tracer particles; moreover, fluorescence correlation spectroscopy as well as DWS require instrumentation that may not be easily implemented in every application. In this work, we have developed a microfluidic platform to measure the viscosity of complex solutions in the absence of shear by following the mass transport of fluorescent tracer particles under steady-state flow conditions, and we have applied this technique to measure the viscosity of protein solutions at high concentrations as well as of a crude cell lyate In comparison to current microfluidic viscometers,3,19 our approach does not involve the measurement of relative flow rates,20,21 or of pressure drops and velocities in capillary


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devices,9,22,23 but relies on the robust evaluation of the diffusivity of tracer particles. This approach avoids the need for the presence of a reference fluid, and the geometry of the device allows the easy integration of the microfluidic viscometer in modular platforms.

Material and Methods Materials Fluorescent polystyrene nanoparticles with nominal diameters of 47 nm (green) or 100 nm (red) and a density of 1.06 kg/dm3 were supplied by ThermoFisher Scientific (UK). Excitation and emission maxima are 468 and 508 nm for the green particles and 542 and 612 nm for the red particles, respectively. Glycerol and bovine serum albumin (BSA) were supplied by Sigma Aldrich (USA). All aqueous solutions were prepared in milli-Q water. Cellular extracts from E. coli BL21 (DE3) gold (Stratagene) were produced as follows. Cells carrying an empty pET17b vector were grown overnight at 28 °C under constant shaking at 250 rpm in 1000 ml of 2xYT (Merck Millipore, UK) and supplemented with ampicillin (100 μg/ml). The cells were then harvested by centrifugation, resuspended in PBS and EDTA-Free Complete Protease Inhibitor Cocktail (one tablet per 1000ml of cell culture, Roche, CH), and lysed by sonication; cell debris was removed by centrifugation at 18,000 rpm with JA25.50 rotor (Beckman Coulter, UK) followed by filtration with a syringe filter with 220 nm cut-off (PES Membrane, Millex-Millipore, IE). The final total concentration of proteins in the crude lysates, evaluated by UV absorbance, was estimated to be roughly about 40 g/L. Fabrication of the microfluidic device and operation of the technique Microfluidic channels were fabricated with standard soft-lithography techniques. Polydimethylsiloxane (PDMS) curing agent and elastomer (Sylgard 184 kit; Dow Corning, MI, USA) were thoroughly mixed at a ratio of 1:10, respectively. The mixture was supplemented with carbon black nanopowder (Sigma Aldrich), stirred and subsequently centrifuged for 10 minutes at 5000 rpm to spin down large clusters of the carbon black. The centrifuged black PDMS was then poured into a petri dish containing the master wafer, and the dish was degassed for 15 minutes in order to eliminate air bubbles before curing the PDMS at 65°C for 75 minutes. The PDMS layer containing the imprinted microchannels was pealed off and bonded to a glass slide after plasma activation.


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The channel height was 25 μm, while the channel width was 300 μm in the detection region, 3000 μm at the nozzle, and 100 μm in the hydrodynamic resistor channels introducing buffer and analyte into the nozzle. Previous to the measurements, air in the system was carefully removed by prefilling the channels with water via a Hamilton glass syringe connected with Neolus Terumo needles (25 gauge, 0.5 x 16 mm) and polythene tubing (inner diameter 0.38 mm, outer diameter 1.09 mm) to the outlet. Samples were introduced in the inlets using gel-loading tips. Afterwards, the flow in the channel was controlled by applying a negative pressure to the outlet by using a syringe pump (neMESYS, Cetoni GmbH, Korbussen, DE). Excitation illumination was provided using a LED light source (Cairn Research, Faversham, UK) equipped with suitable filter sets (Chroma Technology Corporation, Bellows Falls, VT, USA) for the specific fluorophore. In particular, the range of excitation and emission were 450-490 nm and 500-550 nm (49002 ET-EGFP) for the green nanoparticles, and 624-654 nm and 668-718 nm (49009 ET-Cy5) for the red nanoparticles, respectively. Images were collected at twelve different points along the channel (at distances 3.5 mm, 5.3 mm, 8.6 mm, 10.3 mm, 18.6 mm, 20.4 mm, 28.6 mm, 30.4 mm, 58.7 mm, 60.5 mm, 88.7 mm and 90.5 mm) using an inverted microscope (Axio Observer D1, Zeiss, Cambridge, UK) equipped with a cooled CCD camera (Evolve 512, Photometrics, Tucson, AZ, USA) with a 10× objective. Typical exposure times were in the range of 0.5 s.

Microfluidic space-time diffusion measurements For water-glycerol mixtures, measurements were performed at 20°C using green fluorescent nanoparticles with a diameter of 47 nm, applying a flow rate of 40 μl/h and 5 μl/h for mixtures with glycerol concentrations smaller or larger than 40 wt%, respectively. For BSA solutions, measurements were performed at 25°C using 47 nm green fluorescent nanoparticles, applying a flow rate of 40 μl/h. For the crude cell lysate, experiments were carried out at 22 °C using 100 nm red fluorescent nanoparticles, applying a flow rate of 20 μl/h and 30 μl/h. The concentration of the probe nanoparticles was 0.02% in all cases.

Fitting Procedure We simulated numerically the mass transport under steady-state flow by using a particle-based approach to solve the diffusion and convection equation describing the movement of the tracer particles in the system, as discussed in detail previously.24 Briefly, we propagated a large number of particles (at least 2’000’000) introduced at a starting point at a single fixed time, and we calculated the trajectories of the particles transiting in a detection region located at a reference distant from the starting point. We exploited this approach to simulate


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a discrete set of concentration profiles, B(Di,x), for particles of a given diffusion coefficient Di in the microfluidic channel. The measured diffusion profiles c(x) of the analyte at different diffusion times were compared to the profiles of the simulated library to evaluate the diffusion coefficient of the tracer particles. Dynamic light scattering Dynamic Light Scattering (DLS) measurements were carried out on a Zetasizer Nano instrument (Malvern, UK) working in the backscattering mode at 163°, equipped with a light source with wavelength of 633 nm. The viscosity of waterglycerol mixtures was evaluated by measuring the apparent diffusion coefficient of 47 nm particles, while for BSA solutions both 47 nm and 100 nm colloids were used as tracer particles. Results and Discussion The schematic of the microfluidic device is shown in Figure 1a-c. The principle underlying the operation of our microfluidic viscometer consists in the direct monitoring of the motion of tracer particles of known size by recording diffusion profiles at different diffusion times and different positions along a microfluidic channel under steady-state flow conditions.25 The analyte solution is introduced in the lateral inlets (i) at the top of the channel (Figure 1a), while the tracer particles are loaded only in the central inlet (ii) (Figure 1a). The analyte and the tracer particles merge in a nozzle ten times wider than the channel in which diffusion is to be monitored, ensuring an accurate positioning of the tracer particles in a well-defined initial configuration before any diffusion is allowed to take place. In this manner, the entire-cross section of the channel is filled homogeneously with the analyte solution, while the tracer particles are focused in a narrow beam at the centre of the channel. While flowing along the longitudinal direction y, the particles diffuse laterally along the width x of the channel (Figure 1c). The residence time in the channel is controlled by modulating the flow rate, and is selected to ensure that the tracer particles exhibit sufficient diffusional transport in the channel to provide accurate information on the diffusivity, yet at the same time to avoid diffusion of the analyte all the way to the side of the channel, at which point information on diffusion motion would be lost. The possibility to control the diffusivity inside the channel by changing the flow rate represents an attractive feature of the technique, and allows a broad range of viscosities to be probed within the same device simply by adjusting the flow rate. For unknown samples, this adjustment can be easily performed during the measurement by monitoring in real-time the diffusion profiles. Typical values of flow rates are 40 μl/h for viscosity in the range of 1-3 cP and 5 μl/h for viscosities in the range of 4-7 cP. Typical volumes of required samples are 20-40 μl for the analyte solution and 5-10 μl for the tracer particles.


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The diffusive motion is monitored by acquiring density profiles at several different positions along the channel; in this work the number has been fixed to 12 measurements. In this approach, the diffusion profiles are acquired under steady-state flow conditions, which allow to measure samples at lower concentrations with respect to pulse techniques simply by increasing the exposure time. In the microfluidic system, the flow occurs in the laminar regime, with Reynolds numbers in the range 0.07-0.6, and the transport of the particles in the channel is governed by advection and diffusion motions only, which can be readily modelled by the corresponding mass transport equations.24 The diffusion coefficient of the tracer particles is estimated by comparing the experimental concentration profiles c(x) acquired along the lateral direction x with a discrete set of simulated standard profiles corresponding to varying diffusion coefficients Di. The large number of constraints provided by the space-time diffusion measurements increases the robustness of the fit against systematic and random experimental noise, and allows the accurate estimation of the diffusion coefficients. The detailed description of the model simulations and of the fitting procedure can be found in Refs. 24 and 25, and an example of a fit to experimental data is shown in Figure 1e. From the apparent diffusion coefficient of the nanoparticles (D), the viscosity of the solution (η) can be calculated according to the Stokes-Einstein relationship: ߟ=

݇ܶ 6ߨܴ௛ ‫ܦ‬

where T is the temperature, k is the Boltzmann constant and Rh is the known hydrodynamic radius of the standard tracer particles.


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Figure 1: Schematic illustration of the microfluidic viscometer technique. a-c) Design and picture of the device highlighting the most relevant components; d) Diffusion profiles at 12 different positions along the channel for particles with hydrodynamic diameter of 47 nm in aqueous solutions with 10 wt% (blue) and 50 wt% (red) glycerol: the viscosity of the solutions is quantified by evaluating the apparent diffusion coefficient of the nanoparticles in the medium. e) Typical experimental images of diffused test nanoparticles at different positions (corresponding to different diffusion times) along the channel, and comparison between the corresponding measured (dot black lines) and simulated (continuous red lines) diffusion profiles.

We first validated our approach by measuring the viscosity of waterglycerol mixtures, whose behaviour has been studied widely in the literature.26,27 The results of the microfluidic space-time diffusion device have been compared with the values obtained by conventional dynamic light scattering as well as with


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data reported in the literature (Figure 2).26 We have reported the values of viscosity in terms of relative viscosity, ηr, defined as the ratio between the viscosity of a given solution (η) and the viscosity of pure water (η0) at the same temperature. Figure 2 reveals the excellent agreement between the different sets of measurements, confirming the accuracy of our approach. The precision of the technique, defined here as the standard deviation of several independent measurements of the same sample, is c.a. 5%, similar to DLS. We tested samples with viscosity values up to 7 cP, and we predict that even higher viscosities can be evaluated by further decreasing the residence time.

Figure 2: The increase in the relative viscosity (ηr) at 20 °C of water-glycerol mixtures with increasing glycerol content as measured by the microfluidic space-time diffusion approach (circles). The measurements are compared with the values estimated by conventional dynamic light scattering (squares) and with data reported in the literature (triangles)26. The dashed line represents an empirical function reported in the literature.27

We then applied our method to measure the viscosity of solutions of bovine serum albumin (BSA) at high concentrations in 20 mM phosphate buffer at pH 7.0 (Figure 3). Also in this case, the measurements of the microfluidic space-time diffusion device have been compared with the values measured by conventional dynamic light scattering, and the results show an excellent agreement between the two techniques.


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Figure 3: Relative viscosity (ηr) of aqueous solutions at different concentrations of bovine serum albumin (BSA) as measured by our microfluidic approach (circles) and by conventional dynamic light scattering technique (squares) using standard nanoparticles of 100 nm diameter at 25 °C.

a 20

b 25 real diam et er: 47 nm

2.5

η=1.77 Relat iv e viscosit y ηr

20

Intensity %

Convolut ion of t he signal

10

c real diam et er: 100 nm

η=2.21

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10

5 5

0

1

10 100 500 Hydrody nam ic diam et er (nm )

0

2

1.5 1 0.5

1 10 100 1000 Hy drodynam ic diam et er (nm )

0

DLS 100nm

DLS 50nm

Micro 50nm

Figure 4: (a-b) Size distribution as measured by means of dynamic light scattering for a solution of 100 g/L BSA with 0.02% standard nanoparticles of 47 nm diameter (a) or 100 nm diameter (b). In the situation where the tracer particles are not sufficiently larger than the protein molecules (panel a)), the convolution of the light scattering signals from proteins and nanoparticles does not allow the accurate sizing of the tracer particles. (c) This limitation can lead to a wrong estimation of the viscosity of the protein solution.

The microfluidic space-time diffusion method described in this work is particularly attractive for applications that require measurements of the viscosity of protein solutions, which represents a common problem in biology and biotechnology. In these systems, solutions can often contain aggregates with size comparable to the tracer particles. The presence of these aggregates, even at low concentrations, may compromise the application of techniques based on conventional light scattering detection. To illustrate this concept, we show in Figure 4 the intensity size distribution of a solution with 100 g/L BSA and 0.02%


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nanoparticles with diameter of 47 nm or 100 nm as measured by dynamic light scattering. In the case where the tracer particles are not sufficiently larger than the protein molecules (Figure 4a), the light scattering signals from proteins and nanoparticles are convoluted. Under such conditions, the accurate sizing of the peak corresponding to the nanoparticles, and therefore the estimation of the solution viscosity, is challenging. Indeed, the apparent diameter of the nanoparticles as estimated in the intensity size distribution in Figure 4a is 103.9±0.3 nm, corresponding to a relative viscosity of 2.21±0.01, which differs from the value of 1.73±0.06 estimated by the microfluidic diffusion technique, and the value of 1.77±0.01 measured by dynamic light scattering by using larger tracer particles (Figure 4b and 4c). This limitation can be alleviated by increasing the intensity of the light scattering signal from the tracer particles, for instance by increasing either the size or the concentration of the particles. However, this optimization procedure can be challenging in the situations where the composition of the solution is unknown. For instance, a crude cell lysate contains thousands of different proteins as well as residuals of cell debris. The viscosity of this solution represents an important property in biotechnology for the processing required by downstream operations. We prepared a crude cell lysate by E. coli cells (Figure 5a), and we measured the corresponding size distribution by DLS after removing big particulates with a 220 nm cut-off filter (see Material and Methods). The analysis of the cell lysate reveals the presence of a small amount of aggregates with hydrodynamic diameter of the order of few hundreds of nm, which contribute largely to the scattered intensity (Figure 5b). We note that the viscosity of the sample is unknown, and therefore the reported diameters are “apparent” values, evaluated from the measured diffusion coefficients assuming the viscosity of water. The presence of these aggregates compromises the use of tracer nanoparticles in the nanometer scale. By contrast, with the microfluidic device we were able to follow the diffusion of fluorescence tracer nanoparticles with diameter of 100 nm (Figure 5c), and we could therefore measure the viscosity of this complex biological mixture. In particular, we evaluated a viscosity of the cell lysate of 3.12 ±0.002 cP, which decreased to 1.52 ±0.03 cP and 1.37 ±0.09 cP upon dilution of the cell lysate in mQ-water at ratios of 1:2 and 1:4, respectively (inset in Figure 5c).


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Figure 5: (a) Cell lysate obtained from E. coli cells. (b) Intensity and volume distribution of the crude cell lysate as measured by means of dynamic light scattering. The viscosity of the sample is unknown, and therefore the reported diameters are “apparent” values, evaluated from the measured diffusion coefficients assuming the viscosity of water. The presence of few aggregates with diameters of hundreds of nm does not allow the accurate sizing of the tracer particles. (c) By contrast, with the microfluidic techniques we can estimate the viscosity of the cell lysate by monitoring the diffusion of fluorescent tracer particles of 100 nm. The inset shows the viscosity values of the crude cell lysate as well as of 1:2 and 1:4 dilutions in water.

Conclusions We have developed a space-time diffusion method to measure the viscosity of complex solutions in the absence of shear by tracking the mass transport of tracer particles under steady-state conditions on a microfluidic platform. We have demonstrated the potential of this approach by measuring the viscosity of standard water-glycerol mixtures and of protein solutions at high concentrations, as well as of a crude cell lysate. Our microfluidic space-time diffusion viscometer requires low quantities of sample material, affords a short analysis time, and can be easily integrated as part of other microfluidic elements on chip. The technique is largely independent of both the probe size and the sample composition, and can be applied in a non-invasive manner. In addition, a broad range of viscosity values can be explored on the same device simply by adjusting the flow rate. Finally, the method exhibits benefits with respect to conventional dynamic light scattering approaches when solutions containing aggregates of comparable sizes of the tracer particles are considered. These features can make the diffusion viscometer an attractive approach in biotechnological and health-care applications where rapid measurements of viscosity with limited consumption of material are required.


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Acknowledgments We acknowledge financial support from the Swiss National Science Foundation (PA, TM), the Marie Curie Fellowship scheme for career development (PA), the BBSRC (TM, TPJK), the ERC (TPJK) and the Newman Foundation (TPJK). Competing financial interests Part of the work described in this paper has been the subject of a patent application28 filed by Cambridge Enterprise, a wholly owned subsidiary of the University of Cambridge.


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Microfluidic Diffusion Viscometer for Rapid Analysis of Complex

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