Size and surface charge characterization of nanoparticles with a salt gradient

Exosomes are nanometer-sized lipid vesicles present in liquid biopsies and used as biomarkers for several diseases including cancer, Alzheimer’s, and central nervous system diseases. Purification and subsequent size and surface characterization are essential to exosome-based diagnostics. Sample purification is, however, time consuming and potentially damaging, and no current method gives the size and zeta potential from a single measurement. Here, we concentrate exosomes from a dilute solution and measure their size and zeta potential in a one-step measurement with a salt gradient in a capillary channel. The salt gradient causes oppositely directed particle and fluid transport that trap particles. Within minutes, the particle concentration increases more than two orders of magnitude. A fit to the spatial distribution of a single or an ensemble of exosomes returns both their size and surface charge. Our method is applicable for other types of nanoparticles. The capillary is fabricated in a low-cost polymer device.

Accurate particle characterization based on the concentration prole of trapped particles requires that the diusioosmotic velocity is known. The diusioosmotic ow velocity depends on the salinity gradient and the zeta potential of the channel walls ζ ch . We nd the ow rate, and, consequently, ζ ch , following the work by Lee et al. [1]. That is, we measure the ow rate from the position-dependent concentration of a uorescent dye in the nanochannel. The dye concentration ρ is kept constant at the two microchannels, which serve as reservoirs with ρ(x = 0) = ρ N and ρ(x = L) = ρ W .
In the funnel-shaped nanochannel, the position-dependent width is w(x) = w N + ∆wx/L. As the ow rate Q = vhw(x) is constant due to the conservation of mass, the velocity is also position-dependent v(x) = Q/[hw (x)]. The dye current I dye (x) = hw(x)J dye (x) is constant along the nanochannel in steady state, i.e., ∂ x I dye (x) = 0, where J dye (x) = −D∂ x ρ(x) + v(x)ρ(x) due to the nite ow v(x) and D is the diusion coecient of the dye.
The dye concentration thus fullls with the boundary conditions ρ(0) = ρ N and ρ(L) = ρ W . The solution is A t of Supplementary Equation 2 to an experimental intensity prole has the ow rate Q as the only free parameter since the channel geometry, the dye concentrations in the microchannels, and the diusion coecient of the uorescent dye are known. From measurements of Q versus ln(C N /C W ), the diusioosmotic mobility, and nally ζ ch , can be extracted (see the main text). In our experiments, we used streptavidin as the uorescent dye, which has the diusion coecient D = 70 (µm) 2 s −1 at our experimental conditions. Measurements were performed for the two lipid coatings used in the experiments, POPC:POPG 3:1 and POPC:POPG 1:1.
Supplementary Figure 1a shows a uorescence microscope image of the uorescent dye in POPG:POPC 3:1 coated nanochannel for an imposed salinity gradient. Intensity proles and ts to Supplementary Equation 2 are plotted in Supplementary Figure 1b. Fitted values for the ow rates are shown in Supplementary Figure 1c together with linear ts with Q = h L ∆w/ ln 1 + ∆w w N Γ os ln(C N /C W ) + Q res , where Q res is a residual ow in the device due to a pressure dierence ∆P between the channel entries. From Γ os , the values of the channel zeta potentials are ζ = (−24 ± 1) mV for POPC:POPG 3:1 and ζ = (−30 ± 1) mV for POPC:POPG 1:1. The residual ows Q res are (36 ± 15) fL min −1 and (29 ± 13) fL min −1 for POPC:POPG 3:1 and POPC:POPG 1:1 coated nanochannels, respectively. This corresponds to residual pressures ∆P equal to (0.21 ± 0.09) mbar and (0.18 ± 0.08) mbar, respectively, which are within the instrumental error of the pressure pump (±0.3 mbar).

Supplementary Note 2: Diusion of particles in nanochannels
The concentration of trapped particles C p (x) depends on the particles' diusion coecients in the nanochannel (see eq. 7 in the main text). For a particle with diameter d in a solution with dynamic viscosity η, the diusion coecient in bulk is When a particle is placed midway between two innite, parallel walls separated by a distance h, an expansion of the diusion coecient to fth order in d/h is [2]: In our experiments, the nanochannel height is h = 240 nm and particle diameters are in the range from d = 70 nm to d = 150 nm, so D p /D 0 is between 0.7 and 0.5. We experimentally conrm the validity of Supplementary Equation 7 for our experimental conditions by tracking the motion of individual liposomes in a funnel-shaped nanochannel in absence of a salinity gradient. Supplementary Figure 2a,b show the coordinates of a single particle undergoing Brownian motion in a nanochannel. The particle is recorded for N = 200 frames with a time-lapse of ∆t = 73.5 ms. From the coordinates The displacements in the x-direction has a mean value of ∆x = (0.01±0.06) µm, where the uncertainty is the standard error on the mean. As ∆x is within two standard errors from zero, we conclude that the measurement is consistent with the hypothesis of no drift in the x-direction. For the y-direction we nd ∆y = (−0.03 ± 0.06) µm, which is also consistent with no drift. A chi-square goodness-of-t test showed that the distribution of displacements in the x-and y-directions were consistent with normal distributions (full curves in Supplementary Figure 2c,d) as the p-values were 0.12 and 0.66, respectively.
The diusion coecients for the two directions were extracted from the displacements using the co-variance based estimator (CVE) [3,4]. That is, we estimate the diusion coecient in the x-direction aŝ Here · · · means average over ∆x 2 , ∆x 3 ∆x 4 , . . . , ∆x N , and the estimate for the positional error iŝ where R is the motion blur coecient that has the value R = 0.11 for our measurements, as we use an exposure time of 50 ms and a time-lapse ∆t = 73.5 ms [3]. The variance of the estimate is where ε = σ 2 /(D∆t) − 2R. The diusion coecient for the y-direction was found similarly. For a discussion of the advantage of the CVE compared to, e.g., extracting the diusion coecient from the mean-squared displacement (MSD), see, e.g., [3,4].
For the trajectory shown in Supplementary Figure 2, the measured diusion coecients for the two directions arê D x = (4.6 ± 0.8) (µm) 2 s −1 andD y = (3.8 ± 0.7) (µm) 2 s −1 , respectively. As the two values are consistent with a common mean value, we take the averageD = (D x +D y )/2 = (4.1 ± 0.5) (µm) 2 s −1 as the value for the diusion coecient. All diusion coecients in Supplementary Figure 3 were obtained in an identical manner.  Figure 4b compares the calculated concentration proles of trapped exosomes C p (x) for the true size distribution but with a cut-o at 240 nm due to channel height restrictions (blue), and for a monodisperse sample with the diameter obtained from the trapping experiment. Only minor dierences are observed, and the assumption of monodispersity used in the data analysis gives a reasonable estimate for the mean of the particle size distribution.

Supplementary Note 4: Trapping eciency
We dene the trapping eciency of the device as the percentage of nanoparticles introduced in the microchannel that are trapped in the nanochannels. In the experiments nanoparticles are loaded in the upper left inlet and ow to the upper right outlet through the upper microchannel (Supplementary Figure 5). The ow rate of nanoparticles before the nanochannel array is denoted I micro,in (see the lower panel in Supplementary Figure 5). As the nanoparticles pass the nanochannel array, some nanoparticles enter a nanochannel and get trapped (see lower panel in Supplementary Figure 5). The ow rate of nanooparticles into the nth nanochannel is I trap,n . The nanoparticles that remain in the microchannel after the nanochannel array continue toward the outlet with a ow rate I micro,out .
So the trapping eciency of the device is where I trap,total is the total rate of particles entering the sixteen traps. We nd η trap from two measurements. First we record the intensity of the rst eleven nanochannels versus time in a single eld of view for a high concentration of liposomes in the microchannel. Then we make a single-particle measurement with a low concentrations of liposomes in the microchannel, where we measure the trapping rate of the rst nanochannel. All trapping eciency measurements were performed with POPC:POPG liposomes with diameters d DLS = (76 ± 3) nm in a salinity gradient dened by ln(C N /C W ) = −9.2.
Supplementary Figure 5: Schematic of particle trapping. a, Particles (red dots) are loaded in the upper left inlet and ow to the upper right outlet through the upper microchannel. a, As the nanoparticles pass the nanochannel array, some get trapped in one of the sixteen parallel nanochannels, while the rest continues to the upper outlet.
Supplementary Figure 6a shows trapped liposomes in eleven consecutive nanochannels. The concentration of liposomes in the microchannel is 2.1 · 10 11 mL −1 . The number of trapped liposomes in the nanochannels decreases along the ow direction as the nanochannels deplete the microchannel. We record the total uorescence intensity of each channel versus time, see Supplementary Figure 6b. After 40 s, the intensity is proportional to time for all eleven nanochannels, which indicates a constant trapping rate in all of them. Trapping rates I trap,n are obtained from a linear t to data (Supplementary Figure 6b) and plotted versus channel number on a lin-log scale in Supplementary Figure 6c. The trapping rates fall on a straight line, indicating an exponential dependence A t givesn = 5.9, and a value for I trap,1 in units of intensity per time. The total trapping rate for all sixteen nanochannels is thus I trap,total = 16 n=1 I trap,n = I trap,1 15 k=0 e −k/n = I trap,1 1 − e −16/n 1 − e −1/n 5.9 I trap,1 .
For a low concentration of liposomes in the microchannel (2.1 · 10 9 mL −1 ), individual liposomes can be detected when they leave the microchannel and enter the rst trap. Supplementary Figure 6d shows the number of particles trapped in the rst nanochannel versus time. The number of trapped liposomes increases linearly, and the tted trapping rate is I trap,1 1 s −1 . So Supplementary Equation 13 gives I trap,total = 5.9 s −1 .
With a uid ow velocity of 50 µm s −1 in the microchannel, a liposome concentration of 2.1 · 10 9 mL −1 , and a crossssection of the microchannel equal to 150 µm 2 , the ow rate of liposomes in the microchannel before the nanochannel array is I micro,in 16 s −1 . So the rst channel traps I trap,1 /I micro,in 6 % of the total number of liposomes passing through the microchannel.
From the denition of the trapping eciency in Supplementary Equation 11, I trap,total 5.9 s −1 , and I micro,in 16 s −1 , we get that the trapping eciency for the whole device with sixteen nanochannels is The eciency can be increased by decreasing the cross-section of the microchannel or by lowering the uid ow velocity. The trapping position x 0 depends nonmonotonically on ln(C N /C W ), see Fig. 3e-f in the main text. This is because the diusioosmotic uid velocity is proportional to ln(C N /C W ) while the diusiophoretic velocity depends nonlinearly on ln(C N /C W ). The full lines in Supplementary Figure 7 show the calculated diusiophoretic velocities v ph (x) for a particle with a diameter d = 75 nm and a zeta potential ζ = −30 mV for dierent values of ln(C N /C W ). Dashed lines are the diusioosmotic velocities −v os (x) for the same values of ln(C N /C W ). Trapping occurs for v ph (x) + v os (x) = 0 (marked with full dots). The trapping positions correspond to the values on the black curve in Fig. 3e in the main text. [4] Vestergaard, C. L., Blainey, P. C. & Flyvbjerg, H. Optimal estimation of diusion coecients from single-particle trajectories. Phys. Rev. E 89, 022726 (2014).