Label-free nanofluidic scattering microscopy of size and mass of single diffusing molecules and nanoparticles

Label-free characterization of single biomolecules aims to complement fluorescence microscopy in situations where labeling compromises data interpretation, is technically challenging or even impossible. However, existing methods require the investigated species to bind to a surface to be visible, thereby leaving a large fraction of analytes undetected. Here, we present nanofluidic scattering microscopy (NSM), which overcomes these limitations by enabling label-free, real-time imaging of single biomolecules diffusing inside a nanofluidic channel. NSM facilitates accurate determination of molecular weight from the measured optical contrast and of the hydrodynamic radius from the measured diffusivity, from which information about the conformational state can be inferred. Furthermore, we demonstrate its applicability to the analysis of a complex biofluid, using conditioned cell culture medium containing extracellular vesicles as an example. We foresee the application of NSM to monitor conformational changes, aggregation and interactions of single biomolecules, and to analyze single-cell secretomes. Nanofluidic scattering microscopy enables label-free, quantitative measurements of the molecular weight and hydrodynamic radius of biological molecules and nanoparticles freely diffusing inside a nanofluidic channel.

F luorescence microscopy has been a long-standing workhorse in biochemistry and biophysics [1][2][3][4][5] . However, a key limitation is the need for labeling with fluorescent tags. Therefore, one current research frontier is the development of methods that enable label-free studies of single biological nanoparticles (BNPs) and biomolecules to complement fluorescence-based techniques. Label-free methods bypass the following limitations of fluorescence microscopy: (1) attaching a fluorescent label to a target may alter its properties 6,7 ; (2) there is a limited number of label colors that can be used simultaneously; and (3) long-term measurements are complicated by photobleaching. In addition, in cell-secretion-related studies 8 , it is very difficult to specifically label biomolecules of interest and, most importantly, it is only possible to detect predefined labeled secreted entities, which means unlabeled but potentially important entities are probably overlooked.
Label-free single-biomolecule detection has been enabled recently by dielectric microresonators 9 , plasmonic approaches based on metallic continuous films 10 and nanostructures 11 , and interferometric scattering microscopy (iSCAT) [12][13][14][15][16] . iSCAT has been used to investigate, for example, single cell secretion dynamics 13 and protein motion on a dielectric substrate 14 , on a supported lipid bilayer 17,18 or on actin filaments 15 . Furthermore, in contrast to alternative methods, iSCAT enables quantitative molecular weight (MW) measurements of biomolecules, since the signal intensity is proportional to the weight of the imaged object 12,16 . However, and as a key point, these three label-free optical single-molecule detection methods require the investigated species to bind to a surface to be "visible". This requirement can lead to misinterpretations when applied to biomolecular interaction studies because binding to a surface may affect the properties and accessibility of molecular binding sites 19 . In addition, binding is a selective process, meaning that only molecules that actually bind are detected, while a large fraction remains unseen. Consequently, the ability to label-free image and track diffusing single biomolecules directly in solution would constitute an important step in the field. However, the resolution of current state-of-the-art microscopy techniques allows imaging only of much larger diffusing objects, such as viruses 20 , extracellular vesicles 21 (EVs), or dielectric particles 22 . This is mainly because the scattering cross-section of individual biomolecules is very small, preventing their direct detection, and because their fast Brownian motion permits the accumulation of the light they scatter only for the extremely short time they spend in a diffraction limited spot and/or before they diffuse out of the focal plane.
To overcome these limitations, we present NSM, which enables the real-time label-free imaging of single BNPs and biomolecules in solution down to the few tens of kilo-Daltons regime inside a nanofluidic channel, without the need for surface immobilization. Furthermore, it allows the simultaneous determination of MW from the optical contrast of the imaged nano-object, and of its hydrodynamic radius (R s ) and/or conformational state from the measured diffusivity.

Results
Nanofluidic scattering microscopy. NSM works by imaging nanofluidic channels nanofabricated into an optically transparent matrix, such as SiO 2 , by dark-field light-scattering microscopy (Fig. 1a). The channel cross-sectional dimensions can range from tens to hundreds of nanometers, depending on the size of the investigated Label-free characterization of single biomolecules aims to complement fluorescence microscopy in situations where labeling compromises data interpretation, is technically challenging or even impossible. However, existing methods require the investigated species to bind to a surface to be visible, thereby leaving a large fraction of analytes undetected. Here, we present nanofluidic scattering microscopy (NSM), which overcomes these limitations by enabling label-free, real-time imaging of single biomolecules diffusing inside a nanofluidic channel. NSM facilitates accurate determination of molecular weight from the measured optical contrast and of the hydrodynamic radius from the measured diffusivity, from which information about the conformational state can be inferred. Furthermore, we demonstrate its applicability to the analysis of a complex biofluid, using conditioned cell culture medium containing extracellular vesicles as an example. We foresee the application of NSM to monitor conformational changes, aggregation and interactions of single biomolecules, and to analyze single-cell secretomes.
nano-object, while their lengths typically exceed the microscope's field of view (Extended Data Fig. 1 and 2; see 'Nanofluidic chips' and 'Experimental setup' in Methods). In this arrangement, the nanochannels ensure the localization of the nano-objects within the microscope focal plane throughout the entire imaging process, similar to other tether-free microscopy methods 23 . Most importantly, the nanochannels improve the optical contrast of the imaged nano-object by several orders of magnitude.
To introduce the underlying principle, we consider a single biomolecule diffusing inside a nanochannel (Fig. 1a). The biomolecule and the nanochannel scatter light coherently into the collection optics, resulting in a total scattering intensity, It = cI 0 L|αt| 2 k 3 /4, which depends on the incident intensity (I 0 ), the wavenumber of the light (k), the length of the illuminated part of the nanochannel (L), the collection efficiency (c) and the optical properties of the molecule and the nanochannel, defined by the total electric dipole polarizability (α t ) 24 . The α t can be determined by the respective electric dipole polarizabilities of the biomolecule, α m , and of the nanochannel, α c , and can be approximated as αt ≈ αc + αm/L 2 , where the length L stems from the fact that the polarizability of a nanochannel is two-dimensional, whereas the polarizability of a molecule is three-dimensional (see Section 1 in Supplementary Information). The total scattering intensity collected from a region of a nanochannel of length L = 3π/ (2k) that contains a biomolecule can then be written as It ≈ Ic + Im − 2 √ IcIm, where Ic = cI 0 L|αc| 2 k 3 /4 and Im = cI 0 |αm| 2 k 4 / (6π) are the scattering intensities produced by the biomolecule (Fig. 1b) and the nanochannel (Fig. 1c) in isolation, respectively. The minus sign in front of the interference term stems from the fact that the nanochannel resides in a high-refractive-index background (α c < 0 since n H 2 O ≈ 1.33 < n SiO 2 ≈ 1.46), while the opposite is true for the biomolecule (α m > 0 since nm > n H 2 O ). Since scattering from subwavelength objects scales as volume squared, and because the nanochannel volume is much larger than the molecular volume, Ic ≫ Im, the scattering signal stemming from the biomolecule is not directly detectable against the nanochannel background. However, by subtracting the scattering image produced by an empty nanochannel (I c ) from a scattering image of a nanochannel with a biomolecule inside (I t ), the presence of the biomolecule can be revealed through the interference term, which contributes a sizeable (negative) signal ΔIt = It − Ic ≈ −2 √ IcIm (Fig. 1d) that can be several orders of magnitude larger than the scattering intensity produced by the biomolecule alone (I m ) outside the nanochannel. This key feature of NSM, which is related closely to homodyne detection in laser interferometry 16,20 , thus enables the direct imaging of diffusing biomolecules and other nano-objects inside a nanochannel.

Experimental setup and data analysis.
To approach the photon shot noise level necessary for NSM imaging, we used a dark-field microscope (Mad City Labs RM21), a polychromatic light source (NKT Photonics, SuperK EXTREME EXB-6) and a high-speed CMOS camera (Andor, Zyla), enabling the recording of movies at 200 frames per second at an averaged noise level of 0.005%. This is low enough to distinguish the optical contrast generated by single biomolecules with MWs ranging down to tens of kilo-Daltons. At the same time, the temporal resolution is high enough to capture their fast Brownian motion (Fig. 2). To extract single-molecule information from the raw data, every frame of a movie is corrected for long-and short-term mechanical and intensity instabilities, and an empty nanochannel background is estimated from every frame and subtracted from the signal. The resulting time-series of differential dark-field images is normalized by the intensity profile of an empty nanochannel to correct for inhomogeneous illumination (see Section 5 in Supplementary Information). A selection of frames from a video so obtained of a single thyroglobulin protein (669 kDa) diffusing inside a nanochannel is shown in Fig. 2a (Supplementary Movie 1). Plotting the entire time-sequence of obtained images in a corresponding kymograph displays the movement of the protein in the nanochannel, where each horizontal line corresponds to the optical signal averaged across the short axis of the nanochannel (Fig. 2b). A corresponding library of kymographs of different types of protein and double-stranded DNA molecules is displayed in Fig. 2c-h, obtained for the proteins inside a nanochannel with cross-sectional area A I = 100 × 27 nm 2 (Channel I in Extended Data Fig. 3a) and for the DNA molecules inside a nanochannel with cross-sectional area A II = 110 × 72 nm 2 (Channel II in Extended Data Fig. 3b).
MW and R s determination. NSM can not only image individual biomolecules, but also determine their MW and hydrodynamic properties. The hydrodynamic properties contain important information about R s and/or shape. The MW determination is enabled by the integrated optical contrast (iOC) being linearly dependent on the polarizability of a biomolecule, α m , which is linearly proportional to its MW 12,16 as αm ∼ = a · MW, where a = 0.46 Å 3 · Da −1 corresponds to values extracted from both measurements 25 and calculations 16 of optical properties of a large number of proteins (see Section 3 in Supplementary Information). We also note that the linear dependency of α m on MW is connected directly to the f-sum rule that relates the number of electrons in a system to its optical extinction cross-cross section 26 . iOC is also inversely proportional to the cross-sectional area of the nanochannel, A, and proportional to n = ( 1.5n 2 SiO 2 ) (see Section 1 in Supplementary Information). Both these factors are constant during the measurement and can be determined before it. Therefore, MW can be determined from iOC, as The diffusivity of a molecule can be obtained from the statistical analysis of its movement 27 . Subsequently, by approximating it as a hard neutral sphere, its hydrodynamic (Stokes) radius, R s , can be estimated using the Stokes-Einstein equation corrected for hindrance effects associated with the diffusion of small objects in a restricted volume as 28 where k B is the Bolzmann constant, T is temperature, η is the viscosity of the liquid in the nanochannel and K is the hindrance factor that takes particle-wall hydrodynamic interactions and steric restrictions inside a nanochannel into account. It is dependent on the size of the nanochannel relative to the dimensions of the biomolecule, and can be estimated using a phenomenological model suggested by Dechadilok et al. 28 as where λ = Rs/r, r = √ A/π is the radius of a circle defined by an area A. We note here that the diffusivity in principle also can be affected slightly by other surface-related effects that are not included here, such as the partial-slip boundary condition 29 .
To extract iOC and the position of the biomolecule along the nanochannel, x, we used a particle-tracking algorithm (see Section 6 in Supplementary Information). It evaluates each frame in the kymograph (Fig. 2i), finds the responses corresponding to a biomolecule and connects them in a trajectory. Each biomolecule is then represented by N values of iOC n (Fig. 2j) and N-1 values of spatial displacement in time Δx n (Fig. 2k), where N is the number of frames that constitute a single biomolecule trajectory. iOC pertaining to a single biomolecule is defined as mean value of iOC n and its D can be calculated as D = (Δxn) 2 /2Δt + ΔxnΔx n+1 /Δt 27 . Furthermore, we have corroborated these results with an independent analysis employing machine learning (ML) algorithms (see Section 7 in Supplementary Information) to derive iOC and D directly from the raw data, whose results are in very good agreement with those of the standard analysis (SA) above.
As final comment, we note that the 28 nM molecular concentration chosen for the experiments is high enough to ensure sufficient throughput and, at the same time, low enough to enable correct and precise discrimination of individual biomolecules. It corresponds to 0.7 and 2 biomolecules on average per field of view in Channels I and II, respectively. Lower concentrations can be studied by applying a flow rather than relying on diffusion alone to improve throughput. For higher concentrations, more advanced particle trackers are in development.
A single biomolecule library. Having established the theoretical framework of NSM, as well as its two main readout parameters, MW (calculated from iOC using Eq. 1) and R S (calculated from D using Eq. 2), we now apply it to a library of proteins and DNAs, and use the two nanochannels with the different cross-sections introduced above, that is, Channel I and Channel II. Accordingly, each datapoint corresponds to iOC and D determined from a trajectory of a single biomolecule in Channel I (Fig. 3a) and Channel II (Fig. 3b). Each molecular species exhibits distinct populations and there is a clear correlation between R s , MW and the shape of the biomolecules. Specifically, for proteins that are globular in shape, the R s scales approximately as Rs ∼ = b · MW 1/3 , where b = 0.88 nm Da -1 was determined empirically 30 (gray solid lines in Fig. 3a,b). For DNA molecules that have a distinctly different geometry compared with globular proteins, D is distinctly lower at the corresponding MW (Fig. 3b), as expected for elongated molecules 31 .
To further analyze the obtained single biomolecule data, we plot one-dimensional histograms of iOC converted to MW for all biomolecules in Channel I and II obtained by SA (Fig. 3c,d). Each detected trajectory is presented by N/ ∑ N counts of its determined iOC where ∑ N is the sum of the number of frames of all the trajectories that were identified in the sample. This way, the numbers of counts within the peaks correspond to the (relative) concentration of different populations present in the sample. To evaluate the main peaks that correspond to molecular monomers, we fit the histograms with Gaussian distributions using the Matlab curve fitting toolbox. The mean value of iOC (iOC) is thus defined as the center of the Gaussian peaks, while the resolution in iOC is defined by their full-width-at-half-maximum (FWHM). For Channel I this translates into a MW resolution of 20-30 kDa and for Channel II of 30-40 kDa (details in Section 10 in Supplementary  Information), which defines the limits for resolving different populations in a sample. The resolution reached for thyroglobulin in Channel I (30 kDa) corresponds to a threefold improvement compared with iSCAT, which determines MW from single binding/ unbinding events 16 . This improvement is enabled by the ability of NSM to track the diffusing biomolecules during the entire time they spend in the field of view, which, in some cases, can be much longer than the residence time on a surface.
As the final analysis step, we investigate the dependency of experimentally determined iOC on nominal MWs of monomers (see 'Biomolecular solutions' in Methods), compared with Eq. 1 (Fig. 3e). Clearly, the theoretical prediction is reproduced very well for both nanochannels, despite their different cross-sectional dimensions and despite the different shapes of the imaged proteins and DNA molecules.
In a similar fashion, we derive the mean values of D (D) and the resolution in D and compare the dependency of D of the protein monomers on their hydrodynamic radii taken from the literature 32 (R s = 8.6 nm for thyroglobulin, R s = 6.1 nm for ferritin, R s = 4.6 nm for ADH and R s = 3.5 nm for bovine serum albumin (BSA)) with the confinement-corrected Stokes-Einstein equation (Eq. 2) (Fig. 3f). We find that the theoretically predicted values reproduce the experimentally measured D values well, which suggests that potential surface-related effects are negligible.
Further analysis of the data library also reveals molecular populations with higher MW and higher R S than expected for monomers.
Specifically, for thyroglobulin and BSA, we observe indications of a second population with approximately double the MW and approximately 1.3× higher R S , (marked 'Dim' in Fig. 3a,b for thyroglobulin, in Fig. 3c for BSA) that according to theory of asymmetric particle diffusion 33 corresponds to dimers. For ferritin, we also find dimers and, interestingly, also multiple subpopulations characterized by MW values somewhere between the monomer and dimer populations that correspond to molecules with different numbers of coordinated iron (details in Section 11 in Supplementary Information).
We also highlight that iOC and D values determined by ML are in excellent agreement with SA (Fig. 3e,f), as well as their distributions (inset of Fig. 3c for BSA and Extended Data Fig. 4 for all biomolecules). This validates the use of ML and we thus use it exclusively from here forward since it is substantially more efficient in terms of computational time.
Surface passivation by supported lipid bilayer. So far, we had designed our experiments such that the biomolecules were predominantly negatively charged to minimize attractive interaction-and thus nonspecific binding-to the negatively charged nanochannel walls. Nevertheless, we were able to observe rare events of molecular binding and unbinding to and from the nanochannel, respectively (Extended Data Fig. 5). For the data presented above, we excluded these transient binding events from the analysis (see Section 6 in Supplementary Information). At the same time, we also note that the demonstrated observation of nonspecific binding events opens the door to using NSM for affinity-based single molecule detection by analyte-specific receptors immobilized on nanochannel walls 34 .
To now demonstrate the active prevention of nonspecific binding, we applied a supported lipid bilayer (SLB) coating 35   protein aldolase (Fig. 4c), which was impossible to analyze in an uncoated channel due to the strong electrostatic interaction with the negatively charged channel walls. The obtained values for aldolase are in good agreement with the nominal values (Fig. 4d,e) and thus corroborate the wide applicability of NSM, irrespective of analyte charge.
Analysis of extracellular vesicles in cell culture medium. EVs act as mediators of physiological intercellular communication, play key roles in the pathobiology of several diseases 36 and are promising diagnostic biomarkers 37 . Their functionality depends on both their composition and their size. However, these parameters are challenging to define precisely with existing methodologies, such as dynamic light scattering or nanoparticle tracking analysis (NTA), due to the substantial heterogeneity of EVs, in combination with their small sizes down to the tens of nanometers range 38 , and their existence in complex biofluids.
Here, to apply NSM to complex biological sample analysis, we collected conditioned medium from human SH-SY5Y cells (details in 'Conditioned cell culture medium' in Methods), containing a mixture of serum proteins and secreted EVs. To accommodate the size of EVs, we used a 225 × 200 nm 2 nanochannel (Channel V), whose walls were passivated with an SLB to prevent nonspecific binding. To increase the throughput to up to ten particles per minute, we introduced a slow flow by applying a 0.25 Pa pressure drop along the nanochannel, resulting in individual particles being flushed through it, as revealed by the NSM signal (Fig. 5a).
Using this setup, we then collected a significant number of trajectories of different BNPs, from which we derive iOC and D translated to R S using Eq. 2 (the applicability of the no-slip condition is discussed in Section 4 in Supplementary Information). This analysis reveals two distinct populations (Fig. 5b): one in the small iOC/R S regime (red circle) corresponding to most trajectories, and one in the large iOC/R S regime (blue circle) corresponding to a minority of trajectories. A control experiment with cell culture medium that had not been in contact with the cells reveals that the former population can be attributed to entities present in the serum supplement, probably lipoprotein particles (Fig. 5c)  population indeed corresponds to EVs secreted by the cells. The identified R S of 10-13 nm and 20-70 nm (Fig. 5d,e) correspond to values reported for low-density lipoproteins 39 and EVs 38 , respectively. In addition, the obtained size of EVs was validated by a comparative size distribution measurement using NTA (Supplementary Fig. 20; more details in 'NTA' in Methods). This clearly demonstrates the applicability of NSM to detect and, importantly, distinguish nonlabelled analytes of biological relevance in a complex sample mixture retrieved from cell culture. However, we also note that precise translation of iOC into MW is more complicated for BNPs than for single molecules due to a large variety of molecular constituents with different optical properties whose representation and spatial distribution might be different for each BNP (that is, different constant a in Eq. 1). Therefore, we did not further explore the content of the EVs via the measured iOC.

Discussion
We have introduced NSM to quantitatively analyze single biomolecules without the need for labeling or surface attachment, as they diffuse inside a nanofluidic channel. NSM provides spatio-temporal information about MW via optical contrast for biomolecules down to 66 kDa, and reveals R s and molecular conformation via molecular diffusivity D. Furthermore, ferritin monomers with different iron content could be identified, showing the ability of the method to distinguish molecular subpopulations within a sample. Moreover, SLB coating on the nanochannel walls prevented nonspecific binding, thereby enabling analysis of both positively and negatively charged proteins. These key NSM attributes challenge existing label-free single biomolecule detection techniques, which all require analyte binding to a surface for detection, and enable up to threefold improvement in terms of MW resolution compared with state-of-the-art methods. Furthermore, NSM complements single molecule fluorescence microscopy in cases where labeling is unwanted or even impossible. Thus, NSM will find application in studies of conformational changes, aggregation processes or reactions between individual biomolecules, and help unravel the dynamics of such processes and molecule-specific heterogeneities that might be of physiological relevance 40 . As a second aspect, we have analyzed conditioned cell culture medium collected from human SH-SY5Y cells, which contained a complex mixture of proteins and BNPs. We were able to accurately determine and, importantly, distinguish the size and corresponding distributions of lipoprotein particles and EVs in this setting. Looking forward, this advertises NSM for label-free single-cell studies in real time, such as for the analysis of intracellular content or secretomes, for which we predict it to be particularly useful due to minimized sample dilution in the nanofluidic system. Furthermore, rapid progress in detector technologies and ML-based data treatment promises to push the limits of NSM towards even smaller molecules and to enable up to two orders of magnitude increased throughput via parallel analysis of hundreds of nanochannels that fit in the field of view of a microscope 41 . Therefore, we predict NSM to find applications across a wide range of fields, including genomic DNA analysis 42 , single particle counting 43 and single particle catalysis 44 .

Methods
LUVs were prepared by mixing lipids (POPC/Marina Blue (99/1 mol%)) in round-bottom flasks followed by drying of the lipid films overnight under vacuum. The lipid films were rehydrated and mixed with PBS to a total lipid concentration of 1 mg ml -1 . Afterwards, rehydrated lipids were disrupted by five freeze-thaw cycles using liquid nitrogen and a 37 °C heat block except for the last cycle, which was thawed at room temperature. Finally, LUVs were obtained by extrusion using a mini-extruder (Avanti Polar Lipids), with two polycarbonate filters of 100 nm pore diameter (21 passages). To form a SLB in nanochannels of size 225 × 200 nm 2 (Channel V), we let the LUV solution flow through the nanochannels for 30 min by applying the pressure drop of 2 bar. For nanochannel of size 80 × 40 nm 2 (Channel V), the process was prolonged to 12 h. In addition, to prevent eventual clogging, the direction of the flow was switched periodically with a period of 10 s using microfluidic pressure controller MFCS-EX (Fluigent).
Conditioned cell culture medium. Fetal bovine serum (FBS), Ham's F-12 nutrient mixture (F12), DMEM GlutaMAX, nonessential amino acids (NEAA) and trypsin-EDTA were purchased from ThermoFisher Scientific. Amicon Ultra-15 centrifugal filter unit 100 kDa 15 ml and PBS (tablets) were purchased from Sigma-Aldrich. PBS buffers were filtered with Millipore filters (0.1 μm) from Merck and water was deionized and filtered using a Milli-Q system from Merck.
SH-SY5Y human neuroblastoma cells (1.2 × 10 6 ) were seeded in T25 flasks (ThermoFisher Scientific) in 5 ml cell culture medium containing a 1:1 mix of MEM and F12 supplemented with 10% FBS and 1% NEAA and cultured for 48 h at 37 °C with 5% CO 2 . The conditioned medium was then harvested, filtrated through a 0.22 μm filter (VWR) and centrifuged for 20 min at 4,000 rpm at 4 °C in an Eppendorf Centrifuge 5430/5430 R with Rotor F-35-6-30 to remove large cell debris. The supernatant was then loaded onto Amicon Ultra-15 100 kDa filters (pre-equilibrated with 5 ml filtered PBS for 10 min at 5,680 rpm at 4 °C) to concentrate EVs and protein particles. The Amicon tubes were centrifuged for 2 h at 6,350 rpm, 4 °C. Afterwards, flowthrough was discarded and Amicon tubes were loaded with 5 ml filtered PBS and centrifuged for 2 h at 6,350 rpm, 4 °C. Finally, the concentrated conditioned cell culture medium was collected from the filter. For the control experiment, 5 ml cell culture medium that had not been in contact with the cells was concentrated on Amicon filters using the same protocol. For NSM measurements the samples were diluted 130× in PBS to reach a sufficiently low particle concentration.
Nanofluidic chips: design. The nanofluidic chips used in our experiments (Extended Data Fig. 2) contain a series of nanochannels with tailored cross-sectional dimensions and 30 μm length (Channels I-IV and VI) and 200 μm length (Channel V), which are connected to macroscopic in-and outlets through two microchannels with cross-section dimensions of 50 × 1.5 μm 2 . The transport of the 30 μl liquid sample from the inlets to the nanochannels is controlled by pressurizing the inlets to 2 bar. During the measurements in Channels I-IV and VI, the applied pressure is turned off to solely rely on diffusion for molecular motion through the nanochannels during imaging. The dataset corresponding to the ADH molecule in Channel I was collected from three different nanochannels of the same geometry and the same nanofluidic chip. No statistically relevant differences between the results from different nanochannels were found. The other data sets corresponding to a combination of a specific biomolecule and a specific nanochannel were collected from the same volume of biomolecular solutions and the same nanochannel.
To measure the cross-sectional area from the SEM images, the edges of the nanochannels were estimated manually from the positions of the pixels with the most rapid change of the intensity (dashed line in Extended Data Fig. 3) and drawn on top of the SEM image using a computer graphics tool (Affinity Designer). A secondary image containing only the derived shape of a nanochannel with dark pixels inside the area of the nanochannel and white pixels outside the area of the nanochannel was then created. The number of black pixels was then calculated using Matlab and translated into micrometers squared accordingly. The area derived (A) was translated into a format expressing the width × length that correspond to the dimensions of an equal-area rectangle. The measured areas of Channels I-VI correspond to A I = 100 × 27 nm 2 , A II = 110 × 72 nm 2 , A III = 100 × 15 nm 2 , A IV = 145 × 27 nm 2 , A V = 225 × 200 nm 2 and A VI = 82 × 40 nm 2 , respectively. Experimental setup. The optical setup was based on the versatile microscope platform RM21 (Mad City Labs) (Extended Data Fig. 1). A beam of collimated polychromatic light with wavelength range 400-2,350 nm generated by a supercontinuum laser (NKT Photonics, SuperK EXTREME EXB-6) was spectrally filtered by the tunable wavelength filter (NKT Photonics, SuperK VARIA) to a polychromatic beam with wavelength range 450-750 nm. The resulting beam with a total power of 250 mW was focused at the back focal plane of a microscope objective lens (numerical aperture (NA) = 1.49, Nikon), and directed to illuminate the fluidic chip under angle using a micromirror positioned at the back aperture of the objective lens. The effective NA of the objective was then lowered to 1.27 as the back aperture of the objective was partially blocked-decreased from a diameter of 23.8 mm to 16.7 mm. The reflected light was spatially filtered using a second micromirror and the scattered light was imaged via a tube lens by a CMOS camera (Andor, Zyla). The resulting magnification was 220×. In the case of the experiments with 30 μm long nanochannels (Channels I-IV and VI), a beam of 1 mm diameter was used to illuminate an area of the fluidic chip of 10 μm diameter. An area of 30 × 600 pixels of the camera was then acquired at the frame rate of about 5,000 frames per second. In the case of the experiments with 200 μm long nanochannels (Channel V), the beam was expanded fourfold to illuminate an area of the fluidic chip of 40 μm diameter. An area of 30 × 2,160 pixels of the camera was then acquired at the same frame rate.
Nanoparticle tracking analysis. We performed NTA using a Malvern NanoSight LM10 instrument equipped with a 488 nm laser and operating in scattering mode and under a flow rate of 100 (B10 ml min -1 ) obtained with a Nanosight syringe pump module and with the cameral level set to 15. The sample was diluted 1,000× in PBS and analyzed in a set of five videos of 60 s each. The videos were analyzed with the built-in NTA 3.2 software using a detection threshold of five to be able to determine optimized size distributions and concentrations. The buffer viscosity was considered as that of water at 21 °C. Concentration values (particles per milliliter) were extracted and plotted.
Reporting Summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
All sample data are packaged with the code and can be found at gitlab.com/ langhammerlab/NSM-SA. Source data are provided with this paper.

Code availability
The codes for device control and data acquisition can be found at gitlab.com/ langhammerlab/NSM-DeviceControl. The code using SA described in Sections 5-6 in Supplementary Information can be found at gitlab.com/langhammerlab/ NSM-SA. The code using ML described in Section 7 in Supplementary Information can be found at gitlab.com/langhammerlab/NSM-ML.