Method for determining a hydrodynamic size of an object

Abstract

The disclosure relates to a method for determining a hydrodynamic size of an object, such as a nano-sized object, said method comprising the steps of: providing a fluid interface, linking said object to said fluid interface thereby providing a linked object, whereby the movement of said linked object is restricted by virtue of being linked to said fluid interface, providing and determining a hydrodynamic shear force that acts on said linked object, tracking the movement of said linked object, and calculating the hydrodynamic size of the object using the Einstein-Smoluchowski relation.

Claims

1. A method for determining a hydrodynamic size of an object, said method comprising the steps of: providing a substrate having a surface that defines a two-dimensional fluid interface, linking said object to said fluid interface thereby providing a linked object, whereby a movement of said linked object is restricted to a two-dimensional plane extending in a x direction and a y direction by virtue of being linked to said fluid interface, providing a hydrodynamic shear force that acts on said linked object by inducing a fluid flow, tracking the movement of said linked object, determining, from the tracked movement, said object's diffusion coefficient and said object's velocity in the direction of the flow, wherein the movement of said object is analyzed independently in a direction parallel or perpendicular, or a combination thereof to the induced flow, determining said hydrodynamic shear force acting on said object from a relationship between said determined diffusion coefficient and said determined velocity, and determining said hydrodynamic size of said linked object from a relationship between said determined hydrodynamic shear force and the fluid flow rate.

2. A method according to claim 1, wherein the hydrodynamic shear force is combined with at least one additional force being an electrophoretic force, osmotic force, magnetic force, or convection, or a combination thereof.

3. A method according to claim 1, wherein said object is a nano-sized object having a maximum cross-sectional dimension within the range of from 1 nm to 500 nm.

4. A method according to claim 1, wherein the object comprises of a metal, an organic material, an inorganic material, a biological material and any combinations thereof.

5. A method according to claim 4, wherein the object comprises a biological material, wherein the biological material is selected from the group consisting of proteins, viruses, exosomes, lipid assemblies, nucleic acids, and extracellular vesicles, and any combinations thereof.

6. A method according to claim 1, wherein said method involves sorting of a plurality said objects according to their hydrodynamic size.

7. A method according to claim 1, wherein said tracking is carried out in real time.

8. A method according to claim 1, wherein the fluid interface is substantially planar or substantially curved.

9. A method according to claim 1, wherein said fluid interface is comprised within a microfluidic channel or a capillary.

10. A method according to claim 1, wherein the fluid interface is a film, a monolayer, a bilayer, a cell membrane, an air water interface, or an oil water interface.

11. A method according to claim 1, wherein the fluid interface is a supported lipid bilayer.

12. A method according to claim 1, wherein said fluid interface is located on a wall.

13. A method according to claim 1, wherein said method comprises the step of detecting said object.

14. A method according to claim 13, wherein said step of detecting said object involves measurement of fluorescence, refractive index and/or scattering intensity of said object.

15. A method of using a system for determining the hydrodynamic size of an object, said system comprising: a container, a substrate having a surface within the container, wherein the surface of the substrate defines a two-dimensional fluid interface; means for flowing a fluid across the fluid interface to provide a hydrodynamic shear force that acts on an object linked to said fluid interface, and means for tracking an object linked to said fluid interface, the method comprising: linking said object to said fluid interface thereby providing a linked object, whereby the movement of said linked object is restricted to a two-dimensional plane extending in a x direction and a y direction by virtue of being linked to said fluid interface, providing the hydrodynamic shear force that acts on said linked object by inducing a fluid flow, tracking the movement of said linked object, determining, from the tracked movement, said object's diffusion coefficient and said object's velocity in the direction of the flow, wherein the movement of said object is analyzed independently in a direction parallel or perpendicular, or a combination thereof to the induced flow, determining said hydrodynamic shear force acting on said object from a relationship between said determined diffusion coefficient and said determined velocity, and determining said hydrodynamic size of said linked object from a relationship between said determined hydrodynamic shear force and the fluid flow rate.

16. The method of claim 15, wherein the container comprises a microfluidic channel.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a framework for the hydrodynamic size determination of single, nanometer sized objects. The objects (1) are linked (2) to a fluid interface (3) and moved by a hydrodynamic force (4), which is e.g. generated by application of a shear flow (5).

(2) FIG. 2 shows trajectories of single gold nanoparticles that are linked to a SLB and subjected to a hydrodynamic flow.

(3) FIG. 3 shows a representative trajectory of a single gold nanoparticle. The predominantly directed movement in direction of the flow is be used to determine the velocity v.sub.x (induced by application of the hydrodynamic shear force), while 1D diffusion coefficients are extracted from the random movements in both directions.

(4) FIG. 4a shows a comparison of the 1D diffusion coefficients D.sub.x and D.sub.y of gold nanoparticles, which were extracted using the decomposition method shown in FIG. 3.

(5) FIG. 4b shows a histogram of the ratio D.sub.x/D.sub.y (bars), whose deviations from the expectation value 1 can be explained by the measurement resolution (solid line).

(6) FIG. 5a, FIG. 5b and FIG. 5c show the velocity v.sub.x for gold nanoparticles versus nanoparticle diffusion coefficient D for different flow rates.

(7) FIG. 5d show the velocity v.sub.x (after normalization by the flow rate) for gold nanoparticles versus nanoparticle diffusion coefficient D, which collapses all data points from FIGS. 5a to 5c onto a single master curve.

(8) FIG. 6a shows a histogram of the hydrodynamic force for 3 gold nanoparticle batches differing in their size distributions.

(9) FIG. 6b shows the dependence of the hydrodynamic radius on the normalized hydrodynamic force for the 3 calibration batches shown in FIG. 6a.

(10) FIG. 7a and FIG. 7b shows a comparison of the size distributions of a gold nanoparticle batch extracted using electron microscopy (a) or using their 2D movement under flow (b).

(11) FIG. 7c and FIG. 7d show a comparison of the size distributions of another gold nanoparticle batch extracted using electron microscopy (c) or using their 2D movement under flow (d).

(12) FIG. 8a shows the size distribution of a SUV sample as extracted from the 2D movement under flow.

(13) FIG. 8b shows the size distribution of the same SUV sample (as in FIG. 8a) as extracted using NTA.

(14) FIG. 9 compares the size distributions of a SUV sample as extracted using DLS (1) or the 2D movement under flow (2).

(15) FIG. 10 shows a flow chart of real time SPT analysis.

(16) FIG. 11 shows a demonstration of real time tracking analysis.

(17) FIG. 12 shows a framework for the size determination and sorting of single, nanometer sized objects.

(18) The disclosure is illustrated by the following non-limitative examples

EXAMPLES SECTION

Example 1. Demonstration of 2D Size Determination of nm-Sized Objects

(19) As a potential implementation of 2D SPT-based size extraction, a POPC SLB was formed within a microfluidic channel, followed by linking of nm-sized objects to the SLB. These objects had either a well-defined size (determined using e.g. TEM analysis) and were used for calibration measurements, or displayed a broad size distribution (e.g., vesicles), which was determined by the novel approach (using 2D SPT under flow) and compared with result of established approaches like DLS and NTA. A schematic view of the setup is given in FIG. 1.

(20) In a first set of experiments, gold nanoparticles were used (the size distributions of which were determined using electron microscopy). The surface of the gold nanoparticles was functionalized using streptavidin, allowing to link the gold nanoparticles to biotin-conjugated lipids in the SLB. FIG. 2 shows typical trajectories of gold nanoparticles (hydrodynamic diameter 60 nm). The flow rate was adjusted such that the movement in the direction of the flow (denoted as x-axis, see FIG. 2) was dominated by a directed motion. FIG. 3a gives a representative trajectory of a single gold nanoparticle (hydrodynamic diameter 60 nm) and its decomposition into its x- and y-components, i.e., into components parallel and perpendicular to the flow direction (FIG. 3b-c). While the movement along the y-axis appeared to be purely random (FIG. 3c), as indicated by the non-directed fluctuations of the y-position displaying no obvious trend of the movement, a predominantly linear increase of the x-position was observed (FIG. 3b), which indicates presence of a directed movement along the flow direction. This directed movement was superimposed by fluctuations, however, causing minor disturbances from a perfect linear increase in x-position over time.

(21) To investigate if this intuitive analysis holds a more stringent analysis the displacements along the x- or y-coordinates of this trajectory were plotted in FIGS. 3d and e for data points that are separated by 2 frames: x(i)=x(i+2)x(i) and y(i)=y(i+2)y(i) with i denoting the frame number. For a pure 1D diffusion, i.e., in the absence of directed movement, one expects that the average value of this coordinate difference is zero, which is observed for y (FIG. 3e, thin solid line). Furthermore, the variance of y is equivalent to the mean squared displacement observed in y-direction and equals therefore 2.Math.D.sub.y.Math.t (with t denoting the lag time between 2 frames):
var(y)=<(y<y>).sup.2>=<y.sup.2>=2.Math.D.sub.y.Math.t.(7)

(22) Hence, calculating the variance of y allows to directly extract the diffusion coefficient in the y-direction. The same holds for the x-direction with one difference: due to the directed movement, the average value of x is in theory now given by
<x>=v.sub.x.Math.t(8)
and therefore non-zero (as observed for x; FIG. 3d, thin solid line). However, as the variance is invariant on shifting all datapoints by a constant offset (which changes only the average value), the variance of x is still proportional to the diffusion coefficient in the x-direction, despite the non-zero average value:
var(x)=<(x<x>).sup.2>=2.Math.D.sub.x.Math.t.(9)
Hence, the diffusion coefficients in x- and y-direction can be independently extracted by calculating the variance of x and y, while taking the average value of x gives a convenient way to extract v.sub.x from the trajectory (see FIG. 3d, e).

(23) As the SLB is a 2D isotropic medium, one expects that D.sub.x and D.sub.y should be equal. This is tested in FIG. 4, which compares the extracted values for D.sub.x and D.sub.y for each tracked gold nanoparticle and shows that both diffusion coefficients are identical within experimental error (dashed lines in FIG. 4a and solid line in FIG. 4b). This demonstrates that the data extraction procedure successfully decouples the directed and the random particle movement and allows to calculate the 2D diffusion coefficient D.sub.link as arithmetic average of D.sub.x and D.sub.y.

(24) From Eqs 2, 3 and 6 one expects that the observed velocity v.sub.x scales linearly with the flow rate v.sub.0 (of the liquid passing the channel) and the diffusion coefficient D.sub.link, which is generally observed in the experiment (FIG. 5). Hence, after normalizing the extracted velocity v.sub.x by the applied flow rate v.sub.0 (FIG. 5d), all data points collapse onto a single, linear master curve (solid line in FIG. 5d). Note that the fluctuations (noise) in FIG. 5 decrease with increasing flow rate, which is attributed to the fact that higher flow rates induce larger particle displacements between consecutive frames, which in turn increases the signal to noise ratio in the measurement of v.sub.x.

(25) As both the velocity in the direction of the flow, v.sub.x, as well as the diffusion coefficient D.sub.link can be determined, application of Eq. 4 allows to directly extract the hydrodynamic force acting on each tracked nanoparticle. FIG. 6a shows histograms of the normalized hydrodynamic force measured for 60 nm, 100 nm, and 210 nm gold nanoparticles, exhibiting peaks at 1.60 fN/(L/min) for the 60 nm, at 4.05 fN/(L/min) for the 100 nm, and at 10.83 fN/(L/min) for the 210 nm gold nanoparticles. These measurements allowed to determine the calibration parameters A and of Eq. 6 and therefore to calibrate the microfluidic channel for the determination of size distributions (FIG. 6b, lines). This is demonstrated in FIG. 7, which compares hydrodynamically-determined size distributions (as obtained by application of Eq. 6 to the observed hydrodynamic shear forces) with the one obtained by electron microscopy imaging of gold nanoparticles samples. Both methods yield essentially the same distributions if one takes a shift of 5 nm into account, which is caused by a PEG corona formed on the nanoparticle surface (and which is not resolvable in the TEM images). Moreover, the hydrodynamically-determined size distributions were extracted using slip lengths of 24.4 nm (bars in FIGS. 7b and 7d; motivated by the weighted LMS-fit in FIG. 6b) and 64.5 nm (dashed lines in FIGS. 7b and 7d; motivated by the LMS-fit in FIG. 6b), showing that changes in the slip length have only little effect on the size extraction for hydrodynamic diameter below 100 nm.

(26) As a potential application, the size distribution of liposomes was determined using the novel approach. The liposomes (fluorescently labelled by incorporation of lissamine rhodamine-conjugated DOPE) were linked to the SLB using cholesterol-equipped DNA-tethers as recently described in The Journal of Physical Chemistry B, 109(19), 9773-9779 and ChemPhysChem, 11(5), 1011-1017. FIG. 8 and FIG. 9 compare the hydrodynamically-determined size distributions of the liposomes (FIG. 8a and curve 2 in FIG. 9) with the size distributions derived using NTA (FIG. 8b) or DLS (curve 1 in FIG. 9), indicating good agreement of the complementary approaches. This comparison also shows that liposomes with hydrodynamic radii <25 nm, which are practically unresolved in the NTA size distribution (FIG. 8b) are well resolved in the hydrodynamically-determined size distribution (FIG. 8a). The existence of this fraction is confirmed by the DLS measurement (FIG. 9).

Example 2. Demonstration of Real Time Tracking Analysis

(27) Sorting obviously requires the full tracking analysis to be done in real time, i.e., the tracking analysis must be capable to analyse the same number of frames the microscope is able to write per time unit. This is so because otherwise the tracked objects will sooner or later have passed the field of view of the microscope before their properties have been determined by the analysis, making a sorting based on their properties impossible.

(28) In order not to affect the acquisition performance of the software used to record and store the imaging data, it was decided to split the whole tracking analysis into distinct tasks, which are distributed among the available nodes of the CPU. This ensures that each analysis task does not consume more CPU resources than the amount corresponding to a single node, which avoids crosstalk in the CPU usage (during the course of the data analysis) between the nodes hosting the image recording and tracking analysis software, respectively. Or in other words, increases in CPU consumption during the tracking analysis cannot feed through to the recording software, which would cause a negative effect on the image acquisition rate.

(29) The tracking analysis was divided into 5 distinct tasks (FIG. 9): 1. picking: detection and localization (with pixel accuracy) of objects within the images, 2. linking of detected objects between adjacent frames to build up the tracks, 3. refining the localization of the detected objects with sub-pixel accuracy based on a centroid algorithm, 4. if of interest: extraction of the integrated scattering or fluorescence intensity of the detected objects, and 5. interlacing all these distinct data streams into a complete tracking analysis, which is then used to steer the flow through the microfluidic channel. The analysis architecture allows further splitting of the data analysis queues (thereby increasing the total analysis throughput) by running multiple copies of these fundamental tasks, each analysing distinct data heaps. This makes up-scaling of the architecture easy, if the hosting computer offers sufficient nodes and data transfer rates. Additionally, it is possible to sort even those objects, whose track coordinates have only partially refined but already offer sufficiently high accuracy in the determination of properties of interest, as soon as their linking data is available.

(30) The performance of the real time particle tracking analysis was tested on liposomes that were linked to a SLB as described in above. A single computer was used to control the TIRF microscope, to record the SPT movies and to analyse the recorded movies, allowing to test if the CPU usage remains within the assigned limits, i.e. to ensure that a high CPU usage of the analysis nodes does not feed through to the nodes controlling the TIRF microscope. The computer was equipped with a 3.2 GHz Intel i7-3930K CPU supplying 12 virtual nodes (6 hyperthreadable, physical cores that can be split in 2 distinct, virtual nodes each) with 32 GB RAM.

(31) For SPT movies containing 12801024 pixels and less than 100 trackable objects, the current implementation reached the following data throughput per node: picking 30 fps, linking 15 fps, refining 12 fps. Using 1 picking node, 2 linking nodes and 2 refinement nodes ensured a constant data throughput of 20 fps, without affecting the acquisition rate of the nodes controlling the microscope (FIG. 10). To push beyond the limit of 25 fps, which is often referred to as real time imaging, it is necessary to split the data streams once more, i.e. to use 1 picking node, 3 linking nodes and 3 refinement node, requiring 4 physical CPU cores, or to reduce the number of tracked objects.

Example 3. Sorting of nm-Sized Objects Linked to a Fluid Interface

(32) The present disclosure enables sorting of nm-sized objects using the following procedure: 1. The objects are linked to a fluid interface (e.g., located at a wall of a microfluidic channel; 1 in FIG. 12), while their motion is followed in real time using SPT (e.g., using microscopic imaging, 2 in FIG. 12, in connection with real time data analysis, 3 in FIG. 12). Exemplary implementations of this step are disclosed in the sections Example 1 and Example 2. 2. The SPT analysis allows to extract object properties of interest, for example the refractive index contrast, and the scattering or fluorescence intensity of each tracked object. Suitable analysis procedures have been describe in the literature. In addition to these established procedures, the analysis approach introduced in section Theoretical considerations, allows to derive the hydrodynamic size of the objects after linking to a fluid interface. This enables sorting of nm-sized objects based on their hydrodynamic size, which is of special interest for sorting of e.g. exosomes, when combined with parallel identification of protein expression levels or incorporated DNA or RNA (e.g., by measuring the fluorescence intensity of a certain marker relative to the hydrodynamic exosome size). 3. Finally, if an object that fulfils a given sorting criteria reaches the sorting area of the microfluidic channel, the flow between the 2 output channels (4a and 4b in FIG. 12) is switched by a computer controlled valve system (5 in FIG. 12), initiating the actual sorting process. Once the object was successfully moved into the sorting output channel, the valves are switched back and the original flow is restored.

REFERENCES

(33) WO 03/093801 WO 2013/021185 US 2004/0169903 US 2014/0333935 Langmuir, Vol. 2006, 22, pp. 2384-2391 Journal of Physical Chemistry B, 109(19), 9773-9779 Langmuir, Vol. 22(13), pp. 5682-5689 Journal of extracellular vesicles, 2015, Vol. 4, Pospichalova et al. The Journal of Physical Chemistry B, 109(19), pp. 9773-9779 ChemPhysChem, 11(5), pp. 1011-1017