Single-Molecule Detection with Lightguiding Nanowires

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Single-Molecule Detection with Lightguiding Nanowires: Determination of Protein Concentration and Diffusivity in Supported Lipid Bilayers Damiano Verardo, Björn Agnarsson, Vladimir P. Zhdanov, Fredrik Höök, and Heiner Linke Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.9b02226 • Publication Date (Web): 01 Aug 2019 Downloaded from pubs.acs.org on August 1, 2019

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Nano Letters

Single-Molecule Detection with Lightguiding Nanowires: Determination of Protein Concentration and Diffusivity in Supported Lipid Bilayers

Damiano Verardo1, Björn Agnarsson2, Vladimir P. Zhdanov2,3, Fredrik Höök2*, Heiner Linke1*

1. NanoLund and Solid State Physics, Lund University, 22100 Lund, Sweden

2. Department of Physics, Chalmers University of Technology, 41296 Göteborg, Sweden

ACS Paragon Plus Environment

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3. Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia

* Corresponding authors: [email protected], [email protected]


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Abstract

Determining the surface concentration and diffusivity of cell-membrane-bound molecules is central to the understanding of numerous important biochemical processes taking place at cell membranes. Here we use the high aspect ratio and lightguiding properties of semiconductor nanowires (NWs) to detect the presence of single freely diffusing proteins bound to a lipid bilayer covering the NW surface. Simultaneous observation of lightemission dynamics of hundreds of individual NWs occurring on the time scale of only a few seconds is interpreted using analytical models and used to determine both surface concentration and diffusivity of cholera toxin subunit B (CTxB) bound to GM1 gangliosides in supported lipid bilayer (SLB) at surface concentrations down to below one CTxB per μm2. In particular, a decrease in diffusivity was observed with increasing GM1 content in the SLB, suggesting increasing multivalent binding of CTxB to GM1. The lightguiding capability of the NWs makes the method compatible with conventional epifluorescence microscopy, and it is shown to work well for both photostable and photosensitive dyes. These features make the concept an interesting complement to existing techniques for


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studying the diffusivity of low-abundance cell-membrane-bound molecules, expanding the rapidly growing use of semiconductor NWs in various bioanalytical sensor applications and live cell studies.


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TOC

Keywords Biosensing, microscopy, nanowires, waveguide, supported lipid bilayer, single molecule, diffusivity


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Numerous biochemical processes taking place both inside and between cells involve molecular activity at and within lipid membranes. Examples include selective molecular transport,1 signaling controlled by spatial clustering of membrane components,2 viral endocytosis,3 and synaptic vesicle fusion.4 Because of the small dimension of membrane components and the weak contrasts that they offer, fluorescence labeling schemes have emerged as a pivotal approach when striving to gain biophysical insight into the dynamics of lipid membranes in general and diffusivity of membrane-bound proteins in particular. Fluorescence recovery after photobleaching (FRAP) is ideally suited when the fluorophore content is relatively high.5,6 For systems with very low surface concentrations, the diffusivity can be better determined either by probing the temporal correlation of fluctuations caused by single or few molecules upon entering and leaving a fixed illumination volume, as in fluorescence correlation spectroscopy (FCS),7 or by direct single particle tracking (SPT) approaches, in which trajectories of several individual molecules are analyzed.8,9 Lately, nanoparticles and other synthetic nanostructures have also emerged as tools to improve single-molecule detection schemes. For example, both gold nanoparticles10,11 and fluorescent quantum dots12 have been used as tags for SPT,


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mitigating problems related to photobleaching using conventional dyes. FCS has been employed on zero mode waveguides13 and plasmonic nanoantennas14 to confine the detection volume and enhance fluorescence.

In this work, we expand on these existing methods and introduce the use of semiconductor nanowires (NWs)15 for single-molecule studies of lipid-bilayer bound molecules. Because of their high aspect ratio and surface-area-to-footprint ratio, such NWs have been used as a platform to develop a multitude of nanoscale bioanalytical sensors,

for

example

to

detect

biomolecules

using

field-effect

transistor

configurations,16,17 and to measure action potentials across cellular membranes18. More recently, semiconductor nanowires have been applied as cell culturing substrates19, for high-resolution cellular force measurements,20,21 and also to enhance fluorescence-based biomolecule detection.22–27

In particular, due to their high refractive index, semiconductor NWs can be designed to function as nanoscale optical fibers by collecting, guiding and concentrate light from surface-bound fluorophores.24,25,27 It has been shown that a large fraction of the emission


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of a fluorophore placed in close proximity of a NW surface can be coupled into the partially localized waveguide modes of a NW and re-emitted at its tip.24,25,28 Although the fraction of light guided to a NW tip depends on fluorophore emission wavelength and NW diameter,27 the in-coupling is expected to be independent of the fluorophore position on a uniform NW,24,27 and hence these nanostructures act as signal integrators, collecting the emission light from all fluorophores on their surface and re-emitting it in a single focal plane at the NW tip.

Here we explore if these light-collecting and -guiding properties of NWs can be used to detect individual biomolecules bound to a laterally fluid supported lipid bilayer (SLB) formed such that it extends on both free-standing NWs and the substrate in between them. NWs stand perpendicularly on the substrate and their diameter is smaller than the diffraction limit of visible light, making them appear as diffraction limited dots when observed with an optical microscope. Therefore, a fluorescent molecule diffusing on the SLB on the NW surface will effectively move only vertically, along the axis of the NW. This means that its fluorescent emission will be guided to the tip of the NW regardless of its


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vertical position and movement between different focal planes. We hypothesized that this effect should lead to a localization enhancement of the emission, located at the tip of the NW and therefore in a fixed focal plane and at a fixed lateral position (Fig. 1 a,b). Further, because the focus depth of high numerical aperture (NA) objectives is typically shorter than the NWs length (~5 µm), molecules diffusing in the SLB on the substrate between the NWs should remain out of focus and thus escape detection by the microscope (Fig. 1 b,c). Together, this is expected to cause the NW tip to appear significantly brighter than the surrounding areas if there are fluorescent species on their surface, thus increasing the chance to detect individual fluorescent molecules compared with a corresponding measurement performed on a planar substrate (given identical illumination conditions and signal to noise levels of the imaging system).

This idea is in this work tested and verified by demonstrating how individual, lipid-bound fluorescent proteins diffusing on and off NWs cause the wires to light up for short periods, leading to ‘blinking’ over time. We show how the detection of such blinking events with a conventional epifluorescence microscope is aided by a combination of the aforementioned


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lightguiding and localization enhancement phenomena. Further, as the average field of view of a standard microscope objective can encompass hundreds of individual NWs, the simultaneous time-resolved monitoring of these blinking events allows for parallel data collection, which, with the help of statistical analysis, makes it possible to determine both surface concentration and diffusion coefficient of these molecules employing shorter acquisition times (~ 10 sec) than are typically required in FCS using a single read-out spot. Due to the highly spatially-localized signal provided by NWs, the experimental approach

presented

here

offers

single-molecule

detection

using

conventional

epifluorescence microscopy, trading the requirement for a highly sensitive system (often necessary for single-molecule detection schemes) for that of a nanostructured sample surface. As this approach requires only very low concentration of fluorescent species (comparable to what is required for SPT), and can be performed at relatively long (> 100 ms) exposure times, it could prove useful in case of low-brightness dyes or when a highend optical setup is not desirable, such as in the context of miniaturization and automation of the fluorescence readout. A more detailed comparison of different diffusion-measuring techniques is given in Supporting Information.


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As model system to test the concept, we make use of a well-established system composed of fluorescently labelled cholera toxin subunit B (CTxB) bound to GM1 gangliosides in a SLB, and demonstrate how the surface concentration and diffusivity of the CTxB-GM1 complexes can be determined. We also investigate how the diffusivity was influenced by varying the GM1 content in the SLB, and compared the results with previously published reports on how multivalent CTxB binding to GM1 influence the diffusivity.29,30 We also explore the robustness of the analysis to the inevitable effect of photobleaching by compared the diffusivity determination for slow- and fast-bleaching dyes. Based on the outcome of these investigations, the advantages and limitations of this new, single-molecule based detection concept are discussed in the context of alternative methods used to determine diffusivity, such as FRAP, SPT and FCS, as well as applications going beyond pure model systems, such as live cell studies. In the forthcoming sections, we first give a detailed description of the experimental design that made it possible to detect single CTxB-GM1 on individual NWs, followed by a summary of the analytical model used to fit the experimental data, and the detailed insights gained with respect to surface concentration and biomolecular diffusivity.


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Sample preparation and imaging

GaP NWs were grown on a (111)GaP substrate via metalorganic vapour-phase epitaxy (MOVPE) seeded by 50 nm Au nanoparticles that were randomly deposited with a density of approximately 0.35 µm-2.31 The two batches of NWs used in this study were grown (i) axially to a length of 3.7 ± 0.1 µm and then radially to a diameter of 130 ± 5 nm and (ii) to a length of 4.0 ± 0.1 µm and a diameter of 105 ± 5 nm, respectively. Both NW samples exhibit lightguiding properties for the particular fluorophore wavelengths used in this study.27 All samples were coated with ~10 nm of SiOx via atomic layer deposition (ALD) to facilitate SLB formation32 (see Supporting Information). The NW substrates were imaged in epifluorescence using either a 100× or a 60× water dipping objective (NA 1.0), an ORCA-Flash4.0 V2 Digital CMOS Hamamatsu camera (~80% QE in the considered wavelength range) and a HP Hg lamp was used for illumination. Prior to SLB formation, no auto-fluorescence could be detected from the NWs. Because of the relatively large spacing between NWs (~1.7 µm on average), individual NWs could easily be resolved in


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brightfield mode (Fig. 1d). Imaging was carried out through a field diaphragm to enhance the signal-to-background ratio,33 which also resulted in an effectively reduced imaging area of circular shape with radius approximately 18 µm for the 100× objective (~1000 µm2 or ~300 NWs) and 33 µm for the 60× objective (~3500 µm2 or ~1300 NWs).

Figure 1. Principle of detection by lightguiding NWs. (a) Zoom-in of the sample surface: GaP NWs are grown on a GaP substrate and coated with 10 nm of SiOx. On the SiOx surface, a POPC SLB is formed that extends over both the flat substrate and the NWs. GM1 gangliosides, bound to dye-labelled CTxBs, diffuse in the SLB. (b,c) Light emitted from a CTxB diffusing on a NW is coupled into the NW and re-emitted at its tip, independently of the molecule’s position on the NW. CTxBs freely moving on the substrate surface between the NWs are out of focus (grey shaded area) and their emission will not be coupled into the NWs. (d) NW sample observed in brightfield. (e) The same NW sample observed in epifluorescence (FITC, 500 ms


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exposure time), with dye labelled CTxB bound to GM1 on the NWs surface (0.25 w% of GM1) demonstrating that the fluorescent spots in (e) are co-located with the brightfieldNWs positions in (d).

SLB was formed on the silica-coated NW samples via adsorption and subsequent rupture of unilaminar POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) vesicles (approximately 100 nm in diameter) suspended in phosphate buffered saline (PBS) and containing different GM1 fraction (see Supporting Information).34,35 After SLB formation, the sample was rinsed and incubated for 10 min with fluorescently labelled CTxB (~100 nM), resulting in CTxB binding to GM1 under stagnant conditions. Two different fluorescent labels were used in this study, one highly prone to photo-bleaching (CTxBFITC from Sigma-Aldrich) and another brighter and more photo-stable variant (CTxBCF488A from Biotium). Both dyes absorb in the blue regime and emit at similar wavelengths in the green. The CTxB incubation process was monitored in real-time at low frame rates to minimize bleaching, resulting in increased brightness of the NW until the signal saturated at equilibrium (Fig. 1e). After removal of unbound CTxB from the solution via rinsing with PBS, the mobility of GM1-bound CTxB both on the surface of the substrate


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(between NWs) and on the NWs themselves was confirmed by performing FRAP (see Supporting Information).

Evaluation of the detection limit

For bilayers formed with vesicles containing 0.25 w% GM1, all individual NWs appeared clearly brighter than the background and could be easily resolved (Fig. 1e). To explore the detection limit of the system, we progressively reduced the nominal content of GM1 content in the SLB from 0.25 w% down to 0.00008 w% (Tab. 1) and to avoid photobleaching, only a single image frame of the sample was acquired after CTxB exposure. As expected, the average fluorescence signal generated on the NWs decreased with decreasing GM1 content, which is consistent with a reduction of binding sites for labeled CTxB (Fig. 2a). A decrease in the number of bright NWs was also observed for decreasing GM1 content (Fig. 2b), which was attributed to a reduction in the probability of a given NW to have a GM1 on its surface. Since both nanowire surface area and the area of a single POPC lipid36 are known (we use the area per lipid obtained for a flat membrane, as the effect of curvature is expected to be small, see Supporting


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Information), the expected average number of GM1 lipids per NW can be estimated from the GM1 nominal content in the SLB (see Tab. 1). Bright NWs were also observed at extremely low GM1 content ( < 0.00008 w%), where one would expect to have less than one GM1 molecule per NW on average (see Tab. 1). Since CTxB has to bind to at least one GM1, the probability of two CTxB molecules being on the same NW at the same time is very low at these conditions, suggesting that most of the bright NWs were indeed bright because of the presence of a single GM1-bound CTxB on their surface.


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Figure 2. (a) Average fluorescence signal of bright NWs in the field of view, for samples functionalized with FITC-CTxB, versus GM1 content in the SLB. The grey dashed line represents the background value detected at the lowest GM1 content plotted (0.00008 w%); the background detected on a sample with 0 w% GM1 showed a similar value. (b) Fraction of bright NWs in the field of view as function of GM1 content for samples functionalized with FITC-CTxB and CF488A-CTxB.


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Nominal GM1

Nominal GM1

Expected average

Measured % bright

content (w%)

surface

number of GM1

NWs

concentration (µm-

per NW

2)

0.25

1.8 · 103

3.3 · 103

100

0.05

3.8 · 102

6.7 · 102

100

0.01

7.6 · 101

1.3 · 102

100

0.006

4.5 · 101

8.0 · 101

92±13

0.002

1.5 · 101

2.7 · 101

76±10

0.0004

3.0 · 100

5.3 · 100

58±8

0.00016

1.2 · 100

2.2 · 100

36±5

0.00008

0.6 · 100

1.1 · 100

19±5

0.000032

0.2 · 100

0.4 · 100

7±4

0.000016

0.1 · 100

0.2 · 100

3±1

(no GM1) 0.0

-

0

1±1

Table 1. Nominal GM1 content in the SLB, the corresponding nominal surface concentration, the expected average number of GM1 per NW and the measured fraction of NW appearing bright for each GM1 content.

At a GM1 content below 0.002 w%, time-sequence acquisitions (𝑡exp = 200 ms, 5 frames/s) revealed a decrease in the number of bright NWs with time (Fig. 2b). However, some NWs displayed random, momentary increases in brightness, even several seconds after the start of the imaging acquisition. These two observations can be attributed to two competing dynamic processes, namely (i) the overall decrease in number of bright NWs over time due to photobleaching and (ii) the blinking of individual NWs due to GM1-bound


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CTxB diffusing back and forth between the NWs and the SLB-coated substrate supporting the NWs. These two competing processes result in dark NWs turning bright due to diffusion of non-bleached GM1-bound CTxB from the substrate to their surface, and bright NWs turning dark due to either GM1-bound CTxB diffusing off the NW surface or bleaching of the fluorophore.

By establishing the exact position of each NW on the surface using brightfield imaging (left inset in Fig. 3a), the fluorescence signal emitted by each NW (right inset in Fig. 3a) was tracked over time (Fig. 3b), determining in which frames the NW was bright and in which not. This information was then translated into a map showing all the detected blinking events as a function of time (Fig. 3c). In the case of significant photobleaching, the fraction of bright NWs (number of bright NW divided by the total number of NW) at any given moment decreased rapidly with time (green curve in Fig. 3d). However, the photobleaching rate heavily depends on the type of fluorophore used. In our experiments the FITC-labelled CTxB were completely photobleached after about 10 s, while CTxB labeled with the brighter and more photostable CF488A, resulted in NWs remaining bright


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even after several minutes of exposure (see Supporting Information). The fast bleaching observed for FITC is possibly a side-effect of the in-coupling of the excitation light in the NWs,25,37 which results in an enhanced electromagnetic field at the NW surface that can enhance the fluorescence emission rate at the expense of faster photobleaching, similarly to what is observed for plasmonic nanostructures.14,38

Since the field of view of the microscope encompasses several hundred NWs, each single NW can be used as an individual detection site. In the regime of very low GM1 content (< 5 CTxB per µm2) information about both the surface concentration and diffusivity of GM1-bound CTxB molecules in the SLB can, as described in the forthcoming section, be extracted on the basis of some fundamental considerations: As the average surface area of the NWs is known, the surface concentration can be deduced from the number of bright NWs in the first frame of a time acquisition (at 𝑡 = 0, before bleaching becomes relevant) while the diffusivity can be extracted from the variation in the number of bright NWs over time.


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Figure 3. (a) Overlay of NW positions detected in bright field (black dots) and observed blinking events detected in epifluorescence (green dots), on a SLB containing 0.0008% GM1. Events in epifluorescence were detected over a 12 s long acquisition period (200 ms exposure time, 5 frames/s). The greyscale inset shows a bright-field image of all NWs found within the field of view while the green-scale inset shows corresponding fluorescence signal from the same area at 𝑡 = 0. Each detected event can be spatially correlated to the exact position of a NW in the greyscale image. See movie 3 for the original acquisition (before processing). (b) Examples of fluorescence intensity vs. time profiles from four NWs highlighted with a red circle in (a). The profiles display an increase and subsequent decrease in fluorescence signal (blinking


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event) at some point during the acquisition, due to GM1 diffusing onto the NWs and subsequently off (or photobleaching). The red dotted lines indicate the detection threshold used in the analysis. (c) Fluorescence signal above threshold as a function of time obtained from the NW profiles; each row in the image represents a single NW, describing if it was bright (coloured) or not (white) at a certain time. Events that had already started at 𝑡 = 0 (i.e. NWs being bright since the beginning of the acquisition) are shown in blue; events that started after 𝑡 = 0 are labelled in red. Horizontal lines in green highlight the specific examples shown in (a) and (b) as indicated. (d) Fraction of NW that are bright at any time during the acquisition (the total number of NWs in the field of view can be extracted from a brightfield image in (a)). 𝐹1 (blue data) represents NWs that were bright continuously since 𝑡 = 0. 𝐹2 (red data) is the fraction of NWs nanowires turned bright at 𝑡 > 0 and 𝐹br = 𝐹1 + 𝐹2 (green data). 𝐹1and 𝐹2were calculated by summing over each frame (i.e. vertically) the data from (c).

Theoretical analysis

The temporal evolution of the number of bright NWs can be represented with an analytical model, which was derived on the basis of some fundamental assumptions. Since single CTxB-GM1 complexes can be detected on the surface of the NWs, we consider that a NW appears bright in a frame if it has at least one GM1-CTxB complex on


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its surface for the majority of the frame-exposure time. In order to extract information from the blinking behavior of the NWs observed at low GM1 content, the detected blinking events, i.e. a NW being bright at a certain point in time, 𝑡, were divided into two groups, in the following denoted by subscripts 1 and 2. Group 1 contains events where emission from a NW was detected continuously from 𝑡 = 0 until a certain 𝑡 > 0 (shown in blue in Fig. 3c). Group 2 contains instead all other detected events, i.e. those that were initiated at 𝑡 > 0 (shown in red in Fig. 3c). Because the total number of NWs in the field of view is known from brightfield imaging and the number of bright NWs is evaluated in each frame, the fraction of bright nanowires belonging to each group, 𝐹1(𝑡) and 𝐹2(𝑡), can be calculated as a function of time, shown as blue and red curves, respectively, in Fig. 3d. Physically, these fractions can be identified with the probabilities, 𝑃1(𝑡) and 𝑃2(𝑡), for a NW to be bright and belonging to the corresponding group. More specifically, 𝑃1(𝑡) can be defined as the probability at time 𝑡 for a NW to have had at least one GM1-bound CTxB continuously on its surface since 𝑡 = 0, and 𝑃2(𝑡) as the probability at time 𝑡 for a NW to have at least one GM1-bound CTxB on its surface, while not having had one continuously since 𝑡 = 0. The analytical expressions given below for these probabilities (for the


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mathematical derivation, see Supporting Information) can then be used to fit 𝐹1(𝑡) and 𝐹2 (𝑡) and thus used to determine surface concentration and diffusion coefficient of GM1bound CTxB.

Mechanistically, 𝑃1(𝑡) and 𝑃2(𝑡) are determined by the interplay of the diffusion and photobleaching of CTxB-GM1 complexes on NWs. At a GM1 content of less than < 0.5w%, the GM1 molecules are expected to diffuse independently from one another.39 For this reason, at 𝑡 = 0, GM1-bound CTxB are distributed randomly on the sample, and the probability of a NW having at least one GM1-bound CTxB on its surface can be obtained using the Poisson distribution. By definition, at 𝑡 = 0 all bright NWs belong to Group 1 and one obtains

𝑃1(0) = 1 ― exp ( ― 𝑛1(0))

and

𝑃2(0) = 0

(1)

where 𝑛1(0) = 𝑐0 𝑆NW is the average number of GM1-bound CTxB per NW at 𝑡 = 0, with 𝑐0 being the surface concentration of GM1-bound CTxB on the sample and 𝑆NW the surface area of a NW.


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In general, the time evolution of 𝑃1(𝑡) and 𝑃2(𝑡) depends on the detailed dynamics of diffusion and bleaching, which are not explicitly described by the Poisson distribution alone. However, with proper specification, the Poisson distribution can be used to approximate both 𝑃1(𝑡) and 𝑃2(𝑡) if the average number of GM1-bound CTxB per NW is small and their diffusion on and off the nanowires is slow with respect to the frame rate of the acquisitions.

In order to evaluate the timescale of GM1-bound CTxB diffusion on NWs, we approximate the NWs used in our experiments as cylinders of radius 𝑅 = 60 ― 75 nm and length 𝐿 = 3.7 ― 4.0 µm (hence 𝑆NW≅2𝜋𝑅𝐿), standing perpendicularly on a flat substrate. Assuming the diffusion constant of a GM1-bound CTxB in the SLB to be approximately 𝐷≅2 µm2 s-1,29 the timescale of diffusion perpendicular to a cylinder axis is:

𝜏⊥≅

4𝑅2 ≅ 10 ―2s 𝐷

(2)

As this timescale is very short, diffusion in this direction becomes effectively negligible, and hence, diffusion on a NW surface can be approximated as one-dimensional (1D) along a cylinder axis. The mean residence time of a single GM1-bound CTxB on a 1D


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wire of length 𝐿, assuming random distribution along the wire length, is (see e.g. Ref. 40 or Eq. 5 below):

𝜏∥ =

4𝐿2 𝜋2𝐷

≅3 s

(3)

The derivation of this expression is based on the solution of the diffusion equation with the absorbing boundary condition at the foothold of the NW.

Because: (i) at low GM1 concentrations the average number of GM1-bound CTxB per NW is small and (ii) the average residence time on a NW is much longer than the exposure time for a frame (200 ms), the evolution of 𝑃1(𝑡) is primarily determined by the bleaching rate of the GM1-bound CTxB that have been on the NWs since 𝑡 = 0, and by their diffusion from the NWs to the substrate. Under these conditions, 𝑃1(𝑡) can be approximated using the Poisson distribution as

𝑃1(𝑡) = 1 ― exp ( ― 𝑛1(𝑡))

(4)

where 𝑛1(𝑡) is the average number of non-bleached GM1-bound CTxB per NW at a given 𝑡 that have been on the NW continuously since 𝑡 = 0. By solving the diffusion equation


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and imposing the appropriate absorbing boundary conditions at the NW foothold (see Supporting Information), this number can be calculated as

∞

[(

8 exp ―

𝐷𝜋2(1 + 2𝑗)2 4𝐿2

)]

+𝑘 𝑡

)]

(5)

𝑃2(𝑡) = [1 ― 𝑃1(𝑡)] ∙ [1 ― exp ( ― 𝑛2(𝑡))] = exp ( ― 𝑛1(𝑡)) ∙ [1 ― exp ( ― 𝑛2(𝑡))]

(6)

𝑛1(𝑡) = 2𝜋𝑅𝐿𝑐0

∑ 𝑗=0

𝜋2(1 + 2𝑗)2

[(

≅ 2𝜋𝑅𝐿𝑐0 exp ―

𝐷𝜋2 4𝐿2

+𝑘 𝑡

where 𝑘 is the photobleaching rate constant.

In turn, 𝑃2(𝑡) can be estimated as

In this expression, the former term, 1 ― 𝑃1(𝑡) or exp ( ― 𝑛1(𝑡)), simply represents the probability that a NW does not belong to Group 1. The second term, [1 ― exp ( ― 𝑛2(𝑡))], is the probability that such a NW contains at least one non-bleached GM1-bound CTxB. 𝑛2 (𝑡) is the average number, per NW at a given time, of non-bleached CTxB-GM1 complexes that have not been continuously on the NW since 𝑡 = 0. The expression 1 ― exp ( ― 𝑛2(𝑡)) is an approximation based on the assumption that the CTxB-GM1 distribution on NWs belonging to Group 2 is also close to a Poissonian. This approximation is justified by the fact that (i) at the initial stages of the acquisition, 𝑛2(𝑡) is primarily


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determined by CTxB-GM1 diffusion from the substrate onto dark NWs and that, (ii) at late stages the number of NWs belonging to Group 1 is small (as this number decreases over time by definition).

Regarding the estimation of 𝑛2(𝑡), we first notice that 𝑛2(0) = 0, since by definition all GM1-bound CTxB on the NW at 𝑡 = 0 belong to 𝑛1(𝑡). At 𝑡 > 0 CTxB-GM1 complexes on the substrate can diffuse on the NWs, so in the initial period, 𝑛2(𝑡) will increase consistently over time. By assuming the initial period being short and by neglecting the effect of photobleaching (𝑘≅0) and imposing 𝑛2(0) = 0, the initial number of events belonging to group 2 (𝑛in 2 (𝑡)) can be calculated as:

𝑛in 2 (𝑡) = 4𝑅𝑐0 𝜋𝐷𝑡

(7)

The full solution for 𝑛2(𝑡), which depends on the interplay between diffusion and bleaching, can only be obtained numerically, because the approximation 𝑘≅0 is only valid for the first few frames. However, further insight can be gained if we focus on the system at its two extremes, where either bleaching or diffusion dominate, as also aimed for in the design of our experiments.


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The bleaching-dominated regime (in the following identified by a superscript B) is 𝐷𝜋2

realized provided bleaching being appreciably faster than diffusion along a NW (𝑘 ≫ 4𝐿2 ). In this case, the probability that a GM1-bound CTxB leaves a NW before being photobleached becomes negligible and 𝑛1(𝑡) is described only by bleaching, with Eq. 5 reducing to:

𝑛B1(𝑡)≅2𝜋𝑅𝐿𝑐0exp( ―𝑘𝑡)

(8)

In this limit, an analytical expression for 𝑛2(𝑡), after the initial transient period, can be obtained by solving the reaction-diffusion equation in the steady-state approximation (under the reasonable assumption that 1D diffusion along a NW is not only slower than photobleaching, but also than 2D diffusion on the substrate). This yields:

𝑛ss 2 (𝑡) = 2𝜋𝑅𝑐0 𝐷/𝑘 ∙ exp( ―2𝜋𝑅𝑐NW 𝐷𝑘𝑡)

(9)

where 𝑐NW is the number of NW per unit area of the substrate, and the superscript ss stands for steady-state. A reasonable approximation for 𝑛B2(𝑡) is to use the smallest value between 𝑛2ss(𝑡) and 𝑛in 2 (𝑡):


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𝑛B2(𝑡) =

{

𝑛in 2 (𝑡) ss 𝑛2 (𝑡)

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ss for 𝑛in 2 (𝑡) < 𝑛2 (𝑡) for 𝑛2ss(𝑡) < 𝑛in 2 (𝑡)

(10)

The diffusion-dominated regime (identified by a superscript D) is realized in the opposite 𝐷𝜋2

case, i.e. provided 𝑘 ≪ 4𝐿2 . Here, the probability that a GM1-bound CTxB diffuses from a NW to the substrate without being photobleached is high. In this case 𝑛D1(𝑡) is determined primarily by the diffusion process and Eq. 5 reduces to:

𝑛D1(𝑡)≅2𝜋𝑅𝐿𝑐0

(

)

𝐷𝜋2 exp ― 2 𝑡 4𝐿

(11)

The estimate of the mean residence time 𝜏 ∥ for a CTxB-GM1 complex on a NW can help to understand the relative role of diffusion and bleaching and to determine whether the bleaching-dominated or the diffusion-dominated model is better suited to interpret experimental data. At a GM1 content of 0.00008 w% and in the case of (photosensitive) FITC-labelled CTxB, the observed average duration of the blinking events in Group 1 (i.e. how long a NW that is bright at 𝑡 = 0 stays bright) was less than a second, which is about three times less than the estimated 𝜏 ∥ , indicating that in these experiments photobleaching had a timescale appreciably shorter than diffusion. Vice versa, for samples labelled with (photostable) CF488A-CTxB at the same GM1 content the average


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duration was about 3 s (same as 𝜏 ∥ ), indicating that in these experiments the photobleaching rate was considerably slower than that of diffusion. The value of the photobleaching constant was evaluated in both cases during the analysis, verifying the correctness of these assumptions.

Data fitting

Given the analytical model, CTxB-GM1 concentration and diffusivity was estimated by fitting the experimental data: as the geometry of the NWs in each sample can be precisely determined via electron microscopy, the only unknown parameters in the analytical expression for 𝑃1(𝑡) and 𝑃2(𝑡), described by Eqs. 1-10, are 𝑐0, 𝑘, and 𝐷. The surface concentration, 𝑐0, can be directly evaluated from the first frame of the acquisition by Eq. 1, via

𝐹1(0) = 𝑃1(0) = 1 ― exp( ― 2𝜋𝑅𝐿𝑐0)

or

𝑐0 = ―

log (1 ― 𝐹1(0)) 2𝜋𝑅𝐿

(12)

Given 𝑐0, 𝑘 and 𝐷 can then be determined through knowledge of whether the experiment was conducted in the bleaching- of diffusion-dominated regime.


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In case of fast bleaching (FITC-CTxB), 𝑘 can be estimated by first fitting 𝐹1(𝑡) with 𝑃1

[𝑛B1(𝑡)] (combining Eqs. 4 and 8), with 𝑘 being the only dependent variable of the fit. Then, with 𝑐0 and 𝑘 given, 𝐷 can be estimated by fitting 𝐹2(𝑡) with 𝑃2[𝑛B2(𝑡)] (combining Eqs. 6 and 10), which leaves 𝐷 as the only unknown variable for the fit. Assuming 𝐷≅2 µm2 s-1, we expect

𝐷𝜋2 4𝐿2

≅0.3 s-1, which is more than four times smaller than the photobleaching

constant, 𝑘≅1.3 s-1, measured in this case. In other words, in this case the average photobleaching time on the NWs is approximately five times smaller than the average residence time 𝜏 ∥ .

For the diffusion-dominated case (CF488A-CTxB), 𝐷 can be estimated by fitting 𝐹1(𝑡) with 𝑃1[𝑛𝐷1 (𝑡)] (combining Eqs. 4 and 11). Alternatively, since bleaching is considered negligible, 𝐷 can be independently estimated by fitting 𝐹2(𝑡) with 𝑃2[𝑛in 2 (𝑡)] (combining Eqs. 4 and 7). Examples of these fits are given in Figs. 4a and b. The value of 𝑘 can be estimated by observing the bleaching over time of CTxB aggregates that sometimes deposited on the sample surface. In order to ensure that the CF488A system was well represented by the diffusion-dominated case, it was observed at a lower illumination


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intensity than those samples labelled with FITC, resulting in 𝑘≅0.02 s-1, about 10 times smaller than the expected value of

𝐷𝜋2 4𝐿2

, confirming that in this case the photobleaching

process was very slow compared to the average residence time 𝜏 ∥ .

Figure 4. (a) Example of renormalized least-square fit of the fraction of bright NWs 𝐹1(𝑡) (blue) and 𝐹2(𝑡) (red), acquired from a sample labelled with FITC-CTxB. As FITC bleaches relatively fast, the probability of a GM1 molecule to diffuse from a NW to the substrate is low, meaning that the bleaching-dominated approximation applies in this case. (b) Example of renormalized least-square fit of the fraction of bright NWs 𝐹1(𝑡)(blue) and 𝐹2(𝑡)(red), acquired from a sample labelled with CF488A-CTxB. CF488A bleaches at a considerably slower rate than FITC, and the diffusion-dominated approximation applies in this case.


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In every case, the measured value for 𝑐0 corresponded to about 20-25% of the nominal GM1 content used in the sample, which is attributed to the fact that the concentration of CTxB employed to label the sample (~100 nM) and the incubation time (~20 minutes) were not sufficient for CTxB to bind to all GM1 in the SLB.41 Importantly, the relation between nominal GM1 and measured GM1-bound CTxB surface concentration is to a good approximation linear in the measured GM1 content range (Fig. 5a), and data from the experiments done with FITC- and CF488A-labelled CTxB are in good agreement with each other. The diffusivity measured for GM1-bound CTxB surface concentrations lower than 0.2 µm-2 (0.00008w% GM1 content or less ) was 2 µm2 s-1 (Fig. 5b), which is within the range of previously measured values for GM1-bound CTxB at low GM1 content in POPC-based SLBs.29 Interestingly, at increasing GM1 concentrations the diffusivity decreased, which we attribute to binding of single CTxB to multiple GM1 gangliosides (up to five GM1 molecules can bind to a single CTxB).29,30 At GM1 contents 5 times higher (0.0004w%) the measured diffusivity was 4 times lower, which would indicate multivalent binding of CTxB to GM1 with the diffusion coefficient inversely proportional to the number of bonds.42


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Figure 5. (a) Measured GM1-bound CTxB surface concentration 𝑐0 versus the nominal GM1 surface concentration in the samples. The measured surface concentrations are consistently 4-5 times lower than the nominal ones, likely because not all GM1 molecules are bound to CTxB. (b) Measured diffusivity 𝐷 versus the nominal GM1 surface concentration. The diffusivity for CF488A-labelled samples was calculated by fitting 𝐹1(𝑡) using the diffusion-dominated model, while for FITC-labelled samples by fitting 𝐹1(𝑡) and 𝐹2 (𝑡) using the bleaching-dominated model. Error bars represent standard deviation based on multiple measurements.


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Discussion and conclusions

The ability of NWs to both collect and guide light, in combination with a thorough statistical analysis were here used to devise a novel analytical method to simultaneously determine concentration and diffusion constant of molecules in a supported lipid bilayer. The presented approach is applicable using a standard epifluorescence microscope, and while it requires an epitaxially grown nanowire sample, it can provide an estimate of surface concentration and diffusivity with a single, short experiment (total acquisition time ~10 s), without the need for extensive hardware and / or data processing. By simultaneous monitoring of hundreds of NWs in a single field of view, we have characterized the diffusion of GM1-bound CTxB in a SLB and demonstrated how the effect of photobleaching can be accounted for in the analysis, making the method viable for different types of fluorescent dyes. Indeed, with the analytical formulations used, it was possible to determine the diffusivity with different fitting approaches, which all yield similar estimates of 𝐷, as further discussed in Section 4 of the Supplementary Information. The


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𝐷 values measured for samples with low ( ≤ 1 µm-2) GM1 coverage are in good agreement with previous measurements on CTxB-GM1 complexes at similar, or lower, GM1 coverages,29 while the values obtained for ‘high’ GM1 coverages ( > 1 µm-2) are instead consistent with literature data obtained at considerably higher GM1 content.30,43,44 This variation in CTxB-GM1 diffusivity at different GM1 content is generally attributed to multivalent binding, since each pentameric CTxB can bind up to 5 GM1, causing the complex to diffuse significantly slower41 than monovalently-bound CTxB.45 However, the more than fourfold decrease in diffusivity upon an increase the GM1 content from ~0.5 to ~2.5 µm-1 is larger than expected for this fairly small variation in GM1 content, but still tentatively attributed to the ability of CTxB-GM1 clusters to form different populations with diffusivities in the range observed by us,42,46 or lipid raft induced aggregation,47 although these observations were all made at higher GM1 contents. Although these measurements were not performed on a flat SLB, the relatively large NW radius compared with the molecular dimensions of the lipids and proteins suggests that the curvature does not have a significant effect on the diffusivity (see Supporting Information). Our results thus demonstrate that the approach is well suited for analyzing the diffusivity of surface-bound


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molecules at low surface concentrations, and thereby provides a complement to existing techniques, in particular SPT and FCS. However, the advantages that we have put forward comes with certain limitations. In essence, the main difference is that the requirement for confocal optics and/or highly sensitive detectors is replaced by a need for specifically designed NW sample, which our concept shares with many nanostructureaided bioanalytical detection schemes, such as zero mode waveguide- or antennaenhanced FCS.13,14 Further, while our approach lacks the versatility of FCS, which can be used in vivo as well as in vitro using a wide range of dye concentrations, it does not require volume calibration measurement and works optimally at coverages which are lower than those that are optimal for FCS. For confocal volumes typically used in FCS, the lowest surface coverage of fluorescent tracers required for detection of sufficient numbers of independent events is around 10 µm-2 (a molar ratio of about 10-5),5 with 1 µm-2 typically being the typical lower limit,48 while the upper limit being approximately two order of magnitude higher (10 µm-2).49 In our case there should ideally be on average around 0.1 to 4 molecules per NW, since at higher coverage all NWs appear continuously bright and at lower, it becomes difficult to observe a statistically significant number of blinking events.


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For the NW size used in this work, this translates to an optimal surface concentration range between 3.5 and 0.05 µm-2, which is similar to the surface concentration typically used in SPT experiments.48 In comparison with SPT one should also bear in mind that each SPT trajectory must be computed individually, which requires long acquisition times and extensive image analysis to generate statistical significance, while with our approach it is sufficient to detect hundreds of events in a time window of a few seconds. This means that our method can become useful in many biologically relevant concentration ranges, since membrane-bound molecules tend to be expressed in very low copy numbers.50 This would be particularly relevant in applications with cellular assays, having the cell resting on top of standing NWs,51,52 or by forming supported lipid bilayers from near native vesicles,53 possibly making feasible the determination of membrane-protein diffusivity at endogenous concentration levels of membrane proteins. Still, it is indeed the individual analysis of each diffusing particle that makes SPT such an attractive technique, especially in the context of live cell imaging, since it can allow discrimination of subpopulations with fairly small differences in diffusivity. This is not easily possible with ensemble average techniques such as FRAP and FCS, which are restricted to discriminate differences in


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diffusivity on an order of magnitude or larger. It is in this context interesting to note that the autocorrelation function used for FCS scales as 𝑡 ―1, while the analytical functions used for analyzing the NW blinking scale as exp ( ― 𝜅𝑡). Although beyond the scope of this work, this suggests a higher sensitivity for the detection of subpopulations since a stronger time dependence makes it easier to resolve diffusivity values close to each other (in other words, a faster function decay over time means the contribution of a slowdiffusing specie overshadows less that of a fast one).

Finally, although our quantitative diffusivity determinations are in good agreement with previous SPT and FCS estimates, it is worthwhile to keep in mind that our analytical treatment is based on the assumption that the system is either in a bleaching or in a diffusion dominated regime. While the use of analytical expressions is preferable in proofof-concept studies, as they provide a straightforward and transparent way to present and discuss the approach, the potential limitations imposed by the approximations used can be overcome by solving the reaction-diffusion equation numerically, thus taking into account factors such as bleaching on the substrate in between the NWs, lateral diffusion


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on NWs and diffusion from outside the field of view. This would be particularly helpful in case of slow photobleaching, since data can in that case be collected over much longer times ( > 100 s), providing better statistics, but which cannot be fitted with the current model (see Supporting Information). However, depending on the type of dye used, one could potentially tune the geometry of the NW substrate to better fit one of the regimes (the mean residence time of a molecule diffusing on a NW depends on the NW length). More information could also be extracted by further refining the statistical analysis: for example, the diffusivity of a molecule on the surface of a NW could be directly evaluated via its mean residence time, which could also possibly allow for the simultaneous detection of multiple species that exhibit different diffusion behavior, or to probe the effect of highly curved NW surfaces on diffusion.54 The analytical model used to fit the data could also be adapted to measure binding kinetics, having one specie bound to the NW surface and the other, fluorescently labeled, diffusing freely in solution. The sensitivity of the system could also be enhanced by using a more sensitive camera, or by achieving directional emission from the NWs tip,55 maximizing the number of photons collected by the objective. Given the significant room for further improvement of this proof-of-principle study, with respect


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both to sensitivity and analytical precision, and the potential applicability of the method in numerous bioanalytical sensor applications, make us believe that the method can become an attractive complement to alternative methodologies used for concentration and diffusion analysis of cell membranes and mimics thereof.

Acknowledgements For financial support, we thank NanoLund, the Swedish Research Council (project number

2015-0612),

the

European

Union’s

Seventh

Framework

Programme

(PhD4Energy, grant agreement n° 608153), and the Crafoord Foundation. We thank Dr. Stephan Block for helpful discussions.

Supporting Information Supporting Information Available: details on nanowire fabrication, lipid bilayer deposition, imaging, formulation of the analytical model and derivation of the corresponding equations, comparison of results obtained with different fitting approaches, role of lipid


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bilayer curvature, example of data acquired in a long acquisition, and a detailed comparison of different techniques for measuring diffusion in lipid bilayers. Four movies are

included,

demonstrating:

bilayer

formation,

fluorescence

recovery

after

photobleaching, and NWs blinking for two different fluorescent dyes. This material is available free of charge via the Internet at http://pubs.acs.org.

References

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5. Macháň, R. & Hof, M. Lipid diffusion in planar membranes investigated by fluorescence correlation spectroscopy. Biochim. Biophys. Acta 1798, 1377–1391 (2010). 6. Heinemann, F., Betaneli, V., Thomas, F. A. & Schwille, P. Quantifying Lipid Diffusion by Fluorescence Correlation Spectroscopy: A Critical Treatise. Langmuir 28, 13395– 13404 (2012). 7. He, H.-T. & Marguet, D. Detecting Nanodomains in Living Cell Membrane by Fluorescence Correlation Spectroscopy. Annu. Rev. Phys. Chem. 62, 417–436 (2011). 8. Ortega-Arroyo, J. & Kukura, P. Interferometric scattering microscopy (iSCAT): new frontiers in ultrafast and ultrasensitive optical microscopy. Phys. Chem. Chem. Phys. 14, 15625–15636 (2012). 9. Schoch, R. L., Barel, I., Brown, F. L. H. & Haran, G. Lipid diffusion in the distal and proximal leaflets of supported lipid bilayer membranes studied by single particle tracking. J. Chem. Phys. 148, 123333 (2018).


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