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Quantification of Multivalent Interactions by Tracking Single Biological Nanoparticle Mobility on a Lipid Membrane Stephan Block, Vladimir P. Zhdanov, and Fredrik Höök Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b01511 • Publication Date (Web): 31 May 2016 Downloaded from http://pubs.acs.org on June 5, 2016

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Quantification of Multivalent Interactions by Tracking Single Biological Nanoparticle Mobility on a Lipid Membrane

Stephan Block1,*, Vladimir P. Zhdanov1,2, Fredrik Höök1,*

1

Division of Biological Physics, Department of Physics, Chalmers University of

Technology, SE-412 96 Gothenburg, Sweden 2

Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090,

Russia

*Corresponding authors: Prof. Dr. Fredrik Höök

Dr. Stephan Block

mail: [email protected]

mail: [email protected]

Tel: +46 31 772 61 30

Tel: +46 31 772 33 67

1 ACS Paragon Plus Environment

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ABSTRACT Macromolecular association commonly occurs via dynamic engagement of multiple weak bonds referred to as multivalent interactions. The distribution of the number of bonds, combined with their strong influence on the residence time, makes it very demanding to quantify this type of interaction. To address this challenge in the context of virology, we mimicked the virion association to a cell membrane by attaching lipid vesicles (100 nm diameter) to a supported lipid bilayer via multiple, identical cholesterol-based DNA linker molecules, each mimicking an individual virion-receptor link. Using total internal reflection microscopy to track single attached vesicles combined with a novel filtering approach, we show that histograms of the vesicle diffusion coefficient D exhibit a spectrum of distinct peaks, which are associated to vesicles differing in the number, n, of linking DNA-tethers. These peaks are only observed if vesicles with transient changes in n are excluded from the analysis. D is found to be proportional to 1/n, in excellent agreement with the free draining model, allowing to quantify transient changes of n on the single vesicle level and to extract transition rates between individual linking states. Necessary imaging conditions to extend the analysis to multivalent interactions in general are also reported.

Keywords: multivalent interactions, single particle tracking, TIRF microscopy, free draining model, Saffman-Delbrück-model, transition rates


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The involvement of multiple ligand-receptor links that together ensure firm binding is typical for a multitude of biological processes occurring on the length scale from a few to 100 nm, as for example manifested in the attachment of virions to the membrane of their host cells, a dynamic process that eventually leads to internalization and infection.1-3 Understanding the nature of such multivalent interactions is of high relevance not only to gain basic biophysical insights about underlying biological processes; in depth knowledge of this category could also stimulate new means to inhibit infection at the early stages of viral attachment and/or entry. Further, entry of virions often occurs via endocytosis1,

2

and the involved

receptor-mediated viral diffusion along the membrane is expected to be one of the ways of search of optimal regions for the entry. Understanding receptor-mediated diffusion of pathogens on a membrane is thus of considerable intrinsic interest and forms the basis for understanding the mechanism of pathogen entry.4-6 The factor that complicates quantitative analysis of multivalent interactions is that the individual ligand-receptor association, often a protein-carbohydrate interaction, is typically weak in the sense that multiple ligand-receptor bonds are required to establish an association with sufficient residence time to enable cellular entry,7 and accordingly each bond functions in the transient mode, causing temporal fluctuations of the number of engaged bonds.8 For these reasons, significant efforts have over the past decade been focused on characterizing multivalent interactions on the level of single pathogens, since in this way, heterogeneities and dynamics that are typically hidden in conventional ensemble-averaging approaches can potentially be scrutinized. Among the different methods developed in this area (as recently summarized by Fasting et al.9), approaches based on total internal reflection fluorescence microscopy (TIRFM) and single particle tracking (SPT) proved to be very powerful.8, 10-14 TIRFM enables exploring the interaction of individual virions and 3 ACS Paragon Plus Environment

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virus-like particles with their receptors embedded in supported lipid bilayers (SLBs), yielding information on the association and dissociation kinetics.12 However, due to the heterogeneous nature of the interaction, the number of virion-receptor links could not be quantified from the broad distribution in the measured residence times. By instead utilizing the fact that membrane-bound virions are laterally mobile (even when engaged in multiple bonds), evidence for a wobbling movement was obtained from SPT analysis, suggested to originate from transient binding and unbinding of receptors by virion capsid proteins.8 Although these and other studies have provided valuable insights into virion-membrane interactions, understanding the dynamics of such interactions still remains elusive. In particular, efficient means to determine the number of engaged bonds are lacking, and it remains unknown how the virion diffusivity and this number are related, how fast the number of virion-receptor links changes, and how many receptors are required for cellular internalization.6 Several theoretical models predict that the nanoparticle/virion diffusion coefficient, D, decreases with increasing number, n, of bound receptors,15,

16

which

might in theory appear to allow information to be obtained about the binding dynamics using SPT experiments. However, the predicted dependences of D on n are different, and there is currently no consensus regarding which model applies best to different situations. This is mainly due to the fact that most D histograms lack the occurrence of distinct peaks related to different n,17 which are required to unambiguously extract the dependence of D on n. This feature and the observation of peak broadening led to the conclusion that trajectories may be affected by transient sticking of biological nanoparticles to domains, imperfections or contaminations,18 as observed even for well-defined model systems composed of lipid vesicles tethered to SLBs using amphiphilic DNA linkers.19-21


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Herein, we show that transient sticking and also transitions between different linking states (which are likely to occur in multivalent systems) distort peak structures in D histograms. Based on this insight, we propose a novel generic approach including identification and exclusion of trajectories affected by transient sticking and also transitions between different linking states, which allow direct interpretation of D histograms and quantification of multivalent interactions. As a model for enveloped viruses, we employ small fluorescently labeled unilamellar vesicles linked to a SLB via amphiphilic DNA-tethers. Applying our approach to the corresponding TIRFM movies, we demonstrate the possibility to unambiguously identify distinct peaks in the vesicle D histograms, which could be directly related to subpopulations of vesicles differing by the number, n, of DNA-tethers linking them to the SLB. The identified dependence of D on n is found to be in perfect agreement with the free draining model,15,

22, 23

implying that each linker acts as an independent, non-interacting

anchor. The approach developed also allowed translation of fluctuations of D into transient changes of n with subsequent extraction of the rates of transitions between states with different n. Finally, we discuss the experimental requirements to apply the analysis to other systems with different individual ligand-receptor life times, diffusion coefficients and number of bonds.


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Fluorescently labeled, small unilamellar vesicles (SUV; approximately 100 nm in diameter) were linked to a SLB using cholesterol-modified DNA strands (Figure 1) as described earlier17, 20 and as outlined in Section S10 (Supporting Information). Briefly, the SLB and vesicles were incubated separately with 2 different kinds of DNAstrands, which both carry a double-cholesterol group at one end and a conjugated single-stranded part at the other end (Figure 1a). The double-cholesterol group ensures self-insertion of the strands into the respective lipid bilayers (Figure 1b), while their single-stranded parts have complementary sequences, ensuring specific binding of pre-incubated vesicles to the pre-incubated SLB (Figure 1c). These experiments were performed within a home-made polydimethylsiloxane well (PDMS; volume 10 µL) attached to a glass surface, allowing to form a SLB at the glass interface by injecting a POPC vesicle-containing solution (lipid concentration 0.3 mg/mL, average vesicle diameter approximately 100 nm, exact composition as indicated in Section S10). After washing with buffer, the SLB was incubated with a solution containing SLB DNA-strands (concentration 300 nM), while in parallel rhodamine-labeled POPC vesicles (average diameter approximately 100 nm, exact composition as indicated in Section S10) were incubated with solutions containing vesicle DNA-strands (lipid concentration 0.125 µg/mL, corresponding to a vesicle concentration of 1.3 nM; DNA-strand per vesicle ratio of approximately 3, 6, and 9, as outlined in Section S10). After 30 min of incubation, the SLB was washed again with buffer and incubated with 10 µL of the solution containing DNA-equipped vesicles, which yielded within incubation times of few 10 sec a vesicle surface density on the order of 2 vesicles/100 µm2. Afterward, the well was washed again with buffer and SPT movies were recorded. Since only the cholesterol groups are inserted into the fluid SLB and the bilayer of the vesicles, the latter are able to perform 2D diffusion above the SLB, 6 ACS Paragon Plus Environment

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which was monitored using TIRFM (Figure 1c and Movie S1) with an acquisition rate of 1 / t0 = 5 fps (i.e., with a time of t0 = 0.2 sec between consecutive frames). SPT allowed to investigate the 2D movement for each vesicle independently (representative tracks in Figure 1d), and calculation of the mean square displacement (MSD) as a function of the lag time, t, generally showed a linear time dependence, indicating unconstrained random walks (Figure 1e). We observed that during the course of the measurement the majority of the SLB-linked vesicles were mobile (> 90%) and their detachment was negligible, indicating high linking stability of the DNA-tethers. Still, extraction of individual diffusion coefficients, D, from these MSD curves yielded broad distributions, which only occasionally showed hints for a peak structure (Figure 2a), but were rather, in agreement with most other studies,17, 18 featureless in the majority of experiments (Figure 2b). However, these occasionally occurring peak features motivated a numerical analysis of processes that could potentially distort peak structures in the D histograms. Such processes may include transient sticking of vesicles to imperfections or contaminations,18 as well as transitions between the states with different n, a phenomenon of generic relevance for multivalent interactions between for example a virion and its host membrane. In analogy with the attachment of a virus to a cell membrane, transitions between different states are expected also in our case because the conjugated regions in the middle of the fully hybridized DNAstrand are known to dissociate with rate constants on the order 0.005 s -1.24 Both, sticking and transitions change D in the course of vesicle diffusion, and application of averaging over the whole trajectory therefore results in ill-defined D values, which eliminates any peak structure in the D histogram (Supporting Information section S1),


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even if the measurement accuracy is sufficient to resolve individual peaks in an undisturbed system (Figure S1a, b). With the aim to identify such distorted trajectories in our measurements, an approach was developed that quantifies the fluctuations of the time-resolved diffusion coefficients (Supporting Information section S1). In brief, it is based on a subtrajectory analysis, which applies averaging only to a fraction of the whole trajectory, yielding D for that particular trajectory part. A rolling window approach was then used to shift the analysis window over the whole trajectory, yielding a time-resolved D of the respective trajectory. For an undisturbed 2D random walk with a constant D over the entire trajectory, the time-resolved D is known to fluctuate around the true value with a standard deviation, , given by,25

 D



Np 2  3 N  Np

(for N  N p ) ,

(1)

where N is the number of data points within the rolling window and Np the maximum data point separation used in the internal averaging (i.e., the product of Np and t0 gives the maximum lag time involved in the extraction of D). Equation 1 does not contain any contribution from the localization noise,26 as the acquisition rate 1 / t0 can usually be chosen fast enough so that the stochastic noise (given by Equation 1) exceeds the localization noise. However, if the trajectory exhibits two or more intervals with different D values, the fluctuations of the time-resolved D will originate from the stochastic nature of the random walk and from transitions between states of different D values, causing standard deviations of the time-resolved D that exceed the expectation value given by Equation 1.


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Hence, as higher values of  / D are indicative of a higher probability that the underlying trajectory exhibits a transiently changing D, it is straightforward to exclude all trajectories from the calculation of the D histogram that exceed a certain fluctuation threshold. Application of this filtering strategy to the experimentally obtained D histograms (Figure 2a, b) indeed revealed a distinct peak spectrum (Figure 2c, d). In the histogram that already showed hints for peaks, the peak structure became enhanced (Figure 2a, c), while in the other case the peak spectrum was only resolvable after excluding distorted trajectories (Figure 2b, d). These results were confirmed numerically by mimicking SPT-TIRFM movies using Brownian dynamics (BD) simulations (Supporting Information section S1). For the movies containing only single diffusion coefficient trajectories, a broad distribution of relative standard deviations  / D was observed (Figure S1c, red bars), the average value of which was close to the expectation value given by Equation 1. However, vesicles undergoing a change in the D values showed a much broader distribution of relative standard deviations  / D (Figure S1c, blue bars), which was, as expected, also shifted to larger values. Applied to BD TIRFM movies, it was confirmed in silico that this filtering approach is able to restore a peak spectrum that was initially distorted by inclusion of transition-containing trajectories (Figure S1b-e). Moreover, calculations using a quasi-continuous D distribution showed that the filtering approach itself does not cut peaks in the D histogram (Figure S2). Furthermore, note that each peak of the experimentally obtained D histograms is formed by at least 50 individual trajectories (Figure S3a, b) and that the peak positions are well reproduced in individual experiments (Figure 2, dashed lines). These observations thus confirm that the occurrence of peaks in the D histogram is


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not an artifact caused by the filtering process, strongly suggesting that the individual peaks can be attributed to vesicles with a unique number of links to the SLB. To address how the D distributions depend on the average number of linkers (roughly estimated from the concentrations of vesicles and DNA-linkers used during the self-assembly process and under the assumption that there is a 100% linker insertion efficiency; see section S10), the same analysis was applied for experiments in which the DNA concentration during the self-insertion process was varied, revealing minor differences for an average number of 3 and 6 linkers per vesicle (Figure 3, top and middle), while significant shifts of the peak distribution to lower D values were observed for 9 linkers (Figure 3, bottom). This observation is in agreement with the expectation, since with increasing number of DNA-tethers per vesicle the frictional force acting on the linking DNA-tethers is expected to increase and accordingly the D distribution of the whole population should shift to lower values. However, since in previous work it was not possible to resolve peak structures in the D histograms,17 it is not clear if a system of this type is expected to follow the model of Saffman and Delbrück,16 which implies that the tethers aggregate into a single structure causing a logarithmic dependence of the diffusion coefficient on n, or the so-called free draining model,15, 22 implying independent, non-interacting DNA-tethers and predicting D  1/n. To address this unresolved question, we note that at D  0.1 µm2/s (corresponding to –1 at the x-axis in Figure 3) the peak spacing is large enough to allow clear identification of individual peaks, while below 0.1 µm 2/s peaks start to merge, making their identification unreliable. This is in agreement with the accuracy expected from Equation 1, indicating relative standard deviations of the extracted D-values of 8% for the experimental settings (N = 200, Np = 2) and making it theoretically possible to resolve peaks if their relative peak spacing exceeds 11%


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(  2   / D ). Since this is only fulfilled for peaks above 0.1 µm 2/s, the further analysis was restricted to D > 0.1 µm2/s. The Saffman-Delbrück theory describes diffusion of a cylindrical inclusion completely protruding through a membrane (2D viscosity m) that is immersed by a fluid (bulk viscosity fl) from both sides,16 and predicts

D

 kB  T   m  1   ln n  .  ln  4 m   fl  r0  2 

(2)

with r0 (≈ 1 nm)27 denoting the inclusion radius of a single linking DNA-tether (Supporting Information section S6). This model cannot describe the observed peak spectra, as the logarithmic dependence yields positions of the diffusion coefficient peaks, which are far smaller than those resolved in our analysis. In contrast, the data are very well described by the free draining model,15, 28 which yields

D

D* , n

(3)

where D* is the diffusion coefficient of a single DNA-tether. This equation can be rewritten as

1 n np  np,0   . D D* D*

(4)

where np is the apparent number corresponding to an observed peak (after enumerating, beginning with the highest D value) and np,0 is the shift taking into account that the first observed peak does not necessarily correspond to n = 1.


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The linear relationship predicted by Equation 4 is observed in our experiments (Figure 4a and Figure S4), indicating that the peaks in the D histogram comply with the free draining model. Moreover, fitting Equation 4 (lines in Figure 4a and Figure S4, right column) yielded D*  1.1 µm2/s for a single DNA-tether, matching well the values reported for similar linkers.20 Hence, as the data were well described by the free draining model, it became possible to identify the relationship between the D values of each observed peak and the corresponding number of linking DNA-tethers. In particular, the intersection of the linear fit with the abscissa yielded -np,0 (Figure S4, right column), allowing to unambiguously relate np with n using n = np,0 + np (Equation 4) and thus to retrieve the D(n)-relationship. Further, averaging the D values (retrieved from individual D histograms) that corresponded to the same value of n, allowed to resolve the dependence of D on n with even higher accuracy (blue symbols in Figure 4b; values are given in Table S1). Again, the so-determined D values are in excellent agreement with the free draining model (Figure 4b, blue line), which is consistent with the DNA-tethers behaving as independent random walks underneath the vesicle. The analysis above was restricted to the peaks with D values >0.1 µm2/s (as outlined above), since for smaller D values the relative peak spacing became smaller than the expected measurement accuracy and adjacent peaks cannot be unambiguously resolved anymore. However, as adding more and more tethers to the vesicles (indicated by an increase in the average number of DNA-tethers per SUV) shifted the observed D distributions towards smaller values, less peaks are observed above 0.1 µm2/s as, e.g., indicated by a decrease in the number of data points for the 3 conditions shown in Figure 4a. This, however, is only a consequence of the fact that the whole D distribution is shifted across the threshold of 0.1 µm 2/s, and does not indicate a decrease in the number of subpopulations of vesicles with different n. 12 ACS Paragon Plus Environment

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After validation of Equation 3 for our case, it can be used to convert transient changes in D into transient changes in n and therefore to analyze transitions between these states. This conversion was done using a channeling procedure (described in Supporting Information section S7), which assumes that a vesicle remains in the linking state n as long as its time-resolved D value (Figure 5, red and blue symbols) remains within the interval (Figure 5, black dashed lines)

Dlow 

D* n  0.5

and

Dup 

D* . n  0.5

(5)

Some trajectories remain fully within one of these intervals, which is interpreted as if the vesicle remains in its initial linking state throughout the tracking (Figure 5a). However, since in this analysis all tracks are used, including those that were filtered out by the procedure described above, the time-resolved D was for a significant number of traces per measurement also observed to cross the boundaries between adjacent intervals, indicating a change in the number of DNA-tethers that link the respective vesicle to the SLB (Figure 5b, c). For random transitions (with an occurrence being independent of past events), it is possible to extract the transition rates between adjacent linking states (Supporting Information section S7). In brief, this was done by counting the number Pun(n, t) of trajectories with unchanged n throughout the observation time t, and the numbers P+(n, t) and P–(n, t) of trajectories that exhibited either an increase or decrease in n during the observation time t. The “survival” probability psur(n, t) could then be determined as:

psur (n, t ) 

Pun (n, t ) . Pun (n, t )  P (n, t )  P- (n, t )

(6)


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For random transitions between the different linking states, the survival probability is expected to depend on t as

psur (n, t )  exp  (k (n)  k (n))  t 

(7)

where k (n) and k (n) are the rate constants of transitions n → n + 1 or n → n – 1. In addition, one is expected to have

P (n, t ) k (n) .  P- (n, t ) k- (n)

(8)

In our SPT-experiments, however, the survival probability usually deviated from a mono-exponential decay predicted by Equation 7 (Figure 6a, data points). This was attributed (Supporting Information section S7) to two types of distortions caused by the measurement process: (i) the fact that extraction of D requires collection of a certain number N of data points from the trajectory (done in this work using a rolling window) and (ii) the intrinsic noise of random walks (whose variance decreases with increasing N; Equation 1). It was therefore necessary to model the measurement and analysis process using BD simulations taking these distortions into account (Supporting Information section S7), which allowed to fit Eqs 6 and 8 to the experimentally derived psur(n, t) and transition rate ratios, from which the dependence of k  and k  on n could be determined (Figure 6). Application of this approach on the data showed that k (n) generally displayed no significant dependence on n, while k (n) increased significantly from 0.004 s-1 for n = 4 to 0.010 s-1 for n = 7 (Figure 6d).


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To mimic the behavior of cell-membrane bound virions, we here used small unilamellar vesicles linked to a SLB via DNA-tethers,20 while SPT was used to explore the dependence between 2D diffusion and linking state (i.e., the number n of linking DNA-tethers). The linking state can transiently change in the course of the trajectory, as hybridized DNA-tethers may break up (thereby lowering n) and as dissociated or non-hybridized DNA-tethers may re-hybridize again (thereby increasing n).24 This efficiently mimics transient changes in many multivalent systems, such as interactions between virions and cell membranes.7, 8 It was shown that trajectories containing such transitions in n can be identified by analyzing the corresponding time-resolved diffusion coefficient D, as these transitions cause additional fluctuations in D, which then exceed the expectation value for a 2D random walk with a fixed diffusion coefficient (Equation 1). Distinct peaks in the D histograms (which are indicative of vesicle subpopulations differing in n) were in fact only observed if transition-containing trajectories were excluded from the histogram. This is in agreement with expectations, since only trajectories keeping their initial linking state are able to create a distinct peak spectrum, while transition-containing trajectories add ill-defined values to the D histogram, filling up the gaps between the peaks. To our knowledge this is the first demonstration of clearly resolved multiple subpopulations (> 3) in D histograms of this type. In particular, the approach is able to identify peaks with relative spacing between them down to 10% that are difficult to access by alternative approaches based on hidden Markov modelling or Bayesian interference, which are usually reported to require a relative peak spacing beyond 100% to reliably identify individual peaks.29, 30 The large number of resolved peaks allowed us to confirm with high accuracy that the relation between D and n is given by the free draining model,15, 22 while the 15 ACS Paragon Plus Environment

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model of Saffman and Delbrück failed describing the data.16 This indicates that the DNA-tethers behave like independent random walkers underneath the vesicle and that any distortions in the SLB (caused by the movement of DNA-tethers) are local effects, which do not affect the movement of the other DNA-tethers. This is in line with recent numerical calculations showing that such distortions are screened out in the SLB already after very few nm,31 and with recent SPT studies on the movement of proteins that are capable to bind 1, 2 or 3 lipids, which also suggests that the diffusion coefficient follows the free draining model.32 Taking into account that the free draining model is suitable in our case, we notice that the way by which the diffusion of an aggregate composed of n monomers is conventionally derived in the corresponding treatments is somewhat heuristic,15, 22 because instead of explicit description of diffusion the analysis is based on postulation of the relation between the friction coefficient of the whole aggregate with the friction coefficients of its parts, i.e., the analysis does not explicitly pay attention to the fact that the diffusion of monomers is spatially restricted. To illustrate the physics behind this model in more detail focusing on spatial constrains, we have performed the complementary Monte Carlo simulations. The simulations confirm that D is proportional to 1/n (Supporting Information section S8). Furthermore, it was possible to relate changes in the time-resolved D with fluctuations between different linking states, allowing extraction of transition rates between them. The rates involved in decreasing n, indicating a dissociation of a fully hybridized DNA-tether into a vesicle- and SLB-bound fragment (Figure 6d), increased monotonously with increasing n. This is expected for a system of non-interacting DNA-tethers: Because any of the linking DNA-tethers can dissociate, it is obvious that the rate of dissociating one DNA-tether among n linking DNA-tethers increases linearly with the total number of available DNA-tethers (=n). These measurements 16 ACS Paragon Plus Environment

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suggest an off-rate rate of 0.002 s-1 for a single DNA-tether, which is in good agreement with studies on a similar DNA-tether system.24 Contrary, the rates involved in increasing n (indicating re-hybridization of a vesicle-linked DNA-strand with its complementary part linked to the SLB) showed no systematic dependence on the linking state and were on the order of 0.01 s -1. In analogy with the discussion above, the involved vesicle DNA-strands are most likely created by dissociation of fully hybridized DNA-tethers. Assuming a diffusion coefficient of the unhybridized, vesicle-bound DNA-strands on the order of 1 µm2/s (see Figure 4a and Benkoski et al.20), this corresponds to a mean squared displacement of 400 µm2. Hence, unhybridized DNA-strands move (between their creation and re-hybridization) on average over an area that is more than 1000 times larger than the vesicle surface area. This indicates that after their formation, the DNA fragments easily leave the vesicle-SLB interaction area and re-enter that area several times before they re-hybridize again. Hence, the rate of entering the interaction area is much larger than the observed rate of re-hybridization, suggesting that the rate limiting step is the collision of vesicle- and SLB-bound DNA-tether fragments. It is therefore not surprising to observe that the rate k  shows no significant dependence on n (Figure 6c). To generalize our findings to systems in which the links have transition times different from those in this work, a further analysis of the measurement process was done (Supporting Information section S7) that allows to tailor the settings of SPT experiments in order to resolve transitions of any transition rate. This analysis yielded lower limits for the size of the rolling window Nmin and the acquisition rate 1/tmax, which must be exceeded to resolve a transition that involves the binding of n receptor-ligand bonds with a maximum transition rate of kmax: 17 ACS Paragon Plus Environment

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N  N min 

2  N p  (2n  1) 2 3

and t 0  t max 

1 2  N  k max (n)

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(9)

Application of these relations to the DNA-tethers (Np = 2, 4 ≤ n ≤ 7, kmax ≤ 2 10-2) gives Nmin and tmax ranging between 100 and 300 frames and 0.1 s - 1 s, respectively, which is fulfilled in the majority of our datasets. For real virions on a flat membrane, n is expected to be in a similar range,7 suggesting rolling window sizes between 100 to 300 frames to yield sufficient accuracy. However, the transition rates of individual virion-receptor contacts are expected in many cases to be several orders of magnitude larger than the values observed here,7 which requires acquisition rates on the order of several kHz. Such high rates are probably difficult to achieve in conventional fluorescence microscopy, but have already been demonstrated using scattering approaches like iScat,33 yielding acquisition rates of several kHz while keeping localization precisions on the nm-scale.34

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/xxx. Additional information and figures: Concepts and illustration of the trajectory filtering approach, linear versus logarithmic binning in D histograms, filtered D histograms for all SPT data, free draining model vs. the Saffman-Delbrück model, extraction of transition rates, Monte Carlo validation of the free draining model, width of the n distribution, and full materials and methods (PDF).


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AUTHOR INFORMATION Corresponding authors *E-mail: [email protected]. *E-mail: stephan.block @chalmers.se. Notes The authors declare no competing financial interests.

ACKNOWLEDGEMENTS The authors thank the Knut and Alice Wallenberg Foundation, the Swedish Research Council (2014-5557) and the Swedish Foundation for Strategic Research (RMA110104) for funding.


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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

28. 29. 30. 31. 32. 33. 34.

Mercer, J.; Schelhaas, M.; Helenius, A. Annual Review of Biochemistry 2010, 79, 803-33. Barrow, E.; Nicola, A. V.; Liu, J. Virology Journal 2013, 10, 177. Mammen, M.; Choi, S. K.; Whitesides, G. M. Angew Chem Int Edit 1998, 37, (20), 27552794. Zhdanov, V. P. Phys Rev E 2013, 88, (6). Huber, F.; Schnauss, J.; Ronicke, S.; Rauch, P.; Muller, K.; Futterer, C.; Kas, J. Adv Phys 2013, 62, (1), 1-112. Sun, E.; He, J.; Zhuang, X. W. Curr Opin Virol 2013, 3, (1), 34-43. Szklarczyk, O. M.; Gonzalez-Segredo, N.; Kukura, P.; Oppenheim, A.; Choquet, D.; Sandoghdar, V.; Helenius, A.; Sbalzarini, I. F.; Ewers, H. Plos Comput Biol 2013, 9, (11). Kukura, P.; Ewers, H.; Muller, C.; Renn, A.; Helenius, A.; Sandoghdar, V. Nat Methods 2009, 6, (12), 923-U85. Fasting, C.; Schalley, C. A.; Weber, M.; Seitz, O.; Hecht, S.; Koksch, B.; Dernedde, J.; Graf, C.; Knapp, E. W.; Haag, R. Angew Chem Int Edit 2012, 51, (42), 10472-10498. Gavutis, M.; Lata, S.; Piehler, J. Nat Protoc 2006, 1, (4), 2091-2103. Jung, H.; Robison, A. D.; Cremer, P. S. J Struct Biol 2009, 168, (1), 90-94. Bally, M.; Gunnarsson, A.; Svensson, L.; Larson, G.; Zhdanov, V. P.; Höök, F. Phys Rev Lett 2011, 107, (18). Ruthardt, N.; Lamb, D. C.; Brauchle, C. Mol Ther 2011, 19, (7), 1199-1211. Visser, E. W. A.; van IJzendoorn, L. J.; Prins, M. W. J. ACS Nano 2016, 10, (3), 3093-3101. Kucik, D. F.; Elson, E. L.; Sheetz, M. P. Biophys J 1999, 76, (1), 314-322. Saffman, P. G.; Delbruck, M. P Natl Acad Sci USA 1975, 72, (8), 3111-3113. Simonsson, L.; Jonsson, P.; Stengel, G.; Höök, F. Chemphyschem 2010, 11, (5), 1011-7. Yoshina-Ishii, C.; Chan, Y. H. M.; Johnson, J. M.; Kung, L. A.; Lenz, P.; Boxer, S. G. Langmuir 2006, 22, (13), 5682-5689. Yoshina-Ishii, C.; Boxer, S. G. J Am Chem Soc 2003, 125, (13), 3696-3697. Benkoski, J. J.; Höök, F. The Journal of Physical Chemistry B 2005, 109, (19), 9773-9. Yoshina-Ishii, C.; Miller, G. P.; Kraft, M. L.; Kool, E. T.; Boxer, S. G. Biophys J 2005, 88, (1), 233a-233a. Flory, P. J., Principles of polymer chemistry. Cornell Univ. Press: Ithaca u.a., 1953; p XVI, 672 S. Knight, J. D.; Lerner, M. G.; Marcano-Velazquez, J. G.; Pastor, R. W.; Falke, J. J. Biophys J 2010, 99, (9), 2879-2887. Gunnarsson, A.; Jonsson, P.; Zhdanov, V. P.; Höök, F. Nucleic Acids Res 2009, 37, (14). Qian, H.; Sheetz, M. P.; Elson, E. L. Biophys J 1991, 60, (4), 910-21. Michalet, X.; Berglund, A. J. Phys Rev E 2012, 85, (6). Bunge, A.; Loew, M.; Pescador, P.; Arbuzova, A.; Brodersen, N.; Kang, J.; Dahne, L.; Liebscher, J.; Herrmann, A.; Stengel, G.; Huster, D. Journal of Physical Chemistry B 2009, 113, (51), 16425-16434. Weast, R. C.; Chemical Rubber Company (Cleveland Ohio), CRC handbook of chemistry and physics. 1. student ed.; CRC Press: Boca Raton, Fla., 1988. Das, R.; Cairo, C. W.; Coombs, D. Plos Comput Biol 2009, 5, (11). Persson, F.; Linden, M.; Unoson, C.; Elf, J. Nat Methods 2013, 10, (3), 265-269. Camley, B. A.; Brown, F. L. H. Soft Matter 2013, 9, (19), 4767-4779. Ziemba, B. P.; Falke, J. J. Chem Phys Lipids 2013, 172, 67-77. Ortega-Arroyo, J.; Kukura, P. Phys Chem Chem Phys 2012, 14, (45), 15625-15636. Andrecka, J.; Arroyo, J. O.; Takagi, Y.; de Wit, G.; Fineberg, A.; MacKinnon, L.; Young, G. V.; Sellers, J. R.; Kukura, P. Elife 2015, 4.


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Figure Legends Figure 1: DNA-mediated vesicle linking to a SLB (a – c) used for single particle tracking (SPT) and representative examples for 2D tracks of single vesicles (d; monitored using TIRFM) allowing to measure D from the time dependence of their mean squared displacement (MSD) curves (e; see text for details). Vesicle and SLB DNA (black and red strands in a – c, respectively) carry a double cholesterol group at their ends that inserts the strands into bilayers (a). SLB DNA is only pre-incubated with the SLB, while vesicle DNA is only pre-incubated with vesicles (b). Mixing DNAequipped vesicles and SLBs causes hybridization, thereby linking the vesicles via the DNA-tethers to the SLB (c; showing only a single linking DNA-tether for simplicity). PEGylated lipids have been incorporated to decouple the lipid motion from surface effects and to decrease non-specific attachment of vesicles to the SLB. Figure 2: D histograms obtained for SUVs carrying on average 3 DNA-tethers (as estimated from the DNA and vesicle concentrations used during the self-assembly process and the assumption of 100% insertion efficiency). Two representative examples (top and bottom) of the results before and after data filtering (left and right) are shown. Including all trajectories (no data filtering), a broad peak is usually observed, showing a vague (a) or no peak spectrum (b). However, after filtering out corrupted trajectories using a threshold of 60% of Equation 1, peaks are clearly resolvable (dashed lines in c and d indicate their positions), which are related to SUV subpopulations differing in their number n of linking DNA-tethers. For comparison with the histograms presented, we also show the Poissonian and modiﬁed Poissonian n distributions for = 3 (Supporting Information section S9). Figure 3: D histograms of SUV carrying on average 3 (top), 6 (middle), and 9 DNAtethers (bottom) (estimated as in Figure 2) using a filtering threshold of 60% (top, middle) or 50% (bottom) of Equation 1. Dashed red lines were drawn for comparison of peak positions between the histograms. Note the logarithmic binning of the histogram. Figure 4: (a) The inverse peak diffusion coefficient 1/D, extracted from D histograms of SUV carrying on average 3 (blue), 6 (red), or 9 DNA-tethers (green), shows a linear dependence of the respective peak observation number np, as suggested by 21 ACS Paragon Plus Environment

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the free draining model. The slope gives the inverse diffusion coefficient of a single DNA-tether 1 / D* and reproduces well (see also Figure S4). The intersection with the x-axis corresponds to –np,0, allowing to relate a peak with its corresponding number of linking DNA-tethers via n  np  np,0 (see text). (b) Relation between D and n according to the experiment (red dots) and free draining model (blue solid line; Equation 3). Blue symbols give averaged diffusion coefficients that have the same n (the error bars correspond to twice the respective standard deviation). Figure 5: Conversion of the time-resolved D (blue and red symbols) into the underlying linking state. Red dashed lines mark peak positions observed in the D histograms (Figure 3), corresponding to linking states as indicated in the plots, while black dashed lines give the boundaries between these linking states. Some trajectories do not cross any boundary, indicating a constant linking state n (a). A histogram of their time-resolved D (a, right) shows again peaks similar to those exhibited in Figures 2 and 3. However, other trajectories may cross the upper (b) or lower boundary (c), which is interpreted as a transition towards a linking state that has lost (b) or gained (c) one linking DNA-tether. For each case and each n, two representative kinetics are shown in blue and red, respectively, making it easier to follow their course. Figure 6: Extraction of transition rates from vesicle trajectories. (a) Equation 6 is used to extract the probability psur of a vesicle to remain in its initial linking state within the observation time t. Symbols give psur extracted from SPT movies (n as indicated), while solid lines are the best fits (Supporting Information section S7) yielding (for a given n) the total transition rate ksur. (b-d) ksur can be further decomposed into k+ and k– (describing transitions from n → n + 1 or n → n – 1) as the ratio k+ / k– is proportional to P+ / P– (Equation 8), i.e., the number P+ of trajectories showing the transition n → n + 1 during the observation time t divided by the number P– of trajectories showing the transition n → n – 1 during t. (c, d) give k+ and k– as obtained by fitting (lines in b) the experimentally determined ratios P+ / P–. Different symbols correspond to individual experiments, while lines give either the average value of k+ for a given experiment (c) or a linear fit using the data of all experiments, yielding a slope of 0.0022 s-1 (d).


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a

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b

d

c

e

MSD  t

Figure 1:


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raw data

a

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filtered data

c 0.13 µm2/s 0.14 µm2/s 0.16 µm2/s 0.19 µm2/s 0.24 µm2/s 0.28 µm2/s

b

d

Figure 2:


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3 tethers per vesicle



log10(D/[µm2/s]) Figure 3:


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b

a D* = 1.18 µm2/s np,0 = 6

D* = 1.11 µm2/s np,0 = 3 D* = 1.02 µm2/s np,0 = 2

Figure 4:


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a

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n =4

=5 =6

b

n

a

c

n

=4

=4

=5

=5

=6

=6

Figure 5:


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b

a

n=7 ksur = 0.02 s-1

c

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n=6 k+/k– = 0.73 n=5 k+/k– = 1.11

n=4 ksur = 0.014 s-1 n=5 ksur = 0.015 -1 n =s 6

n=4 k+/k– = 1.14

ksur = 0.025 s-1

d

Figure 6:


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TOC-Image


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