Mass-sensitive particle tracking (MSPT) to elucidate the membrane-associated MinDE reaction cycle

In spite of their great importance in biology, methods providing access to spontaneous molecular interactions with and on biological membranes have been sparse. So far, it has been consensus that their observation with sufficient sensitivity and time resolution requires the introduction of - predominantly fluorescent-labels to the system. However, the recent advent of mass photometry to quantify mass distributions of unlabelled biomolecules landing on surfaces raised hopes that this approach could be transferred to membranes. Here, we introduce mass-sensitive particle tracking (MSPT), enabling simultaneous label-free tracking and monitoring of molecular masses of single biomolecules diffusing on lipid membranes. We applied this approach to the highly non-linear reaction cycles underlying MinDE protein self-organisation. MSPT allowed us to determine the stoichiometry and turnover of individual membrane-bound MinD/MinDE protein complexes and to quantify their size-dependent diffusion. We found that MinD assembles into complexes larger than the commonly postulated dimer, through lateral interactions of membrane-bound complexes and subunit recruitment from solution. Furthermore, the ATPase-activating protein MinE interconnects MinD into high-molecular-weight heteromeric complexes and affects their subunit turnover and concerted membrane release. This study demonstrates the potential of MSPT to enhance our quantitative understanding of both prokaryotic and eukaryotic membrane-associated biological systems.


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The recruitment of proteins to lipid interfaces is crucial for various cell biological processes, 64 such as the regulation of membrane trafficking 1 , mediation of signalling cascades 2 , and the This system consists of three proteins -MinC, MinD and MinE -and is essential for the spati-

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First, we set out to assess the quality of mass determination of mobile molecules compared to 165 landing particles in conventional mass photometry. To this end, we used a bilayer supple-166 mented with biotinylated lipids and attached a set of biotinylated standard proteins with known 167 mass via divalent streptavidin 35 . This system has several advantages, such as the ability to 168 cover different protein size regimes, standardised membrane binding, and the added benefit 169 of simplified complex stoichiometries by using divalent streptavidin. For each molecule, we 170 determined its median contrast throughout its trajectory. Analogous to conventional mass pho-

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For our standard proteins, iSCAT contrast as a function of mass exhibited the expected linear 174 relationship 17 . The calibration line obtained from standards diffusing on SLBs was in fact indis-175 tinguishable from the one determined with molecules landing on glass (Fig. 1c). This result 176 suggests that mass calibrations performed with landing assays can be transferred to particles 177 diffusing on membranes. However, this strictly needs to be verified for any new lipid/buffer 178 combination, protein system and imaging condition.

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Besides mass determination, MSPT also enables the analysis of the diffusive behaviour of 181 membrane-bound molecules. For this purpose, it is important to choose the median window 182 size for background estimation such that particles travel sufficient distances during the median 183 period. Hence, we first systematically tested the minimum median window sizes required to extract the correct diffusion coefficients at particle diffusion speeds expected for our SLB sys-185 tem. We generated artificial movies of randomly diffusing particles at varying speeds and com-186 pared the input diffusion coefficients with diffusion coefficients extracted using different median

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In contrast, the major species on the membrane was a MinD dimer already at sparse densities 249 corresponding to one particle per frame in the field of view (31.9 µm 2 ). However, it should be 250 noted that at the chosen imaging conditions for MSPT, the signal-to-noise ratio of monomers (33 kDa) was too low for their quantitative detection ( Supplementary Figures 9 and 10). Hence, 252 an adequate estimate of their membrane abundance cannot be stated.

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One of the major advantages of iSCAT-based imaging is that it provides a direct estimate of 255 the molecular density on a bilayer from the number of detected particles, as compared to sin-

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This result suggested that the WT was able to also recruit MinD monomers forming trimeric 276 species as intermediates, which were not as abundant for the D40A mutant. In order to provide

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These graphs show a sequential appearance of increasingly larger oligomers of MinD for higher molecule densities (Fig. 2f). Compared to the WT, the D40A mutant had a higher ten-288 dency to populate stoichiometries with even numbers of subunits and to transform its dimer 289 state into the tetramer state, likely due to the increased stability of the dimer (Fig. 2h).

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Time-resolved mass analysis of single MinD trajectories 323 Aside from measuring a particle's location frame by frame, MSPT also allows to determine its 324 respective mass in a time-resolved fashion, thus enabling the detection of attachment and 325 detachment events along the trajectory of a single particle (Fig. 3a, Supplementary Fig. 14).

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For MinD, the minimal expected mass increment (33 kDa) for monomer-wise turnover was 327 close to the measurement uncertainty (28 kDa standard deviation) of the mass for a single 328 frame. To minimise user bias, we employed a step-finding algorithm that locates mass change   338 3c), which appeared to mostly (dis-)assemble in one-or two-subunit increments at low particle 339 densities. However, for higher MinD particle densities, when larger oligomers had accumu-340 lated, these complexes often turned-over greater subunits, as indicated by the shift of the dis-341 tribution towards higher mass steps 27 (Fig. 3c, dark blue profile). Moreover, the combined in-342 formation of a mass plateau level and its dwell time as annotated in Fig. 3b could be used to 343 extract the subunit turnover rates of each oligomer species (Fig. 3d). Here, the dwell time 344 preceding a mass increase could be used to deduce subunit attachment rates (Fig. 3d -upper   345 panel), whereas the dwell time followed by a mass decrease provided an estimate of detach-346 ment rates (Fig. 3d -lower panel). The resulting lifetime plots suggested that membrane-at-347 tached dimers had a faster subunit turnover than tetramers, implying higher stability of these 348 larger complexes.

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Plateaus at the end of trajectories (Fig. 3b, bottom panel, last plateau), and trajectories without 351 any mass change at all (Fig. 3b, top panel), could be used to identify the molecular weight of 352 particles completely released (rl) from the membrane (Fig. 3e). Notably, this time-resolved mass analysis of the individual trajectories significantly improved the mass resolution, as com-354 pared to the median-based particle mass estimates used in Figure 2. Hence, MinD dimers, 355 trimers and tetramers were now fully resolved as separate peaks (Fig. 3e). Accordingly, one 356 could now recognize that the major species released from the membrane was a dimer at low 357 particle densities and a tetramer at high particle densities. The corresponding dwell time plot 358 showed that tetramers stayed associated to the bilayer significantly longer than dimers, in line 359 with a higher avidity in membrane binding conferred by additional MTS (Fig. 3f). For compari-360 son, the dimer-arrested mutant MinD D40A almost exclusively dissociated as dimers or te-361 tramers ( Supplementary Fig. 15, 16). Taken together, our detailed trajectory analysis confirms  Fig. 17). In the presence of a sup-400 ported lipid bilayer, however, the MinDE complex existed predominantly in a stable double-401 dimeric state (Fig. 4a -light pink, Supplementary Fig. 18). Furthermore, if the MinDE complex 402 encountered more proteins on a crowded bilayer, MinE promoted the interconnection into very 403 large heteromeric MinDE complexes, a behaviour unexpected considering the common mod-404 els ( Fig. 4a -magenta). One possible explanation for this behaviour is the ability of a MinE 405 dimer to symmetrically bind to both sides of a MinD dimer, thus effectively acting as a bridge 406 between MinD assemblies 49 . Accordingly, our time-resolved mass step analysis revealed that 407 during subunit turnover on membrane-bound particles, predominantly dimeric and tetrameric 408 subunits attached (at) and detached (dt) at high particle densities of 0.6 and 0.8 µm -2 (Fig. 4b,

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Supplementary Fig. 19). This effect required a critical minimum density on the bilayer, since  (Fig. 4c, light pink). Strikingly, on bilayers 413 with high protein density, MinDE complex sizes released from the membrane increased be-414 yond the sizes observed for MinD alone and reached masses of >350 kDa (Fig. 4c, purple).

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Based on our mass dwell time analysis, we found that the presence of MinE generally reduced 417 the diffusion coefficients (Fig. 4d) of MinDE oligomers and slowed down turnover rates (Fig.   418 4e, pink), when compared to their respective MinD versions (Fig. 4e, blue). In addition, MinDE 419 complexes were found to reside significantly longer on the membrane before full release (    analysis of time-resolved subunit turnover and its kinetics by analysing mass changes along a 504 particle's trajectory; 4) Extended observation times due to the absence of photo-bleaching, 505 thus enabling the collection of high particle statistics in a short period of time. Ultimately, we 506 believe that mass-sensitive particle tracking will make a strong contribution to the quantitative 507 understanding of both prokaryotic and eukaryotic membrane-associated biological systems.

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Error bars in Fig 1c represent Fig. 12). Additionally, the sum of contributions of the six components 779 was constrained to add up to unity in the least-squares sense. Prior to fitting, the simulated 780 mass distributions were smoothed using a moving average with a window length of 4.5 kDa.

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To estimate the uncertainty of the extracted abundances of the components, the dataset at 782 each trajectory density was split randomly into three samples before fitting each subset indi-

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vidually. This procedure was repeated 10 times and the average standard deviation of the per-784 split results was calculated. Unless otherwise stated, the reported particle densities throughout