High affinity of Skp to OmpC revealed by single-molecule detection

Outer membrane proteins (OMPs) are essential to Gram-negative bacteria, and they need molecular chaperones to prevent from aggregation in periplasm during the OMPs biogenesis. Seventeen kilodalton protein (Skp) is the major protein for this purpose. Here we used singlemolecule detection (SMD) to study the stoichiometry modulation of Skp in binding with outer membrane protein C (OmpC) from Escherichia coli. To accomplish our task, we developed the tool of portion selectively chosen fluorescence correlation spectroscopy (pscFCS). We found that Skp binds OmpC with high affinity. The half concentration for Skp to form homotrimer Skp3 (C1/2) was measured to be 250 nM. Under the Skp concentrations far below C1/2 OmpC can recruit Skp monomers to form OmpC·Skp3. The affinity of the process is in picomolar range, indicating that the trimerization of Skp in OmpC·Skp3 complex is induced by OmpC-Skp interaction even though free Skp3 is rarely present. In the concentration range that Skp3 is the predominant form, OmpC may directly interact with Skp3. Under micro-molar concentrations of Skp, the formation of OmpC·(Skp3)2 was observed. Our results suggest that the fine-tuned modulation of Skp composition stoichiometry plays an important role in the safe-guarding and quality control mechanism of OMPs in the periplasm.


Introduction
Outer membrane (OM) in Gram-negative bacteria is crucial for bacterial survival because it separates the periplasm and the external environment and protects cells from toxic molecuels 1 . Meanwhile, most outer membrane proteins (OMPs) adopt a porin-like β-barrel conformation to take nutrients and excrete toxic waste products. As OMPs are synthesized in cytoplasm in unfolded state and have to transport through aqueous periplasm to fold in OM, several periplasmic quality control factors such as survival protein A (SurA), seventeen kilodalton protein (Skp) and serine endoprotease DegP are involved to protect OMPs from mis-folding and aggregation [2][3][4][5] . Recent study from our group identifies Skp to be the major protein to prevent OMPs from aggregation 6 . Accumulation of periplasmic OMPs and other survival stress will stimulate the σ E response 7 , which downregulates OMPs expression and upregulates chaperone expression 8 . Crystallographic analysis reveals that Skp exists as a homo-trimer with a "jelly-fish" shape, and the trimeric core is composed of inter-subunit βsheets and the tentacles of hairpin-shaped α-helices 9,10 . The crystallographic structure makes people believe that Skp3 is the basic unit to interact with OMPs. Lyu et al. shows that the N-terminus of OMPs enters Skp3 firstly through the tentacles and Skp3 engulfs entire OMPs via the electrostatic and hydrophobic interactions 11 . The tentacles are remarkably flexible, which modulate the size of cavity to accommodate OMPs with different sizes 12,13 . Meanwhile, only the β-barrel domains of OMPs are captured in the binding cavity 14 and the encapsulated domains populate a dynamic conformational ensemble 15,16 . The global lifetime of OMP·Skp3 complex is hours to ensure OMPs' searching for low-energy conformations in the cavity 15,17 .
Recently, the dynamic equilibrium between Skp and Skp3 has attracted attention. Sandlin et al. shows that dynamic equilibrium exists between Skp monomer and Skp3 at micro-molar physiological concentration 18 , which is significantly larger than the reported nano-molar affinity of Skp to OMPs 19 . It is therefore speculated that Skp monomer may be involved in the chaperone activity 18 . Moreover, two Skp3 are found to bind large OMPs 13 . These studies raise questions on what is the exact composition stoichiometry of Skp in OMPs-Skp complex at low Skp concentration where Skp monomer is the predominant form and under what concentrations these complexes form. Couple obstacles hinder people from getting answers for these questions. Firstly, OMPs are prone to aggregation at ensemble level, which will bring side effect to the experimental phenomenon. Secondly, there are many subpopulations in solution. For example, OMPs are in equilibrium among freely existent (apo-) state and complex formed with chaperones (bound-) state 20 , and Skp has equilibrium between Skp and Skp3 18 . These equilibria will blur the information at ensemble level.
To overcome above problems, subpopulation needs to be separately resolved by, for example, electrophoresis, chromatography, or single-molecule detection (SMD) 6,[21][22][23] . Unlike other separation methods which perturb the molecular interaction and the equilibrium of subpopulations, SMD yields a statistical analysis of individual molecule via ultrahigh spatiotemporal resolution. Furthermore, SMD may prepare and investigate OMP samples under monomeric form, so that the interference of OMP aggregation can be completely removed 6,24 . Here we developed an easy-to-implement SMD method named the portion selectively chosen fluorescence correlation spectroscopy (pscFCS), which takes advantages of single-molecule fluorescence resonance energy transfer (smFRET) and fluorescence correlation spectroscopy (FCS) to get diffusion time of specific subpopulation. We used pscFCS as well as fluorescent sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) to examine the formation and composition stoichiometry of the complexes of Skp and outer membrane protein C (OmpC). We found that under pico-molar concentrations of Skp, OmpC induced the trimerization of Skp to form OmpC·Skp3. Under micro-molar concentrations of Skp, additional Skp3 can bind OmpC·Skp3 to form OmpC·(Skp3)2. Our results provided new information to help better understanding the role of Skp in the safeguarding and quality control mechanism of OMPs.

Development of pscFCS for specific subpopulation
OMPs biogenesis is a complex system, consisting of different subpopulations including OMPs of different states and chaperones of different kinds. To resolve specific subpopulation, we developed pscFCS which utilizes smFRET and FCS 24 . We measured smFRET histogram and chose the fluorescence traces of specific subpopulation (SI methods). Figure 1a shows that under SMD condition the desired fluorescence traces within certain smFRET efficiency portion were selected and the unselected parts of the traces were replaced by random Poisson noise at the experimental level. Figure 1b where I is the fluorescence intensity, .// is the apparent diffusion time and $ is inverse of the number of fluorescent molecules in the focus volume. Obviously, the peak threshold on photon counts in picking up the selected bursts would generate a bias on the apparent diffusion time. Taking Cy3B dye in solution as a real example, the FCS curves of two thresholds are shown in Fig. 1c and the relation between the apparent diffusion time and the peak threshold of three parallel experiments are shown in Fig. 1d. We empirically found that the relation between the apparent diffusion time and the peak threshold can be fitted by where is the peak threshold, t and a are fitting parameters. To correct the bias, an extrapolation procedure was implemented by using equation (2), and t is taken to be the unbiased diffusion time. As a test, the unbiased diffusion time of Cy3B measured by pscFCS was 151±2 μs (n=3, Fig. 1d). While the diffusion time of Cy3B measured by conventional FCS was 162±8 μs (n=5, Supplementary Fig. S9). The relative error was 6.8%, which is sufficient for our goal of identifying the composition stoichiometry of OmpC-Skp complex.
According to the Stokes-Einstein equation, the diffusion coefficient of spherical particles through a liquid with low Reynolds number is where is the dynamic viscosity and is the hydrodynamic radius. is related to the diffusion time in FCS by where :; is the laser beam waist in the plane. To get molecular weight from D by using the Stokes-Einstein equation, we made three reasonable assumptions: 1) Proteins are in spherical shape, 2) the solution is simple so that the Stokes-Einstein equation holds, and 3) all protein species have the same molecular density. Under above assumptions, the following relation holds between two protein species with one of them taken to be a reference, where ) , 0 , ) and 0 are respective molecular weights and diffusion times. The error propagation from the diffusion time to the molecular weight was derived to be

Formation of OmpC·Skp3 complexes in pM range of Skp concentration
The "jellyfish"-like architecture of Skp3 consists of three subunits (Fig. 2a). We first studied the homo-trimerization of Skp by FCS (SI methods and Supplementary Figs. S10 and S11).
The dissociation constant was measured to be (4.6±2.7)×10 4 nM 2 , corresponding to that the half trimerization concentration ( )/0 ) of Skp is (2.5±0.7)×10 2 nM (Supplementary Fig.   S12). Our measured )/0 is smaller than but on the same order of magnitude with the reported )/0 of (4.4±1.3)×10 2 nM under the most similar temperature and salt concentration 18 , confirming that free Skp is not negligible at a physiological concentration.  Figure   2b shows smFRET histogram of OmpC G8C-D335C in presence of certain Skp concentrations. When Skp was absent, only the Eapp=0.78 peak was observed. At Skp concentration of 0.23 nM, an smFRET efficiency peak at Eapp=0.13 was observed besides the 0.78 peak. When Skp was 1.8 nM, only the 0.13 peak remained (more results in Supplementary Fig. S13). The 0.78 peak was assigned to apo-OmpC and the 0.13 peak to bound-OmpC as previously observed 6 . The peak at Eapp=0 (zero peak) was due to missing or inactivated acceptors and was disregarded.
To determine the composition stoichiometry of OmpC-Skp complexes, we used pscFCS to compare the diffusion time of apo-and bound-OmpC in the same smFRET histogram (Fig.   2c). The stoichiometric ratio = Skp: OmpC was derived to be = (?
and was determined to be 2.8±0.4 with the apo-OmpC molecule as the inner reference, indicating that OmpC was already bound by Skp3 even though the concentration of Skp in solution was extremely lower than )/0 .
To accurately quantify the affinity of Skp to OmpC, we conducted colocalization measurement using total internal reflection fluorescence (TIRF) microscope where OmpC G8C-AF555 was immobilized on surface and incubated with freely diffusing Skp D128C-AF647. The concentration of Skp generating half occupation of OmpC ( B ) for the reaction was measured to be (5.5±0.4)×10 2 pM with a Hill coefficient DEFF = 1.6 ± 0.2 (Fig. 3a, SI method). Our measured B is much smaller than previously reported values 19 , which may be due to the high sensitivity of the SMD method. The statistical analysis on the 640 nm-excited fluorescence counts showed that in the OmpC-Skp complex the composition stoichiometry of Skp is larger than 1 ( Fig. 3b and Supplementary Fig. S14), consistent with the pscFCS results that there are 3 Skp molecules in the OmpC-Skp complex.

Discussion
We made thorough study on the equilibrium constants of Skp homo-trimerization and the complex formation between OmpC and Skp. Skp D128C was used for fluorescent dye labelling. Although the residue D128 is at trimeric core of Skp3 structure, our previous study 11 shows that the Skp mutation and dye labelling does not perturb its chaperone activity, and labelled Skp D128C had a minimal self-quenching effect. Since OmpC is unfolded, the mutation and dye labelling do not vary its property 6  where chaperones had to compete with OMPs self-aggregation. In our smFRET experiments, monodisperse OmpC was prepared which removed the side effect of aggregation 6 , and it was a better mimic of the situation in living cells. With SMD, we were able to resolve individual subpopulations, and we showed high affinity ( B = (5.5 ± 0.4) × 10 0 pM) and positive cooperativity ( DEFF = 1.6 ± 0.2) of Skp to form OmpC·Skp3 (Fig. 2 and Fig. 3). Because the immobilized OmpC was limited in phase space compared to freely diffusing OmpC, the affinity in TIRF experiment could be slightly weaker than that in smFRET experiment in solution 32 , but it still resulted in high affinity of Skp towards its client, providing strong evidence to support the proposed unique chaperone function of Skp to dissolve aggregated OmpC 6 . The high affinity of Skp to OmpC is perhaps a result of multiple, non-specific and transient interactions 11,15 . Additionally, Skp has a broad substrate spectrum 33 . We speculate that the high affinity of Skp to OmpC is likely to be prevalent among its other substrates.
The reaction rate of Skp binding OmpC is nearly diffusion limited 30 . The association rate constant could be estimated by where is the diffusion coefficient, and is the radius of molecules. We observed the formation of OmpC·(Skp3)2, but the hydrodynamic radius of OmpC·(Skp3)2 was similar to that of OmpC·Skp3 according our pscFCS results (Supplementary Table S2).
This experimental result strongly suggests that the orientation of the two Skp3 in OmpC·(Skp3)2 is via the "inter-locked" pattern 13 . Our data showed that the intramolecular smFRET efficiency of OmpC is higher in OmpC·(Skp3)2 than that in OmpC·Skp3, indicating that OmpC is compressed tighter in OmpC·(Skp3)2 than in OmpC·Skp3, that also causes the reduction of the complex radius and is consistent with the "inter-locked" model. SANS study reveals that the gyration radius of apo-state Skp3 in solution is larger than Skp3 bound to OmpA or OmpW 34 . OmpA and OmpW are both small OMPs with 8 b-strands. It is reasonable that the complex is larger when Skp3 binds to larger OMPs such as OmpC (16 b-strands).
When apo-state Skp3 in solution was used as reference, we found that indeed the hydrodynamic radius of OmpC·Skp3 is larger than that of Skp3.
The physiological concentration of Skp is around 2.1-3.9 μM at stationary phase growth in LB 6,18 , which is near the dissociation constant B G = 1.2 ± 0.4 µM for second Skp3. The s E response will downregulate OMPs expression and upregulate expression level of chaperones and proteases 40 . Although the whole OMPs biogenesis landscape will be much complicated in vivo, we speculate that the upregulated Skp will increase the population of OMP·(Skp3)2, which may enhance the protection of OMPs from aggregation to help the cell survival.  OmpC·Skp3. When micro-molar of Skp is present, OmpC·(Skp3)2 will appear with an "interlocked" binding pattern.

Protein expression, purification and mutagenesis
The

Monte-Carlo simulation for Brownian motion
Monte-Carlo simulation was performed as described previously 41,42 and simplified by putting 6 diffusing molecules into the volume. Each fluorescence trace was tracked and calculated to obtain smFRET histogram where contribution from each molecule was known. Then all fluorescence traces were added to simulate the signals, which was used to select fluorescence bursts of certain subpopulation in pscFCS, and the generated Boolean array was used in each fluorescence trace to test the contribution of 6 molecules by checking selected fluorescence bursts and recalculating smFRET histogram.

FCS experiments for homo-trimerization of Skp
Homo-trimerization titration of Skp was carried out with a home-built inverted fluorescence confocal microscope based on a TE2000-U microscope (Nikon) equipped with a 532 nm solid-state laser (MLL-III-532-20mW, LD&TEC) as previously described 25,43 . The laser was where is the diffusion time, L is the relaxation time, $ is the inverse of number of fluorescent molecules in the focus volume and is the amplitude of the relaxation.
where .// is the apparent smFRET efficiency, BN and HO are photon counts of every identified fluorescence burst. Statistics of smFRET efficiency yielded smFRET histogram and the histogram was fitted by Gaussian distributions.

pscFCS measurement for stoichiometry
pscFCS experiments were performed as the same of smFRET experiments except that the bintime was taken to be 0.96 μs. The data of every sample was processed by Python scripts to obtain unbiased diffusion time, which was used to derive stoichiometry by where ) , 0 , ) and 0 are the molecular weights and corrected diffusion times of subpopulations. More details about pscFCS is in supplementary information.

TIRF colocalization measurement for affinity
The PEG-passivated slides were prepared as previously described 44 . OmpC G8C-AF555 with AviTag on C-terminus was immobilized on coverslip surface via biotin-streptavidin interaction. The cell was incubated by 0.05 mg/mL streptavidin and washed by buffer C. Then 8 M urea denatured biotinylated OmpC was diluted 50-fold in buffer C to final concentration of 50 pM and added to the cell with streptavidin. Then the cell was washed again by buffer C.
Finally varying Skp D128C-AF647 from 500 pM to 8 nM in buffer C was added to the cell.
Surface adsorption of proteins was prevented by 0.02% (v/v) tween 20 (Surfact-Amps 20, Life Technology) in buffer and an oxygen scavenging system was included in buffer during detection 44 . Colocalization measurement was performed on a home-built TIRF microscope using alternating laser excitation (ALEX) between 532 nm and 640 nm at 23 °C 44 . Emitted fluorescence from the molecules on surface was separated by filters and collected by a dualview EMCCD with frame frequency of 10 Hz. Colocalized fluorescence spots of donor and acceptor excited by 532 nm laser were counted as described before 44 . Traces of monomeric OmpC bound by Skp were selected to yield 640 nm-excited fluorescence counts histogram and apparent smFRET efficiency histogram. Apparent smFRET efficiency was calculated by equation (13). Finally, the sample was diluted in buffer C to single-molecule concentration to carry out the smFRET experiments.

Data Availability
The datasets and code in the study are available from the corresponding author on reasonable request.