Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations

Biochemistry in living cells is an emerging field of science. Current quantitative bioassays are performed ex vivo, thus equilibrium constants and reaction rates of reactions occurring in human cells are still unknown. To address this issue, we present a non-invasive method to quantitatively characterize interactions (equilibrium constants, KD) directly within the cytosol of living cells. We reveal that cytosolic hydrodynamic drag depends exponentially on a probe’s size, and provide a model for its determination for different protein sizes (1–70 nm). We analysed oligomerization of dynamin-related protein 1 (Drp1, wild type and mutants: K668E, G363D, C505A) in HeLa cells. We detected the coexistence of wt-Drp1 dimers and tetramers in cytosol, and determined that KD for tetramers was 0.7 ± 0.5 μM. Drp1 kinetics was modelled by independent simulations, giving computational results which matched experimental data. This robust method can be applied to in vivo determination of KD for other protein-protein complexes, or drug-target interactions.

Where k is the Boltzman constant, T refers to temperature at which measurement was conducted [K], and η is the viscosity of water [Pa•s] in given temperature T.
Hydrodynamic radius of Calcein was obtained from literature (ref. 27).
EGFP and EGFP tagged apoferritin were modelled using HydroPro software.
All hydrodynamic radii for tracers were set together in Table SI1.

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations
3

SI2. Determination of diffusion coefficients of tracers in the cytoplasm of HeLa cells
Dextrans and nanoparticles were introduced into cells by microinjection. Proteins (EGFP and EGFP-apoferritin) were expressed after transfection with proper plasmids. Calcein was introduced to cell culture medium as calcein-AM and spontaneous cellular uptake occurred within minutes.
For each experiment, size of a focal volume (ωxy) was determined during calibration. † Cells filled with tracers were placed in experimental setup and focal volume was positioned in cytoplasmic area. FCS measurements were performed for 0.25-10 minutes, depending on a tracer ‡ . Each tracer was measured in at least 15 cells from at least two different inocula. Diffusion coefficients were calculated according to equation SI1.1 and displayed in

SI3. HydroPro calculations
Diffusion coefficients in water D0 at temperature of 37° C and viscosity of 0.69 mPas were calculated using HydroPro software (Ortega2011) based on the available structural data (RCSB Protein Data Bank and EMDataBank). The size of a given oligomer was estimated as hydrodynamic radius, rp, calculated from respective D0 using Stokes-Sutherland-Einstein relation, (equation SI1.2). The protein data bank (PDB) structures of Drp1 (4BEJ), GFP (1EMA) and ferritin (4YKH) were used to build models of Drp1 and GFP-Drp1 oligomers as well as model molecules † Calibration was performed using 10 nM Rhodamine B in 2.5%w/w glucose in PBS (see reference 36). ‡ Acquisition time was dependent on a fluorophore photostability and expected diffusion time of a tracer.

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations
4 (GFP, ferritin). The structure of GFP-Drp1 was created in Chimera software and saved in pdb format for calculations in HydroPro software. The four Drp1 molecules (monomers) present in the 4BEJ asymmetric unit of 4BEJ structure were used as one of the models of the tetramer. Biological assembly was used as a model of dimer and one selected Drp1 molecule from a dimer was a model of the monomer.

SI4. Drp1 analysis in cell -K668E mutant (monomer)
FCS data was acquired in a cytosol of cells transfected with EGFP-K668E-Drp1 protein. 10 measurements were performed per cell and acquisition time of each curve was 30 s. The FCS autocorrelation curves were normalized and summarized for each cell, and then fitted using two component model. Diffusion coefficients for each component were calculated using equation SI1.1, where τD was a value obtained from fitting and ωxy was determined during calibration (separately for each experiment). Results were summarized in table SI4.1.

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations
Results for bigger oligomers indicate existence of EGFP blinking phenomenon (see SI5, SI6 and SI7 sections). It was expected, that blinking should also occur in EGFP-K668E-Drp1 samples. However, blinking time (approximately 150 µs) was close to monomer diffusion time (approx.. 550 µs, varying according to calibration settings). These two times could not be distinguished by fitting and thus simple two component model was used.

SI5. Drp1 analysis in cell -G363D mutant (dimer)
FCS data was acquired in a cytosol of cells transfected with EGFP-G363D-Drp1 protein. 10 measurements were performed per cell and acquisition time of each curve was 30 s. The FCS autocorrelation curves were normalized and summarized for each cell, and then fitted using two component model with additional component for EGFP blinking (see reference 34). Diffusion coefficients for each component were calculated using equation SI1.1, where τD was a value obtained from fitting and ωxy was determined during calibration (separately for each experiment). Results were summarized in table SI5.1.

SI6. Drp1 analysis in cell -C505A mutant (dimer with fission functionality)
FCS data was acquired in a cytosol of cells transfected with EGFP-C505A-Drp1 protein. 10 measurements were performed per cell and acquisition time of each curve was 30 s. The FCS autocorrelation curves were normalized and summarized for each cell, and then fitted using two component model with additional component for EGFP blinking (see reference 34). Diffusion coefficients for each component were calculated using equation SI1.1, where τD was a value obtained from fitting and ωxy was determined during calibration (separately for each experiment). Results were summarized in table SI6.1. Content of freely diffusing dimer is 44% (on average). This is lower than in G363D mutant (67%), which indicates higher membrane affinity of C505A-Drp1.

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations
7 (see Table 1, main text) and ωxy calibrated for each data set. Results of the fitting were summarized in Table SI7.1.

SI8. Brightness of oligomers
FCS autocorrelation curve G(τ) depends inter alia on a square of molecular brightness of a probe (see reference 36). Therefore, if a mixture of a probes is considered, brightness should be taken into account in analysis of the probes' relative quantities. In case of Drp1 dimer and tetramer, if each of monomers consist of an EGFP tag, then tetramer should be twice as bright as dimer. Thus, tetramer contribution in FCS signal would be 4-times bigger than it would result from its concentration.
Plasmid coding EGFP-Drp1 was introduced into native cells, expressing their endogenous Drp1 levels. According to Western blot analysis (see reference 27), total concentration of endogenous Drp1 in HeLa Kyoto cells is 0.6 mM (counted per monomer). Concentration of EGFP-tagged protein can be calculated basing on FCS autocorrelation curve amplitude, which is equal to N -1 , where N is a number of fluorescent objects in a focal volume. FCS autocorrelation curves of EGFP-Drp1(wt) before normalization were fitted with a three component diffusion model. Obtained N

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations
values were used for calculation of fluorescent objects concentrations (C), according to equation SI8.1.
where NA is Avogadro constant, h is height of detection volume (assumed to be equal to 1•10 -6 m, constant for all measurements) and ωxy is a radius of a focal volume considered for each experiment separately. Geometry of focal volume in a cell is presented in Fig. SI8 (1) decreasing diffusion coefficient, (2) increasing amplitude, and (3) decreasing apparent concentration. As was shown in figure SI8.2, none of these dependences could have been noticed. Thus, we can assume that large oligomers of bigger brightness were immobile in a timescale of FCS measurements and do not contribute in FCS signal. This assumption is in accordance with the fact, that large Drp1 oligomers are formed on mitochondrial membranes as fission complexes and can be detected as immobile bright spots (see reference 23).  Amount of Drp1 in transfected cells is a sum of endogenous Drp1 (580 nM, Western blot) and tagged, EGFP-Drp1 expressed from the introduced plasmid. For FCS experiments only cells with low EGFP-Drp1 expression were picked to obtain N optimal for measurements (see figure 3). Concentration of objects measured by FCS (tagged) was in the range of 42 to 125 nM, which gives fraction of EGFP-Drp1 of 7-22% (average 12 ± 4%). Thus, there is an excess of endogenous Drp1 in examined cells. Moreover, steric limitations account for higher probability of EGFP-Drp1 to Drp1(endo) binding, than of two EGFP-Drp1 molecules (analogous for EGFP-dimers and dimers(endo)). EGFP dimerization has also low probability as it occurs at higher concentrations (approx. 0.1 mM, see reference 38). Following, on average we can assume, that each dimer or tetramer detected by FCS contains only one EGFP-Drp1 molecule. Going further, considerations concerning large component resulted in conclusion, that molecules of a brightness equal to dimers and tetramers have major contribution to the signal. Concluding, we assume equal brightness of all diffusing objects. ** Types of objects present in cytosol of EGFP-Drp1 (wt) expressing cells are presented schematically in Fig. SI8.3.

Determination of oligomerization state of Drp1 protein in living cells at nanomolar concentrations
** Equal to brightness of one EGFP molecule.

SI10. Monte Carlo simulations
The in vivo FCS experiments were supported by simulations of Drp1 diffusion in living cells. Also the kinetics of oligomerization was modelled. The simulations were performed using Monte Carlo cell (Mcell) simulator (references 42-44) supported by CellBlender 1.1 environment. Output of the MCell simulations was piped into the FERNET toolkit where FCS timetraces were generated (reference 44). The dimensions of simulation box were set as 5×5×1 μm and the walls of the simulation box were set as reflecting. The backward rate constant was calculated as koff = K kon. For Reaction 1 and Reaction 2 the forward rates used in simulations was given by equation SI10.1. Due to the character of Reaction 1 however the backward rate was set as koff/2. This is because the amount of dimer molecules D decreases twice faster than increase of tetramer molecules T. For Reaction 2 the backward rate was equal to koff.
Simulations were run for two cases. At each simulation there was an additional fraction of fluorescent molecules that did not take part in the tetramerization reactions but were detectable in the experiments. The concentration of those C molecules was equal to [C] = cf p, where cf denotes total concentration of fluorescent molecules (71.7 or 55.6 nM). The equilibrium concentrations of dimers and tetramers were estimated on the basis of initial simulations -the simulation containing only the total amount of unlabelled monomers [M] = 580 nM and labelled [D*] dimers. Number of simulations steps for initial simulations was equal to 5 × 10 4 and corresponded to 50 ms. The equilibrium was obtained after about 1 ms and the equilibrium concentration of the each type of molecule ([D]eq, [D*]eq, [T]eq, [T*]eq) was calculated as an average concentration for time t > 1 ms. Thus obtained equilibrium concentrations were equal to those calculated from the kinetic equations with approximately 3% of accuracy.