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• W4313463897 abstract "Article Figures and data Abstract Editor's evaluation Introduction Results Discussion Materials and methods Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5 Appendix 6 Data availability References Decision letter Author response Article and author information Metrics Abstract Inside prokaryotic cells, passive translational diffusion typically limits the rates with which cytoplasmic proteins can reach their locations. Diffusion is thus fundamental to most cellular processes, but the understanding of protein mobility in the highly crowded and non-homogeneous environment of a bacterial cell is still limited. Here, we investigated the mobility of a large set of proteins in the cytoplasm of Escherichia coli, by employing fluorescence correlation spectroscopy (FCS) combined with simulations and theoretical modeling. We conclude that cytoplasmic protein mobility could be well described by Brownian diffusion in the confined geometry of the bacterial cell and at the high viscosity imposed by macromolecular crowding. We observed similar size dependence of protein diffusion for the majority of tested proteins, whether native or foreign to E. coli. For the faster-diffusing proteins, this size dependence is well consistent with the Stokes-Einstein relation once taking into account the specific dumbbell shape of protein fusions. Pronounced subdiffusion and hindered mobility are only observed for proteins with extensive interactions within the cytoplasm. Finally, while protein diffusion becomes markedly faster in actively growing cells, at high temperature, or upon treatment with rifampicin, and slower at high osmolarity, all of these perturbations affect proteins of different sizes in the same proportions, which could thus be described as changes of a well-defined cytoplasmic viscosity. Editor's evaluation The work of Bellotto et al. provides a comprehensive and compelling study of the diffusion of proteins in the cytoplasm of the bacterium Escherichia coli, using multiple measurement methods, notably Fluorescence Correlation Spectroscopy. It is found that fast diffusing proteins roughly follow the Stokes-Einstein relation, while proteins that strongly interact with the cytoplasm manifest subdiffusion. This study will be a valuable resource for scientists seeking to understand the temporal dynamics of proteins within cells. https://doi.org/10.7554/eLife.82654.sa0 Decision letter eLife's review process Introduction Diffusion of molecules is important for the function of any cellular system, setting the upper limit for the mobility of proteins and other (macro)molecules and for the rates of many biochemical reactions that rely on random encounters between molecules (Schavemaker et al., 2018). Although the fundamental physics of diffusion in dilute aqueous solutions is well understood and mathematically described (Einstein, 1906; Langevin, 1908; Perrin, 1910), diffusion in a cellular environment may be quite different (Schavemaker et al., 2018; Mika and Poolman, 2011). The concentration of macromolecules in the bacterial cytoplasm, primarily proteins but also ribonucleic acids (RNAs), a phenomenon known as macromolecular crowding, is extremely high. For Escherichia coli, it is around 300 mg/ml, which corresponds to a volume fraction of 25–30% (Cayley et al., 1991; Zimmerman and Trach, 1991). Such macromolecular crowding could hinder free diffusion and influence kinetics of protein association and of gene expression (Klumpp et al., 2013; Tabaka et al., 2014; van den Berg et al., 2017). The effects of crowding on protein diffusion have been demonstrated both in vitro and in vivo (Dix and Verkman, 2008; Rivas and Minton, 2016). Compared to water, the diffusion of a free green fluorescent protein (GFP) was reported to be 3–4 times slower in the eukaryotic cytoplasm (Swaminathan et al., 1997) and up to 10 times slower in the bacterial cytoplasm (Elowitz et al., 1999; Nenninger et al., 2010; Mika et al., 2010; Kumar et al., 2010). In addition to the high density of macromolecules, the diversity in the size and chemical properties of the solutes makes the cytoplasmic environment highly inhomogeneous (Luby-Phelps, 1999; Spitzer and Poolman, 2013). How much the diffusion of a particular molecule is affected by macromolecular crowding might thus depend on the size (Muramatsu and Minton, 1988) and the shape of the molecule (Balbo et al., 2013) as well as on the nature of the crowders (Banks and Fradin, 2005; Goins et al., 2008). The effects of crowding observed in living cells appear to be even more complex, varying not only with the properties of the diffusing particle but also with the physiological state of the cell (Parry et al., 2014; Joyner et al., 2016) and the local cellular environment (Konopka et al., 2006; Persson et al., 2020). Moreover, non-trivial effects on diffusion arise due to reversible assembly and disassembly of the diffusing protein complexes (Agudo-Canalejo et al., 2020), and possibly also due to the active enhancement of enzyme diffusion by catalytic reactions (Golestanian, 2015; Agudo-Canalejo et al., 2018; Zhang and Hess, 2019). The dependence of the diffusion coefficient (D) of a protein in the cytoplasm on its size might thus not necessarily follow the Stokes-Einstein (also called Stokes-Einstein-Sutherland-Smoluchowski) relation that is valid in dilute solutions, D ∝ T/(ηR) (Einstein, 1906), where T is the absolute temperature in Kelvin, η is the viscosity of the medium, and R is the hydrodynamic radius of the particle. For globular proteins, R is given by the radius of gyration (Tyn and Gusek, 1990) and depends on the molecular mass (MM) as R ∝ MMβ, where the exponent β would be 1/3 for perfectly compact and globular proteins but is in practice within the range of 0.35–0.43 for typical proteins, reflecting the fractal nature of the spatial distribution of protein mass (Smilgies and Folta-Stogniew, 2015; Enright and Leitner, 2005). Several studies of protein diffusion in the cytoplasm of E. coli have yielded different dependencies on the molecular mass, from ~0.33 (Nenninger et al., 2010) to ~2 (Kumar et al., 2010), with an average β~0.7 estimated based on the data pooled from multiple studies (Mika and Poolman, 2011; Kalwarczyk et al., 2012), and thus substantially steeper than predicted by the Stokes-Einstein relation. Similar exponent of ~0.7 was observed for limited sets of differently sized proteins (Mika et al., 2010; Stracy et al., 2021). However, neither of these studies took explicitly into account the non-globularity of the used fluorescent constructs, where two or more proteins are typically connected by flexible linkers. For such multidomain proteins, shape fluctuations and hydrodynamic interactions between the different domains can have a sizeable effect on the effective diffusion coefficient of the whole protein (Agudo-Canalejo and Golestanian, 2020), and they might thus be important to consider when interpreting deviations from the Stokes-Einstein relation. Besides macromolecular crowding, the translational diffusion of cytoplasmic proteins is also influenced by intracellular structures, such as cytoskeletal filaments (Sabri et al., 2020), and by (transient) binding to other macromolecules (Saxton, 2007; Guigas and Weiss, 2008; von Bülow et al., 2019). Both these factors can not only reduce protein mobility but also lead to the anomalous subdiffusive behavior, where the mean square displacement (MSD) of diffusing particles does not scale linearly with time, as for Brownian diffusion in dilute solutions, but rather follows MSD α tα with the anomalous diffusion exponent α being <1 (Saxton, 1996; Etoc et al., 2018). Subdiffusion is commonly observed in eukaryotes, particularly at longer spatial scales, primarily due to the obstruction by the cytoskeletal filaments to the diffusion of proteins and larger particles (Di Rienzo et al., 2014; Sabri et al., 2020). The mobility of larger nucleoprotein (Golding and Cox, 2004; Lampo et al., 2017) and multiprotein particles (Yu et al., 2018) in the bacterial cytoplasm is also subdiffusive, while the diffusion of several tested small proteins was apparently Brownian (Bakshi et al., 2011; English et al., 2011). Even for the same protein, for example, GFP or its spectral variants, estimates of the diffusion coefficient in the cytoplasm obtained in different studies vary widely (Schavemaker et al., 2018), which could be in part due to differences in methodologies. Most early studies in bacteria relied on fluorescence recovery after photobleaching (FRAP), where diffusion is quantified from the recovery of fluorescence in a region of the cell bleached by a high-intensity laser (Lorén et al., 2015). These measurements provided values of diffusion coefficient for GFP ranging from 3 to 14 µm2 s–1 (Elowitz et al., 1999; Mullineaux et al., 2006; Konopka et al., 2009; Kumar et al., 2010; Mika et al., 2010; Nenninger et al., 2010; Schavemaker et al., 2017). More recently, single-particle tracking (SPT), where diffusion is measured by following the trajectories of single fluorescent molecules over time (Kapanidis et al., 2018), became increasingly used. Finally, diffusion can also be studied in vivo using fluorescence correlation spectroscopy (FCS) (Cluzel et al., 2000), which measures the time required by a fluorescent molecule to cross the observation volume of a confocal microscope (Elson, 2011). SPT and FCS measure protein mobility locally within the cell, with FCS having also a significantly better temporal resolution than FRAP and SPT. Both methods provided higher but still varying values of DGFP, from 8 µm2 s–1 up to 18 µm2 s–1 (Meacci et al., 2006; English et al., 2011; Sanamrad et al., 2014; Diepold et al., 2017; Rocha et al., 2019). Protein mobility also depends on the environmental and cellular conditions that affect the structure of the bacterial cytoplasm (Schavemaker et al., 2018). Diffusion of large cytoplasmic particles, measured by SPT, was shown to be sensitive to the antibiotics-induced changes in the cytoplasmic crowding (Wlodarski et al., 2020) and to the energy-dependent fluidization of the cytoplasm (Parry et al., 2014). Protein diffusion is also affected by high osmolarity that increases macromolecular crowding and might create barriers to diffusion (Konopka et al., 2006; Konopka et al., 2009; Liu et al., 2019). Furthermore, the surface charge of cytoplasmic proteins has been shown to have a dramatic effect on their mobility (Schavemaker et al., 2017). Variations between values of diffusion coefficients observed even for the same model organism in different studies, each investigating only a limited number of protein probes, using different strains, growth conditions, and measurement techniques, hampered drawing general conclusions about the effective viscosity of bacterial cytoplasm and its dependence on the protein size. Furthermore, while the impact of several physiological perturbations on protein diffusion has been established, most of these previous studies used either large particles or free GFP, and how these perturbations affect the properties of the cytoplasm over the entire physiological range of protein sizes remained unknown. Here, we address these limitations by systematically analyzing the mobility of a large number of differently sized cytoplasmic fluorescent protein constructs under standardized conditions by FCS. We further combined experiments with Brownian dynamics simulations and theoretical modeling of diffusion to correct for effects of confined cell geometry. Our work establishes general methodology to analyze FCS measurements of protein mobility in a confined space, which could be broadly applicable to cellular systems. For the majority of studied constructs, we observe consistent dependence of the diffusion coefficient on the protein size, with a pronounced upper limit on diffusion at a given molecular mass. When corrected for the confinement due to the bacterial cell geometry, the diffusion of these constructs was nearly Brownian. Moreover, part of the deviation of the mass-dependence of their diffusion coefficients from the Stokes-Einstein relation might be explained by the specific shape of the fusion proteins. The slower and more anomalous diffusion of several protein constructs was apparently due to their strong interactions with other cellular proteins and protein complexes, and disruption of these interactions restored a Brownian diffusion close to the upper limit expected for their mass. Proteins that are not native to E. coli were observed to diffuse very similarly to their E. coli counterparts, except for their motion being slightly subdiffusive. Under the same experimental conditions FCS and FRAP measurements yield similar values of diffusion coefficients, suggesting that no pronounced dependence of protein mobility on spatial scale could be observed in the bacterial cytoplasm. Finally, we investigated the effects of environmental osmolarity and temperature, of exposure to antibiotics and of cell growth on the mobility of proteins of different size, demonstrating that the effects of all these perturbations, including cell growth, on protein diffusion could be simply explained by changes in a unique cytoplasmic viscosity. Results Dependence of cytoplasmic protein mobility on molecular mass measured by FCS For our analysis of cytoplasmic protein mobility, we generated a plasmid-encoded library of 31 cytoplasmic proteins (Table 1) of E. coli fused to superfolder GFP (sfGFP) (Pédelacq et al., 2006). We selected proteins that belong to different cellular pathways and, according to the available information, are not known to bind DNA or to form homomultimers, although we did not exclude a priori proteins that interact with other proteins. The structure of all selected proteins is known and roughly globular, avoiding effects of the irregular protein shape on mobility. The expected size and stability of each construct were verified by gel electrophoresis and immunoblotting (Figure 1—figure supplement 1). Only one of the constructs, ThpR-sfGFP, showed >20% degradation to free sfGFP, and it was therefore excluded from further analyses. This was also the sole construct with an atypically high isoelectric point (pI), and all remaining constructs have pI ranging from 5.1 to 6.2, as common for cytoplasmic proteins (Schwartz et al., 2001). We further imaged the distribution of fusion proteins in the cytoplasm. Except for RihA-sfGFP and NagD-sfGFP that were subsequently excluded, all other constructs showed uniform localization (Figure 1A). Expression of most fusion proteins used for the measurements of diffusion had little effect on E. coli growth (Figure 1—figure supplement 2), and even for several proteins where expression delayed the onset of the exponential growth, the growth rate around the mid-log phase when cultures were harvested for the analysis was similar. The mobility of the remaining 28 fusion constructs and of free sfGFP was investigated in living E. coli cells by FCS (see Materials and methods and Appendix 2). In order to reduce the impact of photobleaching on FCS measurements, cell length was moderately (approximately twofold) increased by treatment with the cell-division inhibitor cephalexin for 45 min, yielding an average cell length of ~5 μm (Figure 1A). The resulting larger cell volume indeed reduces the rate of photobleaching. During each FCS measurement, the laser focus was positioned close to the polar region in the cell cytoplasm, in order to keep the confocal volume possibly away from both the cell membrane and the nucleoid, and the fluorescence intensity in the confocal volume was measured over time (Figure 1—figure supplement 3). For each individual cell, six subsequent acquisitions of 20 s each were performed at the same position. The autocorrelation function (ACF) of the fluorescence intensity fluctuations was independently calculated for each time interval and fitted to extract the mobility parameters of the fluorescent proteins. Although we initially considered both the Brownian diffusion and the anomalous diffusion models, the latter model proved to be considerably better in fitting the experimental data (Figure 1—figure supplement 4). The anomalous diffusion model was therefore used to determine the diffusion (or residence) time (τD) of a fluorescent molecule in the confocal volume and the anomalous diffusion exponent α for all ACFs (Figure 1B, Table 1, and Figure 1—figure supplement 3). The averaged values of τD and α for each individual cell were then calculated from these six individual acquisitions (Figure 1C and Figure 1—figure supplement 5). Although, as mentioned above, all finally used protein constructs showed no or little degradation, we tested a possible impact of the fraction of free sfGFP for the construct that displayed the strongest (~15%) degradation, DsdA-sfGFP. To this end, we fitted the FCS data using a model of two-components anomalous diffusion, where the weight of the fast component was fixed to 15% and its values of τD and α to the average values obtained for sfGFP (Figure 1—figure supplement 6). The average value of τD for the slow component was only ~7% lower compared to our regular fit using the one-component model, and the value of α remained unchanged, suggesting that the impact of an even smaller fraction of free GFP for other constructs could also be neglected. As another control, we observed no significant correlation between the values of 1/τD or α and the length or the width of individual cells, although a weak trend of α increasing with cell width might exist (Figure 1—figure supplement 7). Finally, when individual cephalexin-treated and untreated cells of similar length were compared, we observed no effect of the treatment on the value of α and only marginal (p=0.08) increase in the mobility of sfGFP (Figure 1—figure supplement 8). Table 1 Molecular mass, biological function, and measured parameters for all studied sfGFP fusion constructs. The concentration of expression inducer and the number of cells measured with each technique is also indicated. Protein nameMolecular mass of sfGFP fusion constructBiological function in E. coliIPTG concentration used for FCS (FRAP)Number of cells analyzed by FCSτD (µs; mean ± SEM)α (mean ± SEM)Diffusion coefficient, FCS (μm2/s, mean ± SEM)Number of cells analyzed by FRAPDiffusion coefficient, FRAP (μm2/s, mean ± SEM)sfGFP26.9–5 µM (15 µM)52561±140.86±0.0114.7±0.31111.3±1.3YggX39.2Probable Fe (2+)-trafficking protein5 µM (5 µM)8611±190.85±0.0112.9±0.4109.4±1.6ClpS39.2ATP-dependent Clp protease adapter protein0 µM111054±330.75±0.01FolK45.12-amino-4-hydroxy-6-hydroxymethyldihydropteridine pyrophosphokinase0 µM8734±240.87±0.0111.6±0.4Crr45.2Component of glucose-specific phosphotransferase enzyme IIA0 µM141065±360.87±0.01UbiC45.7Chorismate pyruvate-lyase15 µM141140±580.87±0.01ThpR46.9RNA 2′,3′-cyclic phosphodiesteraseDiscarded due to instability of sfGFP fusion constructCoaE49.6Dephospho-CoA kinase0 µM11854±470.87±0.019.8±0.6Adk50.6Adenylate kinase5 µM (15 µM)23802±260.88±0.0010.6±0.4169.8±1.5Cmk51.7Cytidylate kinase5 µM161163±580.87±0.01NagD54.1Ribonucleotide monophosphataseDiscarded due to non-uniform protein localizationKdsB54.63-deoxy-manno-octulosonate cytidylyltransferase0 µM111659±700.84±0.01Map56.3Methionine aminopeptidase0 µM201830±780.81±0.01MmuM60.4Homocysteine S-methyltransferase5 µM142241±1380.73±0.01RihA60.8Pyrimidine-specific ribonucleoside hydrolaseDiscarded due to non-uniform protein localizationPanE60.82-dehydropantoate 2-reductase0 µM (5 µM)181059±260.85±0.017.8±0.2115.2±0.6SolA67.9N-methyl-L-tryptophan oxidase0 µM7795±310.82±0.019.9±0.5Pgk68.1Phosphoglycerate kinase0 µM16991±410.90±0.018.6±.0.3EntC69.9Isochorismate synthase15 µM151777±1190.82±0.01AroA73.13-phosphoshikimate 1-carboxyvinyltransferase5 µM9995±690.86±0.018.7±0.7ThrC74.1Threonine synthase0 µM14908±280.87±0.019.1±0.3MurF74.4UDP-N-acetylmuramoyl-tripeptide--D-alanyl-D-alanine ligase0 µM71008±760.85±0.028.3±0.7DsdA74.9D-serine dehydratase0 µM141017±530.89±0.018.4±0.4107.8±0.7HemN79.7Oxygen-independent coproporphyrinogen III oxidase0 µM131262±540.86±0.016.7±0.4PrpD80.92-methylcitrate dehydratase0 µM121866±1400.84±0.01DnaK96.0Molecular chaperone5 µM102296±780.76±0.01MalZ96.0Maltodextrin glucosidase0 µM93725±2290.77±0.01GlcB107.5Malate synthase G5 µM (15 µM)161315±450.86±0.016.4±0.2106.7±1.1MetE111.75-methyltetrahydropteroyltriglutamate--homocysteine methyltransferase5 µM81137±530.87±0.017.4±0.3LeuS124.2Leucine--tRNA ligase0 µM141637±750.86±0.015.1±0.2AcnA124.7Aconitate hydratase A5 µM (15 µM)191415±560.86±0.016.1±0.2104.3±0.4MetH163.0Methionine synthase0 µM (5 µM)91402±450.81±0.015.8±0.1154.0±0.5 Figure 1 with 10 supplements see all Download asset Open asset Dependence of protein mobility in bacterial cytoplasm on molecular mass and cellular interactions. (A) Examples of fluorescence microscopy images of Escherichia coli cells expressing either sfGFP or the indicated sfGFP-tagged cytoplasmic proteins. Scale bars are 2 μm. (B) Representative autocorrelation functions (ACFs) measured by FCS for the indicated protein constructs. Data were fitted using the anomalous diffusion model (solid lines). All ACF curves were normalized to their respective maximal values to facilitate comparison. (C) Diffusion times (τD) measured for the indicated protein constructs. Each dot in the box plot represents the value for one individual cell, averaged over six consecutive acquisitions (Figure 1—figure supplement 3). The numbers of cells measured for each construct are shown in Appendix 6. ***p<0.0001 in a two-tailed heteroscedastistic t-test. Exact p-valuescan be found in Appendix 5. (D, E). Dependence of protein mobility (1/τD; D) and apparent anomaly of diffusion (α; E) on molecular mass. Each symbol represents the average value for all individual cells that have been measured for that particular construct and the error bars represent the standard error of the mean. Individual values are shown in Figure 1—figure supplement 5 and the numbers of measured cells for each construct are shown in Appendix 6. Protein constructs with low mobility for which effects of specific interactions were further investigated are highlighted in color and labeled. The values of 1/τD and α for both the original constructs (diamonds) and the constructs where mutations were introduced to disrupt interactions (circles) are shown. For Map, two alternative amino acid substitutions that disrupt its interaction with the ribosome are shown (see Figure 1—figure supplement 10). (F–H) Cartoons illustrating the cellular interactions that could affect mobility of ClpS (F), Map (G), and DnaK (H). ClpS engages with the ClpAP protease and with substrates, cartoon adapted from Figure 1A from Román-Hernández et al., 2011. Map interacts with the actively translating ribosomes, cartoon adapted from Figure 3A from Sandikci et al., 2013. DnaK interacts with unfolded client protein. Amino acidic residues that were mutated to disrupt interactions are highlighted (see text for details). FCS, fluorescence correlation spectroscopy. Figure 1—source data 1 Individual τD measurements from Figure 1C. Individual mean and standard errors of the mean of 1/τD values from Figure 1D. Individual mean and standard errors of the mean of α values from Figure 1E. https://cdn.elifesciences.org/articles/82654/elife-82654-fig1-data1-v2.xlsx Download elife-82654-fig1-data1-v2.xlsx Despite their substantial intercellular variability, the obtained mean values of the diffusion time were clearly different between protein constructs (Figure 1C and Table 1). We next plotted the mean values of 1/τD, which reflect protein mobility, against the molecular mass of protein constructs (Figure 1D). This dependence revealed a clear trend, where mobility of more than half of the constructs decreased uniformly with their molecular mass, while some exhibited much lower mobility than the other constructs of similar mass. In contrast, the anomalous diffusion exponent α showed no apparent dependence on the protein size, ranging from 0.8 to 0.86 for most of the constructs (Figure 1E). Notably, the few protein constructs with α of ~0.8 or lower were also among the ones with low mobility for their molecular mass (Figure 1D and E, colored symbols). Macromolecular interactions reduce protein mobility We reasoned that the main group of constructs that exhibit mobility close to the apparent mass-dependent upper limit represents proteins whose diffusion is only limited by macromolecular crowding, and that the lower 1/τD and α of other constructs might be due to their specific interactions with other cellular proteins or protein complexes. Indeed, for three of these proteins (ClpS, Map, and DnaK) such interactions are well characterized and can be specifically disrupted. ClpS is the adaptor protein that delivers degradation substrates to the protease ClpAP (Román-Hernández et al., 2011). The substrate-binding site of ClpS is constituted by three amino acid residues (D35, D36, and H66) that interact with the N-terminal degron of target proteins (Figure 1F). If these residues are mutated into alanine, substrate binding in vitro is substantially reduced (Román-Hernández et al., 2011; Humbard et al., 2013). Additionally, ClpS directly docks to the hexameric ClpA. Consistently, we observed that while the stability of the mutant construct ClpSD35A_D36A_H66A-sfGFP was not affected (Figure 1—figure supplement 9), its mobility in a ΔclpA strain became significantly higher and less anomalous, with both 1/τD and α reaching levels similar to those of other proteins of similar mass (Figure 1D and E and Figure 1—figure supplement 10). Similar results were obtained for the other two constructs. Map is the methionine aminopeptidase that cleaves the N-terminal methionine from nascent polypeptide chains (Solbiati et al., 1999). Map interacts with the negatively charged backbone of ribosomes through four positively charged lysine residues (K211, 218, 224, and 226) located in a loop (Figure 1G). If these residues are mutated into alanine, the in vitro affinity of Map for the ribosomes is reduced (Sandikci et al., 2013). The mobility of Map-sfGFP was indeed much increased by alanine substitutions at all four lysine sites (Figure 1D and E and Figure 1—figure supplement 9 and Figure 1—figure supplement 10). Interestingly, charge inversion of lysines to glutamic acid did not further increase Map-sfGFP mobility as was expected based on in vitro experiments (Sandikci et al., 2013). DnaK is the major bacterial chaperone that binds to short hydrophobic polypeptide sequences, which become exposed during protein synthesis, membrane translocation, or protein unfolding (Genevaux et al., 2007). DnaK accommodates its substrate peptides inside a hydrophobic pocket (Figure 1H). The substitution of the valine residue 436 with bulkier phenylalanine creates steric hindrance that markedly decreases substrate binding to DnaK in vitro (Mayer et al., 2000), and both the 1/τD and α of DnaKV436F-sfGFP were significantly higher than for the correspondent wild-type construct (Figure 1D and E and Figure 1—figure supplement 9 and Figure 1—figure supplement 10). Nevertheless, in this case, the 1/τD did not reach the levels of other proteins of similar molecular mass, which is likely explained by multiple interactions of DnaK with other components of the cellular protein quality control machinery besides its binding to substrates (Kumar and Sourjik, 2012). Apparent anomaly of diffusion could be largely explained by confinement When FCS measurements are performed in a confined space with dimensions comparable to those of the observation volume, such confinement may affect the apparent mobility of fluorescent molecules (Gennerich and Schild, 2000; Jiang et al., 2020). To investigate the effect of confinement on our FCS measurements, we performed Brownian dynamics simulations of FCS experiments with particles undergoing three-dimensional, purely Brownian diffusion inside a bacterial cell-like volume (Figure 2A Inset; see Materials and methods). For the values of cell diameter commonly observed under our growth conditions, 0.8–0.9 μm, and over a wide range of particle diffusion coefficients, simulated ACFs could be indeed successfully fitted with the anomalous diffusion model, yielding an anomalous diffusion exponent of around 0.8–0.9 (Figure 2A and B). This made us hypothesize that the relatively small apparent deviation from Brownian diffusion in the fit, with α between 0.82 and 0.9 common to most constructs, may primarily reflect a confinement-induced effect rather than proper subdiffusion. Figure 2 with 8 supplements see all Download asset Open asset Protein diffusion in bacterial cytoplasm corrected for confinement. (A) Representative ACFs of simulated fluorescence intensity fluctuations. Simulations were performed in a confined geometry of a cell with indicated length L and diameter d, and dimensions of the measurement volume ω0 and z0, representing an experimental FCS measurement (Inset; see Materials and methods) for two different values of the ansatz diffusion coefficient. Solid lines are fits by the models of unconfined Brownian diffusion, anomalous diffusion and by the Ornstein-Uhlenbeck (OU) model of Brownian diffusion under confinement, as indicated. (B) The exponent α extracted from the fit of the anomalous diffusion model to the ACFs data that were simulated at different values of the cell diameter. Corresponding values of the diffusion coefficient are shown in Figure 2—figure supplement 7. (C, D) Escherichia coli cells treated with cephalexin alone or with cephalexin and 1 µg/ml of A22 (see Materials and methods), show A22-dependent in" @default.
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• W4313463897 title "Author response: Dependence of diffusion in Escherichia coli cytoplasm on protein size, environmental conditions, and cell growth" @default.
• W4313463897 doi "https://doi.org/10.7554/elife.82654.sa2" @default.
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