Antibiotic Resistance via Bacterial Cell Shape-Shifting

ABSTRACT Bacteria have evolved to develop multiple strategies for antibiotic resistance by effectively reducing intracellular antibiotic concentrations or antibiotic binding affinities, but the role of cell morphology in antibiotic resistance remains poorly understood. By analyzing cell morphological data for different bacterial species under antibiotic stress, we find that bacteria increase or decrease the cell surface-to-volume ratio depending on the antibiotic target. Using quantitative modeling, we show that by reducing the surface-to-volume ratio, bacteria can effectively reduce the intracellular antibiotic concentration by decreasing antibiotic influx. The model further predicts that bacteria can increase the surface-to-volume ratio to induce the dilution of membrane-targeting antibiotics, in agreement with experimental data. Using a whole-cell model for the regulation of cell shape and growth by antibiotics, we predict shape transformations that bacteria can utilize to increase their fitness in the presence of antibiotics. We conclude by discussing additional pathways for antibiotic resistance that may act in synergy with shape-induced resistance.

caused by the antibiotic or if these are active shape changes that promote bacterial fitness for surviving antibiotic exposure. While the roles of cell size and shape in bacterial growth and motility have been characterized (15,17,(19)(20)(21)(22), the effect of cell shape on antibiotic resistance remains poorly understood.
Changes in cell size and shape can be physiologically beneficial to antibiotic-treated bacteria in several ways. An increase in the cell volume can dilute the antibiotic concentration inside a cell, thereby promoting cell growth. A reduction in S/V can reduce the flux of antibiotics coming into the cell (Fig. 1B). An increase in S/V can also provide adaptive benefits by increasing the rate of nutrient uptake or by increasing the rate of antibiotic efflux. An outstanding question is how bacteria modulate their cell morphologies to promote resistance to different types of antibiotics that target different cellular components. In this article, we use quantitative modeling and data analysis to propose that cell shape-shifting via changes in S/V promotes antibiotic resistance by effectively diluting the intracellular antibiotic concentration. In particular, by developing a mathematical model for antibiotic transport and kinetics coupled to bacterial cell shape and growth, we show that by changing S/V of the cell, bacteria can effectively dilute the intracellular antibiotic concentration by decreasing antibiotic influx (Fig. 1B). The model allows us to predict the quantitative range for antibiotic dilution via reduction in S/V. The model also explains how bacteria can increase S/V to promote resistance to membrane-targeting antibiotics (Fig. 1B), in agreement with experimental data (13). To understand how antibiotics induce cell shape transformations, we develop a whole-cell model for bacterial growth and shape regulation using the particular example of ribosome-targeting antibiotics for which the biochemical pathways are quantitatively  ) via changes in the cell surface-tovolume ratio (S/V) when the bacterial cell is exposed to a constant extracellular antibiotic concentration (a out ). Pathways for reducing intracellular antibiotic concentrations by solely reducing S/V, lowering porin expression, or overexpressing efflux pumps are shown with dashed lines. In the schematic, P in and P out represent the membrane permeability coefficients in the inward and outward directions, respectively. (Bottom) For membrane-bound antibiotics, an increase in S/V decreases the antibiotic surface density (a on ). Here, P on and P off are the rates of antibiotic binding to the membrane and unbinding from the membrane, respectively.
characterized. Using this model, we show that antibiotic-induced shape changes are dependent on nutrient availability such that it is beneficial for cells to increase S/V in nutrientrich media (to promote nutrient influx) and to decrease S/V in nutrient-poor media (to inhibit antibiotic influx). We conclude by discussing additional mechanisms of countering antibiotics via regulating metabolic pathways and membrane porin and efflux pump expression that may act in synergy with shape-induced resistance.

ANTIBIOTIC-INDUCED CELL SHAPE CHANGES IN ROD-SHAPED BACTERIA
To understand the effect of antibiotics on bacterial cell shape, we first analyzed the morphological data for E. coli cells treated with 42 different antibiotics belonging to 5 different categories based on their binding targets (see Fig. 3B; see also Fig. S1 in the supplemental material) (13). While the cell volume and surface area increased for antibiotics that target DNA, RNA, ribosomes, or the cell wall, membrane-targeting antibiotics induced reductions in both the surface area and the volume of the cell (Fig. S1). Surprisingly, all antibiotics decrease S/V except for membrane-and membrane transport-targeting antibiotics, which increase S/V ( Fig. 2A). Similarly, a decrease in S/V was previously observed in cells treated with cell wall-targeting antibiotics (A22, amdinocillin, and fosfomycin) (23), and an increase in S/V was previously observed for the membrane-targeting antibiotic cerulenin (24). We find that the Gram-negative bacterium Acinetobacter baumannii also decreases S/V for most antibiotics, including the membrane-targeting antibiotic triclosan (Fig. 2B). For the Gram-positive bacterium Bacillus subtilis, with a thick, less plastic cell envelope (25,26), S/V decreases for all groups of antibiotics ( Fig. 2C) (22). While these shape changes could represent a passive side effect of the antibiotic, they could also represent adaptive responses to counter the antibiotic's action. In particular, we note that S/V is one of the key physical parameters that regulate nutrient influx and waste efflux (19) as well as the rates of influx and efflux of antibiotics. To quantitatively understand the role of S/V in regulating antibiotic flux across the cell membrane, we developed a mathematical model of antibiotic transport into a rod-shaped bacterial cell, with binding/unbinding interactions with its specific targets in the cytosol or on the membrane.

THE CELL SURFACE-TO-VOLUME RATIO REGULATES INTRACELLULAR ANTIBIOTIC CONCENTRATIONS
When antibiotics are passively translocated into the cell thorough membrane porins or lipids (Fig. 3A), antibiotic transport is diffusion limited, and flux is given by Fick's law (27,28). The dynamics of the intracellular antibiotic concentration, a in , and the substrate concentration, x, are given by where a out is the concentration of the antibiotic in the extracellular medium, x 0 is the substrate concentration in the absence of the antibiotic, k x is the rate of substrate production, k on is the rate of binding of the antibiotic to the substrate, k off is the antibiotic unbinding rate, and P in and P out are the membrane permeability coefficients in the inward and outward directions, respectively. The last term on the right-hand side of equations 1 and 2 represents the dilution of the antibiotic and the substrate due to cell growth, where k is the bacterial growth rate. Using model parameters provided in Text S1 in the supplemental material (section 4), the numerical solution of the above-described system of equations for different values of S/V predicts the time evolution of the intracellular antibiotic concentration ( Fig. 3B), where the steady-state concentration of the antibiotic decreases with decreasing S/V (Fig. 3C). Here, for simplicity, it is assumed that the antibiotic binds irreversibly to the substrate, k off = 0 h 21 . Changes in k off do not strongly impact the dependence of the antibiotic concentration on S/V (Fig. S1B). Since all antibiotics, apart from membrane- To conceptually understand these numerical results, we note that the flux balance is reached at steady state such that in the limit of strong antibiotic-substrate binding (Text S1, section 1). Therefore, the strategy to decrease S/V upon antibiotic treatment (Fig. 2) results in a reduction in the antibiotic  Opinion/Hypothesis mBio influx term on the left-hand side of equation 3. In the case where efflux pumps are effective, where P out is .0, S/V reduction also leads to an overall decrease in antibiotic efflux.
To quantify the effect of S/V reduction on the intracellular antibiotic dilution (Fig. 3C), we introduce the antibiotic dilution factor d jDa in j=a out , defined as the absolute change in the intracellular antibiotic concentration (Da in ) relative to the extracellular concentration, as S/V is varied between a chosen minimum, (S/V) min , and a maximum value, (S/V) max . The dilution factor is thus dependent on the variation in S/V, growth rate k, influx permeability P in , and outflux permeability P out (Fig. 3D; Fig. S2). The maximum dilution is obtained for P out = 0 ( Fig. 3C and D), while a lesser dilution is obtained for a higher P out (Fig. S2D). To determine the maximum d due to shape variations, we optimize P in and k for P out = 0. We find that d is maximized when P in ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðS=VÞ min ðS=VÞ max p ¼ k (Fig. 3D, dashed line; Text S1, section 1), given by Thus, the maximum value of the dilution factor is dependent only on the surface-to-volume ratios before and after antibiotic application. The above-described equation predicts a maximum of an ;15% dilution in the intracellular antibiotic concentration for cephalexin-treated E. coli, where (S/V) max and (S/V) min are taken to be the surface-to-volume ratios for the untreated cell and the antibiotic-treated cell, respectively. Similarly, meropenem-treated A. baumannii cells undergo a maximum of a 22% dilution in the intracellular antibiotic concentration. Antibiotic dilution mediated by changes in S/V could provide a significant fitness advantage for antibiotics with steep growth inhibition curves (29,30) since a small reduction in the antibiotic concentration via shape variation could lead to a significant increase in the bacterial growth rate. For spherocylindrical cells of widths w min and w max before and after antibiotic treatment, the maximum dilution factor can be approximated as suggesting that the maximum antibiotic dilution depends predominantly on cell width for rod-shaped bacteria (Text S1, section 1). In contrast to cytosolic antibiotics, when E. coli cells are treated with membrane-targeting and membrane transport-targeting antibiotics, the cell surface area and volume decreased (Fig. S1), whereas the surface-to-volume ratio increased ( Fig. 2A). The decrease in surface area is expected since these antibiotics induce membrane damage or a reduction in membrane synthesis. However, the benefits of an increase in S/V could be interpreted as follows. If the membrane-targeting antibiotic binds directly to the membrane, the dynamics of the surface-bound antibiotic is given by P off a on |{z} unbinding from membrane 2 ka on |{z} dilution by growth (6) where a on is the surface density of the antibiotic and P on and P off are the rates of binding to and unbinding from the membrane surface, respectively (see Text S1, section 2, for derivation).
The first term on the right-hand side of equation 6 represents the total amount of antibiotic molecules (a out V) that can bind to the membrane per unit surface area and per unit time with a probability P on . Therefore, an increase in S/V decreases the density of membrane-bound antibiotics, thereby providing a beneficial morphological adaptation for countering the action of the antibiotic.

MECHANISMS OF CELL SHAPE CHANGES BY ANTIBIOTIC ACTION
The mechanisms by which antibiotics induce cell shape changes are specific to the type of antibiotic treatment (13). DNA-targeting antibiotics induce an SOS response that inhibits cell Opinion/Hypothesis mBio division, resulting in longer filamentous cells (13, 29) (Fig. 2). Cell wall-targeting antibiotics such as b-lactams bind to penicillin binding proteins and inhibit peptidoglycan synthesis. This affects septal cell wall synthesis, leading to longer filamentous cells, while the inhibition of peptide cross-linking by b-lactams can result in wider cells with a lower surface-to-volume ratio. Ribosome-targeting antibiotics inhibit translation, inducing a variety of shape changes depending on the nutrient availability in the growth environment (15,18,20). Below, we specifically focus on the case of ribosome-targeting antibiotics, for which the biochemical reactions are well characterized (31), in order to elucidate how the coupling between cell growth, shape, and protein synthesis regulates the cellular morphological response. One of the most commonly used ribosome-targeting antibiotics is chloramphenicol (CHL), which inhibits bacterial translation. When actively translating ribosomes are blocked by CHL, cells synthesize new ribosomes in excess to counterbalance their Here, a out is 5 mM, and P in /P out is 1. (D) Bacterial growth rate versus time obtained from simulations for two different cases as described above for panel C. The decrease in S/V results in a fitness gain. (E) Heat map of antibiotic dilution factors predicted from simulations as functions of membrane permeability ratios (P in /P out ) and the ratio of antibiotic-ribosome binding and unbinding rates (k on /k off ). The antibiotic dilution was calculated when the bacterial S/V was altered from 15 to 3 mm 21 , as in Fig. 3C. Membrane permeability ratios shown with horizontal arrows were estimated (see Text S1, section 1, in the supplemental material) for growing wild-type (WT) (G) and stationary-phase wild-type (S) E. coli cells and OmpF porin-deficient (DompF) and efflux-pump deficient (DtolC) cells (35). Experimentally measured k on /k off values for different ribosome-targeting antibiotics are shown with vertical arrows (58)(59)(60).
Opinion/Hypothesis mBio inactivation (32). This increase in ribosome abundance requires bacteria to strategically focus their ribosomal resources toward growth rather than division, causing an increase in the cell volume (33). Interestingly, when E. coli cells are exposed to nutrient or CHL perturbations, the bacterial cell aspect ratio remains constant at ;4 (17), implying a simple scaling relation between surface area and volume, S = 2p V 2/3 , yielding S/V = 2p V 21/3 (17). Therefore, if the bacteria increase their volume upon CHL treatment, due to excess ribosome synthesis, S/V would then decrease ( Fig. 4A and B). Experimental data, however, show that S/V increases or decreases upon chloramphenicol treatment depending on nutrient availability in the growth environment (20) (Fig. 4B). In nutrient-rich medium, S/V decreases upon chloramphenicol treatment, whereas in nutrient-poor medium, S/V increases upon chloramphenicol treatment (Fig. 4B). To interpret these results and quantitatively explain the data, we applied a previously developed whole-cell model for bacterial growth and division control (33) in the context of translation inhibition. In this model, the cell volume grows exponentially at a rate, k, whereas division proteins are synthesized at a volume-specific rate, k F . The cell divides when a threshold amount of division proteins is synthesized, resulting in the relation V = k/k F . This implies for E. coli cells that S/V = 2p (k F /k) 1/3 ( Fig. 4A; see also Text S1, section 3, in the supplemental material). The data in Fig. 4B can now be interpreted using the framework of cellular resource allocation (34). Upon treatment with chloramphenicol, cells upregulate ribosome synthesis to compensate for ribosome inhibition by chloramphenicol (32). The excess ribosomes that are produced are allocated differentially to growth (k) or division protein synthesis (k F ) depending on nutrient availability. In nutrientrich medium, cells allocate more ribosomes to division than growth (k/k F decreases), resulting in smaller cells and higher S/V. The increase in S/V provides an adaptive benefit by importing more nutrients to counter growth inhibition by the antibiotic. In contrast, in nutrient-poor medium, cells tend to allocate more ribosomes to growth than division (k/k F increases), resulting in larger cells and smaller S/V. A reduction in S/V reduces antibiotic influx, which is more beneficial for survival if nutrient availability is low.
To estimate the amount of antibiotic dilution due to cell shape changes, we simulated the whole-cell model to evolve the coupled dynamics of cell size and shape, division proteins, ribosomes, and the antibiotic (Text S1, section 3) (33). Using parameters benchmarked for E. coli cells, our model can quantitatively capture the experimentally observed trends for the dependence of S/V on the antibiotic concentration in different nutrient environments (Fig. 4B, solid lines). We find that under conditions where S/V remains unchanged, the intracellular antibiotic concentration is higher and the growth rate is lower than in the case where S/V spontaneously decreases over time ( Fig. 4C and D). Our simulations revealed that the maximum antibiotic dilution was obtained for antibiotics with high affinity constants (k A = k on /k off . 1 mM 21 ) typical for aminoglycosides: hygromycin B (k A = 5 mM 21 ), chloramphenicol (k A = 5.8 mM 21 ), streptomycin (k A = 10 mM 21 ), and paromomycin (k A = 19 mM 21 ). Depending on the ratio of the membrane permeability constants (P in /P out ), the antibiotic dilution factor is nonmonotonic and reaches a maximum for a P in /P out value of ;1 (Fig. 3C and Fig. 4E). Since aminoglycosides are predominantly transported inside the cell by porins, we estimated the permeability coefficients for the fluorescent antibiotic ofloxacin, which is also translocated by porins (35). By analyzing time traces of fluorescent-antibiotic accumulation inside the cell, we estimated that growing E. coli cells readily accumulate antibiotics, with a P in / P out value of ;0.54, while for stationary-phase cells, the P in /P out value is ;0.11. Interestingly, for bacterial cells lacking porins (DompF), P in /P out is ;0.18, and for bacteria lacking efflux pumps (DtolC), P in /P out is ;0.66 (Text S1, section 1). Therefore, these results suggest that the antibiotic dilution by changes in S/V could approach the maximum value achieved for P in P out and a large k on /k off (Fig. 4E).

CONCLUSION
In this article, we used quantitative modeling and morphological data analysis to demonstrate that bacteria can develop antibiotic resistance purely by cell shape changes. By analyzing cell size and shape data for three different bacterial species treated with 46 different antibiotics, we find that bacterial cells robustly reduce surface-to-volume ratios when treated with cytosolic antibiotics. A reduction in S/V comes with the adaptive benefit of decreasing antibiotic influx, which can effectively dilute the concentration of intracellular antibiotics. For membrane-bound antibiotics that induce membrane damage, an increase in S/V promotes drug dilution, in agreement with experimental observations. By developing a whole-cell model for bacterial growth, we further show how antibiotic-induced shape changes can provide fitness advantages in the presence of antibiotics and compare the model predictions with experimental data.
Since antibiotic dilution predominantly depends on cell width (equation 5), a central question is how width is determined (36)(37)(38) and how fast width is remodeled in response to antibiotic treatments. During steady-state growth, cell width is one of the most tightly controlled cellular parameters in both E. coli and B. subtilis (39,40) such that fluctuations in width are restored within 4 to 5 generations (17), commensurate with the typical time necessary for bacterial width remodeling (41). Under non-steady-state conditions, the cell width reaches a new equilibrium only within a few generations after nutrient shifts (42) or antibiotic exposure (15,18). Cell width control is achieved by cell wall synthesis machinery such as MreB, RodZ, and penicillin binding proteins (43) as well as by physical forces, including mechanical stress on the cell envelope and osmotic pressure (44)(45)(46). Understanding the mechanisms of cell shape regulation therefore requires an integrative approach, combining cellular mechanics and biochemical regulation.
In addition to the surface-to-volume ratio, recent work found that Vibrio bacteria can also alter curvature when exposed to antibiotics (18). In particular, when C. crescentus is treated with sub-MICs of chloramphenicol (CHL), the cell becomes more curved, and the cell width increases (18). Immediately upon CHL treatment, the cell growth rate decreases, but over ;10 generations, the growth rate is gradually restored to the preantibiotic level. While the cell S/V decreases during CHL exposure, the contribution of a lowered S/V cannot solely explain the almost full growth rate recovery. This adaptive response via cell shape changes can be explained by a model of negative feedback between the cellular growth rate and cell envelope mechanical tension (18). Translation inhibition by CHL reduces the rate of synthesis of cell envelope material, which leads to an initial fast drop in the growth rate. The reduced rate of surface area synthesis also reduces the effective tension that works against the compressive bending forces acting on the cell surface. As a result, reduced tension leads to cell surface bending until a new mechanical equilibrium is reached with a higher curvature. Lower cell envelope tension promotes cell wall synthesis (45), thereby increasing the growth rate to its prestimulus value. Future experiments are needed to further test the role of cell curvature and wall tension in the maintenance of growth rate homeostasis. In particular, it will be interesting to test whether Caulobacter mutant cells with straight morphologies are poor at adapting to chloramphenicol (47) or whether Vibrio bacteria adapt better than straight rod-shaped cells.
A reduction in the surface-to-volume ratio not only decreases antibiotic influx but also leads to reduced nutrient influx that may in turn decrease cellular metabolic activity. In recent work, Lopatkin et al. showed that metabolism plays a crucial role in the bacterial response to antibiotics such that cells with decreased metabolic activities are more antibiotic resistant (48). Metabolic mutations in response to antibiotic exposure suggest adaptive mechanisms in central carbon and energy metabolism. Interestingly, some of the advantageous metabolic mutations that mitigate antibiotic susceptibility have been identified in .3,500 clinically relevant pathogenic E. coli isolates (48). These findings point toward a new pathway of antibiotic resistance mediated by mutations in the core metabolic genes. Decrease in cell surface-to-volume ratio may act in synergy with the metabolic slowdown to confer stronger antibiotic resistance.
In synergy with shape changes, bacteria can actively regulate the antibiotic concentration inside the cell by controlling porin and efflux pump expression (Fig. 1B) (49,50). Cell wall-targeting antibiotics, such as b-lactams, that disrupt the stability of the peptidoglycan meshwork are translocated by OmpF porins to induce the envelope stress response (Cpx) (51). The activation of the Cpx system decreases ompF expression (52), creating a negative-feedback loop (Fig. 1B), resulting in lower porin numbers and lower inward membrane permeability (P in ). Similarly, when E. coli cells are exposed to DNA-targeting antibiotics that are also translocated inside the cell by OmpF, the expression level of ompF decreases within 30 to 120 min after antibiotic treatment (49). A reduction in porin numbers will act in synergy with a reduction of S/V to confer stronger resistance phenotypes. In addition to controlling antibiotic influx, bacteria can decrease the intercellular antibiotic concentration through the overexpression of efflux pumps (49,53,54) (Fig. 1B). In the future, time-lapse experiments are necessary to reveal the time scales associated with the onset and completion of morphological transformation under antibiotic perturbations and how these time scales compare with changes in the expression profiles of proteins responsible for regulating antibiotic influx and efflux. These studies would be essential to quantify the contributions of the different resistance pathways and their synergistic effects responsible for increasing bacterial fitness.

SUPPLEMENTAL MATERIAL
Supplemental material is available online only. TEXT S1, PDF file, 0.1 MB. FIG S1, EPS