article: Myxococcus xanthus is a model organism for studying bacterial social behaviors due to its ability to form complex multi-cellular structures. Knowledge of M. xanthus surface gliding motility and the mechanisms that coordinated it are critically important to our understanding of collective cell behaviors. Although the mechanism of gliding motility is still under investigation, recent experiments suggest that there are two possible mechanisms underlying force production for cell motility: the focal adhesion mechanism and the helical rotor mechanism, which differ in the biophysics of the cell–substrate interactions. Whereas the focal adhesion model predicts an elastic coupling, the helical rotor model predicts a viscous coupling. Using a combination of computational modeling, imaging, and force microscopy, we find evidence for elastic coupling in support of the focal adhesion model. Using a biophysical model of the M. xanthus cell, we investigated how the mechanical interactions between cells are affected by interactions with the substrate. Comparison of modeling results with experimental data for cell-cell collision events pointed to a strong, elastic attachment between the cell and substrate. These results are robust to variations in the mechanical and geometrical parameters of the model. We then directly measured the motor-substrate coupling by monitoring the motion of optically trapped beads and find that motor velocity decreases exponentially with opposing load. At high loads, motor velocity approaches zero velocity asymptotically and motors remain bound to beads indicating a strong, elastic attachment.
  Myxococcus xanthus is a predatory soil bacterium that has been widely used as a model organism for studies of bacterial social behaviors [1], [2]. Under different environmental conditions M. xanthus cells display a range of complex multi-cellular behaviors, including groups of cells moving together (often referred to as swarms), periodic bands of high cell density travelling waves (termed ripples), and aggregates of more than 105 cells containing environmentally-resistant myxospores (termed fruiting bodies) [3]. Formation of these complex self-organized patterns requires coordination and collective motility among the cells [4]–[6]. The biophysical mechanisms underlying the cell motility and intercellular interactions that generate these collective behaviors are still not completely understood. M. xanthus cell movement is limited to translocation on solid surfaces using two different flagella-independent motility systems [7]. Gliding motility, previously termed adventurous (A) motility, is defined as active surface translocation along the long cell axis without the aid of flagella or pili and is responsible for individual cell movement. Twitching motility, previously termed social (S) motility, appears similar to gliding motility, but is limited to cells within at least a cell length of another cell and is known to be powered by type IV pili extension and retraction [8]. The biophysical mechanism of gliding motility in M. xanthus and other bacteria is the subject of active research. Earlier studies on the mechanism of gliding motility hypothesized that the exopolysaccharide (EPS) slime secretion at the cell' s lagging pole and the expansion of slime due to hydration was responsible for the motility [9]–[11]. However, subsequent experimental studies [12], [13], indicated that force generation in gliding motility is likely to be distributed along the cell length. Recently, an alternative view of the gliding motility mechanism has emerged. Using fluorescently tagged proteins recent experiments identified a few components of the machinery responsible for the distributed force-generation: gliding motility regulatory protein (AglZ) [14] and motor proteins (AglRQS) [15]. These studies showed clustering of these proteins at regular intervals along the cell length. These clusters appear to form at the cell' s leading pole and disperse at the lagging pole, while remaining stationary with respect to the substrate during cell movement. Further, depolymerization of the cell cytoskeleton elements (MreB) dispersed these clusters and inhibited the gliding motility [15]. Based on the above observations, a focal adhesion mechanism (FAM) of gliding motility was proposed [14], [15] (Fig. 1A). The mechanism hypothesizes that intracellular motor proteins moving on helical cytoskeletal filaments are somehow connected to the focal adhesion complexes attached to a substrate. The cell movement is therefore generated by motors pushing against these focal adhesion complexes. However, it is not clear which molecules adhere cells to the substrate and how their connection to the motor complex is able to move through the peptidoglycan layer of the cell wall. Another study observed that AgmU, a gliding motility protein, is part of a multi-protein complex that spans cell' s inner membrane and periplasm [16]. Additionally, it was found that AgmU decorates a looped continuous helix that rotates as the cell moves forward [17]. It was shown that rotation of the helix stopped when MreB cytoskeletal filaments were depolymerized [17]. The authors also observed that a periodic distortion of cell wall that is consistent with periodicity of the MreB helices. Based on these observations, a helical rotor mechanism (HRM) [9], [17] (Fig. 1B) of gliding motility was proposed. In this mechanism motor proteins (AglR) [18] distort cell surface by interacting with the gliding motility proteins (AglZ, AgmU) in protein clusters and create drag forces between cell surface and substrate. These drag forces propel the cell forward. Even though these studies provide ample evidence for both FAM and HRM mechanisms of gliding motility, neither mechanism has been conclusively proven or eliminated. We note that the major biophysical distinction between the mechanisms is in the nature of cell-substrate interactions – elastic force coupling in FAM vs. viscous drag coupling in HRM. Hence, by studying the mechanical interactions of motile cells it may be possible to distinguish between the two mechanisms of gliding motility. We tested the effect of mechanical forces on motility in two ways: (i) by examining the outcome of physical collisions between moving cells, and (ii) by probing the effect of applied load to the motion of individual motor complexes. We hypothesize that the outcome of mechanical collision between a pair of cells will be different in the two models of motility because of the differences of the nature of cell-substrate interaction (see Fig. 1C). Specifically, during a cell-cell collision FAM-based cell motility would offer high resistance to the cell displacement because of the adhesive attachment between the cell and substrate. In contrast, HRM-based cell motility would result in a larger cell displacement, as the resistance due solely to viscous interactions would be weak. To test this hypothesis, we built a computational model (see Methods for details) that represents the biophysical characteristics of M. xanthus cells and used it to investigate how the outcomes of cell-cell collisions depend on the gliding motility mechanism. Since the individual components of gliding motility and their interactions are not completely known at present, we simplified the two mechanisms of gliding motility in our model to focus exclusively on their cell-substrate interactions. As such we employed the viscous coupling model (VCM), which is similar the HRM and the elastic coupling model (ECM), which is similar to the FAM. We analyzed the modeling results for both mechanisms of cell - substrate interactions and compared them with quantified experimental data on isolated cell-cell collisions. Furthermore, we investigated the robustness of our results to variations in mechanical and geometrical parameters of the collision events. As an additional test for the coupling of motors to the substrate, we used optically trapped beads to directly test the mechanics of motor coupling and the effect of load on motor movement. While the details of how applied hindering load affects the speed of the gliding motors themselves remain unknown, the two models of motility make qualitatively different predictions near the motor stall force due to the difference in coupling. Regardless of the shape of the motor force-velocity relationship, as the force is increased to high enough levels, the VCM predicts that beads should cease motion at the stall force and move backwards for higher loads. In contrast, the ECM predicts that applied force should stop bead motion even for loads well above stall.
  To study the mechanical cellular interactions, we simulated a head-to-side collision between two cells moving on crossing paths. To differentiate the two mechanisms of gliding motility, we assumed strong attachments between the cell and the substrate in the ECM. The results show qualitatively distinct interaction behaviors of cells for the two alternative mechanisms (Fig. 2A and 2B). In these simulations, we define a primary cell as the one whose side is hit by the first node of another (secondary) cell. We observed that in the simulations of both the mechanisms, primary and secondary cells align with each other and move in a common direction after the collision. However, this common direction differed in the two mechanisms. In the VCM (Fig. 2A), both the cells changed their direction after the collision. In contrast, in the ECM (Fig. 2B), the new common direction is the same as the direction of the primary cell before collision. Thus, the primary cell maintained its direction, whereas the secondary cell aligned with the former. This contrasting cell-cell collision behavior in the two mechanisms can be explained by observing the cell' s resistance to shape deformation (bending). During collision the primary cell nodes are displaced due to the contact with the secondary cell, thereby leading to local deformation of the primary cell. This deformation results in counterforces on the cell nodes. In both of the mechanisms cell deformation produces viscous drag forces and angular spring forces on nodes. In addition, in case of the ECM a strong restoring force acts on nodes due to the substrate attachments. These forces do not allow the deformations to propagate to the front nodes of the primary cell and as a result limits its change in direction. Since no such force exists in VCM, cell-cell collision results in cell deformation that propagates to its front node, and in turn significantly changes the cell travel direction. To identify which of the two scenarios resembles the behavior of colliding M. xanthus cells, we examined similar collisions in the time-lapse images of wild-type M. xanthus cells under low cell density (8×107 cells/ml). We chose these conditions to easily identify isolated cells and their pairwise interactions. Fig. 2C shows a typical cell-cell collision observed in experiments. In this case, the direction of the primary cell has not changed after collision. This behavior is similar to the simulations using the ECM of gliding motility. Thus, comparison of our simulations with experimental observations indicates that there is an elastic coupling between the cell and substrate for M. xanthus gliding cells. Nevertheless, these conclusions may be sensitive to the parameter values used in our simulations or to the particular collision geometry. We therefore examined the robustness of these results. To further investigate the role of substrate adhesions during cell-cell collisions we needed a quantitative metric to characterize the outcome of collision events. Since the major difference between the two mechanisms is the change in the primary cell orientation during collision, we focused on this value (see Methods for details). We note that the collision outcome greatly depends on some aspects of the collision geometry, especially the collision position (defined from leading end of the primary cell, see Fig. S3A) and collision angle. Therefore, we set the collision angle as ∼90 deg (that produces maximum change in cell orientation) and choose the maximum change in cell orientation () from all possible node collision positions () as the metric that describes the cell-cell collision behavior for a specific parameter set. Nodes 1 and N were excluded from this analysis since we assume no adhesion complexes at these nodes (see Methods for details). Fig. 3A depicts how varies in the ECM model as a function of attachment strength. Each adhesive attachment is modeled by an elastic spring with a spring constant and a bond-breaking distance. By keeping the bond-breaking distance constant we vary the elastic spring constant () and thereby change the maximal force to break the bond. corresponds to the case in which no bond is formed with the substrate, and therefore only viscous interactions with substrate exist (VCM). Intermediate values of correspond to weak and non-specific interactions with substrate therefore may correspond to viscoelastic properties of EPS slime surrounding cells. Large values of correspond to a strong specific binding which resembles the ECM. Fig. 3A shows that the value of starts at approximately 40 degrees for and then decreases to values below 15 degrees for pN/µm. pN/µm corresponds to a bond-breaking force of 50 pN (), which is roughly the order of integrin bond-breaking forces (∼50–250 pN) [19]–[21]. This behavior is expected as the adhesion complex force will only be relevant if it resists the force generated by cell motility (∼60 pN). When the attachment strength exceeds this threshold it results in small node displacements and hence small changes in cell orientations after collision. For comparison we quantified the change in primary cell orientation () in isolated cell collisions under experimental conditions for 97 cell pairs (Fig. 3D). As these measurements also contain the spontaneous change in the orientation of cells, we measured the mean spontaneous orientation change () of isolated cells (Fig. 3F, measurements from ∼50 cells; see Methods and Fig. S4A, S4B for details) and subtracted it from experimental data (). The mean value and standard deviation of the net change in cell orientation () from experimental images is shown in Fig. 3A (gray area). Since these experimental results were based on wild-type cells (DK1622) that exhibit both gliding and twitching motility, we replicated the analysis with DK10407 (ΔpilA A+S−) cells that exhibit only gliding motility. The results from 58 isolated collision events for DK10407 cells are shown in Fig. 3E. We observed that the mean change in primary cell orientation () in isolated cell collision events for pure gliding motility cells is ∼14±12 deg (n = 58). This value is very close to that of the wild-type cells (∼15±15 deg). These results indicate that the contribution of twitching motility to our analysis of gliding motility is negligible which is expected as twitching pili are located only at the poles and should not affect cell bending. Thus we used only wild-type cell data in our further analysis. We observe that the modeling results match with the experimental observations only for adhesion strength () values greater than 200 pN/µm (Fig. 3A). Whereas, model results with no adhesion complexes (, VCM) show very large changes in cell orientation and do not match the experimental observations for the chosen parameters. However, we are uncertain whether the results will hold if some mechanical parameters (see Table S1 for model parameters) of the model are changed. We therefore systematically varied the model parameters over two orders of magnitude (from 0. 1× to 10×, see Table S2) and investigated their effect on cell-cell collisions. These results are combined in Fig. 3B, which shows the mean values and standard deviations of the cell orientation changes for different adhesion strengths (). As before, we find that only the ECM model at very high adhesion strength values (pN/µm) matches the experimental values. We also noted that despite the large variability of the parameters, the standard deviations in the model results at high adhesion strengths are quite small. Thus, we conclude that our results are robust to variation in all model parameters except for the strength of adhesion complex. We have also quantified the minimum strength () required for a focal adhesion complex in the cell model to match the experimental cell orientation change in a collision for different cell propulsive force () (Fig. 3C). The results indicate that values increased with an increase in the cell propulsive force and are similar in magnitude to that of propulsive force. As noted earlier, the outcomes of cell-cell collisions depend on the mechanical parameters of the cell and on the collision geometry, specifically the collision position along the cell length and collision angle (the angle between the cell orientations at the start of the collision) (Fig. 4). To this point, our analysis focused on the maximum change in cell orientation as we varied the position of the colliding nodes and used a collision angle near 90 degrees at which the maximal cell deformation is expected. However, it is not clear if the experimental collision events correspond to these amplified effect scenarios or whether it is possible that a model with very weak or no elastic coupling can be consistent with the experimental collisions at some conditions. Thus, we systematically explored how variability in the geometrical model parameters affects the outcome of the collision. In these simulations we chose for the adhesion strength value () of 2000 pN/µm in the ECM, a value for which the model results closely match the experimental observations. In addition, all the experimental observations were corrected for spontaneous orientation change of cells (). First, we compared the orientation change from the two mechanisms as a function of the collision position for the default parameter set (Fig. 4A). We note that both models produced a much smaller change in cell orientations for collisions near the lagging end of the primary cell. This is an expected behavior of the model, as small node displacement near the lagging end of the cell may not produce sufficient cell deformation to significantly change the cell travel direction. However, collisions in the forward and middle section of the cell produced significantly larger orientation changes for the VCM model as compared to the ECM model. We note that the collision at the first node of primary cell produced very large orientation change in both mechanisms. This large change is due to the assumption that no adhesive attachment present at the first node of the cell (see Methods for details). As a consequence we observed a large displacement of nodes even in the ECM. Thus, we excluded the first node collisions from our analysis. For comparison, we next quantified the changes in cell orientation as a function of the collision position from experiments (black circles in Fig. 4A). We note that only the results of the ECM model match with the mean experimental values for all collision node positions, whereas the results of the VCM model deviated significantly from the experimental values. We also found that these results are also robust to variation in mechanical parameters of the model (see Fig. S5A) and for small perturbations in collision positions (see Fig. S5B). Next we investigated the effect of collision angle on cell-cell collision behavior. We varied the collision angle between 15–165 deg (corresponding to the experimental data, see Fig. S4C) and measured the maximum orientation change of the cell across all node collision position at each collision angle. We observed that the cell orientation changes with both the mechanisms are similar at both extremes of the collision angle range, but vary significantly in the middle (Fig. 4B). We compared these results with the observations from experimental cell collisions as a function of collision angle. We determined that results from the ECM model match closely with the experimental observations, whereas the results from the VCM model deviated significantly (Fig. 4B). We also observed similar results for variation in cell length and number of adhesion complexes per cell (see Fig. S5C, S5D). Thus, the results from the VCM model consistently showed large cell orientation changes compared with the ECM model for various collision geometries. Further, the results from the ECM model match with mean values from the experimental data for all the collision scenarios considered. To directly test the coupling of single motor complexes to external objects such as the gliding substrate, we applied controlled loads to micron-sized beads being transported by gliding motors on immobilized cells [15]. We designed a transient force clamp that isolates the effects of force on the motor-driven ‘runs’ even from the complex pause dynamics and occasional directional reversals seen in bead motion (Fig. 5A, see [15] and Methods for experimental procedure). This procedure uses an optical trap to apply fixed loads to beads, but only after being triggered by a motor-driven displacement of 63 nm in less than 3 s. Trap position feedback was then used to maintain a constant force on the bead for approximately 8 s after which the trap was shut off. If the bead velocity and direction before and after force application was nearly the same, we concluded that the motor did not reverse or pause during the force-clamped period. Fig. 5B–D show the measurements of bead linear velocities under various loading conditions in force clamp experiments. We observe that after some initial period of inactivity bead starts moving (green lines) at which point a preset opposing force is applied on the bead. We found that opposing forces of ∼12 pN (Fig. 5C) cause stalling of the bead whereas for forces below 12 pN (Fig. 5B) bead movement is continued albeit slower than load free conditions. We estimated this stall force by finding those events in which the linear velocity was zero within twice the standard error of the linear velocity measurement. Interestingly, beads remained motionless for loads well-beyond the stall force (18 pN, Fig. 5D) and we never observed a bead to reverse its direction in response to high loads over the eight seconds of force application. The lack of backwards motion at super-stall forces is consistent with the ECM, but inconsistent with the viscously-coupled VCM model which predicts significant backwards motion at these loads. We measured the force-velocity response of at least 108 motor complexes on 40 different M. xanthus cells. We chose the preset force to probe the complete force-velocity relationship for opposing loads from 0 to 20 pN (Fig. 5E) and also varied the concentration of nigericin (a drug that reduces pH gradient/proton motive force across cell membrane there by decreases the motor function/bead motion [15]) in solution. We find that opposing loads slow gliding motors exponentially with a characteristic decay force of 2. 3±0. 1 pN. In addition, we find that with increasing nigericin concentration, bead velocity decreased but force production did not (Fig. S6A–C). When normalized by the unloaded velocity, force-velocity curves from different nigericin concentrations collapse onto a single exponential curve (Fig. 5F) with a characteristic force independent of nigericin. This is again inconsistent with the VCM in which decrease in velocity would lead to decrease in force production.
  Despite progress in elucidating the mechanism of M. xanthus gliding motility, its biophysical mechanism is still not fully understood. Based on recent experimental evidence two alternative mechanisms: FAM and HRM of gliding motility are proposed but to date neither model has been conclusively proven. A key difference between the two models is in the biophysics of the interactions between cells and substrate. We hypothesized that this difference will affect cell behavior during cell-cell collisions. To test this, we constructed mathematical models of the M. xanthus cell with either viscous (VCM) or elastic (ECM) interactions with substrate and studied the mechanical behavior in isolated cell-cell collision events. As expected, we found that both models differed in their cell interaction outcome, which was quantified by cell orientation changes. We compared the results from both the models with experimental observations of isolated cell-cell collisions events under similar conditions. We found that experimental cell behavior differs from that of the VCM model and agrees with the ECM model in which there is strong adhesion between the cell and substrate. Variations of the mechanical and geometrical parameters in the cell model for the collision process further confirmed these findings and indicated the robustness of the model. Thus our analysis predicts strong elastic attachments between the cell and substrate, which is consistent with a focal adhesion mechanism for gliding motility. As a further test of the mechanics of cell attachment, we then studied the effect of load on motor attachment and speed. We found that motors stalled to zero speed for loads about12 pN. Even when the loads exceeded this stall force value (up to 20 pN), the beads remained strongly attached to the cells and did not show motion in the opposite direction. This behavior is expected in an elastic-coupling model. In total, our simulations and measurements are consistent with the ECM and inconsistent with the VCM. The strong attachment between cell and substrate indicated by our analysis are realistic and are similar in the range of other biological cell-substrate interactions (e. g. integrin focal adhesions in eukaryotic cells [19], [20]). Further, we observed that the minimum adhesive strength per node required to match the experimental observations increased with an increase in cell propulsive force, but remained within same magnitude (0. 5×–5×) of cell propulsive force. Based on the force-clamp experimental estimate of ∼12 pN force generated at each focal adhesion node, and assuming ∼5 adhesion nodes per cell [14], [22], we estimate the gliding motility apparatus generates ∼60 pN of force. This estimate is of the same order as the force generated by the twitching motility engine [23], [24] which is not surprising given that M. xanthus cells using either gliding or twitching motility move at approximately the same speed [25]. In light of this estimate, our model (Fig. 3C) would predict at least 80 pN of adhesion force. In support of this, force-clamp experiments never observed bead detachments for forces up to 20 pN. While the work here probed the attachment of motor bound-bead cargos to immobilized cells, it should be possible in the future to directly test the ECM model using optical tweezers and moving cells to measure the cell detachment force along the cell length. Large detachment forces with the existence of multiple peaks in the cell displacement curve along the cell length would provide support for multiple strong attachment sites. Although our biophysical model that includes strong adhesion, similar to the FAM, explains the observed experimental cell collision behavior, a number of issues remain unresolved regarding the focal adhesion model of gliding motility. First, while it is observed that clusters of AlgZ proteins, which are predicted to form the focal adhesions, remain stationary during cell movement [4], [9], [14], this behavior requires that the adhesion complexes move through the peptidoglycan layer. Second, the adhesive proteins/molecules that bind the motor complexes to the substrate have not been identified. A recent study by Durcet et al. [26] speculated that slime acts as a binding agent between the cell and substrate. In this context it is worth noting that our biophysical cell model incorporates a simplistic viscoelastic model for cell-substrate interactions. However, a non-isotropic viscoelastic model for attachment may provide a better description of the substrate interactions [27]. Third, strong cell-substrate attachments pose an additional problem for cell by restricting its movement at the lagging pole. Since the attachments remain stationary during cell movement, the elastic nature of the attachment at the lagging pole would be expected to cause an increasingly opposing force for cell movement as the cell moves forward until the attachment is broken causing its lagging pole to snap back. This type of jerky motion is commonly seen in fibroblasts that utilize substrate attaching lamellopods for movement [28]–[30]. However, since this type of motion is absent in M. xanthus gliding, it suggests that the cells actively destroy attachment complexes at the lagging pole. The critical role of substrate adhesion in the mechanism of gliding motility of M. xanthus may have analogues in other bacteria. Recent studies have demonstrated that gliding motility in Flavobacterium johnsoniae is dependent of the cell-surface adhesion protein SprB [31]. As in M. xanthus, these adhesion proteins appear to rapidly move along the cell surface on helical filaments and this movement is powered by the PMF [31]. F. johnsoniae cells are also capable of binding and propelling latex beads [32] but the force-velocity relationship has not been measured. These observations bring an intriguing possibility that the biophysical mechanism of gliding motility in evolutionary distant F. johnsoniae and M. xanthus could share some similarities. Is there any physiological role for the strong adhesion with substrate? We speculate that the strong attachment between the cell and substrate helps the cells align at high cell density. Indeed, the simulations of Janulevicius et al. [33] lacking substrate adhesion, indicated that M. xanthus cells with the bending modulus reported in literature [34], [35] cannot maintain alignment. In our model we have observed that when strong substrate adhesion is included the orientation of one of the cells remains unchanged during cell collisions, whereas the orientation of the other cell aligns to this orientation. This reflects the natural arrangements of high density M. xanthus cells that self-organize into well-aligned clusters [36], [37]. As new cells join and align with the existing cells in a cluster, strong substrate attachments prevents the change in orientation of the cell clusters, thus preserving the mean orientation of the cluster. This effect appears to explain that flexible cells can maintain their alignment using strong adhesive attachment with the substrate.
  We developed a biophysical model of the M. xanthus cell by extending the linear flexible cell model by Janulevicius et al. [33]. In our model, each cell is represented as a connected string of circular nodes with a total cell length and width (Fig. S1A). Each circular node is modeled as a rigid body of radius. Circular nodes are kept at a fixed distance apart by rectangular spacers of length () and width (). Each body of mass () is identified by its position () and heading direction (). Neighbor circular and rectangular bodies are connected by a rotational joint at the center of the circular node (Fig. S1B). Each circular node is connected to the neighboring circular nodes by angular springs () that resist bending of the nodes from straight line position (Fig. S1C). Spring constants for the angular springs () can be tuned to achieve the desired flexibility of the cell that matches with the actual bacterium. Various forces () (e. g. propulsive forces that move cell forward, drag forces on the cell surface due to contact with surrounding fluid) act on the nodes that affect the velocity () of the nodes. In the following sections we describe the equations that model the cell motion. In these equations letters represent magnitudes and bold letters represent vectors.
summary: Studies of collective bacterial motility on solid surfaces are essential for understanding self-organization of biofilms. The Gram-negative bacterium Myxococcus xanthus has long been used as a model organism for studying surface motility but its mechanism of gliding is still under investigation. Recent experiments point to two potential mechanisms for gliding motility that differ qualitatively in the details of their cell-substrate interactions. To investigate the biophysical nature of this interaction (viscous vs. elastic coupling), we developed a synergistically multidisciplinary approach combining computational modeling, time-lapse microscopy, and biophysical optical trap experiments. First we studied the mechanical cell interaction behavior in isolated cell pair collisions in a computational model and compared the results with experimental cell behavior. The results indicated a strong adhesive attachment between cell and substrate which is further confirmed by applying opposing loads on beads attached to cell surface in an optical trap. Thus our results conclusively showed strong adhesive attachments between cell and substrate, providing support for an elastic rather than viscous coupling between cell and substrate similar to phenomena observed in focal adhesions from eukaryotic cells.
keywords: biofilms
  bacteriology
  cell motility
  microbiology
  prokaryotic models
  model organisms
  bacteria
  research and analysis methods
  biophysics
  myxococcus
  microbial ecology
  bacterial biofilms
  cell biology
  ecology
  biology and life sciences
  computational biology
  myxococcus xanthus
  organisms
  biophysical simulations
title: Myxococcus xanthus Gliding Motors Are Elastically Coupled to the Substrate as Predicted by the Focal Adhesion Model of Gliding Motility