Cell-body curvature reduces stall frequency to reinforce Vibrio cholerae swimming and chemotaxis by way of hydrogels

Bacterial strains and progress situations

V. cholerae C6706str2 wild-type (wt) and its non-curved mutant obtained by deletion of curvature-inducing proteins CrvA and CrvB (ΔcrvAB) originated from Martin et al.⁵. Overnight cultures had been inoculated in 2 ml LB (1% Bacto Tryptone, 0.5% Bacto Yeast extract, 0.5% NaCl, pH 7) from particular person colonies grown on 2% agar LB plates streaked from frozen glycerol shares lower than 1 week earlier, and grown to saturation at 30 °C, 250 rpm. Day cultures had been inoculated with the in a single day cultures at 1:200 dilution in 10 ml TB (1% Bacto Tryptone, 0.5% NaCl, pH 7) in and grown in parallel at 30 °C, 250 rpm in 100-ml glass tradition flasks with ventilated caps (DWK Life Sciences), till they reached an optical density (OD) at 600 nm between 2.2 and a pair of.4 and inside 0.01 of one another (to make sure comparability, see SI Fig. 3). Volumes of 0.5 ml of bacterial tradition combined with 0.5 ml of M9TB had been washed as soon as by centrifugation in 1.5 ml microcentrifuge tubes (7 min at 2500 rcf), adopted by mild resuspension in 1 ml of M9TB. M9TB consisted of M9 salts (M6030 Sigma-Aldrich) sterile filtered and 0.01% (v/v) TB (autoclaved) added to it. Bacterial suspensions had been diluted to a goal OD of roughly 0.005 for chemotaxis experiments in buffer, 0.003 for polymer options, or 0.002 for chemotaxis experiments in agar, both in M9TB (chemotaxis experiment in buffer or agar) or in M9TB with PVP K90 (chemotaxis experiment in viscous media), with or with out chemoattractant, for injection into the chemotaxis gadget. For bulk viscosity estimates of 5% PVP K90 options, a beforehand established relationship was used¹².

Chemotaxis assay preparation in buffer or polymer answer

The chemotaxis assays had been carried out utilizing a high-throughput chemotaxis assay¹⁰ the place micro organism are tracked in 3D in a managed chemical gradient established in a commercially accessible microfluidic gadget (µ-slide Chemotaxis, IBIDI), consisting of two reservoirs of various chemical concentrations related by a small channel through which a linear gradient is fashioned. The gadget’s reservoirs had been respectively crammed with bacterial options with or with out 200 µM L-serine (84959, Sigma-Aldrich), as beforehand described¹¹, in order to acquire a 200 µM/mm steady and repeatable linear gradient inside roughly 40 minutes after closing the gadget¹⁰. The full characterization of gradient institution and stability, carried out with fluorescein (approx. 332 Da) may be present in Reference 11 (Supplementary Materials). As gradient institution is ruled right here by diffusion, the gradients of L-serine (approx. 105 Da) are anticipated to ascertain in a similar way. Each unbiased organic replicate reported is a set of acquisitions made in a pair of microfluidic gadgets, one for every phenotype, on the identical day and with parallel preparation steps.

Chemotaxis assay preparation in agar

For chemotaxis assays carried out in agar, the central channel of the microfluidic gadget was crammed upfront with molten agar (0.19–0.21% w/v Bacto agar in M9TB). For filling the gadget, every reservoir is successively emptied, crammed with bacterial answer with or with out chemoattractant, after which closed. Biological replicates evaluating phenotypes at a given agar focus had been ready in parallel to restrict the affect of technical variability in agar gel properties. Chemotaxis experiments in buffer and polymer options had been concluded usually inside 60 min after closing the chamber for experiments. Experiments in agar concluded usually inside 1.5 hours, maximally 2 hours.

Motility experiments

After washing and resuspension in M9TB as described above, cells had been diluted to a goal OD of roughly 0.005 in M9TB, incubated at room temperature for not less than 15 minutes, to permit adaptation to the medium. Preliminary experiments adopted an analogous protocol however with totally different resuspension media or preincubation time, as indicated in Supplementary Fig. 1. Sample chambers with a peak of roughly 300 µm had been created as described beforehand²², by utilizing three layers of parafilm as spacers between a slide and a canopy glass, crammed, sealed with Valap, and instantly delivered to the microscope for information acquisition.

Data acquisition

Phase distinction microscopy recordings had been obtained at room temperature (∼21 °C) on a Nikon Ti2-E inverted microscope utilizing an sCMOS digital camera (PCO Edge 5.5) and a 40x goal lens (Nikon CFI S Plan Fluor ELWD 40x ADM Ph2, correction collar set to 1.2 mm to induce spherical aberrations²²) centered on the heart of the channel in all three dimensions. The integration time was 3 ms. The body price was 30 fps for recordings in buffer, 15 fps in agar, and 5% PVP K90 options. Typical cumulative acquisition time for one situation in a single chemotaxis experiment (one level in Fig. 2b,c) ranged from 4 to 10 minutes in buffer, 6 to 12 minutes in viscous medium, and 15 to twenty minutes in agar. All acquisitions had been made inside 150 minutes of resuspension in motility medium after washing.

Data processing and 3D monitoring

Video recordings had been binned by an element of two × 2 pixels by averaging pixel counts after which subjected to a background correction process based mostly on dividing the picture by a pixel-wise median computed throughout a sliding time window of 101 frames, apart from information acquired for agar experiments, the place a sliding window of 2001 frames was used to make sure that stalled micro organism weren’t erased. 3D trajectories had been extracted from phase-contrast recordings utilizing a high-throughput 3D monitoring methodology based mostly on picture similarity between diffraction rings of micro organism and people in a reference library with recognized vertical positions²² improved in earlier works by correcting photographs for the diffraction rings of already tracked micro organism¹¹.

Positions had been smoothed utilizing 2nd-order ADMM-based development filtering²³ with regularization parameter λ = 0.1 in agar and λ = 0.3 in any other case. Three-dimensional velocities had been computed as ahead variations in positions divided by the point interval between frames. In chemotaxis experiments, the vertical place of the highest and backside of the chamber was recognized by visible inspection of trajectory information. All trajectory segments inside not less than 12 µm of the highest or backside of the central channel had been eliminated to keep away from floor interplay results¹⁰, besides within the delicate agar experiments. The variety of motile micro organism tracked for one situation in a single chemotaxis experiment was not less than 2000 bacterial trajectories in buffer (usually 3000–6000), 900 in agar (typ. 2000–4000), 500 in PVP (typ. 800–1200). A dataset abstract is offered in Table 1, and the primary bacterial trajectory datasets may be present in ref. 24.

Run-reverse-flick evaluation in buffer

The turning occasion detection that we beforehand utilized to a different V. cholerae pressure (together with sharing of the code)¹², relies on the native price of angular change, computed from the dot product between the sums of the three consecutive velocity vectors previous and subsequent to a time level. The threshold for a flip to start is a 7-fold price relative to the median price of angular change of the run segments, as decided in three iterations of the process. A brand new run begins with not less than one time level (not less than 0.033 s) underneath this threshold. The 3D turning angle for a flip starting at body i and ending at body j is computed because the angle between the sum of the instantaneous velocity vectors at frames i-2 and i-1 and the sum of these at frames j and j + 1. Backward (CCW rotation) and ahead (CW rotation) runs had been recognized as runs with a flip underneath 140°, respectively on the finish or at first of the run, and a flip above 150° on the different finish of the run. All trajectories with a minimal velocity of 15 µm/s and with a minimal length of 0.8 s had been analyzed.

Stall-swim evaluation in delicate agar hydrogels

The stall occasion detection relies on the instantaneous velocity: If the velocity is underneath 1 µm/s for 0.2 s or extra, a stall begins. During a stalling occasion, if the instantaneous velocity exceeds 1 µm/s for 0.2 s or extra, the stall ends, and a brand new swimming part begins. All trajectories with a minimal length of 1 s entered stall-swim evaluation. For every phenotype, in every of the 7 replicates, this resulted in evaluation of greater than 80% of all trajectories (totaling 28,984 and 20,937 analyzed trajectories for wt and ΔcrvAB, respectively), of which not less than 90% had not less than one stall occasion detected. Swim-stall evaluation outcomes are detailed in SI Table 2.

Simulation mannequin

Coarse-grained molecular dynamics simulations are performed utilizing the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS²⁵). In the simulations, the gel matrix is represented as a crosslinked community of chains of spherical beads of 1 µm diameter and 9.42478 pg mass. The beads inside a polymer chain are interconnected by stretchable bonds, outlined by vitality:

the place Okay is 2.2 nN/µm and ({r}_{0}) is 1.25 µm. The swimming cell is modeled as a inflexible physique consisting of 13 spherical beads, every of 1 µm diameter and 1 pg mass. For the straight cell, all beads are aligned linearly, whereas for the curved cell, the beads type an arc. Interactions between gel-cell beads and gel-gel beads are modeled by a purely repulsive Lennard-Jones potential outlined as:

the place ϵ is 0.0001fJ, σ is 1 µm. The equations of movement are built-in within the microcanonical ensemble (NVE), making certain conservation of vitality by way of direct integration of Newton’s equations. Simultaneously, a Langevin thermostat is utilized to take care of the system at every desired temperature (see under).

Gel initialization

First, a gel matrix formation course of is simulated. 125 chains, every consisting of 150 beads, are launched right into a simulation field of dimension 100 µm × 100 µm × 100 µm with periodic boundary situations. To higher replicate the compactness and pore dimension distribution typical of a hydrogel, the system is geometrically reworked: all bead coordinates (x, y, z) and the simulation field are scaled by an element of 0.5 to uniformly shrink the system, producing a compact preliminary configuration. The system is then absolutely relaxed for 3 × 10⁵ time steps (the timestep is 1 µs) at 300 Okay. Following this, crosslinking between gel beads is allowed throughout 3 × 10⁵ time steps, whereas the system is cooled down from 300 to 100 Okay. During the crosslinking part of the simulation, bond formation is carried out by the repair bond/create command in LAMMPS. A verify for doable new bonds is carried out each 100 time steps. If two beads i and j are inside a distance of 1.125 µm of one another, and if a bond doesn’t exist already between i and j, and if each i and j are under their respective most bond restrict (not more than 4 bonds), then i and j are labeled as a “possible” bond pair. If a number of beads are near a bead, it might have a number of doable bond companions. Every bead checks its record of doable bond companions and labels the closest such associate as its “sole” doable bond associate. After that is carried out, if bead i has bead j as its sole doable associate and bead j has bead i as its sole doable associate, then the i,j bond is fashioned with a chance of 0.5. Note that these guidelines imply {that a} bead will solely be a part of at most one newly created bond at a given time step. It additionally signifies that if i chooses j as its sole doable associate, however j chooses okay as its sole doable associate (as a result of distance_jk < distance_ji), then i is not going to type a bond on this time step, even when it has different doable bond companions. This crosslinking part is then adopted by a remaining cool-down, from 100 Okay to 0 Okay throughout one other 3 × 10⁵ timesteps, with no new crosslinking. To mimic the tensioned construction of hydrated gels, the simulated polymer community is once more geometrically reworked (within the method described above) previous to introducing swimming cells: to impose mechanical stress, the coordinates are uniformly expanded by an element of 1.2. This process yields a beginning conformation that’s each dense and underneath stress, reflecting the structural traits of actual hydrogels, which swell underneath hydration. Subsequently, the system is allowed to mechanically equilibrate for a further 3 × 10⁵ time steps at 0 Okay.

Simulation process

Within the constructed gel matrix, a swimming cell is launched at a random location, making certain no overlap with the gel matrix by briefly enjoyable any intersecting gel beads. To mimic bacterial swimming, together with each rotational and translational movement, a torque of 500 pN.nm about its axis and an exterior pressure of 0.1 pN alongside its axis are utilized, similar to roughly one full rotation per cell-length of ahead displacement throughout free swimming. For the simulation of various curvatures, a smaller torque (100 pN.nm) is utilized. The movement of the swimming cell within the gel is then simulated at 0 Okay, and the positions and velocities of all cell beads are recorded each 500 timesteps (every timestep is 0.5 µs) for subsequent evaluation. Each simulation is ran for two × 10⁷ timesteps. To decide when a swimming cell stopped transferring, displacements are calculated over a time interval of 10⁴ timesteps. At every body, the Euclidean distance between the present place and the place 10⁴ timesteps later is computed. If this displacement is lower than 2 µm for 4 × 10⁴ consecutive timesteps, the cell is taken into account to have stopped. The first body assembly this situation is recorded because the stopping level. If no such occasion happens, the cell is classed as motile all through the trajectory. A complete of 1000 simulations per situation (e.g., per curvature) are carried out.

Gel shear modulus measurement

Following an preliminary equilibration part and a leisure part of the gel as described above, shear deformation is launched by making use of an affine field deformation within the xy airplane at a relentless pressure price of 0.001 ms⁻¹. During the next simulation, which lasts 5 × time steps at 0 Okay, the shear stress σ_xy of the gel matrix, field tilt L_xy, and field size L_y (see SI Fig. 6c) are recorded each 500 time steps. The shear pressure is calculated as (gamma ={L}_{{XY}}/{L}_{Y}), and the shear modulus is decided from (G=Delta {sigma }_{{xy}}/Delta {gamma }_{{xy}}).

Cell curvature measurement

To estimate cell curvature, we match a circle that passes by way of two central physique atoms and is tangent to the instructions of the 2 arms (see SI Fig. 6b). Specifically, we first extract two brief segments representing the left and proper arms of the cell, every comprising 3–4 beads. Linear regression is used to suit a line to every arm section, yielding estimates of their orientations. Two beads positioned close to the midpoint of the physique — one on the junction with every arm — are used to outline the arc of the cell physique. We then compute the place and radius of the circle that passes by way of these two central atoms and is tangent to the beforehand fitted arm instructions. The circle is decided by minimizing a value operate that penalizes deviation from each distance constraints (factors mendacity on the circle) and angular constraints (tangency with arm instructions), utilizing nonlinear optimization. The fitted radius is used to quantify cell curvature.

Reporting abstract

Further data on analysis design is out there within the Nature Portfolio Reporting Summary linked to this text.