Detachment and successive re-attachment of multiple, reversibly-binding tethers result in irreversible bacterial adhesion to surfaces

Bacterial adhesion to surfaces occurs ubiquitously and is initially reversible, though becoming more irreversible within minutes after first contact with a surface. We here demonstrate for eight bacterial strains comprising four species, that bacteria adhere irreversibly to surfaces through multiple, reversibly-binding tethers that detach and successively re-attach, but not collectively detach to cause detachment of an entire bacterium. Arguments build on combining analyses of confined Brownian-motion of bacteria adhering to glass and their AFM force-distance curves and include the following observations: (1) force-distance curves showed detachment events indicative of multiple binding tethers, (2) vibration amplitudes of adhering bacteria parallel to a surface decreased with increasing adhesion-forces acting perpendicular to the surface, (3) nanoscopic displacements of bacteria with relatively long autocorrelation times up to several seconds, in absence of microscopic displacement, (4) increases in Mean-Squared-Displacement over prolonged time periods according to tα with 0 < α ≪ 1, indicative of confined displacement. Analysis of simulated position-maps of adhering particles using a new, in silico model confirmed that adhesion to surfaces is irreversible through detachment and successive re-attachment of reversibly-binding tethers. This makes bacterial adhesion mechanistically comparable with the irreversible adsorption of high-molecular-weight proteins to surfaces, mediated by multiple, reversibly-binding molecular segments.


Table S1
Physiological status and metabolic activity of the bacteria used during AFM and bacterial vibration spectroscopy, assessed by dead/live staining 1 and fluorescence microscopy a and metabolic activity determined with an MTT 2 (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) reduction colorimetric assay b . Data immediately after harvesting were identical to data obtained 2 h after harvesting, representing the maximum duration of either experiment. All experiments were carried out in triplicate with separately cultured bacteria. ± Signs indicate standard deviations.  In silico modeling of tethered particle motion with detaching and successively re-attaching tethers Tethered particle motion of an adhering (bio) particle in three dimensions is described in the Langevin equation as being governed by deterministic and stochastic forces. Deterministic forces include the viscous drag force arising from the surrounding fluid and elastic forces that individually attached tethers exert on a substratum surface after elongation or compression, while stochastic Brownian-motion forces are generated by the thermal motion of the surrounding fluid molecules. Accordingly

BACTERIAL
in which ⃗ is the viscous drag force, ⃗ , the elastic force from the tether and ⃗ the Brownianmotion force, m is the particle mass and ⃗ is the resulting acceleration acting on the particle. Gravity and buoyancy forces were neglected. In our simulation program (see Fig. S2 for an overview), Brownianmotion forces for each time point i, after each time increment ∆t, were computed as a white noise term from random numbers w i , derived from a standard Gaussian distribution with mean of zero and standard deviation of unity 3,4 . Random numbers generated were scaled to the same level as the other forces appearing in Eq. S1 using in which m the particle mass (5.7 x 10 -16 kg) particle diameter (1000 nm) µ dynamic viscosity of the surrounding fluid (1 x 10 -3 Pa s) T absolute temperature of the surrounding fluid (293 K) Cunningham correction factor; set to 1 due to negligible slip in liquid media Boltzmann constant (1.38 x 10 -23 m 2 kg s -2 K -1 ) Δt Time step for each iteration (1 x 10 -6 s) Figure S2. Schematics of the algorithm developed to simulate tethered particle motion accounting for detachment and re-attachment of binding tethers.
For the simulations in this paper, elastic forces from the tethers were calculated using a spring constant, k of 1.2 x 10 -5 N/m, representing the average value over a variety of different bacterial strains and species measured using vibration spectroscopy 5 . Accordingly, elastic tether forces were computed based on the previous radial position ( ⃗ −1 ) of the center of the bacteria, assumed constant throughout the i th time step, ∆ . Elastic forces of each individual binding tether were summed over all tethers in which N t is the number of binding tethers, ds the relative extension or compression of the tether, and ̂ is the unit vector in the direction of the tether. For all simulations, 252 tethers were equally distributed over the particle surface, of which 12 were assumed to be involved in initial binding. In the current simulations, all tethers were taken of an equal length of 50 nm. Once the substratum surface came within reach of the tether length, the tether was allowed to bind to the substratum surface. Viscous drag forces were accounted according to Stokes law in which ⃗ is the radial position of the center of an adhering particle.
Subsequently, a first and second order backward difference algorithm was implemented to calculate the location of the center of a particle, based its previous two positions. Initially, all tethers were oriented radially outwards as they would be in the planktonic phase prior to adhesion. Simulated particle adhesion and tethered particle motion was initiated by allowing the 12 initially binding tethers to adhere to the substratum surface and exposing the particle to the prevailing forces listed in Eq. S1. When the distance between the tether origin at the particle surface and the substratum surface was less than the tether length, taken as 50 nm within the current simulations, the tether was allowed to bind in addition to the 12 initial ones (of which a number may have detached within the process). During simulation, the elastic tether force was assumed to be radially directed in order to avoid particle torsion.
Tethers were detached in this simulation when the elastic force generated in an elongated tether exceeded the tether adhesion force, an input parameter to the program. Moreover, the probability, P det , that a tether detached from the substratum surface was programmed to increase when the elastic force generated in the tether due to Brownian-motion and viscous drag forces increased according to in which F T, elastic is the elastic tether force at the current position of the particle, i.e. the current elongation of the tether and F T, adhesion the individual tether adhesion force. Accordingly, position-maps were generated in silico under different conditions that account for the dynamics of tether binding, including the final number of binding tethers and their residence times. The in silico generated position-maps can subsequently be analyzed in exactly the same way as experimentally observed position-maps.
VIDEO V1. Time-lapse series of binding tethers of a simulated adhering particle initially binding with 12 tethers, each with a tether adhesion force of 0.18 pN. The dots indicate the positions of the binding tethers. Time step for each iteration in the simulation program was 1 x 10 -6 s.