Layered Structure and Complex Mechanochemistry Underlie Strength and Versatility in a Bacterial Adhesive

ABSTRACT While designing synthetic adhesives that perform in aqueous environments has proven challenging, microorganisms commonly produce bioadhesives that efficiently attach to a variety of substrates, including wet surfaces. The aquatic bacterium Caulobacter crescentus uses a discrete polysaccharide complex, the holdfast, to strongly attach to surfaces and resist flow. The holdfast is extremely versatile and has impressive adhesive strength. Here, we used atomic force microscopy in conjunction with superresolution microscopy and enzymatic assays to unravel the complex structure of the holdfast and to characterize its chemical constituents and their role in adhesion. Our data support a model whereby the holdfast is a heterogeneous material organized as two layers: a stiffer nanoscopic core layer wrapped into a sparse, far-reaching, flexible brush layer. Moreover, we found that the elastic response of the holdfast evolves after surface contact from initially heterogeneous to more homogeneous. From a composition point of view, besides N-acetyl-d-glucosamine (NAG), the only component that had been identified to date, our data show that the holdfast contains peptides and DNA. We hypothesize that, while polypeptides are the most important components for adhesive force, the presence of DNA mainly impacts the brush layer and the strength of initial adhesion, with NAG playing a primarily structural role within the core. The unanticipated complexity of both the structure and composition of the holdfast likely underlies its versatility as a wet adhesive and its distinctive strength. Continued improvements in understanding of the mechanochemistry of this bioadhesive could provide new insights into how bacteria attach to surfaces and could inform the development of new adhesives.

where D is the distance between the surfaces, Γ is the brush layer density, k B is the Boltzmann constant, and T is temperature. It can be shown that in the range 0.2 < D/2L 0 < 0.9, the expression in Eq. 3 is approximately exponential For a bare spherical tip interacting with a polymer brush, the pressure is obtained by substituting L 0 /2 for L 0 , and dividing the pressure by 2. Using the Derjaguin approximation, the total force for a parabolic tip profile (Z − D = r 2 /2R tip ) becomes [12] F (D) The validity of brush models is usually evaluated retrospectively after finding the brush parameters, in particular L 0 . When the AFM probe-surface distance, D, is less than approximately 20% of the brush layer thickness, L 0 , the brush layer response is no longer strictly entropic in nature. Recent work has shown that at high compression, the brush behaves as an elastic layer [4], contributing to an effective elastic modulus for the underlying sample.

Simultaneous fits to Hertz and brush layer models
We extract parameters describing holdfast material properties from least-squares fits to the raw AFM data given by cantilever deflection, d, and piezo height, Z. Specifically we plot Z − d versus d, and fit the data in selected regions to functional forms describing the bulk of the holdfast and a surface brush layer, as described below. We chose to plot the data in this way in order that the fit procedure is most robust for portion of the data at large d, where Z − d varies slowly with d, allowing reliable extraction of the modulus of elasticity, E, which constitutes a central result of our work.
In this section, we describe two approaches to fitting the AFM data: In the first approach, we fit the brush layer model all the way to the surface. In the second approach, we exclude the transition region corresponding to D/L 0 less than ∼ 0.1 − 0.2, wherein the brush layer force is not strictly entropic. Our results demonstrate that while the Young's modulus characterizing the material properties of the bulk of the holdfast is different in these two approaches, the results are consistent and vary by less than an order of magnitude. However, we emphasize that in the transition region at the surface of holdfast, neither the Hertz nor brush layer model strictly holds. In using the Hertz and brush layer models to describe the stiff elastic bulk region coated with biopolymer, first we allow the boundary between these regions to float as a free parameter in the least-squares minimization process. For values of d greater than this value, the fit function is the Hertzian form, given by where the Young's modulus is obtained from the fit parameter γ as E = 3γ For values of d less than the boundary, the fit function represents a description of the brush layer, where the brush layer density is obtained from the fit parameter α as Γ = (αk c /50k B T R tip ) 2/3 .
To allow for an assessment of goodness of fit via a χ 2 metric, we assign an uncorrelated 0.25 nm experimental uncertainty to every value of Z − d, based on empirical evaluation of instrumental drift over the measurement time frame. This value represents an upper bound, in the sense that both the point-by-point fluctuations and perceived unphysical drifts within measurements of most samples are smaller than this. For our fits we have not incorporated the corresponding uncertainties on what we take as the independent observable (d). We have excluded from the fits the points with (d − d 0 ) ∼ 0, since they fall outside the range of applicability of the brush layer model (D > 0.9L 0 ).
With the approach described above, it is possible for most samples to obtain fits to the data with satisfactory χ 2 values, in which the model used for the brush layer gives a prediction for Z − d that matches that of the Hertzian model at the boundary between the two. However we have also observed that (1) the values of L 0 are driven to be progressively smaller than what we find when we successively include more data points at low d − d 0 values, and (2) in some cases the best-fit values for d 0 deviate significantly from what is expected based on visual inspection of the low (d − d 0 ) region. This deviation is likely due to the fact that by requiring the fits based on the two functions to be continuous at the surface of the holdfast where D < 0.2L 0 , the brush layer is highly compressed and the model does not strictly hold, as described above.
As a result we have also carried out fits where, in addition to points at very low d − d 0 , we exclude data points in the transition region approximately centered on the boundary between the brush layer and bulk behaviors. By excluding the transition region from the fit, the two problems noted above are avoided. Determination of the limits of the excluded region is done empirically on a sample-by-sample basis, but is not highly tuned in order to avoid the introduction of significant biases that might result from fine-tuning based on the data itself.
We show representative fits to 16 h and 64 h data where the transition region at the surface is excluded (Fig. A and Fig. C, respectively) and the brush layer and Hertz models are continuous at the surface of the holdfast (Fig. B and Fig. D, respectively). In Table 1, we summarize fit results for the parameters characterizing the material properties of the holdfast (E, L 0 , Γ) using the two fitting approaches.

Surface layer as an elastic material
We also investigated a description of the data wherein the surface layer and bulk of the holdfast are both characterized as elastic materials and described by the Hertzian model, with different elastic moduli. We find that the data does not support this description as well as the brush layer model for the surface layer. As an example, in Fig. E

Finite thickness correction to Hertz model
In been obtained for the Green's function for the deformation of the finite sample free surface [5,6], and for a spherical tip in the limit of small indentation (δ/h 1), it is given by: where χ = R tip δ/h. heights but varying elastic moduli, we find that with increasing sample stiffness, this ratio decreases. This result is consistent with the expectation that for stiffer samples and at small indentations, the strain field in Figure S3 is less influenced by the substrate. The

Young's modulus as a spring constant
To make connection between the fitted results for the holdfast Young's modulus and effective spring constant, we consider holdfast as an elastic bar comprised of a bundle of ideal springs of length h, compressed by δ along the length dimension. The number of springs in parallel is proportional to the cross-sectional area A * of the bar. Hence, the force applied to each spring is proportional to the total applied force F divided by the cross-sectional area A * . Hooke's law for each spring in the bundle is where E is Young's modulus. Therefore, k = EA * /h. We take A * to be an effective cross-sectional area of the tip during indentation, A * = απR 2 tip , where α < 1. While the indentation is not uniform across the cross-sectional area of the tip (i.e., each spring in the bundle is not compressed by the same amount), we approximate it as constant. For an indentation of δ/R tip ∼ 2/3, for a spherical indenter, we have A * ∼ (5/9) A. Using typical holdfast parameter values E ∼ 0.36 ± 0.12 × 10 9 Pa, h ∼ 30 nm, R tip = 15 nm, and α ∼ 5/9, we find k ∼ 5 ± 1.7 N/m, consistent with the fitted value of k = 7.1 ± 0.5 N/m.