A new approach to decoupling of bacterial adhesion energies measured by AFM into specific and nonspecific components

Abstract

A new method to decoupling of bacterial interactions measured by atomic force microscopy (AFM) into specific and nonspecific components is proposed. The new method is based on computing the areas under the approach and retraction curves. To test the efficacy of the new method, AFM was used to probe the repulsion and adhesion energies present between L. monocytogenes cells cultured at five pH values (5, 6, 7, 8 and 9) and silicon nitride (Si₃N₄). Overall adhesion energy was then decoupled into its specific and nonspecific components using the new method as well as using Poisson statistical approach. Poisson statistical method represents the most commonly used approach to decouple bacterial interactions into their components. For all pH conditions investigated, specific energies dominated the adhesion and a transition in adhesion and repulsion energies for cells cultured at pH 7 was observed. When compared, the differences in the specific and nonspecific energies obtained using Poisson analysis and the new method were on average 2.2% and 6.7%, respectively. The relatively close energies obtained using the two approaches demonstrate the efficacy of the new method as an alternative way to decouple adhesion energies into their specific and nonspecific components.

Keywords: AFM; Listeria monocytogenes; adhesion energy; pH and Poisson model; repulsion energy.

Figure 1

(A) An example of an AFM retraction curve of L. monocytogenes EGDe cultured in BHIB at pH 7. The gray shadowed area represents the adhesion energy in aJ. The black arrows at the top of the curve indicate the bounds of integration where the adhesion energy was computed using eq. 1. (B) An example of an AFM approach curve of L. monocytogenes EGDe cultured in BHIB at pH 7. The gray shadowed area represents the repulsion energy in aJ. The black arrows at the top of the curve indicate the bounds of integration where the repulsion energy was computed using eq. 2.

Figure 2

(A-E) Histograms that show the distribution of the adhesion energies (aJ) quantified from retraction curves (white-filled) and the repulsion energies computed from approach curves (gray-filled) between the biopolymers of L. monocytogenes EGDe cells cultured at pH values of 5, 6, 7, 8, and 9 and Si₃N₄ under water. For comparison purposes, the absolute values of the repulsion energies were plotted on the same figure. Solid lines in white-filled histograms indicate the theoretical Poisson distribution fits to the distributions of adhesion energies. The ability of the Poisson model to fit the distribution of adhesion energies was judged by the values of coefficient of correlation (r²); which averaged 0.90 for all histograms. Solid lines in the gray-filled histograms indicate the log-normal probability distribution function with three parameters fits to the distributions of repulsion energies. The coefficient of correlation (r²) values for the log-normal fits were 0.88, 0.89, 0.88, 0.75 and 0.83, respectively. (F) A scatter graph that shows the means of all data included in the histograms shown in panels A-E of this Figure as a function of the pH of the bacterial growth media. Absolute values of repulsion energies were used in this scatter graph. Error bars indicate the values of the standard error of the mean.

Figure 2

(A-E) Histograms that show the distribution of the adhesion energies (aJ) quantified from retraction curves (white-filled) and the repulsion energies computed from approach curves (gray-filled) between the biopolymers of L. monocytogenes EGDe cells cultured at pH values of 5, 6, 7, 8, and 9 and Si₃N₄ under water. For comparison purposes, the absolute values of the repulsion energies were plotted on the same figure. Solid lines in white-filled histograms indicate the theoretical Poisson distribution fits to the distributions of adhesion energies. The ability of the Poisson model to fit the distribution of adhesion energies was judged by the values of coefficient of correlation (r²); which averaged 0.90 for all histograms. Solid lines in the gray-filled histograms indicate the log-normal probability distribution function with three parameters fits to the distributions of repulsion energies. The coefficient of correlation (r²) values for the log-normal fits were 0.88, 0.89, 0.88, 0.75 and 0.83, respectively. (F) A scatter graph that shows the means of all data included in the histograms shown in panels A-E of this Figure as a function of the pH of the bacterial growth media. Absolute values of repulsion energies were used in this scatter graph. Error bars indicate the values of the standard error of the mean.

Figure 3

(A) A representative scatter plot of the variance, σ_E², versus the mean, μ_E, of the adhesion energies measured between L. monocytogenes cells cultured at pH 7 and Si₃N₄ in water. Each point represents the variance and the mean of all adhesion energies quantified from retraction force-distance curves collected on one cell. The solid line represents the linear regression fit to the data and was used to obtain the specific and nonspecific components of the adhesion energies (Table 1, eq. 8). The error bars represent the standard errors of the means. Figure S2 in the supplementary materials shows similar scatter plots for L. monocytogenes cells cultured at the other four investigated pH conditions of growth. The coordinates of the data points used in constructing Figures 3A and S2 are given in Table S1 in the supplementary materials. (B) A scatter-graph that shows the specific and nonspecific energy components predicted using Poisson statistical analysis of the adhesion energies as a function of the pH of the bacterial growth media.

Figure 4

Scatter graphs that show the relationship between (A) specific energies and (B) nonspecific energies, respectively estimated using Poisson statistical model and our new proposed methodology. Solid lines indicate linear fits to the data. In (A), the equation is described by Y=1.02X, r²=0.97 and in (B), the equation is described by Y=1.08X with r² value of 0.99.

Figure 4

Scatter graphs that show the relationship between (A) specific energies and (B) nonspecific energies, respectively estimated using Poisson statistical model and our new proposed methodology. Solid lines indicate linear fits to the data. In (A), the equation is described by Y=1.02X, r²=0.97 and in (B), the equation is described by Y=1.08X with r² value of 0.99.