Entropic bonding of the type 1 pilus from experiment and simulation

Abstract

The type 1 pilus is a bacterial filament consisting of a long coiled proteic chain of subunits joined together by non-covalent bonding between complementing $\beta$ -strands. Its strength and structural stability are critical for its anchoring function in uropathogenic Escherichia coli bacteria. The pulling and unravelling of the FimG subunit of the pilus was recently studied by atomic force microscopy experiments and steered molecular dynamics simulations (Alonso-Caballero et al. 2018 Nat. Commun. 9, 2758. (doi:10.1038/s41467-018-05107-6)). In this work, we perform a quantitative comparison between experiment and simulation, showing a good agreement in the underlying work values for the unfolding. The simulation results are then used to estimate the free energy difference for the detachment of FimG from the complementing strand of the neighbouring subunit in the chain, FimF. Finally, we show that the large free energy difference for the unravelling and detachment of the subunits which leads to the high stability of the chain is entirely entropic in nature.

Keywords: atomic force microscopy; pilus; steered molecular dynamics.

Figure 1.

Atomic force microscopy (AFM) force-extension experiment. (a) Schematic view of the experimental set-up; the FimG protein domain is attached in between two dimers of I91 domains used as markers. The polyprotein sequence is held between a cantilever with spring constant k and a gold surface retracted at speed v; the extension x of the whole sequence and the force F on the cantilever are recorded. (b) An example force–time trace (after downsampling). (c) The corresponding force–extension trace, with the fitted curves from the WLC model for each branch and the automatically determined maxima and minima. The contour length increment s_i owing to the unfolding of each domain is also shown. (d) The final force–extension trace using the fitted curves; the shaded areas give the quasi-static work across the transitions $W_i^{\mathrm{rip}}$.

Figure 2.

Distribution of experimental peak force values. The dashed lines show normal distributions fitted to the data. Distribution of the tip detachment peak not shown.

Figure 3.

Steered molecular dynamics (SMD) simulation. (a) Schematic view of the FimG protein (in red) with the linker to the next subunit (L, in blue), connected together by a sequence of four amino acids (C, in green) to form a single chain. The pulling is done from the N and C-terminal amino acids (NT and CT, respectively), and the extension is measured as the distance x between them. The lower diagram shows an abstract view of the entire sequence of amino acids, with the HBs between them illustrated by dashed black lines, and the DB as the full yellow line. (b) An example force–time trace. (c) The corresponding force–extension trace, with the fitted curves from the FJC model for each branch, and the automatically determined maxima. Only the final FJC curve is used in determining the unfolding work.

Figure 4.

Distribution of work values for the unfolding of FimG, W^unfold. Note the different scales for experiment and simulation. There are a total of 186 traces from experiment, and 10 traces from simulation. The dashed lines show normal distributions fitted to the data.

Figure 5.

Free energy difference for the unfolding using the mean work estimator 〈W^unfold〉. The error bars for both experiment and simulation are the instantaneous standard deviations from the respective distributions. The internal energy of the system from the simulation is also shown by the full black line. The free energy for detachment between FimG and FimF in simulations without the linker is shown by the dotted horizontal line.