Stochastic model for Soj relocation dynamics in Bacillus subtilis

Abstract

The Bacillus subtilis Spo0J/Soj proteins, implicated in chromosome segregation and transcriptional regulation, show striking dynamics: Soj undergoes irregular relocations from pole to pole or nucleoid to nucleoid. Here, we report on a mathematical model of the Soj dynamics. Our model, which is closely based on the available experimental data, readily generates dynamic Soj relocations. We show that the irregularity of the relocations may be due to the stochastic nature of the underlying Spo0J/Soj interactions and diffusion. We propose explanations for the behavior of several Spo0J/Soj mutants, including the "freezing" of the Soj dynamics observed in filamentous cells. Our approach underlines the importance of incorporating stochastic effects when modeling spatiotemporal protein dynamics inside cells.

Fig. 1.

Schematic representation of the model for the Spo0J/Soj dynamics. Soj-ATP undergoes spontaneous cooperative nucleoid binding (9, 28); nucleoid-bound Soj induces Spo0J condensation (9). Condensed Spo0J stimulates the ATPase activity of Soj, leading to cooperative expulsion (9) of Soj-ADP from the nucleoid into the cytoplasm. Once most of the Soj has been expelled, the Spo0J begins to revert back to its uncondensed form. Expelled Soj binds to the cell membrane in the presence of MinD (29). MinD is a polar membrane-associated protein meaning that, in our model, Soj can only bind close to the cell poles. Soj is then released back into the cytoplasm, where it is now able to rebind to the nucleoid, and the cycle repeats. When in the cytoplasm, Soj may diffuse and then rebind to the closest nucleoid/polar membrane or, with a lower probability, it may relocate to the other nucleoid/polar membrane. This behavior leads to spontaneous dynamic Soj relocations.

Fig. 2.

Stochastic simulations of normal length B. subtilis cells. (A, C, E, and G) Space-time plots of nucleoid-bound Soj concentration; bright colors represent high concentration on a nucleoid. (B, D, F, and H) Number of Soj proteins on each nucleoid (+, o), and at the left hand polar membrane (B only, full line, copy number exaggerated by a factor of 10), as a function of time. (A and B) Example of wild-type cell simulation showing stochastic relocation. (C and D) Example of wild-type cell simulation where the Soj patch fails to relocate to another nucleoid. (E–H) Spo0J19 mutant simulations. (E and F) Model I. (G and H) Model II, showing much more rapid Soj relocation dynamics.

Fig. 3.

(A, C, and E) Space-time plots of nucleoid-bound Soj concentration; bright colors represent high concentration on a nucleoid. (B, D, and F) Number of Soj proteins on each nucleoid as a function of time. (A and B) Stochastic simulations of filamentous cells depleted for FtsZ. (C–F) Simulated Spo0J19 mutants lacking FtsZ. (C and D) Model I. (E and F) Model II. In both cases, the dependence on the poles is lost, and Soj is able to relocate from nucleoid to nucleoid well away from polar regions.