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Dislocation-Mediated Elongation of Bacteria David R. Nelson, Harvard University, DMR 1005289 INTELLECTUAL MERIT ●Recent experiments have illuminated a remarkable growth mechanism for rod-shaped bacteria: proteins associated with “strand extension centers” in the cell wall move at constant velocity on circles around the cell circumference.[1] ● These defects are in fact dislocations in a partially ordered peptidoglycan meshwork, driven by specialized glycan strand extension machinery. Unlike most dislocations, the motion is dominated by climb, i.e., motion perpendicular to the Burgers vector. ● Generation and motion of these interacting defects lead to surprising effects associated with the cylindrical geometry, with important implications for growth.[2] ● The dynamics is influenced in important ways by long range elastic interactions between defects and by turgor pressure Model of bacterial elongation: up- and down- pointing arrows represent moving dislocation defects activated by strand extension machinery. Asterisks represent static, inactive dislocations. [1] D. R. Nelson, Annual Reviews of Biophysics, 41, 371, (2012). [2] A. Amir and D. R. Nelson, Proceedings of the National Academy of Science, 109, 9833 (2012) Numerical simulation: trajectories of ~30 active dislocations, driven by a combination of chemical forces and turgor pressure ; black dots indicate 10,000 inactive dislocations, which create a disordered potential for the active ones.

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BROADER IMPACT It is important to understand how cell walls endow bacteria with a shape and a shear modulus. Of particular interest are gram- negative bacteria whose cell walls consist of a giant macromolecule composed of glycan strands cross-linked by peptides. Recent experiments on labeled strand extension machinery” reveal how dislocations systematically add material to cell walls. This dynamics can be understood using ideas from materials science such as Peach-Kohler forces and mobilities describing dislocation climb. Our theoretical work also treats the two dimensional “chemical kinetics” of a relatively small number of interacting dislocations, as an alternative to brute force simulations of ~2.75 peptidoglycan unit cells. A simplified model of the dynamics of n ac (t) and n in (t), the areal densities of active and inactive dislocations, is illustrated at left. Simplified model of the dynamics of active and inactive dislocation densities. Here, γ 1 and γ 2 are respectively dislocation processivity and activation rates. The nonlinear terms arise from a novel “geometrical dilution” effect within the bacterial cell wall. Inactive dislocation pairs are created at a rate γ 4. Active dislocation pulled past an inactive one by enzymatic machinery: An initially inactive dislocation pair is created by an enzyme that cuts a vertical glycan strand (rate constant γ 4 ) in the cell wall. The elongation machinery then assembles around one inactive defect, turning it into an active one (rate constant γ 2 ). Dislocation-Mediated Elongation of Bacteria David R. Nelson, Harvard University, DMR 1005289

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