Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

tagO is involved in the synthesis of all anionic cell-wall polymers in Bacillus subtilis 168.

Sequence homologies suggest that the Bacillus subtilis 168 tagO gene encodes UDP-N-acetylglucosamine:undecaprenyl-P N-acetylglucosaminyl 1-P transferase, the enzyme responsible for catalysing the first step in the synthesis of the teichoic acid linkage unit, i.e. the formation of undecaprenyl-PP-N-acetylglucosamine. Inhibition of tagO expression mediated by an IPTG-inducible P(spac) promoter led to the development of a coccoid cell morphology, a feature characteristic of mutants blocked in teichoic acid synthesis. Indeed, analyses of the cell-wall phosphate content, as well as the incorporation of radioactively labelled precursors, revealed that the synthesis of poly(glycerol phosphate) and poly(glucosyl N-acetylgalactosamine 1-phosphate), the two strain 168 teichoic acids known to share the same linkage unit, was affected. Surprisingly, under phosphate limitation, deficiency of TagO precludes the synthesis of teichuronic acid, which is normally induced under these conditions. The regulatory region of tagO, containing two partly overlapping sigma(A)-controlled promoters, is similar to that of sigA, the gene encoding the major sigma factor responsible for growth. Here, the authors discuss the possibility that TagO may represent a pivotal element in the multi-enzyme complexes responsible for the synthesis of anionic cell-wall polymers, and that it may play one of the key roles in balanced cell growth.

Scaling behavior and equilibrium lengths of knotted polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease. on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.

High throughput 3D super-resolution microscopy reveals Caulobacter crescentus in vivo Z-ring organization.

We created a high-throughput modality of photoactivated localization microscopy (PALM) that enables automated 3D PALM imaging of hundreds of synchronized bacteria during all stages of the cell cycle. We used high-throughput PALM to investigate the nanoscale organization of the bacterial cell division protein FtsZ in live Caulobacter crescentus. We observed that FtsZ predominantly localizes as a patchy midcell band, and only rarely as a continuous ring, supporting a model of "Z-ring" organization whereby FtsZ protofilaments are randomly distributed within the band and interact only weakly. We found evidence for a previously unidentified period of rapid ring contraction in the final stages of the cell cycle. We also found that DNA damage resulted in production of high-density continuous Z-rings, which may obstruct cytokinesis. Our results provide a detailed quantitative picture of in vivo Z-ring organization.

Magistri Petri Rogerii, Prioris sancti Baudilii, qui fuit postea Clemens Papa VI.lectura super Decretalem Joannis Papae XXII. Quia quorumdam mentes.

Baluzianus

1.° Joannis de Sacrobosco tractatus de sphaera, cum Joannis Anglici commentario. — 2.° Summa Lamberti de logica. — 3.° Communia super totam logicam, grammaticam, et super mathematicas scientias : authore anonymo.

Colbertinus