Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

The Becker-Döring equations with monomer input, competition and inhibition

We investigate the Becker-Döring model of nucleation with three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentation rates. Initially we consider the problem of constant monomer input and determine the steady-state solution approached in the large-time limit, and the manner in which it is approached. Secondly, in addition to a constant input of monomer we allow a constant input of inhibitor, which prevents clusters growing any larger and this removes them from the kinetics of the process; the inhibitor is consumed in the action of poisoning a cluster. We determine a critical ratio of poison to monomer input below which the cluster concentrations tend to a non-zero steady-state solution and the poison concentration tends to a finite value. Above the critical input ratio, the concentrations of all cluster sizes tend to zero and the poison concentration grows without limit. In both cases the solution in the large-time limit is determined. Finally we consider a model where monomers form two morphologies, but the inhibitor only acts on one morphology. Four cases are identified, depending on the relative poison to monomer input rates and the relative thermodynamic stability. In each case we determine the final cluster distribution and poison concentration. We find that poisoning the less stable cluster type can have a significant impact on the structure of the more stable cluster distribution; a counter-intuitive result. All results are shown to agree with numerical simulation.

Structure of the N-terminal oligomerization domain of DnaD reveals a unique tetramerization motif and provides insights into scaffold formation

DnaD is a primosomal protein that remodels supercoiled plasmids. It binds to supercoiled forms and converts them to open forms without nicking. During this remodeling process, all the writhe is converted to twist and the plasmids are held around the periphery of large scaffolds made up of DnaD molecules. This DNA-remodeling function is the sum of a scaffold-forming activity on the N-terminal domain and a DNA-dependent oligomerization activity on the C-terminal domain. We have determined the crystal structure of the scaffold-forming N-terminal domain, which reveals a winged-helix architecture, with additional structural elements extending from both N- and C-termini. Four monomers form dimers that join into a tetramer. The N-terminal extension mediates dimerization and tetramerization, with extensive interactions and distinct interfaces. The wings and helices of the winged-helix domains remain exposed on the surface of the tetramer. Structure-guided mutagenesis and atomic force microscopy imaging indicate that these elements, together with the C-terminal extension, are involved in scaffold formation. Based upon our data, we propose a model for the DnaD-mediated scaffold formation.