The packaged state of bacteriophage genome is among the simplest examples of condensed DNA found in nature; however, the details of genome packing and organization have eluded full characterization. One avenue toward resolution of the packaged state concerns analysis of DNA knots obtained from bacteriophage capsids. Work in this vein has demonstrated a relative absence of simple, achiral knots in DNA extracts taken from P4 bacteriophage. This chiral organization can be explained by a biasing in a fundamental knotting parameter - the writhe. Thus, successful genome packing models must account for the chiral nature of genomic knots while also proposing a mechanism mediating writhe-bias.
The following work builds upon the notion of writhe-bias, simulating its effects upon knotting parameters relevant to phage genome packing – the knotting probability (KP) and the radius of gyration (RoG, a measure of knot compactness). KnotPlot was used to generate raw data sets comprised of random knots of predefined lengths and their associated knotting parameters (i.e. writhe, RoG, evaluated Alexander polynomials). Writhe-biased data sets were generated by imposing arbitrary minimum writhe requirements upon raw data sets.
Unbiased KP's tend to decay with decreasing knot length. Writhe-biased KP's alter this trend displaying sharp growth for shorter knot lengths followed by decay and subsequent growth at larger lengths. Writhe-biased RoG's are shifted to lower values over all lengths relative to the unbiased case. Thus writhe-biasing appears to increase the probability of knotting particularly for knots of short length while also producing more compact knots.