||Supercoiling: Gyrase, TopoI, TopoIV
We use a calculation of the DNA's linking number (LK) in order to track the supercoiling of the DNA. The ΔLK is the difference between the current level of DNA supercoiling and the relaxed level of DNA supercoiling. The LKrelaxed is defined as # of base pairs/10.5, in which 10.5 is the number of bases per turn in a relaxed double helix. As the replication loops move, the LKcurrent deviates from this relaxed state, and gyrases and topoisomerases help bring the DNA back to the relaxed state. We model two regimes on the chromosome and track their ΔLKs separately. Unreplicated DNA is that downstream of the two replication loops. As the replication loop progresses the number of bases in this regime decreases, meaning that the LKrelaxed decreases. The LKcurrent then, is too high, and must be brought down towards the LKrelaxed by inducing negative supercoils with DNA gyrase and topoisomerase IV. The second regime is the replicated DNA upstream of the replication loops. As new uncoiled DNA is formed, it needs to be positively supercoiled. The number of bases in this regime is increasing, meaning that the LKrelaxed is increasing. As the LKcurrent relative to the LKrelaxed is too low, positive supercoils are induced by topoisomerase I.
DNA Condensation: SMC
Chromosome segregation requires that the DNA be highly compacted. Structural maintenance of chromosome (SMC) complexes are V shaped proteins (with an head and two legs) that induce positive supercoils in double stranded DNA (Porter et al., 2004). The complexes are believed to work with a lock and key mechanism in which first DNA is looped around the legs of the SMC complex, and then an ATP is bound between the two tails to lock the SMC complex in place. The complexes bind and clamp the DNA causing many loops in the DNA and compacting it. The loops around each leg occupy 90bp. A loop of about 450bp forms between the two SMC complex legs (Jensen and Shapiro, 2003, Strick and Kawaguchi, 2004). Further, it has been inferred that there is about 1 SMC complex per every 7000bp (Jensen and Shapiro, 2003). In our model, SMC complex binding is included in the supercoiling module. The initial chromosome is bound by SMC complexes averaging 7000bp spacing. As the replication loop proceeds, the SMC complexes that it encounters are displaced. Once the DNA has been replicated, SMC complexes are randomly bound to the DNA such that their spacing averages 7000bp. Each SMC complex occupies 630bp, and no two SMC complexes can occupy the same space. Both the decision of whether an SMC complex will bind at a given time point and the binding location are random. SMC complexes do not fall off the chromosomes unless due to the force of the replication loop. The two chromosomes are tracked separately.
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