1 can perform a statistical mechanical evaluation of your transition within a superhelical domain possessing any base sequence, as NS-018 manufacturer described below.Nevertheless, it doesn’t hold for the B-Z transition simply because the repeat unit of Z-DNA is two base pairs (dimeric), whilst that on the B-form is actually a single base pair (monomeric). We will initial derive an expression for the amount of Z-form states out there to a linear molecule of N base pairs, and after that use this outcome to ascertain the number of states of a circular molecule possessing exactly the same length. Let Sl (N) denote the amount of states available to a linear molecule comprised of N base pairs experiencing the B-Z transition. In any offered state each base pair within the sequence isPLoS Computational Biology | www.ploscompbiol.orgThe Equilibrium Statistical Mechanics of a Conformational TransitionIn principle all states accessible towards the molecule compete for occupancy. As soon as the absolutely free energy GS connected to each and every state S has been evaluated, the partition function Z could possibly be calculated as Z XSe({bGS ) ,where the sum is over all states, and b 1=kB T, where kB is the Boltzmann constant and T is the temperature. At thermodynamic equilibrium the available states are weighted according to the Boltzmann distribution. That is, in the equilibrium distribution each state S occurs with relative frequency e({bGS ) : Zp(S)Stress Induced B-Z TransitionsThis means that the occupancy of states decreases exponentially as their free energies increase, so only the relatively low energy states are significantly occupied. At equilibrium the ensemble average value of a parameter A, that has value AS in state S, is given by XSP AS p(S)vAwSAS exp ({bGS PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20151456 ) : ZThe equilibrium probability p(x) of transition for base pair x is found by averaging the parameter nx according to the above equation, where nx 1 in any state where base pair x is transformed, and nx 0 in all other states. The transition profile is the graph of p(x) vs x. It shows the probability of transition for each base pair in the sequence under the assumed conditions. As will be shown below, this profile can change significantly as the imposed superhelix density changes.States and Their EnergiesWe consider a DNA molecule containing N base pairs of defined sequence, on which a superhelical density s is imposed. Here s AB a=N, where AB 10:4 bp/turn is the helical twist rate for the B-form. A state of this molecule assigns to each base pair one of two conformations, either B-form or Z- form. This is done in a manner consistent with the dinucleotide repeat unit of ZDNA, as described below. The residual superhelicity in that state is the linking difference remaining to stress the molecule after the change of twist consequent on transition. This includes the untwisting of the transformed base pairs from the right-handed Bform to the left-handed Z-form, together with a small amount tz of untwisting of the two stands at each B-Z junction [21]. Thus, in a state where n bases pairs are in the Z-form the residual superhelical linking difference is given by 1 1 {2tz nr : { ar azn AB AZ one in anti and the other in syn conformation. As the values in the table show, the transition energy of a particular dinucleotide depends strongly on whether it is AS (59 anti 39 syn) or SA (59 syn 39 anti). A Z-Z junction occurs when adjacent dinucleotides have different anti-syn alternations, either (AS)(SA) or (SA)(AS). This violation is energetically costly, as shown in the last column of the Table. Some.