The iso-competition point for counterion competition binding to DNA: calculated multivalent versus monovalent cation binding equivalence.

In this paper we introduce an important parameter called the iso-competition point (ICP), to characterize the competition binding to DNA in a two-cation-species system. By imposing the condition of charge neutralization fraction equivalence theta1 = ZthetaZ upon the two simultaneous equations in Manning's counterion condensation theory, the ICPs can be calculated. Each ICP, which refers to a particular multivalent concentration where the charge fraction on DNA neutralized from monovalent cations equals that from the multivalent cations, corresponds to a specific ionic strength condition. At fixed ionic strength, the total DNA charge neutralization fractions thetaICP are equal, no matter whether the higher valence cation is divalent, trivalent, or tetravalent. The ionic strength effect on ICP can be expressed by a semiquantitative equation as ICPZa/ICPZb = (Ia/Ib)Z, where Ia, Ib refers to the instance of ionic strengths and Z indicates the valence. The ICP can be used to interpret and characterize the ionic strength, valence, and DNA length effects on the counterion competition binding in a two-species system. Data from our previous investigations involving binding of Mg2+, Ca2+, and Co(NH3)63+ to lambda-DNA-HindIII fragments ranging from 2.0 to 23.1 kbp was used to investigate the applicability of ICP to describe counterion binding. It will be shown that the ICP parameter presents a prospective picture of the counterion competition binding to polyelectrolyte DNA under a specific ion environment condition.