By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 +/- 0.1 A characteristic decay length and the attractive component of the free energy is always 2.3 +/- 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 +/- 0.5 A characteristic decay length for intermolecular attractions between condensed DNA molecules.
We have measured forces generated by multivalent cation-induced DNA condensation using single-molecule magnetic tweezers. In the presence of cobalt hexammine, spermidine, or spermine, stretched DNA exhibits an abrupt configurational change from extended to condensed. This occurs at a well-defined condensation force that is nearly equal to the condensation free energy per unit length. The multivalent cation concentration dependence for this condensation force gives the apparent number of multivalent cations that bind DNA upon condensation. The measurements show that the lower critical concentration for cobalt hexammine as compared to spermidine is due to a difference in ion binding, not a difference in the electrostatic energy of the condensed state as previously thought. We also show that the resolubilization of condensed DNA can be described using a traditional Manning–Oosawa cation adsorption model, provided that cation–anion pairing at high electrolyte concentrations is taken into account. Neither overcharging nor significant alterations in the condensed state are required to describe the resolubilization of condensed DNA. The same model also describes the spermidine3+/Na+ phase diagram measured previously.
We have measured the interaction force between a silicon nitride scanning force microscopy (SFM) probe and the basal plane of highly oriented pyrolitic graphite as a function of pH and ionic concentration in aqueous solutions. Forces in the range +/- 50 pN were reconstructed from measured signals using dynamical analysis of the cantilever. We modeled the force-separation data using a flat plate electric double-layer interaction and assumed the Derjaguin approximation to adapt the flat plate geometry for the SFM probe shape. Measured forces were well modeled by the theory at high ionic concentrations (10 and 100 mM), where Debye lengths were 3.0 and 0.96 nm, respectively. The theory failed to model forces at a lower ionic concentration (1 mM), where the Debye length was 9.6 nm. To investigate this, we calibrated the SFM probe geometry using blind reconstruction and obtained an apex radius of 7 nm. This value suggested that failure of the theory was due to an invalidation of the Derjaguin approximation at long Debye lengths, where the characteristic length scale for the interaction was larger than the size of the SFM probe. The errors were reduced by replacing the Derjaguin approximation with a surface element integration. The result experimentally demonstrates the limitations of the Derjaguin approximation for predicting interactions of nanoscale colloids.
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