The condensation of stiff, highly charged DNA molecules into compact structures by condensing agents ranging from multivalent ions 1 to small cationic proteins 2,3 is of major biological and therapeutic importance 4,5 , yet the underlying microscopic mechanism remains poorly understood 1,6-9 . It has been proposed 7,10 that DNA condensation is a purely electrostatic phenomenon driven by the existence of a strongly correlated liquid (SCL) of counterions at the DNA surface. The same theoretical argument predicts that multivalent counterions overcompensate the DNA charge when present at high concentration 11 , in turn destabilizing the condensates 12 . Here, we demonstrate the occurrence of DNA charge inversion by multivalent ions through measurements of the electrophoretic mobility of condensed DNA. By observing the multivalent-ioninduced condensation of a single DNA molecule using magnetic tweezers, we further show that charge inversion influences condensation by modulating the barrier for condensate nucleation in a manner consistent with the SCL mechanism.The role played by spatial correlations of screening ions in biological systems remains poorly understood. Definitive experimental evidence is particularly difficult to obtain because of the short length scales involved. The strongly correlated liquid (SCL) mechanism predicts that charge inversion necessarily accompanies and influences counter-ion-induced like-charge attraction 12 , thus providing a unique opportunity to test this mechanism. We concentrate on DNA because of its high charge density, the level of experimental control that it provides and the direct relevance of condensation to genome packaging.To verify the existence of DNA charge inversion, we measured the electrophoretic mobility, µ, of DNA condensates in solution using dynamic light scattering (DLS). The mobility, µ, reflects the bare charge of DNA plus that of counterions at its surface, and its sign is expected to reverse on charge inversion [13][14][15] . In DLS, the phase of laser light scattered from the condensates is monitored over time; condensates drifting at constant velocity in an electric field yield a phase that evolves linearly in time at a rate proportional to their mobility. Figure 1a shows the measured phase for concentrations c = 0.1 and 3 mM of the quadrivalent cation spermine ([C 10 N 4 H 30 ] 4+ ). The two signals have opposite slopes, indicating a sign reversal of µ (negative for c = 0.1 mM and positive for c = 3 mM). This is to our knowledge the first experimental report of DNA charge inversion induced solely by simple multivalent ions. Figure 1b shows the measured mobility of condensed DNA as a function of the concentration of spermine and buffer conditions. In 1 mM TRIS buffer, the mobility is positive for spermine concentrations greater than the charge-inversion concentration c 0 = 0.5 mM. Increasing the TRIS buffer concentration to 10 mM hinders charge inversion, causing c 0 to increase to 1 mM. Further adding 50 mM monovalent KCl salt causes charge inversion to disa...

DNA in solution can be condensed into dense aggregates by multivalent counterions. Here we investigate the effect of a nearby surface on the morphology of DNA condensates. We show that, contrary to what has often been assumed, interactions between DNA condensates and the surface can strongly influence the observed morphology. This limits the usefulness of surface probes such as atomic force microscopy for studying the morphology of condensates in bulk solution. Surprisingly, we find that the most negatively charged surface disturbs the condensate morphology most, suggesting that the microscopic mechanism resulting in DNA condensation is also responsible for the attractive force between DNA and the surface.