Reentrant Condensation of DNA induced by Multivalent Counterions

A theory of condensation and resolubilization of a dilute DNA solution with growing concentration of multivalent cations, N is suggested. It is based on a new theory of screening of a macroion by multivalent cations, which shows that due to strong cation correlations at the surface of DNA the net charge of DNA changes sign at some small concentration of cations N_0. DNA condensation takes place in the vicinity of N_0, where absolute value of the DNA net charge is small and the correlation induced short range attraction dominates the Coulomb repulsion. At N > N_0 positive DNA should move in the oppisite direction in an electrophoresis experiment. From comparison of our theory with experimental values of condensation and resolubilization thresholds for DNA solution containing Spe$^{4+}$, we obtain that N_0 = 3.2 mM and that the energy of DNA condensation per nucleotide is $0.07 k_B T$.Comment: 8 pages, 4 figures, references correcte

Effects of mechanical strain on thermal denaturation of DNA

As sections of a strand duplexed DNA denature when exposed to high temperature, the excess linking number is taken up by the undenatured portions of the molecule. The mechanical energy that arises because of the overwinding of the undenatured sections can, in principle, alter the nature of the thermal denaturation process. Assuming that the strains associated with this overwinding are not relieved, we find that a simple model of strain-altered melting leads to a suppression of the melting transition when the unaltered transition is continuous. When the melting transition is first order in the absence of strain associated with overwinding, the modification is to a third order phase transition.Comment: 4 pages, 5 figures, RevTe

Unzipping Kinetics of Double-Stranded DNA in a Nanopore

We studied the unzipping kinetics of single molecules of double-stranded DNA by pulling one of their two strands through a narrow protein pore. PCR analysis yielded the first direct proof of DNA unzipping in such a system. The time to unzip each molecule was inferred from the ionic current signature of DNA traversal. The distribution of times to unzip under various experimental conditions fit a simple kinetic model. Using this model, we estimated the enthalpy barriers to unzipping and the effective charge of a nucleotide in the pore, which was considerably smaller than previously assumed.Comment: 10 pages, 5 figures, Accepted: Physics Review Letter

The bend stiffness of S-DNA

We formulate and solve a two-state model for the elasticity of nicked, double-stranded DNA that borrows features from both the Worm Like Chain and the Bragg--Zimm model. Our model is computationally simple, and gives an excellent fit to recent experimental data through the entire overstretching transition. The fit gives the first value for the bending stiffness of the overstretched state as about 10 nm*kbt, a value quite different from either B-form or single-stranded DNA.Comment: 7 pages, 1 figur

The HIV-1 nucleocapsid chaperone protein forms locally compacted globules on long double-stranded DNA

The nucleocapsid (NC) protein plays key roles in Human Immunodeficiency Virus 1 (HIV-1) replication, notably by condensing and protecting the viral RNA genome and by chaperoning its reverse transcription into double-stranded DNA (dsDNA). Recent findings suggest that integration of viral dsDNA into the host genome, and hence productive infection, is linked to a small subpopulation of viral complexes where reverse transcription was completed within the intact capsid. Therefore, the synthesized dsDNA has to be tightly compacted, most likely by NC, to prevent breaking of the capsid in these complexes. To investigate NC\u27s ability to compact viral dsDNA, we here characterize the compaction of single dsDNA molecules under unsaturated NC binding conditions using nanofluidic channels. Compaction is shown to result from accumulation of NC at one or few compaction sites, which leads to small dsDNA condensates. NC preferentially initiates compaction at flexible regions along the dsDNA, such as AT-rich regions and DNA ends. Upon further NC binding, these condensates develop into a globular state containing the whole dsDNA molecule. These findings support NC\u27s role in viral dsDNA compaction within the mature HIV-1 capsid and suggest a possible scenario for the gradual dsDNA decondensation upon capsid uncoating and NC loss

Negative electrostatic contribution to the bending rigidity of charged membranes and polyelectrolytes screened by multivalent counterions

Bending rigidity of a charged membrane or a charged polyelectrolyte screened by monovalent counterions is known to be enhanced by electrostatic effects. We show that in the case of screening by multivalent counterions the electrostatic effects reduce the bending rigidity. This inversion of the sign of the electrostatic contribution is related to the formation of two-dimensional strongly correlated liquids (SCL) of counterions at the charged surface due to strong lateral repulsion between them. When a membrane or a polyelectrolyte is bent, SCL is compressed on one side and stretched on the other so that thermodynamic properties of SCL contribute to the bending rigidity. Thermodynamic properties of SCL are similar to those of Wigner crystal and are anomalous in the sense that the pressure, compressibility and screening radius of SCL are negative. This brings about substantial negative correction to the bending rigidity. For the case of DNA this effect qualitatively agrees with experiment.Comment: 8 pages, 2 figure

Theory of High-Force DNA Stretching and Overstretching

Single molecule experiments on single- and double stranded DNA have sparked a renewed interest in the force-extension of polymers. The extensible Freely Jointed Chain (FJC) model is frequently invoked to explain the observed behavior of single-stranded DNA. We demonstrate that this model does not satisfactorily describe recent high-force stretching data. We instead propose a model (the Discrete Persistent Chain, or ``DPC'') that borrows features from both the FJC and the Wormlike Chain, and show that it resembles the data more closely. We find that most of the high-force behavior previously attributed to stretch elasticity is really a feature of the corrected entropic elasticity; the true stretch compliance of single-stranded DNA is several times smaller than that found by previous authors. Next we elaborate our model to allow coexistence of two conformational states of DNA, each with its own stretch and bend elastic constants. Our model is computationally simple, and gives an excellent fit through the entire overstretching transition of nicked, double-stranded DNA. The fit gives the first values for the elastic constants of the stretched state. In particular we find the effective bend stiffness for DNA in this state to be about 10 nm*kbt, a value quite different from either B-form or single-stranded DNAComment: 33 pages, 11 figures. High-quality figures available upon reques

Kinetics of macroion coagulation induced by multivalent counterions

Due to the strong correlations between multivalent counterions condensed on a macroion, the net macroion charge changes sign at some critical counterion concentration. This effect is known as the charge inversion. Near this critical concentration the macroion net charge is small. Therefore, short range attractive forces between macroions dominate Coulomb repulsion and lead to their coagulation. The kinetics of macroion coagulation in this range of counterion concentrations is studied. We calculate the Coulomb barrier between two approaching like charged macroions at a given counterion concentration. Two different macroion shapes (spherical and rod-like) are considered. A new "self-regulated" regime of coagulation is found. As the size of aggregates increases, their charge and Coulomb barrier also grow and diminish the sticking probability of aggregates. This leads to a slow, logarithmic increase of the aggregate size with time.Comment: Some formulas correcte

Potential of mean force and the charge reversal of rodlike polyions

A simple model is presented to calculate the potential of mean force between a polyion and a multivalent counterion inside a polyelectrolite solution. We find that under certain conditions the electrostatic interactions can lead to a strong attraction between the polyions and the multivalent counterions, favoring formation of overcharged polyion-counterion complexes. It is found that small concentrations of salt enhance the overcharging, while an excessive amount of salt hinders the charge reversal. The kinetic limitations to overcharging are also examined.Comment: To be published in the special issue of Molecular Physics in honor of Prof. Ben Wido

Denaturation transition of stretched DNA

We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent $c$ for which we find the new value $c=4\nu-1/2$ such that the transition is second order with $c=1.85<2$ in $d=3$. We show that a finite stretching force $F$ destabilizes DNA, corresponding to a lower melting temperature $T(F)$, in agreement with single-molecule DNA stretching experiments.Comment: 5 pages, 3 figure