Linearity, saturation and blocking in a large multiionic channel: Divalent cation modulation of the OmpF porin conductance
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Saturation (graph theory)
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We prepared salt-free polystyrenesulfonate (PSS) solutions with various ratios α of univalent and divalent counterions, i.e., X 0.5α Na 1-α PSS (X=Mg,Ca), and investigated them in the dilute region by means of the electrostatic birefringence spectroscopy that detects the rotational relaxations of polyelectrolyte chains. The obtained relaxation spectra show that, with replacing univalent counterions by divalent ones, the relaxation strengths decrease and the relaxation times gradually shift to higher values. From the rotational relaxation times, the electrostatic persistence length L p for 0≤α≤1 is also evaluated using the worm-like chain model, which reveals that L p with divalent counterions (i.e., α=1) becomes approximately half of that with univalent ones (α=0). The result suggests that the divalent counterion effect on conformations of intrinsically flexible polyelectrolyte is weaker than that expected from theoretical considerations.
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We unambiguously demonstrated DNA attraction and its regulation mediated by divalent cations Mg2+ and Ca2+ by tethering a DNA single chain at various pH solutions. It is found that DNA is compacted when the pH of the solution containing these divalent counterions is decreased below 5. When the pH of the medium is ∼4, DNA is in an unstable transition state, being able to switch between compact and extensible states. We can also regulate the DNA attraction through a cyclic process of DNA compaction and unraveling by alternating the pH of the solution between 3 and 8. The corresponding change of morphology of DNA modulated by pH is also confirmed by atomic force microscopy (AFM). In the theoretical aspect, the present experimental finding is consistent with the coarse-grained simulation of Langevin dynamics on the effect of pH on DNA in a solution of divalent counterions.
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Counterion Condensation
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The problem of DNA− DNA interaction mediated by divalent counterions is studied using a generalized grand-canonical Monte-Carlo simulation for a system of two salts. The effect of the divalent counterion size on the condensation behavior of the DNA bundle is investigated. Experimentally, it is known that multivalent counterions have strong effect on the DNA condensation phenomenon. While tri- and tetra-valent counterions are shown to easily condense free DNA molecules in solution into toroidal bundles, the situation with divalent counterions is not as clear cut. Some divalent counterions like Mg+2 are not able to condense free DNA molecules in solution, while some like Mn+2 can condense them into disorder bundles. In restricted environment such as in two dimensional system or inside viral capsid, Mg+2 can have strong effect and able to condense them, but the condensation varies qualitatively with different system, different coions. It has been suggested that divalent counterions can induce attraction between DNA molecules but the strength of the attraction is not strong enough to condense free DNA in solution. However, if the configuration entropy of DNA is restricted, these attractions are enough to cause appreciable effects. The variations among different divalent salts might be due to the hydration effect of the divalent counterions. In this paper, we try to understand this variation using a very simple parameter, the size of the divalent counterions. We investigate how divalent counterions with different sizes can lead to varying qualitative behavior of DNA condensation in restricted environments. Additionally, a grand canonical Monte-Carlo method for simulation of systems with two different salts is presented in detail.
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Counterion Condensation
DNA condensation
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The problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulation. Although divalent counterions cannot condense free DNA molecules in solution, we show that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetra-valent counterions. DNA-DNA interaction is strongly repulsive at small or large counterion concentration and is negligible or slightly attractive for a concentration in between. Implications of our results to experiments of DNA ejection from bacteriophages are discussed. The quantitative result serves to understand electrostatic effects in other experiments involving DNA and divalent counterions.
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Counterion Condensation
DNA condensation
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The problem of DNA$-$DNA interaction mediated by divalent counterions is studied using computer simulation. The effect of the counterion size on the condensation behavior of the DNA bundle is investigated. Experimentally, it is known that multivalent counterions has strong effect on the DNA condensation phenomenon. While tri- and tetra-valent counterions are shown to easily condense free DNA molecules in solution into torroidal bundles, the situation with divalent counterions are not as clear cut. Some divalent counterions like Mg$^{+2}$ are not able to condense free DNA molecules in solution, while some like Mn$^{+2}$ can condense them into disorder bundles. In restricted environment such as in two dimensional system or inside viral capsid, Mg$^{+2}$ can have strong effect and able to condense them, but the condensation varies qualitatively with different system, different coions. It has been suggested that divalent counterions can induce attraction between DNA molecules but the strength of the attraction is not strong enough to condense free DNA in solution. However, if the configuration entropy of DNA is restricted, these attractions are enough to cause appreciable effects. The variations among different divalent salts might be due to the hydration effect of the divalent counterions. In this paper, we try to understand this variation using a very simple parameters, the size of the divalent counterions. We investigate how divalent counterions with different sizes can leads to varying qualitative behavior of DNA condensation in restricted environments.
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Counterion Condensation
DNA condensation
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The problem of DNA-DNA interaction mediated by divalent counterions is studied using computer simulation. Although divalent counterions cannot condense free DNA molecules in solution, we show that if DNA configurational entropy is restricted, divalent counterions can cause DNA reentrant condensation similar to that caused by tri- or tetra-valent counterions. DNA-DNA interaction is strongly repulsive at small or large counterion concentration and is negligible or slightly attractive for a concentration in between. Implications of our results to experiments of DNA ejection from bacteriophages are discussed. The quantitative result serves to understand electrostatic effects in other experiments involving DNA and divalent counterions.
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Counterion Condensation
DNA condensation
Reentrancy
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