The study investigates the elastic properties of λ-bacteriophage DNA under different ionic conditions and the presence of multivalent cations. Key findings include: 1. **Electrostatic Contribution to Persistence Length**: The electrostatic contribution to the persistence length \( P \) decreases as the inverse of the ionic strength in monovalent salt, as predicted by the worm-like polyelectrolyte model. However, ionic strength is not the sole determinant of DNA elasticity, as monovalent and multivalent ions have distinct effects even at the same ionic strength. 2. **Multivalent Ions and Persistence Length**: Multivalent ions (e.g., Mg²⁺ and Co(NH₃)₆³⁺) reduce \( P \) values more significantly than monovalent ions (e.g., Na⁺), leading to persistence lengths as low as 250-300 Å, compared to 450-500 Å in monovalent salt. 3. **Elastic Stretch Modulus and Persistence Length**: The elastic stretch modulus \( S \) and \( P \) show opposite trends with ionic strength, contradicting predictions from macroscopic elasticity theory. 4. **WLC Model at Trivalent Cations**: DNA remains well described by the worm-like chain (WLC) model at concentrations of trivalent cations that induce condensation, provided the molecule is kept stretched to prevent condensation. 5. **Retractile Force and Condensation Mechanism**: A retractile force is observed in the presence of multivalent cations at molecular extensions allowing intramolecular contacts, suggesting a "thermal ratchet" mechanism for condensation in stretched DNA. 6. **Behavior of Multivalent Cations**: Di- and trivalent cations (e.g., Mg²⁺, Co(NH₃)₆³⁺) stabilize λ DNA against enthalpic elongation, similar to the effect of monovalent salt. This supports the idea that cations may oppose forces that destabilize or melt DNA duplexes during processes like supercoiling, replication, and transcription. The study highlights the complex interactions between ionic strength, cation valence, and DNA elasticity, providing insights into the biologically significant behavior of DNA.The study investigates the elastic properties of λ-bacteriophage DNA under different ionic conditions and the presence of multivalent cations. Key findings include: 1. **Electrostatic Contribution to Persistence Length**: The electrostatic contribution to the persistence length \( P \) decreases as the inverse of the ionic strength in monovalent salt, as predicted by the worm-like polyelectrolyte model. However, ionic strength is not the sole determinant of DNA elasticity, as monovalent and multivalent ions have distinct effects even at the same ionic strength. 2. **Multivalent Ions and Persistence Length**: Multivalent ions (e.g., Mg²⁺ and Co(NH₃)₆³⁺) reduce \( P \) values more significantly than monovalent ions (e.g., Na⁺), leading to persistence lengths as low as 250-300 Å, compared to 450-500 Å in monovalent salt. 3. **Elastic Stretch Modulus and Persistence Length**: The elastic stretch modulus \( S \) and \( P \) show opposite trends with ionic strength, contradicting predictions from macroscopic elasticity theory. 4. **WLC Model at Trivalent Cations**: DNA remains well described by the worm-like chain (WLC) model at concentrations of trivalent cations that induce condensation, provided the molecule is kept stretched to prevent condensation. 5. **Retractile Force and Condensation Mechanism**: A retractile force is observed in the presence of multivalent cations at molecular extensions allowing intramolecular contacts, suggesting a "thermal ratchet" mechanism for condensation in stretched DNA. 6. **Behavior of Multivalent Cations**: Di- and trivalent cations (e.g., Mg²⁺, Co(NH₃)₆³⁺) stabilize λ DNA against enthalpic elongation, similar to the effect of monovalent salt. This supports the idea that cations may oppose forces that destabilize or melt DNA duplexes during processes like supercoiling, replication, and transcription. The study highlights the complex interactions between ionic strength, cation valence, and DNA elasticity, providing insights into the biologically significant behavior of DNA.