Lars Nordenskiöld

Theory of nuclear spin relaxation in paramagnetic systems in solution

Interactions mettant en jeu le spin electronique; theorie de Solomon-Bloembergen (MSB); effets de la relaxation de spin electronique; theories sur la relaxation de spin nucleaire suivie dune discussion des modeles dynamiques; comparaison avec des donnees experimentales selectionnees

On the Competition between Water, Sodium Ions, and Spermine in Binding to DNA: A Molecular Dynamics Computer Simulation Study

The interaction of DNA with the polyamine spermine(4+) (Spm(4+)), sodium ions, and water molecules has been studied using molecular dynamics computer simulations in a system modeling a DNA crystal. The simulation model consisted of three B-DNA decamers in a periodic hexagonal cell, containing 1200 water molecules, 8 Spm(4+), 32 Na(+), and 4 Cl(-) ions. The present paper gives a more detailed account of a recently published report of this system and compares results on this mixed Spm(4+)/Na(+)-cation system with an molecular dynamics simulation carried out for the same DNA decamer under similar conditions with only sodium counterions (Korolev et al., J. Mol. Biol. 308:907). The presence of Spm(4+) makes significant influence on the DNA hydration and on the interaction of the sodium ions with DNA. Spermine pushes water molecules out of the minor groove, whereas Na(+) attracts and organizes water around DNA. The major binding site of the Spm(4+) amino groups and the Na(+) ions is the phosphate group of DNA. The flexible polyamine spermine displays a high presence in the minor groove but does not form long-lived and structurally defined complexes. Sodium ions compete with Spm(4+) for binding to the DNA bases in the minor groove. Sodium ions also have several strong binding sites in the major groove. The ability of water molecules, Spm(4+), and Na(+) to modulate the local structure of the DNA double helix is discussed.

Nuclear spin relaxation in paramagnetic systems

A theory of nuclear spin relaxation in paramagnetic systems, allowing for the electron spin relaxation to be in the slow motion regime, is presented. The formulation is general and can, for example, be used to derive formally the modified Solomon-Bloembergen equations. The theory is applied to the specific problem of nuclear spin lattice relaxation caused by the dipole-dipole interaction between the nuclear spin and an electron spin (S = 1). The lattice is described in terms of the electron Zeeman interaction, a zero field splitting of cylindrical symmetry and isotropic rotational diffusion. The resulting equations are solved numerically for a range of parameter values of practical interest and limiting cases are discussed. In the slow motion regime for the electron spin relaxation (that is, where the zero field splitting is larger than the rotational diffusion constant), the behaviour of the nuclear spin-lattice relaxation rate predicted using the present formalism differs qualitatively from the predicti...

A Monte Carlo simulation study of electrostatic forces between hexagonally packed DNA double helices

The electrostatic contribution to the force between hexagonally packed B‐DNA double helices has been studied using different statistical mechanical descriptions and the Monte Carlo simulation method. The effects of small ion correlations and sizes are considered, and comparison with experimental results is made. It is found that for monovalent counterions, the mean field Poisson–Boltzmann theory can give a reasonable reproduction of the experimental data, even though the simulations show that its description of the electrostatic interaction can be qualitatively wrong. The chemical equilibrium of the ordered DNA phase with the surrounding bulk salt solution is found to be an important feature. Furthermore, the simulations show that the correlation between the ion clouds of different DNA polyions gives rise to a significant attractive contribution to the interaction when divalent cations are present. It is suggested that this electrostatic attraction is an important driving force for the experimentally obse...

Competitive binding of Mg2+, Ca2+, Na+, and K+ ions to DNA in oriented DNA fibers: experimental and Monte Carlo simulation results.

Competitive binding of the most common cations of the cytoplasm (K(+), Na(+), Ca(2+), and Mg(2+)) with DNA was studied by equilibrating oriented DNA fibers with ethanol/water solutions (65 and 52% v/v EtOH) containing different combinations and concentrations of the counterions. The affinity of DNA for the cations decreases in the order Ca > Mg >> Na approximately K. The degree of Ca(2+) and/or Mg(2+) binding to DNA displays maximum changes just at physiological concentrations of salts (60-200 mM) and does not depend significantly on the ethanol concentration or on the kind of univalent cation (Na(+) or K(+)). Ca(2+) is more tightly bound to DNA and is replaced by the monovalent cations to a lesser extent than is Mg(2+). Similarly, Ca(2+) is a better competitor for binding to DNA than Mg(2+): the ion exchange equilibrium constant for a 1:1 mixture of Ca(2+) and Mg(2+) ions, K(c)(Ca)(Mg), changes from K(c)(Ca)(Mg) approximately 2 in 65% EtOH (in 3-30 mM NaCl and/or KCl) to K(c)(Ca)(Mg) approximately 1.2-1.4 in 52% EtOH (in 300 mM NaCl and/or KCl). DNA does not exhibit selectivity for Na(+) or K(+) in ethanol/water solutions either in the absence or in the presence of Ca(2+) and/or Mg(2+). The ion exchange experimental data are compared with results of grand canonical Monte Carlo (GCMC) simulations of systems of parallel and hexagonally ordered, uniformly and discretely charged polyions with the density and spatial distribution of the charged groups modeling B DNA. A quantitative agreement with experimental data on divalent-monovalent competition has been obtained for discretely charged models of the DNA polyion (for the uniformly charged cylinder model, coincidence with experiment is qualitative). The GCMC method gives also a qualitative description of experimental results for DNA binding competitions of counterions of the same charge (Ca(2+) with Mg(2+) or K(+) with Na(+)).

Metal ion-induced lateral aggregation of filamentous viruses fd and M13

We report a detailed comparison between calculations of inter-filament interactions based on Monte-Carlo simulations and experimental features of lateral aggregation of bacteriophages fd and M13 induced by a number of divalent metal ions. The general findings are consistent with the polyelectrolyte nature of the virus filaments and confirm that the solution electrostatics account for most of the experimental features observed. One particularly interesting discovery is resolubilization for bundles of either fd or M13 viruses when the concentration of the bundle-inducing metal ion Mg(2+) or Ca(2+) is increased to large (>100 mM) values. In the range of Mg(2+) or Ca(2+) concentrations where large bundles of the virus filaments are formed, the optimal attractive interaction energy between the virus filaments is estimated to be on the order of 0.01 kT per net charge on the virus surface when a recent analytical prediction to the experimentally defined conditions of resolubilization is applied. We also observed qualitatively distinct behavior between the alkali-earth metal ions and the divalent transition metal ions in their action on the charged viruses. The understanding of metal ions-induced reversible aggregation based on solution electrostatics may lead to potential applications in molecular biology and medicine.

Application of Polyelectrolyte Theories for Analysis of DNA Melting in the Presence of Na+ and Mg2+ Ions

Numerical calculations, using Poisson-Boltzmann (PB) and counterion condensation (CC) polyelectrolyte theories, of the electrostatic free energy difference, DeltaGel, between single-stranded (coil) and double-helical DNA have been performed for solutions of NaDNA + NaCl with and without added MgCl2. Calculations have been made for conditions relevant to systems where experimental values of helix coil transition temperature (Tm) and other thermodynamic quantities have been measured. Comparison with experimental data has been possible by invoking values of Tm for solutions containing NaCl salt only. Resulting theoretical values of enthalpy, entropy, and heat capacity (for NaCl salt-containing solutions) and of Tm as a function of NaCl concentration in NaCl + MgCl2 solutions have thus been obtained. Qualitative and, to a large extent, quantitative reproduction of the experimental Tm, DeltaHm, DeltaSm, and DeltaCp values have been found from the results of polyelectrolyte theories. However, the quantitative resemblance of experimental data is considerably better for PB theory as compared to the CC model. Furthermore, some rather implausible qualitative conclusions are obtained within the CC results for DNA melting in NaCl + MgCl2 solutions. Our results argue in favor of the Poisson-Boltzmann theory, as compared to the counterion condensation theory.

Dipole-dipole nuclear spin relaxation: A cross correlation correction to the Solomon-Bloembergen equation forT2

The transverse spin relaxation of a spin I in a IS pair is analysed for the dipole-dipole relaxation mechanism. It is shown that, when for the S-spin there is an additional efficient relaxation mechanism, which is of a second order tensorial rank, there can exist substantial corrections to the Solomon-Bloembergen equation for T 2. The correction terms are found to be non-negligible in the non-extreme narrowing limit. The correction terms are due to a cross correlation effect between the dipole-dipole interaction and the interaction causing the efficient relaxation of the S spin. As shown in the Appendix the correction appears as a near divergence of a fourth order term in the Redfield type expansion of the equation of motion of the density matrix. The explicit expressions for T 2 are, however, derived using a Liouville operator formalism combined with a perturbation expansion. For the relaxation of the S-spin a zero field splitting term is considered for a paramagnetic system with S ≥ 1. Similarly for a n...

A nonempirical SCF–MO study of the validity of the Solomon–Bloembergen equation for the hexa‐aquonickel (II) ion

Nonempirical SCF–MO calculations of the effective distance between the ligand nuclei and the unpaired electron spins in the triplet ground state (3Ag) of the hexa‐aquonickel (II) ion are presented and the validity of the point dipole approximation in the Solomon–Bloembergen equation is discussed. The calculations show that the effective distance between the oxygen atom and the unpaired electron is significantly shorter than the internuclear oxygen–nickel distance. For the case of the hydrogen atom, the point dipole approximation functions very well. Calculations of the isotropic hyperfine coupling constants are also reported.

Nuclear spin-lattice and spin-spin relaxation in paramagnetic systems in the slow-motion regime for the electron spin. III. Dipole-dipole and scalar spin-spin interaction for S = 32 and S = 52

Abstract The theory for nuclear spin relaxation in paramagnetic complexes, where the electron spin relaxation is allowed to be in the slow-motion regime, [Mol. Phys. 48, 329 (1983)] is generalized to spin states of multiplicity higher than triplet. Numerical calculations of nuclear spin-spin and nuclear spin-lattice relaxation rates are reported for electron spin systems ( S = 3 2 , S = 5 2 ), coupled to the nuclear spin system via dipole-dipole and scalar spin-spin interaction. Analogous to the S = 1 case, in the region when the zero-field splitting interaction is larger than the electron Zeeman interaction, the spectral densities show qualitatively different behavior than that described by the Solomon-Bloembergen (SB) theory. Furthermore, the spectral densities show an additional structure, a “soft plateau,” compared to the S = 1 case. This extra structure is a characteristic feature for half-integer electron spin systems ( S ⩾ 3 2 ). It is shown that this structure is mainly due to the lifting of the Kramers degeneracy of the |S ± 1 2 〉 level. The results show that the interference spectral density at zero frequency K0,0DD-SC(0), i.e., the contribution to the nuclear spin-spin relaxation due to the interference term when both dipole-dipole and scalar coupling are present, does not vanish in the Redfield region for the electron spin system.