Quantum Magnetism of the Iron Core in Ferritin Proteins-A Re-Evaluation of the Giant-Spin Model

Abstract

The electron-electron, or zero-field interaction (ZFI) in the electron paramagnetic resonance (EPR) of high-spin transition ions in metalloproteins and coordination complexes, is commonly described by a simple spin Hamiltonian that is second-order in the spin S: H=D[Sz2-SS+1/3+E(Sx2-Sy2). Symmetry considerations, however, allow for fourth-order terms when S ≥ 2. In metalloprotein EPR studies, these terms have rarely been explored. Metal ions can cluster via non-metal bridges, as, for example, in iron-sulfur clusters, in which exchange interaction can result in higher system spin, and this would allow for sixth- and higher-order ZFI terms. For metalloproteins, these have thus far been completely ignored. Single-molecule magnets (SMMs) are multi-metal ion high spin complexes, in which the ZFI usually has a negative sign, thus affording a ground state level pair with maximal spin quantum number m_S = ±S, giving rise to unusual magnetic properties at low temperatures. The description of EPR from SMMs is commonly cast in terms of the 'giant-spin model', which assumes a magnetically isolated system spin, and in which fourth-order, and recently, even sixth-order ZFI terms have been found to be required. A special version of the giant-spin model, adopted for scaling-up to system spins of order S ≈ 10³-10⁴, has been applied to the ubiquitous iron-storage protein ferritin, which has an internal core containing Fe³⁺ ions whose individual high spins couple in a way to create a superparamagnet at ambient temperature with very high system spin reminiscent to that of ferromagnetic nanoparticles. This scaled giant-spin model is critically evaluated; limitations and future possibilities are explicitly formulated.

Keywords: EPR; core; ferritin; giant spin; higher-order terms; metal-ion clusters; single-molecule magnets; spin Hamiltonian; superparamagnetism; zero-field interaction.

Figure 1

Crystallographic model of the ferritin from Pyrococcus furiosus. The structure (2JD7.pdb [11]), obtained from an Fe-soaked crystal, consists of 24 identical subunits each of mass 20.3 kD and each with a five-helical bundle fold. Twelve subunits have been colored in groups of three to emphasize 3-fold symmetry (e.g., three red subunits) and 4-fold symmetry (where red, green, yellow, and blue subunits meet). The other 12, in the back, are all in black. The most conspicuous aspect of the figure is the complete absence of an internal core structure, reflecting the fact that atomic-structure resolution has never been obtained for any core in any ferritin.

Figure 2

Very similar simulations of a g = 4.3 signal based on very different spin Hamiltonians. The ubiquitous g = 4.3 signal is generally considered to stem from maximally rhombic high-spin Fe³⁺ with E/D = 1/3. The blue trace was generated with the spin Hamiltonian in Equation (1) with D = −0.9 cm⁻¹ and E = −0.3 cm⁻¹. The red trace is based on Equation (1) extended with the fourth-order term in Equation (5e) using D = −0.9 cm⁻¹, E = −0.14 cm⁻¹, and B⁴₄ = 0.24 cm⁻¹. For both traces, g_iso = 2.00, and the temperature T = 15 K. The line shape is Gaussian with FWHM = 100 gauss.

Figure 3

Non-scalability of axial higher-order ZFI terms for giant spins. Based on a reported value of D = −1.2 × 10⁻⁵ cm⁻¹ with a spin of S = 5000 for the core of Pyrococcus furiosus ferritin [19], values of B⁰₂ = −2 × 10⁻³, −2 × 10⁻⁴, and −2 × 10⁻⁵ cm⁻¹ are deduced with Equation (13) for S_eq = 10, 100, 1000. Values for B⁰₄ and B⁰₆ are then taken to be less than B⁰₂ by a factor of 10⁴ and 10⁸, respectively. The plotted number is the magnitude of the largest diagonal element in the energy matrix: $<m_{S_{eq}}\left|\mathcal{H}\right|m_{S_{eq}}>$ for $\mathcal{H}=B_k^0{O}_k^0$ with k = 2, 4, 6, respectively.

Figure 4

Comparison of EPR spectra from Fe-loaded Pyrococcus furiosus ferritin based on two different loading procedures. The blue trace, reported by Tatur et al. [87] for sample T = 110 K, is for ferritin loaded with 1140 Fe²⁺ using O₂ as the oxidant at ambient temperature and pH = 7.0, in a procedure with small stepwise additions and long incubation times [87,90]. The red trace, reported by Fittipaldi et al. [19] for sample T = 130 K, and here digitalized from their Figure 1, is for ferritin overloaded with 4500 Fe²⁺ using H₂O₂ as the oxidant at a temperature of 65 °C and pH = 8.6 in a titration procedure with constant flow of Fe and H₂O₂. The two core signals differ in width by a factor of circa three.

Figure 5

Inventory of line shapes from randomly oriented giant spins that result from switching on individual ZFI coefficients. The orthorhombic-spin Hamiltonian is the sum of Equations (1), (3), and (7), with g_iso = 2.00 and a Gaussian line shape with FWHM = 300 gauss. Each coefficient B^q_k is switched on individually (that is, all other B^q_ks are set to zero) except for B²₂, which is assumed to be equal to B⁰₂ (that is, maximal rhombicity, E/D = 1/3). The value for B^q_k, except B²₂, is chosen such that induced spectral changes (red traces) are just resolved from the basic spectrum without ZFI (black traces). Subsequently, this value is doubled (green traces) and tripled (blue traces).