Molecular understanding of Ni ²⁺ -nitrogen family metal-coordinated hydrogel relaxation times using free energy landscapes

Abstract

Incorporating dynamic metal-coordination bonds as cross-links into synthetic materials has become attractive not only to improve self-healing and toughness, but also due to the tunability of metal-coordination bonds. However, a priori determination of bond lifetime of metal-coordination complexes, especially important in the rational design of metal-coordinated materials with prescribed properties, is missing. We report an empirical relationship between the energy landscape of metal-coordination bonds, simulated via metadynamics, and the resulting macroscopic relaxation time in ideal metal-coordinated hydrogels. Importantly, we expand the Arrhenius relationship between the macroscopic hydrogel relaxation time and metal-coordinate bond activation energy to include width and landscape ruggedness identified in the simulated energy landscapes. Using biologically relevant Ni 2+ -nitrogen coordination complexes as a model case, we demonstrate that the quantitative relationship developed from histidine-Ni 2+ and imidazole-Ni 2+ complexes can predict the average relaxation times of other Ni 2+ -nitrogen coordinated networks. We anticipate the quantitative relationship presented here to be a starting point for the development of more sophisticated models that can predict relaxation timescales of materials with programmable viscoelastic properties.

Bond clusters control rupture force limit in shear loaded histidine-Ni2+ metal-coordinated proteins

“…The following parameters are used to determine the N cr prediction for the histidine-Ni 2+ bonds: characteristic time scale of τ = 0.06 s (ref. 40) (for reference, τ ∼ 0.1 s for a 4PEG-His3 polymer in TRIS buffer which likely forms only 1 coordination bond), 24 applied pulling distance at the moment of rupture x B of 2 Å, persistence length l p of 0.4 nm, 41–43 and a bond energy E 0 of ∼11 kcal mol −1 based on the SMD studies done in this work on the (histidine) 2 -Ni 2+ complex (Fig. 1a).…”

“…While this lack of tetradentate stability may be due to challenges with the force field modeling for metal ions, speciation models predict a dominance of bidentate coordination stoichiometry in aqueous conditions between histidine and Ni 2+ . 40,69,70 Further, though the short peptides are equilibrated for a significant amount of time, we note that the peptide structures used in this paper are not necessarily the equilibrium binding state of the peptide with the metal ion, because the peptide may be trapped in a local minima. We also enforce a trans bidentate binding configurations on the metal ions to most closely replicate the hydrogen-bonded beta-sheets.…”

Moduli of Mussel‐Inspired, Metal‐Coordinated Hydrogels Comprising Four‐, Six‐, and Eight‐Arm Polymers

“…The pH of each gel is measured before every rheological test. The pH probe we use has been used with reasonable success in supramolecular hydrogel work, [18,20,32,59,68] despite being primarily designed for use in soil rather than hydrogels. After loading, gels rest between plates at the testing gap until the axial force is zero.…”

“…Before testing, the pH of a sample was measured using a ParWest Turf Soilstik pH probe. [ 18,20,59,68 ] Gels were tested over a range of 400–0.1 rad s −1 at 0.1% strain, which was well within the linear viscoelastic region of these gels. In slow relaxing samples, tests were allowed to continue to 0.01 rad s −1 .…”

“…Once the ligands are deprotonated by adding sodium hydroxide (NaOH), they coordinate with the metal ions and percolate into a network (Figure 1c) forming tris-, bis-, mono-, and free species (3, 2, 1, and 0 ligands bound to a metal ion, respectively). [35,[54][55][56][57][58][59] The distribution of these species can be calculated using their ther-modynamic equilibrium constants. Experimentally, we confirm that the modulus increases with increasing number of arms per macromolecule and show the effect of pH on cross-linking.…”