Free Energy Change during the Formation of Crystalline Contact between Lysozyme Monomers under Different Physical and Chemical Conditions

We use the MM/GBSA method to calculate the free energies of dimer formation by binding two monomers with different combinations of precipitant ions, both embedded in the structure of monomers and in the crystallization solution. It shows that the largest difference in free energy values corresponds to the most accurate dimer model, which considers all precipitant ions in their structure. In addition, it shows that in the absence of precipitant ions in the solution of lysozyme molecules, a monomer is a more energetically favorable state.

Crystal Structure Reveals the Full Ras–Raf Interface and Advances Mechanistic Understanding of Raf Activation

Ras and Raf-kinase interact through the Ras-binding (RBD) and cysteine-rich domains (CRD) of Raf to signal through the mitogen-activated protein kinase pathway, yet the molecular mechanism leading to Raf activation has remained elusive. We present the 2.8 Å crystal structure of the HRas–CRaf-RBD_CRD complex showing the Ras–Raf interface as a continuous surface on Ras, as seen in the KRas–CRaf-RBD_CRD structure. In molecular dynamics simulations of a Ras dimer model formed through the α4–α5 interface, the CRD is dynamic and located between the two Ras protomers, poised for direct or allosteric modulation of functionally relevant regions of Ras and Raf. We propose a molecular model in which Ras binding is involved in the release of Raf autoinhibition while the Ras–Raf complex dimerizes to promote a platform for signal amplification, with Raf-CRD centrally located to impact regulation and function.

Absence of Superconductivity in the Hubbard Dimer Model for κ-(BEDT-TTF)2X

In the most studied family of organic superconductors κ-(BEDT-TTF)2X, the BEDT-TTF molecules that make up the conducting planes are coupled as dimers. For some anions X, an antiferromagnetic insulator is found at low temperatures adjacent to superconductivity. With an average of one hole carrier per dimer, the BEDT-TTF band is effectively 12-filled. Numerous theories have suggested that fluctuations of the magnetic order can drive superconducting pairing in these models, even as direct calculations of superconducting pairing in monomer 12-filled band models find no superconductivity. Here, we present accurate zero-temperature Density Matrix Renormalization Group (DMRG) calculations of a dimerized lattice with one hole per dimer. While we do find an antiferromagnetic state in our results, we find no evidence for superconducting pairing. This further demonstrates that magnetic fluctuations in the effective 12-filled band approach do not drive superconductivity in these and related materials.

Site-Monotonicity Properties for Reflection Positive Measures with Applications to Quantum Spin Systems

We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates—improving previous positivity results which hold for the Cesàro sum. We also derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model and lattice permutations, thus extending the previous results of Lees and Taggi (2019).

Miquel dynamics, Clifford lattices and the Dimer model

Miquel dynamics was introduced by Ramassamy as a discrete time evolution of square grid circle patterns on the torus. In each time step every second circle in the pattern is replaced with a new one by employing Miquel’s six circle theorem. Inspired by this dynamics we consider the local Miquel move, which changes the combinatorics and geometry of a circle pattern. We prove that the circle centers under Miquel dynamics are Clifford lattices, an integrable system considered by Konopelchenko and Schief. Clifford lattices have the combinatorics of an octahedral lattice, and every octahedron contains six intersection points of Clifford’s four circle configuration. The Clifford move replaces one of these circle intersection points with the opposite one. We establish a new connection between circle patterns and the dimer model: If the distances between circle centers are interpreted as edge weights, the Miquel move preserves probabilities in the sense of urban renewal.