We discuss the phase diagram of the Bose-Hubbard (BH) model in the leading-order auxiliary field (LOAF) theory. LOAF is a conserving nonperturbative approximation that treats on equal footing the normal and anomalous density condensates. The mean-field solutions in LOAF correspond to first-order and second-order phase transition solutions with two critical temperatures corresponding to a vanishing Bose-Einstein condensate Tc and a vanishing diatom condensate Tẫ†. The second-order phase transition solution predicts the correct order of the transition in continuum Bose gases. For either solution, the superfluid state is tied to the presence of the diatom condensate related to the anomalous density in the system. In ultracold Bose atomic gases confined on a three-dimensional lattice, the critical temperature Tc exhibits a quantum phase transition, where Tc goes to zero at a finite coupling. The BH phase diagram in LOAF features a line of first-order transitions ending in a critical point beyond which the transition is second order while approaching the quantum phase transition. We identify a region where a diatom condensate is expected for temperatures higher than Tc and less than T0, the critical temperature of the noninteracting system. The LOAF phase diagram for the BH model compares qualitatively well with existing experimental data and results of ab initio Monte Carlo simulations. © 2013 American Physical Society.

The two genes most commonly associated with mutations linked to hypertrophic or dilated cardiomyopathies are β-myosin and cardiac myosin binding protein-C (cMyBP-C). Both of these proteins interact with cardiac actin (ACTC). Currently there are 16 ACTC variants that have been found in patients with HCM or DCM. While some of these ACTC variants exhibit protein instability or polymerization-deficiencies that might contribute to the development of disease, other changes could cause changes in protein-protein interactions between sarcomere proteins and ACTC. To test the hypothesis that changes in ACTC disrupt interactions with cMyBP-C, we examined the interactions between seven ACTC variants and the N-terminal C0C2 fragment of cMyBP-C. We found there was a significant decrease in binding affinity (increase in Kd values) for the A331P and Y166C variants of ACTC. These results suggest that a change in the ability of cMyBP-C to bind actin filaments containing these ACTC protein variants might contribute to the development of disease. These results also provide clues regarding the binding site of the C0C2 fragment of cMyBP-C on F-actin.