Chiral Symmetry Breaking in Liquid Crystals: Appearance of Ferroelectricity and Antiferroelectricity

Uniaxial Symmetry Breaking in Bacteriorhodopsin at the Thermal Phase Transition of Lipids of Purple Membranes

The article correlates between symmetry breaking and phase transition. An analogy, extending from physics to biology, is known to exist between these two topics. Bacteriorhodopsin (bR) as a paradigm of membrane proteins has been used as a case study in the present work. The bR, as the sole protein embedded in what is called a purple membrane (PM), has attracted widespread interest in bionanotechnological applications. The lipids of PM have a crucial role in maintaining the crystal lattice of bR inside PM. For this reason, the present work has been concerned with elucidating the thermal phase transition properties of the PM lipids in orthogonal directions. The results indicated that the axial symmetry of bR exhibits considerable changes occurring at the thermal phase transition of lipids. These changes are brought by an anomaly observed in the time course of orthogonal electric responses during the application of thermal fields on PM. The observed anomaly may bear on symmetry breaking in bR occurring at the phase transition of lipids based on such analogy found between symmetry breaking and phase transition. Lipid-protein interactions may underlie the broken axial symmetry of bR at such lipid thermal transition of PM. Accordingly, thermally perturbed axial symmetry of bR may be of biological relevance relying on the essence of the crystal lattice of bR. Most importantly, a question has to be raised in the present study: Can bR, as a helical protein with broken axial symmetry, affect the symmetry breaking of helical light? This may be of potential technical applications based on a recent discovery that bR breaks the symmetry of helical light.

Variety of subphase emerging sequences, the frustration of three main phases, SmC_{A}^{*}, SmC^{*}, and SmA, and the long-range interlayer interactions

Prompted by the existence of biaxial subphases 1/4, 2/5, and 3/7 [Phys. Rev. E 96, 012701 (2017)2470-004510.1103/PhysRevE.96.012701], we reconsidered the three-phase frustration and the resulting degeneracy lifting by combining the phase diagram of SmC_{A}^{*}, SmC^{*}, and SmA with the discrete flexoelectric effect. We systematically calculated the phase diagrams and tried to understand the overall picture of the phenomena by means of a simple and intuitively clear way in terms of minimal number of parameters. The treatment naturally explains the highly distorted helical structures of the biaxial subphases as well as the microscopic helical short-pitch of SmC_{α}^{*} which increases or decreases accordingly with rising temperature. The regular subphase emerging sequence is SmC_{A}^{*}(SmC_{α}^{*})-1/4-1/3-2/5-3/7-1/2-SmC^{*}(SmC_{α}^{*}), where the subphases other than 1/3 and 1/2 may or may not emerge. At the same time, we can see a variety of irregular sequences; in particular, any one of the biaxial subphases may singly emerge between SmC_{A}^{*}(SmC_{α}^{*}) and (SmC^{*})SmC_{α}^{*}. Moreover, the experimentally confirmed extraordinary subphase emerging sequence SmC^{*}-1/2-SmC_{α}^{*} appears for particular parameter values. Contrastingly to these affirmative aspects, some calculated results are contradictory to the previously reported experimental results: the change from SmC_{A}^{*} and SmC^{*} to SmC_{α}^{*} is always continuous, the 6-layer 2/3 subphase is not stabilized, and the subphase emerging sequence SmC_{A}^{*}-1/3-SmC^{*} does not appear. The causes of inconsistency and how to resolve them were discussed in comparisons with experimental findings.