Liquid crystal models of biological materials and processes

Abstract

This paper presents an overview of liquid crystal (LC) models of phase diagrams, phase transitions, self-assembly, interfaces, defects, and rheology and their integrated applications to biological mesophase materials and processes. Biological liquid crystals, classified into analogues (helicoidal plywoods), biopolymer solutions (in vitro DNA, polypeptides, collagen solutions) and in vivo LCs (membranes, silk, DNA), are discussed in terms of molecular characteristics and the symmetry of the thermodynamic phases. The thermodynamics and self-assembly of biological liquid crystals (BLCs) are discussed in terms of the Doi-Maier-Saupe lyotropic model and its extensions to chiral phases, showing the role of excluded volume and chirality. The defect physics of BLCs is described using the Landau-de Gennes model of chiral and achiral nematostatics to identify (i) thermodynamic phases, and (ii) observed textures and defect lattices under confinement and flow. The rheology and flow properties of BLCs are described using the Leslie-Ericksen and the Landau-de Gennes models of nematodynamics. The applications of integrated thermodynamic/defect/rheology modeling to the experimental characterization of several BLCs, including collagen and DNA solutions, are shown to provide organizing principles and quantitative tools to establish the properties of these natural materials. The phase transitions, tactoidal spherulites, flow-birefringence in dilute solutions, and banded textures in sheared concentrated solutions of collagen show how the principles of LC physics operate in BLC materials. Drying and spreading drops of DNA solutions leading to the formation of nematic monodomain aligned along the contact line are shown to follow self-assembly structuring under the action of interfacial, bulk, and contact line torques. Finally modeling of spider and silkworm LC spinning is presented as an example of biological polymer processing, where a high performance fiber material is produced through a lyotropic LC protein solution. The concerted structuring action of capillary confinement, strong anchoring, and nematic flow leads to predictions in agreement with the reported textural transitions in the duct of spiders and silkworms. The quantitative description of BLC materials and processes using mesoscopic models provides another tool to develop the science and future biomimetic applications of these ubiquitous natural anisotropic soft materials.

Actuation of flexoelectric membranes in viscoelastic fluids with applications to outer hair cells

“…which coincides with E H , and gives 4k c = (K 1 + 8K 24 ),k c = −2K 24 ; the surface gradient is given by the tangential projection of the total gradient: ∇ s (·) ≡ I s · ∇(·), I s = I − kk, since thin layers and membranes behave like LCs, membranes should also exhibit flexoelectricity or couplings between polarization and bending [1][2][3][4]7,11,[17][18][19]. Figure 2 shows a schematic of flexoelectric polarization in rod-like and banana-like molecules and the corresponding membrane flexoelectric polarization; as noted above the physics and modelling are affected by identifying the director field n with the membrane normal k. Using the same approach as above, equation (1.4) gives the membrane polarization P due to membrane bending (∇ s · k): 10) where c f is the membrane flexoelectric coefficient, as indeed found experimentally [4].…”

“…A distinguishing and novel property of nematics is flexoelectricity [1][2][3][4]11], which describes the coupling between orientational gradients and electric polarization, such that an applied electric field creates orientational distortions and distortions create macroscopic polarization [1][2][3][4]11,[17][18][19]. The polar nature of splay S = n∇ · n and bend B = −n × ∇ × n orientational deformations can polarize the nematic LC medium [11][12][13] (b) Flexoelectricity in biological membranes due to bending curvature described by surface gradients of the unit normal k. The correspondence between nematic flexoelectricity and membrane flexoelectricity is obtained when the director n is identified with the membrane unit normal k (adapted from [11]).…”

“…The phase angle φ in equation (1.2) is φ = arctan Im{F D (jw)} Re{F D (jw)} , (1.3) and it represents the tendency to delay the input signal and is intimately related to the memory of the fluids. Besides the role of fluid viscoelasticity, the functioning of OHCs is based on LC flexoelectricity [1][2][3][4]. Hence, a key to OHC modelling that we have performed in this paper is to determine and characterize F D (jw) in terms of LC membrane flexoelectric elasticity and frequency-dependent fluid viscoelasticity.…”

“…In nature and physiology, biological liquid crystals (LCs) play significant roles as multifunctional materials [1]. This paper presents theory and simulation of a Schematic of the processes and mechanisms currently accepted to be involved in the functioning of OHCs.…”

“…The functioning of outer hair cells (OHCs) in the inner ear involves electric field-driven periodic curvature oscillations of LC elastic membranes that impart momentum and flow to the contacting viscoelastic fluids; the electric field actuation of the LC membrane is known as flexoelectricity [1][2][3][4][5][6][7][8][9][10][11][12]. The key role of OHCs is sound amplification in the presence of viscous dissipation and elastic storage [10].…”