Microfibril organization modes in plant cell walls of variable curvature: a model system for two dimensional anisotropic soft matter

Self-assembly Mechanisms in Plant Cell Wall Components

“…This reasoning is further supported by wide variations in observed microfi bril orientation in the innermost layers of S 3 among different tree species [78]. The model when solved on a membrane of spatially varying curvature, results in membrane with spatially graded fi ber orientation and order [58]. This numerical prediction is consistent with an abrupt change in fi ber angle in S 2 and S 3 at the corners reported in plant cell walls of juniper tracheid.…”

“…Periodic relief arising at the free surface of a helicoidal plywood in some fl owers' petals, and beetle exocuticle surfaces that play a key role in the iridescence of these structures, have been simulated using a mathematical model based on chiral self-assembly with air-surface interface driven by chiral capillarity [53]. This review article emphasizes the capability of theory and simulations based on anisotropic soft matter models [54][55][56][57][58] to yield testable and verifi able predictions of textural and rheological phenomena observed in real plant cell walls, in an attempt to verify the LC self-assembly model for plant cell wall synthesis and highlight the versatility of these models to simulate other biological/biomimetic systems. For an extensive review on mesoscopic models employed to quantitatively describe the structures and processes in biological systems, refer to [31,59].…”

“…Planar self-assembly mechanisms in these materials remain partially understood despite their biological and biomimetic relevance. An integrated mechanical model for curvature-driven planar self-assembly of rigid rods on an arbitrarily curved fl uid membrane through novel surface phenomena such as curvophobic and curvophilic effects, by extending the Helfrich elastic theory of curved isotropic membranes to anisotropic curved membrane, has been applied to predict the uniaxial modes in plant cell walls [56][57][58]. Curvophilic (curvophobic) effects seek to align the CMFs along high (zero) curvature directions [56].…”

“…On the other hand, curvophobic interactions may originate from any of the following mechanisms: (i) the fi bers exhibiting preferential orientation over corrugated grooves on the membrane surface, known as Berreman anchoring [75], (ii) intrinsic nanoscale coiling of biological fi bers predominantly modeled by the Helfrich elastic chiral fi lament model or Kirchhoff elastic theory of rods [76], (iii) membrane curvature induced by soft-mode instability of membranes caused due to the adsorbed fi bers [77]. The total free energy of the fi ber-laden membrane system per unit area F is posited to be [56][57][58]:…”

“…where b is the tensor that quantifi es the ambient curvature of the membrane and S is the fi ber order parameter in 2D. When the free energy of the ensemble is minimized, the equilibrium fi ber alignment and order are obtained as a function of dimensionless radius of the membrane [58]. Figure 12 depicts the fi ber orientation modes in terms of cosine of Figure 12 Fiber structure plot for cylindrical membranes of circular cross-section [58].…”