Multi-lamellar Dorsoventral Architecture

• Multi-lamellar dorsoventral architecture is defined by spatially organized, repetitive layers exhibiting asymmetry along a dorsal-to-ventral axis that determines mechanical and functional properties.
• In biological systems like embryogenesis, collective tension forces across apical, basal, and lateral membranes drive invaginated morphologies without requiring predetermined cell fates.
• Engineered materials and neural models exploit these architectures to achieve tunable mechanical responses and hierarchical information processing through controlled interlayer interactions.

A multi-lamellar dorsoventral architecture refers to structured, spatially organized stacks of layered domains or cell populations arranged along a dorsoventral axis, where the properties, connectivity, and function of the layers exhibit coordinated, often directional variation. This concept appears in a range of biological, synthetic, and theoretical systems—from embryonic epithelial morphogenesis to the design of advanced materials, from lipid tubule stability to information processing in neural architectures. At its core, multi-lamellar dorsoventral systems are defined by their lamellarity (repetitive, layered structure) and dorsoventral polarity (structural or functional asymmetry along an axis traversing “dorsal” to “ventral” regions).

1. Collective Mechanical Principles in Embryonic Dorsoventral Lamellae

A paradigmatic example is Drosophila embryogenesis, in which the formation of the ventral furrow demonstrates key mechanical principles underlying multi-lamellar dorsoventral architecture (Hocevar et al., 2011). The embryo cross-section is modeled as a closed sheet composed of $N$ identical epithelial cells, each with three mechanical tension parameters: $\Gamma_a$ (apical), $\Gamma_b$ (basal), and $\Gamma_l$ (lateral). The total energy of the tissue is:

$$W = \sum_{i=1}^{N} \left( \Gamma_a L_a^i + \Gamma_b L_b^i + \tfrac{1}{2}\Gamma_l L_l^i \right)$$

When recast in dimensionless form using reduced tensions $\alpha = \Gamma_a/\Gamma_l$ and $\beta = \Gamma_b/\Gamma_l$, the equilibrium morphologies (circular, elliptical, biconcave, invaginated) arise from collective minimization of membrane energy—without requiring differentiated cell properties. The thickening of the epithelial layer (increasing lamellarity) amplifies the mechanically stable invaginated shapes, suggesting that dorsoventral polarity and multi-layered structures emerge from the coordinated, system-wide mechanics.

A critical insight is that tissue morphogenesis, including the establishment of dorsoventral polarity, can result from generic collective line-tension mechanics. Rather than requiring precise local triggers, axis formation and multi-lamellar architeture in early development are regulated by the balance of apical, basal, and lateral tensions over the entire tissue.

2. Coupled Orders in Hybrid Multi-lamellar Materials

Multi-lamellar dorsoventral architectures arise in engineered materials, where layered domains interact and exhibit directional anisotropy. In a hybrid mesophase of lyotropic lamellar surfactant stacks doped with magnetic nematic nanorods (Constantin et al., 2015), the organization is structurally and functionally multi-lamellar, with distinct dorsoventral stacking arising from confinement and coupling effects.

Surfactant bilayers of thickness $\delta \approx 2.9$ nm alternate with water layers, each confining nematic goethite nanorods:

• The lamellar repeat distance $d$ enforces vertical ordering (dorsoventral axis), while in-plane nematic order parameter $S$ describes rod alignment within layers.
• Coupling between lamellar and nematic orders is bidirectional: Nanorod concentration pins and stiffens the bilayer stack (sharper Bragg peaks in SAXS), while confinement dramatically reduces nematic $S$ (from 0.75 in bulk to 0.45 in layered arrangement).
• Magnetic field control enables reorientation of nanorod directors, manipulating both local (nematic) and global (lamellar) order along the stacking axis.

The result is a multi-lamellar system where vertical coherence (enforced by surfactant stacking) coexists with lateral functional domains (nematic nanorod order), with overall dorsoventral architecture sensitive to both internal composition and external fields.

3. Asymmetric Hard–Soft Multi-lamellar Nanomaterials

The mechanical architecture of alternating hard/soft nanolayers is essential in functional materials. As shown in asymmetric lamellar block copolymers (Shi et al., 2017), multi-lamellar stacks can be engineered for directional properties by controlling layer thickness and composition.

Table: Layer thickness versus mechanical response in miktoarm PS–PI–PS star block architectures

Hard Layer Thickness	Soft Layer Thickness	Mechanical Response
< 100 nm	13 nm	Ductile, kinks, PI cavitation
> 100 nm	13 nm	Brittle, PS crazing, voids in both domains

The stacking (lamellarity) and dorsoventral polarity (differential deformation across layers) yield materials with tunable modulus, high ductility, and spatially resolved energy dissipation. Deformation phenomena such as kinks and void formation differ sharply between dorsal-most (hard) and ventral-most (soft) layers, underscoring the importance of lamellar thickness and structural polarity.

Self-consistent field theory (SCFT) and SAXS confirm the universal features of elastic deformation, mechanical homogenization, and damage, informing the design of synthetic systems and providing analogies to biological multi-lamellar dorsoventral structures.

4. Thermodynamic Coexistence in Multi-lamellar Surfactant Architectures

Complex multi-lamellar assemblies often involve distinct lamellar domains stacking along a dorsoventral axis, each domain characterized by composition and spacing (Sou et al., 2017). Theoretical treatments using free energy functionals predict coexistence diagrams that illustrate these architectures:

For binary systems:

$$f(\phi) = a\phi (\ln\phi - 1) - \chi\phi^2 + \frac{\phi^3}{2(1 - \phi)^2} - \mu\phi$$

For ternary systems:

$$g(\phi, \psi) = \phi(\ln\phi-1) + \psi(\ln\psi-1) - \chi_{AA}\phi^2 - \chi_{BB}\psi^2 - \chi_{AB}\phi\psi + \frac{(\phi+\psi)^3}{2(1-\phi-\psi)^2} - \mu_A\phi - \mu_B\psi$$

Critical points and tie-lines in the Gibbs triangle reveal regions where two or three distinct lamellar phases coexist, each with discrete repeat distances and compositions. Finite surface tension, modeled as a suppression of membrane undulations, exponentially stabilizes lamellar domains, favoring sharp dorsoventral stacking. Thus, dorsoventral multi-lamellar architectures in both biological and synthetic contexts reflect underlying thermodynamic phase separation driven by composition, tension, and undulation suppression.

5. Elastic Stability in Multi-lamellar Lipid Tubules

The mechanical stability of multi-lamellar lipid tubules (MLTs) depends on hydrostatic equilibrium and elastic properties (Bhatia, 2023). Here, coaxially stacked bilayers trap solvent and maintain shape via compression modulus $B$ and bending modulus $\kappa$. The elastic free energy is given by

$$F_{el} = \int r\,dr\,d\phi\,dz\ \left[ \frac{B}{2}(\partial_r u)^2 + \frac{\kappa}{2}(\partial_r^2 u + \frac{1}{r}\partial_r u)^2 \right]$$

Solving the variational equations with boundary conditions matching solvent pressures at inner and outer radii yields density profiles $v(r)$ that remain stable with minor pressure differences (e.g., 0.1 atm). The dorsoventral polarity is manifest in higher normal stress on the “dorsal” (core) side due to curvature, with ventral (external) layers under lower stress. This arrangement is not only robust against external perturbations but is universal for stacked membrane systems sustained by hydrostatic balance and elastic restoring forces.

6. Multi-lamellar Dorsoventral Information Processing in Neural Systems

In computational neuroscience, the multi-lamellar dorsoventral architecture achieves directional information processing, exemplified by the Generalization and Associative Temporary Encoding (GATE) model for hippocampal formation (Liu et al., 22 Jan 2025). Here, lamellae arranged along the DV axis connect EC3-CA1-EC5-EC3 in re-entrant loops:

• EC3 encodes sensory inputs with persistent dynamics via an ODE,

$\frac{dr}{dt} = (1 - r) p_{01} - r p_{10}$

where $p_{01}$ and $p_{10}$ depend nonlinearly on EC3 input; $r_\infty = p_{01}/(p_{01} + p_{10})$, $\tau = 1/(p_{01} + p_{10})$.

• CA1 reads out EC3 memory only when CA3 gating opens the basal dendrite,

$$b_j(t) = \text{ReLU}\left(W_{jm}^{(basal)} g_m(t)\right), \quad a_j(t) = \sigma(W_{ji}^{(apical)} r_i(t) - \alpha_j)$$

• EC5 integrates signals, adjusting EC3's phase of writing/keeping/forgetting.
• Multiple lamellae operate in parallel; dorsal lamellae encode detail, ventral lamellae abstraction, enabling rapid generalization as cue, environment, or task parameters change.

Neuron representations in CA1—splitter, lap, evidence, trace, delay-active, conventional place cells—emerge during learning and are inherited across task generalization. The multi-lamellar dorsoventral design thus enables hierarchical processing, gating, and flexible memory—mirroring the organizational principles observed in biological neural systems.

7. Contextual Significance and Applications

Multi-lamellar dorsoventral architectures, whether formulated as tissue models, material stacks, membrane assemblies, or computational frameworks, are central to organizing complexity with directionality. In biological development, they underlie axis formation and morphogenesis; in materials science, they offer tunable mechanical and functional interfaces; in membrane physics, they stabilize large-scale shape and pressure equilibrium; in neuroscience, they support dynamic, hierarchical learning and generalization within lamellar computational substrates.

The recurring theme across domains is the emergence of directional, multi-layered structure through the balance of mechanical, thermodynamic, or information-processing principles. A plausible implication is that further exploration of multi-lamellar dorsoventral stacks may yield new paradigms for robust, adaptable systems—both in natural and synthetic contexts—by leveraging the interplay of lamellarity, polarity, and collective interactions.