Search bioRxiv⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/2021.10.30.466618

Mem3DG: Modeling Membrane Mechanochemical Dynamics in 3D using Discrete Differential Geometry

Zhu, C.·Lee, C. T.·Rangamani, P.
View original source ↗Export metadata ↓

Abstract

Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to approximation-based methods (e.g., finite element method), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, Mem3DG, for modeling 3D mechanochemical dynamics of membranes based on Discrete Differential Geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, Mem3DG is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumb-bell, and unduloid and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions. Why it mattersCellular membranes have shapes and shape changes which characterize cells/organelles, and support nutrient trafficking among other critical processes. Modeling membrane shape changes using mechanical principles can provide insight into how cells robustly bend membranes to support life. Mathematical and computational strategies to solve the equations describing membrane shape evolution can be complex and challenging without simplifying assumptions. Here, we present a new, general, numerical approach to model arbitrary 3D membrane shapes in response to interaction with curvature sensing and generating membrane proteins. The accompanying implementation, Mem3DG, is a software tool to make computational membrane mechanics accessible to the general researcher. HighlightsO_LIIntroduces a discrete theory for membrane mechanics which connects with smooth theory C_LIO_LIDiscrete energy/force are functions of basic geometric quantities C_LIO_LIRecipes for extending the discrete framework with additional physics are provided C_LIO_LIDescribes a user-friendly software implementation called Mem3DG C_LIO_LIMem3DG is designed to facilitate modeling in tandem with experimental studies C_LI Significance and noveltyHelfrich Hamiltonian is widely used to model biomembranes. Many numerical methods have been developed to solve the geometric PDE. Compared to approximation-based methods, discrete-mesh-based models have many advantages when incorporating multiphysics in 3D due to their flexibility, efficiency, and straightforward implementation. However, there is no consensus on which mesh-based model is optimal, and a connection between the discrete and smooth geometric theory remains obscure. In this work, we provide a unifying perspective by identifying fundamental geometric invariants of the discrete force derived from a discrete energy. As a demonstration of generality of the framework to various physics, we follow a formulaic procedure to derive additional physics such as interfacial line tension, surface-bulk adsorption, protein lateral diffusion, and curvature-dependent protein aggregation.

Source connections

Explore related subjects

biophysicsPreprint

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zhu, C., Lee, C. T., Rangamani, P.. 2021-10-31. Mem3DG: Modeling Membrane Mechanochemical Dynamics in 3D using Discrete Differential Geometry. https://doi.org/10.1101/2021.10.30.466618

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

Autonomous Homeostatic Synthetic Cells via Self-Gating DNA Nanopores

Homeostasis is a fundamental hallmark of living organisms, arising from the complex interplay between biochemical reactions and regulatory feedback systems. Reconstituting such self-regulating behaviour in minimal synthetic cells enables continuous, persistent operation of biochemical reactions for extended amount of time. In this work, we demonstrate a minimal homeostatic synthetic cell capable of autonomous flux regulation using DNA nanotechnology and bottom-up synthetic biology. Our homeostatic architecture consists of Giant Unilamellar Vesicles (GUVs) equipped with gated DNA nanopores, encapsulated in vitro transcription (IVT) machinery, and an RNA degradation system. We achieve homeostasis under varying external chemical stimuli specifically varying concentrations of rNTPs by implementing a negative feedback loop between rNTP influx and RNA production. In our system, DNA nanopores facilitate the influx of rNTPs from the external environment, driving internal transcription. Crucially, the transcription process generates RNA "blockers" designed to bind and gate the DNA nanopores, thereby attenuating further rNTP influx. Our system is dynamic as encapsulated RNases slowly degrade the RNA blockers, allowing the pores to reopen as blocker concentration goes down. We first characterise the functionality and gating efficiency of the DNA nanopores using both pre-synthesised and in situ produced DNA and RNA blockers. We then demonstrate that rNTP flux through these pores is sufficient to drive IVT within the GUVs. Finally, by integrating these modules, we demonstrate robust homeostasis: the system maintains a steady-state level of RNA production for up to 16 hours. By harnessing the controllability of negative feedback loop, we demonstrate thresholding of the homeostasis level using single-stranded regulator DNA. This work establishes a versatile framework for engineering adaptive and self-sustaining responsive nanomaterials and synthetic cell chassis.

biophysics↗
bioRxiv2026

A Generic Numbering Scheme for TMEM16 Scramblases

The TMEM16 family of calcium-activated phospholipid scramblases (CaPLSs) and chloride channels (CaCCs) performs diverse physiological functions that include regulation of blood coagulation and apoptotic signaling, through a shared ten-transmembrane-helix (TM) architecture organized around a hydrophilic lipid-translocating groove. Mechanistic studies of TMEM16 family members have been hampered by the absence of a unified positional reference framework that would permit direct comparison of structurally equivalent residues across paralogs with different sequence numbering systems. Here we introduce a generic numbering scheme for TMEM16 scramblases (GNS-TMEM16), modeled on the Ballesteros & Weinstein system established for class A G protein-coupled receptors. A reference alignment (TMEM16-RA) was constructed from twelve human and mouse TMEM16 scramblases (TMEM16C/D/E/F/G/J) using structure-based ClustalW alignment of the ten TM helices. From this alignment, a TM-specific reference residue (TsRR) was identified for each helix by hierarchical application of three criteria: (1) 100% conservation in the core TMEM16-RA; (2) conservation in an augmented reference alignment (TMEM16-ARA) incorporating a group of phylogenetically more distant homologs composed of nhTMEM16, afTMEM16, TMEM16K, TMEM16A, and TMEM16B; and (3) structural and functional considerations, including helix-perturbing character, groove localization, conserved motif membership, and central TM position. The resulting ten TsRRs are Y1.50, W2.50, R3.50, E4.50, F5.50, P6.50, E7.50, D8.50, W9.50, and E10.50, and are illustrated in mTMEM16F. Each residue is assigned the identifier N.m(k), where N is the TM number, m is the position relative to the TsRR (for which m = 50), and k is the absolute sequence number. Loop residues receive dual identifiers referenced to the TsRRs of both flanking helices. Application of the GNS-TMEM16 is illustrated with the comparisons of the groove-opening measurements using pairwise distances between residues identified by their N.m indices to be corresponding across mTMEM16F, afTMEM16, and nhTMEM16. The results bring to light the advantages of corresponding residues identification in different TMEM16 proteins and show that the mammalian scramblase undergoes substantially larger separation at the extracellular groove entrance than either fungal homolog. Comparison of mutagenesis data guided by N.m correspondence shows at the conserved (E3.55,R6.26) salt-bridge locus, Ala substitution reduces activity more than 100-fold in nhTMEM16 but less than 2-fold in afTMEM16, illustrating that the GNS identifies structural equivalence of position without implying functional equivalence of the residue, which is a distinct advantage of GNS in providing mechanistic interpretation across paralogs. Also described is a protocol for extending the GNS-TMEM16 to uncharacterized protein sequences, including AlphaFold-predicted models, using structural superposition to mTMEM16F. Thus, the presented GNS-TMEM16 provides a stable positional reference for the integration and comparative analysis of structural, computational, and functional data across the TMEM16 family, utilizing a construction strategy applicable to yet other polytopic membrane protein families sharing a common transmembrane fold.

biophysics↗
bioRxiv2026

An agent-based 3D model of non-genetic adaptation in cancer tissues under electrical, mechanical, and hypoxic stress

Non-genetic adaptation enables cancer cells to alter their phenotype under stress without requiring new mutations. However, the mechanisms by which electrical, mechanical, and hypoxic cues combine to shape this process in 3D tissues remain poorly understood. This work presents an agent-based tumor model that integrates vascular oxygen supply, a globally imposed electric field, mechanically mediated crowding and compression cues, phenotype transitions, cell growth, mitosis, death, and inheritance of adaptive memory across division. The simulated tumors exhibit a three-stage trajectory consisting of necrosis onset, transient collapse of live mass, and partial regrowth accompanied by progressive accumulation of adapted cells. Continuous electrical stimulation produces a dose-dependent reduction in live mass while markedly increasing the adapted fraction, with comparatively limited changes in final necrotic burden. This response is strongly conditioned by mechanics and reshapes (and is reshaped by) adaptive capacity. Pulsed stimulation further shows that, in the model, electric field amplitude and temporal schedule jointly determine memory phenomena, phenotypic diversification, and growth recovery. These results show that coupling local oxygen availability, mechanical constraints, electrical forcing, and history-dependent phenotype transitions can generate distinct tissue-level patterns of phenotypic heterogeneity. Both stimulus magnitude and temporal protocol influenced the resulting population structure, suggesting that the history of physical stress may be an important determinant of adaptive dynamics in spatially organized tumor models.

biophysics↗