Beyond static geometry: dynamic curvature in mechanobiology

1 Dynamic curvature: beyond a geometric descriptor

Initially considered a purely geometric property, curvature is increasingly recognized as an active regulator of biological function rather than a passive characteristic (Luciano et al., 2024a). Recent advances in mechanobiology have revealed that curvature not only reflects underlying mechanical forces but also directly influences cellular behaviour, force transmission, and biochemical signalling (Hirashima and Matsuda, 2024). Dynamic curvature refers to the time-dependent evolution of geometric curvature in biological membranes, cells, and tissues, and to its intimate coupling with mechanical forces and biochemical signalling. Curvature can emerge from internally generated processes such as apical constriction (Martin and Goldstein, 2014; Pérez et al., 2021), compressive stresses (Tozluoǧlu et al., 2019; Trushko et al., 2020), hydrostatic and osmotic pressure (Latorre et al., 2018; Dumortier et al., 2019), and collective tissue remodelling.

Unlike stretch or compression, curvature intrinsically couples geometry and mechanics by generating spatial gradients of deformation and stress. Importantly, dynamic curvature is not defined solely by its magnitude (κ) but can be described by several independent physical parameters, including curvature sign (positive or negative), rate of change (dκ/dt), oscillation frequency (f), and persistence time (τ). Together, these variables define a multidimensional geometric landscape that evolves over time. In turn, changing curvature redistributes mechanical stresses, alters membrane tension, reorganizes the cytoskeleton, and modulates signalling pathways involved in migration, differentiation, and morphogenesis.

This raises the possibility that cells do not simply sense curvature itself but rather decode a multidimensional curvature signal integrating both geometric and temporal information. In living systems, such signals are ubiquitous: cells are continuously exposed to dynamically evolving curvature landscapes generated by tissue deformation, morphogenesis, and physiological organ activity (Vikran and Hirashima, 2025). These curvature fluctuations span multiple spatial and temporal scales, from millisecond membrane remodelling events to large-scale tissue shape changes occurring over hours or days during development, regeneration, and disease progression.

Such observations challenge the conventional view of curvature as a static structural parameter and instead suggest that biological shape may constitute a dynamic form of physical information. Within this emerging paradigm, curvature is not merely an outcome of mechanics but a dynamic physical variable capable of encoding, transmitting, and modulating biological information across scales.

A fundamental question therefore emerges: can the spatiotemporal dynamics of curvature themselves act as a biophysical signal, coordinating cellular and tissue behaviour through their interplay with mechanics, geometry, and biochemical signalling? Addressing this question requires bridging traditionally separate fields, from membrane biophysics and mechanotransduction to tissue morphogenesis and bioengineering.

In this Perspective, we explore the emerging idea that dynamic curvature constitutes a previously underappreciated layer of biological regulation. We propose that evolving geometries may actively encode physical information, coordinate collective behaviours and couple mechanical and biochemical processes across scales. Understanding how living systems generate, interpret, and potentially remember dynamic curvature could reveal a new organizing principle of mechanobiology, in which geometry is not merely a consequence of biological activity but a dynamic and programmable regulator of cellular and tissue function.

2 Dynamic curvature as an independent physical variable: a geometry–force–time framework

Mechanobiology has established that biological systems continuously sense and respond to a broad spectrum of biochemical and physical cues, including forces, matrix mechanics, geometry and tissue architecture. Here, we propose a complementary conceptual framework in which dynamic curvature constitutes an independent physical variable that actively regulates biological functions across scales. Rather than viewing curvature as a static geometric descriptor or merely a passive consequence of force generation, we argue that its spatiotemporal evolution represents a distinct form of mechanical information continuously generated during membrane remodelling, cell deformation, tissue morphogenesis and organ function (Figures 1A,B).

The key conceptual shift is therefore from curvature as a state to curvature as a trajectory. Two cells exposed to the same instantaneous curvature may nevertheless experience fundamentally different mechanical signals depending on how that curvature was generated: whether it developed rapidly or gradually, persisted over time, or oscillated repeatedly. Dynamic curvature is therefore defined not only by its magnitude and sign, but also by its temporal characteristics, including the rate of change, frequency, duration and previous history of geometric deformation (Figure 1A).

Within this framework, time becomes an intrinsic component of the mechanical signal rather than an experimental variable. Cellular responses may therefore depend not only on the current geometric state but also on the path through which it was reached, implying that cells can discriminate between distinct temporal patterns of otherwise identical curvature. This raises a fundamental question: how is this geometric information encoded, transmitted and integrated across biological scales?

We propose that dynamic curvature is decoded through a hierarchical mechanotransduction cascade. At the plasma membrane, evolving geometry is sensed by curvature-sensitive proteins and changes in membrane tension (Figure 1B). These signals are relayed through the cytoskeleton to the nucleus, where they influence nuclear mechanics, chromatin organization and gene expression (Figure 1B). When sufficiently persistent, these responses may outlast the original geometric stimulus, providing a mechanism by which transient geometric experiences generate mechanical memory and shape future cellular behaviour.

At the tissue level, dynamic curvature is unlikely to act as a simple upstream cue but instead participates in reciprocal feedback loops. Changes in geometry alter cellular forces and signalling, which remodel tissue architecture and continuously generate new curvature. Dynamic curvature therefore functions simultaneously as a mechanical input, an emergent signal and a consequence of tissue self-organization (Figure 1B).

Viewed from this perspective, dynamic curvature is not simply another form of deformation but a time-dependent physical variable that carries information across molecular, cellular, tissue and organ scales. Establishing this geometry–force–time framework provides a conceptual foundation for integrating dynamic geometry into mechanobiology and offers new opportunities for the design of dynamic biomaterials, organ-on-chip systems, mechanomedicine and regenerative medicine.

3 Curvature sensing and generation at the molecular and membrane scale

Dynamic curvature is an intrinsic property of biological membranes, which continuously undergo deformation, remodelling, and shape fluctuations driven by membrane trafficking, cytoskeletal forces, and protein–lipid interactions (McMahon and Gallop, 2005). Unlike static membrane geometries commonly reproduced in simplified experimental systems, cellular membranes constantly generate, amplify, and dissipate curvature over time (Figure 1B). Endocytosis, exocytosis, organelle biogenesis and intracellular transport therefore occur within continuously evolving geometric landscape, suggesting that membrane-associated proteins are exposed not to fixed membrane shape but to dynamic curvature signals.

Considerable progress has identified the molecular machinery responsible for membrane curvature sensing and generation. BAR-domain proteins, clathrin, dynamin, septins and other related curvature-sensitive proteins assemble preferentially on curved membranes while simultaneously remodelling membrane shape (Curtis et al., 2022; Zimmerberg and Kozlov, 2006; Jarsch et al., 2016; Shi et al., 2023; Itoh et al., 2005). These reciprocal interactions established membrane curvature as a key regulator of membrane trafficking and organization. However, almost all current models implicitly assume that proteins respond to static or quasi-static membrane geometries, whereas living membranes rarely experience such conditions.

This raises a fundamentally different question: can curvature-sensitive proteins decode how curvature evolves over time rather than simply sensing its instantaneous value? Two membrane regions may transiently exhibit identical curvatures while differing completely in their history having arisen through rapid bending, slowly remodelling, oscillatory deformation or a persistent curvature. If cells distinguish between these situations, membrane-associated proteins would effectively encode a multidimensional curvature signal integrating curvature magnitude together with temporal descriptors such as curvature rate, oscillation frequency, and persistence. Dynamic membrane curvature would therefore represent more than a structural property of membranes, but a physical signal carrying information about ongoing cellular activity.

Recent advances make this hypothesis experimentally accessible. Reconstituted membrane systems based on giant unilamellar vesicles (GUVs) and synthetic liposomes allow membrane curvature to be generated under highly controlled conditions (Shi et al., 2023; Nakazawa et al., 2023) while fluorescent membrane-tension reporters have revealed rapid spatiotemporal fluctuations in membrane mechanics during membrane remodelling (Roffay et al., 2021; Colom et al., 2018). Complementing these approaches, recently developed DNA-based mechanosensors can quantify membrane-associated tensile forces while recording their cumulative mechanical history, providing a means to integrate mechanical signals over time rather than measuring only instantaneous force events (Bhattacharyya et al., 2026; Singuru et al., 2025a). Although originally developed to probe force transmission, these tools offer an attractive conceptual framework for dynamic curvature studies, as they raise the possibility of determining whether cells similarly integrate the temporal history of curvature signals.

Together, these emerging technologies provide unprecedented opportunities to investigate how dynamic curvature, membrane tension and curvature-sensitive proteins are functionally coupled and to establish a framework describing dynamic curvature as a true spatiotemporal signal. Such efforts could reveal that membrane curvature functions as more than a structural regulator of trafficking and membrane organization, acting instead as an information-processing layer through which cells integrate geometry, mechanics, and biochemical signalling.

Despite substantial progress in identifying the molecular machinery involved in membrane curvature sensing, the temporal dimension of membrane curvature remains largely unexplored.

It is still largely unknown whether curvature-sensitive proteins respond solely to the instantaneous membrane shape or whether they can also detect how membrane curvature changes over time. Addressing this question may fundamentally change how membrane mechanosensing is viewed. Rather than acting as simple detectors of membrane geometry, curvature-sensitive proteins may function as dynamic signal decoders, extracting spatiotemporal information from continuously remodelling membranes. More broadly, membrane curvature sensing would constitute the first layer of a multiscale hierarchy through which dynamic geometric information is encoded, propagated and ultimately translated from molecular assemblies to cellular and tissue-level behaviour.

4 How single-cells sense and adapt to dynamic substrate curvature

At a larger scale, dynamic curvature emerges from continuous shape changes generated by cytoskeletal remodelling and external mechanical constraints. Studies on static curved substrates have revealed that cells sense local geometry by modulating their morphology (Mukherjee et al., 2019), cytoskeletal architecture (Bade et al., 2018; Bade et al., 2017), nuclear organization (Werner et al., 2017), and migration (Pieuchot et al., 2018; Werner et al., 2018). These discoveries have positioned curvature as a major regulator of cell–environment interactions and have laid the foundations for a broader investigation of how dynamic changes in tissue geometry may influence cellular responses in living systems.

Emerging evidence suggests that cells do not simply adapt to instantaneous curvature but also integrate its temporal characteristics. Dynamic curvature continuously remodels cell polarity, cytoskeletal organization, focal adhesions, and nuclear mechanics (Figure 1B). Among the determinants of curvature adaptation, the spatial organization of focal adhesions (FA) appears particularly important. Rather than cellular contractility itself, the recently introduced “free spanning distance” (FSD), reflecting the spatial distribution of focal adhesion clusters of the cell, predicts the ability of cells to bridge curved geometries, highlighting that geometric sensing primarily depends on how mechanical forces are spatially transmitted (Herrera et al., 2026).

Experimental evidence supporting dynamic curvature sensing has recently emerged using a micro-pneumatic platform capable of dynamically controlling surface curvature over time. Adipose-derived stem cells (ASCs) exhibit responses that depend not only on curvature magnitude but also on stimulation frequency progressively reorganizing actin filaments, focal adhesions, and nuclear orientation while aligning preferentially along regions of lower curvature (Saporito et al., 2024). These observations suggest that cells may decode temporal features of curvature dynamics rather than geometry alone. Such findings support the emerging view that dynamic curvature constitutes a biologically relevant signal capable of transmitting information beyond its instantaneous shape.

Consistent with this view, photoresponsive hydrogels capable of repeatedly switching between flat and curved states have revealed nuclear mechanoprotection responses (Bril et al., 2025). Fibroblasts reposition their nuclei away from regions undergoing deformation while remodelling nuclear architecture and chromatin organization through actin- and vimentin-dependent mechanisms. These adaptations are accompanied by epigenetic modifications that protect the genome from mechanically induced DNA damage, raising the intriguing possibility that dynamic curvature leaves long-lasting nuclear imprints and contributes to mechanical memory.

If dynamic curvature can indeed be integrated over time, an important conceptual question follows: can it also instruct cell behaviour rather than simply perturb it? Recent computational work introducing the concept of dynamic curvotaxis provides a first indication that this may be the case (Manifacier et al., 2024). In contrast to classical curvotaxis on static substrates (Pieuchot et al., 2018; Sadhu et al., 2024), it has been suggested that time-dependent changes in substrate curvature can act as directional signals, guiding cell migration over long distances with the nucleus acting as a curvature-sensitive mechanical sensor that biases migration toward concave regions. Although experimental validation remains to be established, this framework suggests that dynamic curvature may function as an active guidance cue generated during tissue folding, contraction, or morphogenesis and may actively encode migratory information.

Together, these studies support a conceptual shift in how dynamic geometry is viewed. Rather than representing a transient mechanical perturbation, dynamic curvature may constitute a genuine spatiotemporal signal whose magnitude, frequency, persistence, and history are decoded by cells to regulate cytoskeletal remodelling, nuclear organization, mechanical memory, and migration. Understanding how these temporal geometric cues are integrated may therefore reveal a previously unrecognized layer of mechanotransduction linking dynamic tissue architecture to cellular decision-making.

5 Collective and tissue-scale response to substrate curvature changes

While single cells adapt to dynamic geometric cues through cytoskeletal remodelling, nuclear mechanosensing, and transcriptional reprogramming, tissues introduce an additional level of complexity in which curvature becomes both a sensed signal and an emergent property of collective behaviour. Dynamic curvature is a hallmark of morphogenetic processes such as epithelial folding, invagination, and organ shaping, where tissues continuously generate, remodel, and respond to evolving geometries (Figure 1). Rather than being a passive consequence of development, curvature increasingly appears as an active variable participating in feedback loops that couple mechanics, cell behaviour, and tissue architecture.

Recent experimental systems capable of inducing curvature have begun to reveal how epithelial tissues decode dynamic geometric changes. Self-rolling substrates trigger rapid and transient adaptation involving osmotic swelling, membrane tension changes, and cytoskeletal remodelling (Tomba et al., 2022). Importantly, tissue responses depend strongly on curvature sign, negative curvature induces tissue tension, nuclear deformation, Ca²⁺ wave propagation, but also a transcriptional reprogramming associated with altered adhesion states (Blonski et al., 2021). Together, these observations suggest that tissues not only sense dynamic curvature but can also discriminate between distinct geometric configurations and translate them into specific collective responses.

Conversely, dynamic curvature can also emerge spontaneously from the intrinsic mechanics of multicellular systems. Epithelial monolayers curl at free edges through the coupling between tissue tension and active bending (Fouchard et al., 2020) while rapid deflation of epithelial domes induces buckling, supracellular folds, and transient cortical wrinkles (Chahare et al., 2025). Likewise, epithelial domes display active superelastic behaviour, highlighting how tissue architecture redistributes mechanical stresses during large deformations (Latorre et al., 2018). Together, these observations highlight that dynamic curvature is both an input sensed by tissues and an output generated by collective mechanical behaviour.

Beyond conventional 2D systems, 3D organoid models further illustrate this reciprocal relationship. In intestinal organoids, dynamic modulation of epithelial curvature regulates membrane tension, YAP activity and crypt formation (Yavitt et al., 2023), while mechanochemical feedback between crypt curvature and actomyosin tension drives robust transitions between bulged and budded morphologies (Xue et al., 2025). Similar curvature-dependent feedback loops operate during lung branching morphogenesis where tissue curvature and ERK signalling reciprocally regulate one another (Hirashima and Matsuda, 2024). These examples support the concept that tissues do not simply adapt to dynamic curvature but actively regulate it through coupled mechanical and biochemical feedback loops capable of stabilizing tissue architecture or amplifying geometric fluctuations into morphogenetic transitions.

A major unresolved question is therefore what tissues actually sense when curvature changes. Do collective responses depend primarily on curvature magnitude, curvature sign, the rate of curvature change, oscillatory dynamics or the persistence of geometric states across space and time? More fundamentally, how are these dynamic geometric signals integrated with biochemical pathways to coordinate tissue-scale organization? Addressing these questions will require experimental platforms capable of precisely controlling curvature dynamics while simultaneously quantifying tissue mechanics, signalling activity and cell behaviour. Such technologies will be essential to establish causal relationships between dynamic geometry and collective biological responses, providing the foundation for the next generation of engineered dynamic curvature systems.

6 Engineering dynamic curvature in vitro

The increasing recognition of dynamic curvature as a biologically relevant signal calls for experimental platforms capable of reproducing controlled geometric changes in vitro. Unlike classical stretch or compression assays, dynamic curvature generates asymmetric mechanical environments by simultaneously imposing tension and compression across tissues. Consequently, it cannot be reproduced using conventional mechanobiology platforms (Luciano et al., 2021; Yevick et al., 2015; Luciano et al., 2024b) and requires systems capable of generating, maintaining, and imaging dynamically evolving 3D geometries. Importantly, these platforms enable independent control of dynamic curvature key features, including curvature magnitude, sign, frequency, persistence, and reversibility, providing a unique opportunity to determine which components of the curvature signal are biologically decoded.

Several complementary strategies have recently emerged to achieve this goal. Mechanical instabilities (Fouchard et al., 2020) and self-rolling substrates (Tomba et al., 2022; Luciano et al., 2026) provide simple approaches to induce rapid curvature formation and have revealed acute epithelial adaptation to changing geometries. Photo-responsive materials enable spatiotemporal control of tissue geometry through light stimulation (Bril et al., 2025; Yavitt et al., 2023; Wang et al., 2021; Puliafito et al., 2019), whereas pressure-driven systems (Saporito et al., 2024; Weber et al., 2026; Brun-Cosme-Bruny et al., 2022) reproduce reversible and cyclic curvature deformations that closely mimic physiological processes such as breathing-like motions (Hajari et al., 2025). More recently, magnetic actuation has introduced contactless and reversible curvature control while preserving optical accessibility for live imaging (Chalut et al., 2024). Rather than competing technologies, these approaches provide complementary experimental framework to investigate how cells and tissues interpret dynamic geometric environments.

Together, these approaches are beginning to provide independent control over key parameters of dynamic curvature (including magnitude, sign, rate of change, persistence, and reversibility) thereby transforming curvature from a static architectural feature into an experimentally tunable variable. Such platforms now offer a unique opportunity to determine which temporal aspects of curvature are biologically sensed and how dynamic geometric information is integrated into cellular and tissue-scale responses. Beyond technological innovation, future systems should aim to reproduce the dynamic geometric complexity of living tissues rather than isolated curved structures.

The next challenge is no longer simply to generate dynamic curvature, but to reproduce the complexity of physiological curvature dynamics while integrating quantitative measurements of mechanotransduction. Future platforms should combine precise control of dynamic geometry with high-resolution imaging, force measurements and molecular readouts in physiologically relevant 3D architectures (Figure 2A). Such systems will be essential to establish causal relationships between curvature dynamics and biological functions, transforming dynamic curvature from an experimental perturbation into a quantitative and predictive variable of mechanobiology.

7 Biological and medical relevance of dynamic curvature

Dynamic curvature is increasingly emerging as an active regulator of cellular and tissue function rather than a simple geometric consequence of biological activity. Recent studies in intestinal organoids demonstrate that locally controlling epithelial curvature through photo-patterned hydrogels regulates crypt morphogenesis by modulating membrane tension, YAP activation, and Paneth cell positioning (Yavitt et al., 2023; Yavitt et al., 2025). These findings suggest that dynamic curvature actively participates in tissue self-organization and morphogenesis (Vikran and Hirashima, 2025), opening new perspectives for mechanobiology and mechanomedicine (Kalukula et al., 2025b). More broadly, if dynamic curvature constitutes an independent physical variable, defects in its generation, transmission, or interpretation may represent a previously unrecognized class of mechanopathologies.

This concept is beginning to emerge across multiple biological scales (Figure 2B). At the intracellular level, dynamic membrane curvature is essential for organelle architecture and trafficking. In the endoplasmic reticulum, the curvature-generating receptor FAM134B is required for vesicle formation, while organelle turnover and its dysregulation has been linked to severe neurological and vascular disorders (Schamberger et al., 2023). Many pathological processes similarly exploit or disrupt the machinery responsible for membrane remodelling, including viral infections that disrupt curvature-dependent endocytic and exocytic pathways (Wölk et al., 2024). At the tissue scale, dynamic curvature also appears to influence disease progression. Shape-shifting magnetic hydrogels have recently demonstrated that dynamically changing curvature directly modulates the expression of genes involved in inflammation, tumor progression and metastasis (Manjua et al., 2025). Likewise, the mammary gland continuously remodels its geometry during ductal branching and alveolar morphogenesis. Perturbation of these evolving curvature landscapes has been linked to altered epithelial organization and breast cancer progression (Fernández et al., 2021; Boghaert et al., 2012). Together, these observations support the idea that abnormal curvature dynamics may not simply accompany disease but actively contribute to its initiation and progression. Deciphering these relationships may reveal new diagnostic and therapeutic targets that remain largely unexplored.

Beyond disease progression, dynamic curvature may also provide a new class of physical biomarkers. Alterations in tissue geometry are hallmarks of numerous pathologies and often precede the onset of obvious functional disorders. Changes in cortical curvature have already been proposed as quantitative biomarkers for traumatic brain injury (TBI) where significant differences in mean cortical curvature are observed between healthy and injured brains (King et al., 2016). Similarly, cancer progression is frequently accompanied by increasingly irregular and heterogeneous curvature landscapes that may actively influence tumor growth, invasion, and cell dissemination (Messal et al., 2019). Dynamic curvature measurements within pulmonary acinus have also been proposed to improve the diagnosis and prognosis of idiopathic interstitial pneumonia and pulmonary fibrosis (Chen et al., 2019). These observations suggest that curvature could evolve from a descriptive measure of pathological architecture into a quantitative readout of disease state and progression.

Conversely, dynamic geometry may also act as a protective mechanical signal. In the beating heart, cyclic mechanical loading suppresses tumor proliferation through Nesprin-2–dependent chromatin remodelling, whereas mechanical unloading restores tumor growth (Ciucci et al., 2026). Whether the continuously changing curvature associated with cardiac deformation contributes to this protective effect remains an intriguing and largely unexplored question. More broadly, this raises a fundamental possibility: if pathological curvature dynamics can be detected, could physiological curvature dynamics also be restored?

Such a shift from measuring geometry to manipulating geometry could open an entirely new dimension of mechanomedicine. Proof-of-concept already exists for mechanically activated therapeutics: DNA-based nanovehicles anchored to the plasma membrane release anticancer drugs upon sensing receptor-generated tensile forces (Singuru et al., 2026; Singuru et al., 2025b). Extending this concept, future biomaterials could become curvature-responsive, using spatiotemporal geometric cues rather than forces alone to trigger drug delivery, regulate tissue repair or guide regeneration. In this view, dynamic curvature would evolve from a descriptor of tissue architecture into a therapeutically actionable physical variable, establishing a new dimension of mechanomedicine that complements biochemical signalling, matrix mechanics, and force transmission.

This emerging perspective is also reshaping biomedical engineering. Organ-on-chip systems and advanced tissue-engineering platforms increasingly integrate dynamically curved environments to reproduce physiologically relevant tissue deformations. Lung-on-chip devices mimic cyclic alveolar curvature to investigate fibrosis and respiratory diseases under realistic mechanical conditions (Weber et al., 2026), while hydraulically actuated organ-chip platforms demonstrate that dynamic curvature regulates corneal stromal cell alignment, focal adhesion, phenotypic transitions, and gene expression (Kim et al., 2025). These systems provide not only more physiologically relevant disease models but also experimental platforms in which geometry can be independently manipulated and quantitatively controlled.

As dynamic biomaterials continue to evolve, controlling curvature in both space and time could transform geometry from a passive feature of biological systems into a programmable design parameter. This may enable new approaches to disease modelling and drug screening while opening the possibility of curvature-based therapeutic strategies for regenerative medicine and pathological tissue remodelling. In this emerging framework, mechanomedicine would move beyond manipulating biochemical signals, matrix stiffness, or mechanical forces alone to actively design the geometry–force–time environment experienced by cells and tissues.

8 Outlooks and future directions

Dynamic curvature emerges as a fundamental physical signal through which living systems couple geometry, mechanics, and biochemical regulation across biological scales (Figure 2C). The central challenge ahead is therefore not simply to determine whether cells respond to curvature, but to understand what information is encoded through its dynamics and how this information is decoded. Curvature magnitude and sign may represent only the most elementary features of the signal; rate of change, frequency, persistence, and temporal sequence may provide additional layers of information. Determining whether cells sense these parameters independently or integrate them into a higher-order geometric code will require quantitative approaches capable of treating curvature as a truly spatiotemporal variable.

A second frontier is to determine how dynamic curvature is sensed and integrated across biological scales. Although curvature-dependent responses have been described at the membrane, cytoskeletal, nuclear, and tissue levels, these processes are still largely investigated independently. A major challenge will therefore be to establish whether dynamic curvature information is progressively encoded and transmitted through a hierarchical mechanosensing network, from membrane-associated molecular assemblies to the cytoskeleton, nucleus, and ultimately multicellular tissues. Addressing this question will require combining dynamic biomaterials with quantitative live-cell imaging, force measurements, and multiscale modelling. In this context, dynamic curvotaxis offers an intriguing example of how evolving curvature fields could act as guidance signals, linking local geometric dynamics to collective cell migration and tissue organization (Manifacier et al., 2024).

An additional and largely unexplored question is whether dynamic curvature contributes to the establishment of mechanical memory. Cells can retain information from past events during which they experienced dynamic curvature modulation through for instance persistent changes in cytoskeletal organization (Kalukula et al., 2025a), chromatin structure, and gene expression (Lee et al., 2026). Because curvature is inherently dynamic, cells may integrate not only their current geometric environment but also the history of previous curvature exposures. Determining whether transient geometric events can generate persistent changes in cellular state would establish a direct link between dynamic curvature, mechanical memory, and cell fate, and could reveal that tissue geometry itself carries a form of biological memory.

Translating dynamic curvature into mechanomedicine will require the development of dynamic biomaterials capable of reproducing the evolving geometries encountered in living tissues. Future organ-on-chip platforms and engineered tissue models will need to combine precise control of curvature dynamics, physiologically relevant three-dimensional architectures, and high-resolution imaging to capture adaptive and out-of-equilibrium cellular behaviors. Such systems will not only provide powerful tools to investigate the fundamental mechanisms of curvature sensing but may also enable new strategies to guide tissue regeneration, control cell fate, and prevent pathological remodelling. By integrating mechanobiology, materials science, and bioengineering, dynamic curvature could ultimately emerge as a new dimension of mechanomedicine (Kalukula et al., 2025b), complementing existing approaches based on biochemical signalling and matrix mechanics (Figure 2D).

Ultimately, the field may need to move beyond the question of how cells respond to curvature toward a broader question: how do living systems sense, integrate, and remember evolving geometry? By explicitly incorporating time into the study of biological shape, dynamic curvature could redefine mechanobiology by establishing biological geometry as a time-dependent and potentially programmable form of information–one that cells can sense, process, and remember to coordinate tissue function, adaptation, and disease.

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Footnotes

Edited by: Shubham Garg, Cincinnati Children’s Hospital Medical Center, United States

Reviewed by: Dhiraj Indana, Stanford University, United States

Murali Mohana Rao Singuru, University of Massachusetts Amherst, United States