# Nuclear Envelope Rupture Initiation in Confined Migration: A Geometric-Kinetic Framework

Navinkumar Patil

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Navinkumar Patil. Nuclear Envelope Rupture Initiation in Confined Migration: A Geometric-Kinetic Framework. 2026. hal-05532179

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# Nuclear Envelope Rupture Initiation in Confined Migration: A Geometric–Kinetic Framework

Navinkumar Patil*

## Abstract

Cells migrating through tight tissue spaces must squeeze the nucleus through constrictions smaller than its resting diameter. Such deformation can transiently rupture the nuclear envelope, yet rupture initiation varies widely even at matched constriction size, indicating that pore diameter alone is insufficient. This review synthesizes evidence into a geometric-kinetic framework that places each confinement event at an operating point defined by two coupled contributors. Geometric stress focusing localizes demand to a small patch at the leading nuclear apex and is captured by a curvature-weighted loading coordinate normalized by nuclear resistance. Rate-limited remodeling captures regimes in which deformation outpaces effective nuclear relaxation and is summarized by a window-defined rate-relaxation index. LINC complexes and perinuclear cytoskeletal assemblies are discussed as candidate force-routing modules that can shift operating points by redistributing loading and entry kinematics. The emphasis is on mechanical determinants of rupture initiation rather than downstream damage, which additionally depends on repair and stress-response programs. A regime map, a minimal measurement checklist, and falsifiable perturbation tests are provided to support cross-platform calibration and to generate gated hypotheses for cancer invasion, immune trafficking, and fibrotic remodeling.

*Keywords:* Nuclear envelope rupture, confined cell migration, geometric stress focusing, rate-limited remodeling, nuclear mechanics

## 1. Introduction

Cells migrating through tissues routinely squeeze through gaps narrower than their own diameter, for example basement membrane pores during invasion, endothelial junctions during immune surveillance, and dense collagen-rich networks during

<footnote>*Independent Researcher, Mumbai, India.</footnote>

<footnote>Email address: navinjpatil@gmail.com (Navinkumar Patil)</footnote>
fibrotic remodeling (Friedl et al., 2011; Kalukula et al., 2022; McGregor et al., 2016; Paul et al., 2017; Stroka et al., 2014). In these confined spaces the nucleus is often the mechanical bottleneck because it is both the largest and the stiffest organelle, with micropipette aspiration and related measurements reporting stiffness contrasts over the cytoplasm ranging from several fold to nearly an order of magnitude depending on probe geometry, strain regime, loading rate, and cell state (Davidson et al., 2014; Guilak et al., 2000; Kalukula et al., 2022; McGregor et al., 2016). This bottleneck reflects the laminated architecture of the nuclear envelope because a thin cross-linked lamin meshwork underlies the double membrane and transmits and resists localized loading during severe confinement (Dahl et al., 2008; Goelzer et al., 2021; Nmezi et al., 2019; Turgay et al., 2017). When deformation is sufficiently extreme the nuclear envelope can rupture transiently, mixing nuclear and cytoplasmic contents, herniating chromatin, and triggering DNA damage (Chen et al., 2019; Denais et al., 2016; Hatch, 2018; Maciejowski and Hatch, 2020; Raab et al., 2016; Shah et al., 2017; Vargas et al., 2012; Xia et al., 2019). Because downstream consequences depend strongly on lineage-specific repair kinetics and stress responses, the present scope is limited to mechanical conditions that bias rupture initiation during confined deformation rather than to longer term damage, signaling, or fate (Chu et al., 2025; Schultz et al., 2025). Rupture initiation as used here refers to the onset of envelope discontinuity rather than to the duration, extent, or repair outcome of the resulting breach (Denais et al., 2016; Raab et al., 2016; Vargas et al., 2012).

Rupture initiation outcomes are nonetheless highly heterogeneous. Nominally similar constrictions yield widely different rupture initiation outcomes across lineages, within single populations, and across platforms that impose different loading histories and boundary conditions (Denais et al., 2016; Kalukula et al., 2022; McGregor et al., 2016; Wolf et al., 2013). This review proposes that much of this heterogeneity can be organized by two coupled but distinguishable contributors, geometric stress focusing and rate-limited remodeling, rather than by constriction size alone. Geometric stress focusing arises when high curvature at the leading nuclear apex concentrates mechanical demand onto a small envelope region. Rate-limited remodeling arises when deformation proceeds faster than viscoelastic relaxation and structural reorganization so that transient stresses exceed quasi-static expectations. Operationally, geometric stress focusing is captured by a curvature-weighted loading proxy normalized by nuclear resistance, and rate-limited remodeling is captured by a dimensionless rate–relaxation index that compares deformation rate with an effective nuclear relaxation time. Because contact-dominated boundary conditions and nonuniform wall reaction forces can strongly shape the local stress state in many confinement assays, apex geometry and deformation history can be more informative
predictors of rupture initiation risk than pore diameter alone. A practical barrier to reconciling results across platforms is that curvature, loading, deformation rate, relaxation, and nuclear resistance are rarely co-measured within a single workflow in a form that supports quantitative calibration and cross-study comparison, and the measurement checklist proposed in this review is intended to help address this gap (Baird et al., 2026; Kalukula et al., 2022; McGregor et al., 2016; Patel et al., 2026; Stroka et al., 2014).

Within single confinement workflows, reducing actomyosin-dependent nuclear loading decreases rupture initiation at fixed constriction size, which is consistent with cytoskeletal force transmission contributing to rupture initiation risk (Denais et al., 2016; Lammerding and Wolf, 2016; Wu et al., 2014). In the same general setting, changes in entry kinematics also modulate rupture initiation at fixed geometry, which is consistent with a rate-limited remodeling contribution in at least some regimes (Pfeifer et al., 2022). Live imaging in microfluidic constrictions localizes rupture initiation to the leading nuclear region, frequently at highly deformed blebs where lamin signal is weak or absent, supporting localized failure rather than uniform envelope breakdown (Denais et al., 2016). Complementary height-controlled confinement devices identify a threshold nuclear deformation above which the lamina breaks and blebs form with persistent misshapen nuclei, further supporting the view that specific highly deformed regions fail first under increasing confinement (Le Berre et al., 2012). In a curvature- and deformation-rate-resolved confinement workflow, lamin B1 dilution aligns most strongly with local curvature, whereas lamin A/C dilution becomes prominent when high curvature combines with fast deformation (Pfeifer et al., 2022), which aligns with the distinct spatial organization and stability contributions of A- and B-type lamin networks (Nmezi et al., 2019). This pattern motivates treating geometric stress focusing and rate-limited remodeling as interacting contributors rather than interchangeable descriptors.

The remainder of this review is organized as follows. Section 2 operationalizes geometric stress focusing and rate-limited remodeling as measurable proxy coordinates and introduces candidate force-routing modules that may shift cellular operating points within this two-axis landscape. Section 3 evaluates mapping constraints and current evidence through the geometric-kinetic lens, develops reconciliation hypotheses for apparent cross-platform contradictions, and formulates falsifiable perturbation tests that stress-test the axis mapping. Section 4 translates the framework into conditional, explicitly gated hypotheses for cancer metastasis, immune trafficking, and fibrosis that are framed as testable predictions rather than intervention claims. Section 5 summarizes scope limits, coupling and implementation priorities, and the measurement deliverables needed for cross-workflow calibration.
## 2. A Two-Axis Framework for Rupture Initiation Risk

To move beyond constriction size as a sole descriptor, rupture initiation risk is framed here as an operating-point problem in which local geometry and deformation history jointly shape the mechanical demand experienced by the nuclear envelope. This section synthesizes observations into two measurable proxy coordinates that can be extracted within common confinement workflows, with one capturing geometric stress focusing normalized by nuclear resistance and the other capturing whether deformation outpaces effective relaxation. It then proposes how LINC composition and perinuclear cytoskeletal architecture may bias force transmission and shift operating points, and it introduces a minimal measurement and reporting set to support cross-platform calibration.

### 2.1. Geometric Axis and Curvature-Weighted Apex Loading Proxy

As a nucleus is driven into a constriction narrower than its resting diameter, its leading surface sharpens into a high-curvature apex that focuses mechanical demand onto a small envelope patch (Deserno, 2015; Xia et al., 2018). Comparing this geometric stress focusing across platforms requires a proxy that does not presuppose a particular constitutive model. The proxy used here, $\sigma_{apex}^{eff}$, is defined from the loading variable a workflow controls or can credibly infer and is intended for within-workflow ranking rather than absolute stress inference (Deserno, 2015).

In aspiration and other pressure-controlled assays, the applied pressure difference $\Delta P$ is the directly controlled normal load, so $\sigma_{apex}^{eff} \approx \Delta P$ is taken as the apex loading proxy in that class, with $\Delta P$ treated as a workflow-anchored loading scale rather than reinterpreted as a membrane tension when boundary conditions differ across studies (Guilak et al., 2000; Hochmuth, 2000). Because the estimator differs across assay classes, absolute values of $\sigma_{apex}^{eff}$ are generally not comparable between aspiration-derived and migration-derived workflows unless loading assumptions and boundary conditions are matched.

In migration and constriction assays, a Laplace-type scaling provides a convenient curvature-weighted estimator linking geometric stress focusing to mean curvature and a workflow-anchored tension-like prefactor,

$$ \sigma_{apex}^{eff} \approx 2 T_{NE} H, \qquad (1) $$

where $T_{NE}$ is an effective envelope tension-like prefactor and $H$ is the mean curvature (Deserno, 2015). This form is most informative in workflows that also constrain an effective $T_{NE}$, because the loading scale is then anchored within matched boundary conditions (Dahl et al., 2008; Davidson et al., 2019). When such an estimate is
not available, reporting the apex mean curvature $H$ together with an independent loading or traction readout, such as entry force or a contractility proxy, preserves the geometric information while avoiding an implied but unconstrained tension scale (Deserno, 2015).

For reporting consistency, mean curvature is defined as

$$H = \frac{1}{2} \left( \frac{1}{R_1} + \frac{1}{R_2} \right), \qquad (2)$$

and is evaluated on a stated apical surface patch, where $R_1$ and $R_2$ are the principal radii of curvature (Deserno, 2015). In many confinement regimes, $H$ alone is a useful focusing metric. Some datasets stratify lamina dilution and rupture signatures by curvature sign structure, but mean curvature is used as the primary geometric descriptor in this framework (Pfeifer et al., 2022). Curvature extraction is method-dependent, so cross-study comparability benefits from reporting the three-dimensional reconstruction method, apex patch definition, and smoothing parameters, as summarized in Table 1, and this patch-scale curvature proxy cannot resolve nanoscale envelope heterogeneity including nuclear pore complex microdomains that may influence local failure susceptibility (Heemskerk and Streichan, 2015; Maćiejowski and Hatch, 2020; Pfeifer et al., 2022).

Within this framework, $\sigma_{apex}^{eff}$ is a phenomenological, curvature-weighted loading proxy rather than a constitutive membrane stress and is intended to be monotonic with local apex loading under the stated measurement operations. In rigid microfluidic constrictions, wall contact and frictional shear can contribute substantially to the local stress state. Accordingly, larger $H$ is interpreted primarily as sharper geometric load localization for comparable entry loading, but the curvature-weighted estimator fails when wall reaction forces and frictional shear dominate the failure pathway and curvature decouples from rupture initiation (Chen et al., 2018; Deserno, 2015). In those regimes, especially when $T_{NE}$ is not independently constrained, curvature is best reported as geometric metadata together with an independent loading proxy under matched boundary conditions rather than interpreting $2T_{NE}H$ as an apex-loading estimate.

A thin-shell motivation is supported by scale separation. Cryo electron tomography reports a lamina meshwork adjacent to the inner nuclear membrane with thickness on the order of $h \sim 10-20$ nm (Turgay et al., 2017). For micrometre-scale curvature radii this implies $h/R \ll 1$, which motivates treating the lamina as a thin shell in the pre-rupture regime (Pfeifer et al., 2022; Turgay et al., 2017). Curvature estimates are therefore treated as geometric metadata that identify where mechanical demand is focused rather than as a complete specification of the local stress state,
and this scale-separation motivation should not be read as a constitutive description near failure events (Turgay et al., 2017).

$T_{NE}$ is treated as workflow-dependent because the nuclear membranes are continuous with the endoplasmic reticulum and envelope folds provide a membrane reservoir that can buffer tension changes during entry, so reported values depend on structural state and observation window (Dahl et al., 2008; Goelzer et al., 2021; Lammerding et al., 2006; McKee et al., 2025). For comparability, any $T_{NE}$ estimate should be reported with assay class, boundary conditions, estimator type, and time window, as summarized in Table 1 (Davidson et al., 2019). LINC tension sensors provide local molecular-force constraints, but mapping them to an isotropic tension-like $T_{NE}$ requires additional assumptions and is best treated as complementary rather than interchangeable with aspiration- or model-derived estimates (Arsenovic et al., 2016). Matched proxy values across assays do not guarantee matched failure mechanisms because dominant contributors to envelope loading can differ by regime (Ungricht and Kutay, 2017).

Comparing geometric loading across lineages with different nuclear resistance requires normalization. The proxy is therefore divided by an entry-relevant, large-strain effective nuclear resistance scale $E_{nuc}$, a system-level stiffness measured under stated probe geometry and loading rate and not a material constant (Davidson et al., 2019). The resulting geometric coordinate is

$$ \frac{\sigma_{\text{apex}}^{\text{eff}}}{E_{\text{nuc}}} \approx \frac{2 T_{\text{NE}} H}{E_{\text{nuc}}}, \qquad (3) $$

which is used as a phenomenological strain-scale measure and, in contact-dominated regimes, is read as nondimensionalization by a resistance scale rather than as a literal local strain estimate (Deserno, 2015; Pfeifer et al., 2022). Measurement operations for $H$, $T_{NE}$, and $E_{nuc}$ are summarized in Table 1. This geometric coordinate captures how strongly mechanical demand is focused at the apex, but it is silent on whether the envelope can reorganize fast enough to accommodate the imposed deformation, which motivates introducing a kinetic axis.

## 2.2. Kinetic Axis and Nuclear Rate–Relaxation Index $Wi_{nuc}$

Geometry alone does not account for a central observation. Identical constraints can rupture some nuclei while sparing others, even within the same lineage and at matched curvature (Denais et al., 2016; Pfeifer et al., 2022). The missing variable is time, specifically whether the lamina and associated nucleoskeletal networks can reorganize fast enough to accommodate the imposed deformation. This observation motivates a second, kinetic coordinate that captures the competition between deformation rate and nuclear relaxation (Dahl et al., 2005).
Two timescale regimes must therefore be distinguished. Lamin A/C turnover, as measured by FRAP, operates on tens of minutes to hours in interphase and reflects network maintenance rather than mechanically relevant relaxation during a single constriction transit (Goldman et al., 2002; Moir et al., 2000; Shimi et al., 2008). Mechanically relevant nuclear relaxation during deformation occurs on seconds-to-minutes timescales and is often well described by broad-spectrum, multi-timescale viscoelastic behavior over the experimental window (Cao et al., 2016; Dahl et al., 2005; Davidson et al., 2019; Hertzog and Erdel, 2023; Pajerowski et al., 2007).

Accordingly, $\tau_{\text{eff}}$ is defined as an operational relaxation time, a windowed quantity $\tau_{\text{eff}}[t_1, t_2]$ extracted from a stated fit form over a stated post-peak interval aligned to constriction entry. Because broad-spectrum relaxation implies that fitted timescales depend on the analysis window, values from different windows are treated as different coordinate definitions rather than inconsistent estimates of a single constant. Cross-study comparability requires reporting $[t_1, t_2]$, the fit form, and, when power-law or stretched-exponential surrogates are used, the exponent, as specified in Table 1 (Dahl et al., 2005; Davidson et al., 2019). As a recommended starting convention, the first post-peak half-decade of time can be used as a default window and sensitivity to window choice should be reported across at least one alternative interval.

The kinetic coordinate is then defined as a nuclear rate-relaxation index

$$Wi_{\text{nuc}} = \tau_{\text{eff}}[t_1, t_2] \dot{\epsilon}, \quad (4)$$

which compares the operational relaxation timescale to an apex deformation-rate proxy $\dot{\epsilon}$. Although the symbol borrows rheology notation, $Wi_{\text{nuc}}$ is used here as a window-defined operational rate-relaxation index for a viscoelastic nucleus during constriction entry (Dahl et al., 2005). $Wi_{\text{nuc}} > 1$ is therefore read as deformation outpacing relaxation and structural reorganization within the chosen window rather than as a flow-to-elastic transition (Bird et al., 1987; Dahl et al., 2005; Kröger and Vermant, 2000).

$Wi_{\text{nuc}}$ is comparable across studies only when the strain definition, apex patch size, smoothing and derivative window, and the $\tau_{\text{eff}}[t_1, t_2]$ fit form and window are reported and aligned for comparison (Dahl et al., 2005; Davidson et al., 2019; Pfeifer et al., 2022). A strain-rate formulation is preferred over a transit-time Deborah number because transit time conflates local deformation with path length and motility history. $\dot{\epsilon}$ is preferably computed from apex areal strain on a stated patch using three-dimensional surface tracking, and defaults and fallback proxies are summarized in Table 1 (Pfeifer et al., 2022).

Experimental evidence supports $Wi_{\text{nuc}}$ as an independent organizing axis at fixed geometry. At fixed constriction geometry, interventions that slow entry dynamics or
reduce actomyosin-dependent nuclear loading are associated with reduced rupture initiation frequency in confined migration assays, which is consistent with deformation rate and deformation history modulating rupture initiation risk even when curvature is similar (Denais et al., 2016; Pfeifer et al., 2022). Osmotic perturbations shift baseline geometry and mechanics on short timescales and are therefore treated as state perturbations that may move cells along both axes unless local geometry and kinematics are co-measured.

The two coordinates are not fully independent because $E_{nuc}$ can be rate dependent and $\tau_{eff}[t_1, t_2]$ can vary with deformation geometry, so calibration is most reliable when resistance and relaxation are extracted in strain and time windows aligned to constriction entry, and in vivo studies further show that mechanical decoupling under high load can attenuate recovery and thereby alter the effective $E_{nuc}$ and $\tau_{eff}[t_1, t_2]$ inferred from deformation (Dahl et al., 2005; Davidson et al., 2019; Zuela-Sopilniak et al., 2020). This coupling is biologically meaningful because force-dependent chromatin transitions and active remodeling during entry can shift both $E_{nuc}$ and $\tau_{eff}[t_1, t_2]$ simultaneously, driving diagonal trajectories that neither coordinate alone would predict (Dahl et al., 2005; Davidson et al., 2019; Schreiner et al., 2015; Stephens et al., 2019). Within this two-axis scope, rupture initiation propensity is thus organized as a position in ($\sigma_{apex}^{eff}/E_{nuc}$, $W i_{nuc}$) space. When repair reporters are available, a persistence overlay such as the ratio $\tau_{repair}/t_{transit}$ can extend the map from initiation risk to net damage, since identical initiation events can yield different biological outcomes when repair kinetics and DNA damage responses differ across lineages and states (Denais et al., 2016; Olmos et al., 2015; Raab et al., 2016; Xia et al., 2019). The key prediction of this framework is that organizing rupture initiation risk by these two proxy coordinates should outperform constriction-size-only rules when curvature, deformation rate, and rupture timing are co-measured within the same workflow.
<caption>**Table 1. Proposed measurement approaches for framework parameters.**</caption>

Parameter ranges are conservative estimates from published studies and values depend on cell lineage, differentiation state, and loading history. FRAP-derived lamin exchange times are not included because this framework uses mechanically inferred $\tau_{eff}[t_1, t_2]$ for single-transit calibration.

<table><thead><tr><th>Parameter</th><th>Measurement approach</th><th>Key considerations</th><th>Range</th><th>Units</th><th>References</th></tr></thead><tbody><tr><td>H (apex mean curvature)</td><td>3D confocal z-stacks with surface fitting or level-set reconstruction</td><td>2D projections underestimate H; compute on 2–3 µm apex patch; report patch size and smoothing method. If 3D surface tracking is available, report apex areal strain as a parallel geometric readout since local area change captures deformation magnitude independently of curvature extraction.</td><td>0.2–1.5</td><td>µm<sup>-1</sup></td><td>(Heemskerk and Streichan, 2015; Pfeifer et al., 2022)</td></tr><tr><td>T<sub>NE</sub> (workflow-anchored effective envelope tension-like prefactor)</td><td>Micropipette aspiration, LINC tension sensors, inverse modeling</td><td>Composite membrane–lamina–LINC contribution and assay-dependent. Report assay class and boundary conditions, assumed geometry and isotropy, estimator type (global, local, inferred), and time window. Do not mix aspiration-derived, sensor-derived, and model-derived values across workflows unless equivalence is justified.</td><td>~10<sup>-2</sup>–10<sup>-1</sup>†</td><td>mN m<sup>-1</sup></td><td>(Arsenovic et al., 2016; Davidson et al., 2019; Evans and Skalak, 2018; Hochmuth, 2000)</td></tr><tr><td>E<sub>nuc</sub> (large-strain effective modulus / resistance scale)</td><td>Micropipette aspiration, AFM, micromanipulation</td><td>Rate-match to entry when possible; probe into large-strain regime; report probe geometry and modulus definition. Within this framework E<sub>nuc</sub> serves as a resistance normalizer for the geometric coordinate.</td><td>1–30</td><td>kPa</td><td>(Currey et al., 2022; Davidson et al., 2019; Stephens et al., 2017; Swift et al., 2013)</td></tr></tbody></table>

*Continued on next page*
<table><caption>Table 1 continued from previous page</caption><thead><tr><th>Parameter</th><th>Measurement approach</th><th>Key considerations</th><th>Range</th><th>Units</th><th>References</th></tr></thead><tbody><tr><td>τ<sub>eff</sub>[t<sub>1</sub>, t<sub>2</sub>] (mechanical relaxation)</td><td>Creep, stress-relaxation, or recovery after unloading</td><td>Define τ<sub>eff</sub>[t<sub>1</sub>, t<sub>2</sub>] on a reported post-peak window matched to constriction entry. Report the window and fit form, and report an exponent when using power-law or stretched-exponential surrogates because broad spectra imply no single relaxation time.</td><td>5–300</td><td>s</td><td>(Dahl et al., 2005; Davidson et al., 2019; Guilluy et al., 2014)</td></tr><tr><td>ε̇ (apex deformation rate)</td><td>3D time-lapse with optical flow or kinematic surface fitting</td><td>Local ε̇ exceeds the nuclear average and is computed on an apex patch. Report patch size, frame rate, smoothing, differentiation window, and normalization length. Peak ε̇ can vary by ~2× across reasonable choices, so report a sensitivity band. When only 1D entry traces are available, entry speed divided by a stated nuclear length scale provides a coarse proxy.</td><td>0.001–0.1</td><td>s<sup>-1</sup></td><td>(Pfeifer et al., 2022)</td></tr></tbody></table>

*Derived coordinates used in this framework.* Geometric coordinate: $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}} \approx 2 T_{\text{NE}} H/E_{\text{nuc}}$. Kinetic coordinate: $W i_{\text{nuc}} = \tau_{\text{eff}}[t_1, t_2] \dot{\epsilon}$.

† $T_{\text{NE}}$ values are method-anchored and should not be compared across aspiration-derived, sensor-derived, and model-derived estimates.
## 2.3. Cytoskeletal Force Transmission and Proposed Routing to Nuclear Axes

With the geometric and kinetic coordinates in hand, a natural next question is how cells shift their operating point within this two-axis space. LINC complexes and perinuclear cytoskeletal networks are primary candidates because they provide direct mechanical connectivity between cytoskeletal force generation and nuclear deformation. This review proposes that LINC composition and perinuclear architecture function as force-routing modules that shift operating points by altering tension delivery to the envelope, shaping curvature at the leading apex, and changing the timescale over which stresses are redistributed around the nucleus (Davidson et al., 2020; Patteson et al., 2019; Vahabikashi et al., 2022).

Within this framework, isoform-specific axis routing is treated as an axis-biased hypothesis with measurable coupling rather than an axis-specific mapping, since LINC assemblies can distribute forces across multiple cytoskeletal systems and can therefore shift operating points along both coordinates simultaneously (Chang et al., 2015; Starr and Fridolfsson, 2010; Vahabikashi et al., 2022). LINC complex composition is dynamically regulated across tissues and contexts (King, 2023), which supports treating LINC assemblies as tunable force-transmission modules, and this routing assignment is the framework's highest-risk mechanistic prediction, so different nesprin linkages may nonetheless bias which coordinate is most affected.

Nesprin-2G is a candidate modulator of front-localized force delivery during constriction entry, increasing the effective loading prefactor $T_{NE}$ within a workflow-defined estimator for $\sigma_{apex}^{\text{eff}}$ and biasing deformation toward higher $\sigma_{apex}^{\text{eff}}/E_{\text{nuc}}$ under matched kinematics. Nesprin-2G polarizes toward the leading nuclear edge in confined migration and supports actomyosin-dependent coupling to the nuclear envelope (Davidson et al., 2020; Padmakumar et al., 2005). Molecular tension sensor measurements report pN-scale forces across nesprin-based constructs under actomyosin-dependent loading, which supports using an effective tension scale that includes LINC-transmitted contributions (Arsenovic et al., 2016). Actomyosin contractility is dynamically regulated during transit with potential surges at constriction entry, so $T_{NE}$ should be interpreted as a workflow-anchored effective prefactor over a stated time window rather than as an assay-invariant material parameter depending on the measurement context. Reduced actomyosin contractility can decrease the effective loading prefactor or reduce independent loading readouts such as entry force or traction in workflows that do not estimate $T_{NE}$, and it can shift $\sigma_{apex}^{\text{eff}}/E_{\text{nuc}}$ leftward under matched kinematics (Davidson et al., 2020).

Whereas nesprin-2G couples primarily to actomyosin, nesprin-3 can couple the nuclear envelope to intermediate filaments through plectin, which provides a structural route for perinuclear intermediate filament networks to redistribute loading
(Ketema et al., 2013; Wilhelmsen et al., 2005). Vimentin forms a perinuclear cage, and vimentin loss increases rupture and DNA damage during confined migration with rescue upon re-expression, consistent with a buffering role potentially including kinetic contributions (Patteson et al., 2019). At the materials level, vimentin networks exhibit nonlinear viscoelastic responses with timescale dependence, which supports the plausibility of rate-sensitive buffering that can alter the effective re-modeling burden during rapid deformation (Aufderhorst-Roberts and Koenderink, 2019; Charrier and Janmey, 2016; Pogoda and Janmey, 2023). A candidate mechanism is load redistribution that reduces peak local deformation-rate excursions at the nuclear surface, contributing to lower $W_i_{nuc}$ under matched geometry, although direct quantitative tests in confined migration remain limited (Lorenz and Köster, 2022; Patteson et al., 2019). Nesprin-4 links the nuclear envelope to kinesin-1 and can modulate entry kinematics through microtubule-dependent nuclear positioning in cell types where it is expressed, although its axis-level impact on rupture initiation risk remains insufficiently constrained in confinement workflows (Lele et al., 2018; Roux et al., 2009).

This review therefore treats rupture initiation risk during constriction entry as jointly dependent on the geometric coordinate $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$ and the kinetic coordinate $W_i_{\text{nuc}}$, and Figure 1 illustrates how cell types and interventions may map onto this proposed two-axis framework (Deserno, 2015; Kalukula et al., 2022).

# 3. Current Evidence and Field Reconciliation

The utility of this framework rests on two empirical tests. First, diverse cell types should map reproducibly onto the same geometric and kinetic space. Second, perturbations should shift operating points in axis-consistent directions across platforms. This section evaluates current mapping constraints and within-workflow evidence for partial axis separability, proposes reconciliation hypotheses for apparent cross-platform contradictions, and outlines falsifiable perturbation tests designed to stress-test the axis mapping.

## 3.1. Cell-Type Positioning and Mapping Constraints

Different lineages are expected to occupy characteristic regions of the two-axis space because lamin composition, chromatin state, and perinuclear cytoskeletal architecture vary systematically across cell types (Buxboim et al., 2010; Kalukula et al., 2022). However, the placements in Figure 1 are best read as inferred operating tendencies rather than calibrated coordinates, because co-measurement of all framework parameters within a single workflow remains rare. Most published datasets
cannot yet be mapped directly into ($\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$, $W_i_{\text{nuc}}$) space because key geometric and kinetic quantities are seldom co-measured under matched boundary conditions (Kalukula et al., 2022; McGregor et al., 2016).

Figure 2 exposes this gap across major assay classes. The regime envelopes in Figure 2A are conservative operating windows obtained by propagating literature-reported parameter ranges through the framework coordinates, so they should be read as assay-class envelopes rather than as single-study placements. Solid envelopes indicate regimes with more directly constrained coordinate inputs within the cited workflow, whereas hatched envelopes indicate assumption-dependent placement because one or more coordinate inputs are not co-measured. The regime envelopes show that pressure-controlled aspiration, rigid micro-constrictions, and compliant confinement devices sample partially overlapping but distinct regions of the two-axis space, so cross-platform placement comparisons embed boundary-condition assumptions that are rarely stated or tested.

The reporting audit in Figure 2B indicates that no single assay class routinely co-reports all five Table 1 parameters, with apex curvature and local deformation rate most often absent or only derivable under additional assumptions. Together these panels identify where coordinate extraction is currently most constrained and where reporting improvements would most directly enable framework calibration. A minimum viable dataset for two-axis placement requires a time-aligned rupture read-out together with the Table 1 quantities, since datasets that match in constriction size can still separate in curvature and deformation-rate history and therefore differ in operating region (Baird et al., 2026; Chu et al., 2025; Elacqua et al., 2018).

With these reporting constraints in view, lineage-specific evidence can be interpreted as shifting inferred operating tendencies within the two-axis landscape in Figure 1 rather than as providing definitive coordinate placement. Immune lineages provide instructive corner cases for this qualitative mapping. Interstitial dendritic-cell migration often proceeds in low-adhesion modes with limited measured nuclear damage, which is consistent with relatively low effective loading and moderate deformation rates in those workflows, placing operating tendencies toward lower kinetic coordinate values within this framework when entry remains slow (Alraies et al., 2024; Renkawitz et al., 2019). Neutrophils exhibit low or absent lamin A/C together with lobulated nuclear architecture, so by definition, for comparable apex loading the geometric coordinate $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$ increases through reduced nuclear resistance, although lobulation may redistribute curvature across multiple lobes and reduce peak geometric stress focusing relative to a single-apex geometry (Lammerding et al., 2006; Ng et al., 2019; Thiam et al., 2016). Perinuclear intermediate filament buffering remains a plausible kinetic contributor in these contexts, although curvature-resolved rupture
measurements in immune lineages remain limited (Patteson et al., 2019). Immune-
lineage operating tendencies are therefore expected to depend strongly on whether
a given assay constrains local $\dot{\epsilon}$ and $\tau_{\text{eff}}[t_1, t_2]$ in the entry window rather than on
constriction size alone.

Mesenchymal cancer models illustrate a contrasting regime in which inferred op-
erating tendencies can plausibly span broad regions of Figure 1. In rigid confinement
assays these models often show frequent rupture together with heterogeneous nuclear
properties, which is consistent with dispersion along both the geometric coordinate
$\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$ and the kinetic coordinate $W i_{\text{nuc}}$ rather than clustering at a single oper-
ating point (Baird et al., 2026; Chu et al., 2025; Denais et al., 2016; Vashisth et al.,
2021). Within a given model, increased lamin A/C is expected to increase $E_{\text{nuc}}$ and
shift $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$ leftward under matched loading, while remodeling dynamics and en-
try history can shift $W i_{\text{nuc}}$ independently (Harada et al., 2014; Vahabikashi et al.,
2022). Whether these tendencies form stable subpopulations or drift with mechani-
cal history remains a priority for single-cell calibration studies (Stöberl et al., 2024).
This heterogeneity motivates within-workflow mapping using the Table 1 measure-
ment operations rather than interpreting Figure 1 placements as universal lineage
coordinates.

## 3.2. *Experimental Evidence for Partial Axis Separability*

A testable prediction of this framework is that geometric stress focusing and
rate-limited remodeling are partially separable in some confinement regimes, mean-
ing that manipulating curvature at matched deformation rate or manipulating de-
formation rate at matched geometry should produce dominant main effects along
the corresponding axis. Direct within-workflow tests that jointly constrain curvature
and local deformation rate remain uncommon, and inference is further limited by
pleiotropy, since reduced contractility can decrease rupture incidence while simul-
taneously altering force transmission pathways, nuclear shape evolution, and entry
kinematics (Denais et al., 2016; Pfeifer et al., 2022). The reported curvature-rate
partition of lamina dilution aligns with this prediction. Lamin B1 dilution is consis-
tent with a geometry-dominant signature, while lamin A/C dilution is consistent with
a rate-sensitive signature most evident in fast, high-curvature entry, as schematized
in Figure 3 (Pfeifer et al., 2022). The discussion below focuses on mechanistic plau-
sibility, interpretation caveats, and what additional experiments would be needed to
test generalizability beyond the originating workflow.

This curvature-rate partition is mechanistically plausible because lamin A/C con-
tributes strongly to nuclear mechanical resistance in deformation assays that probe
large shape changes (Lammerding et al., 2006; Vahabikashi et al., 2022). Lamin A/C
abundance scales with tissue stiffness and has been linked to time-dependent nuclear
mechanical behavior and migration through confinement, consistent with deforma-
tion speed and history shaping nuclear responses even when nominal geometry is
similar (Harada et al., 2014; Swift et al., 2013). Measurements across strain regimes
further indicate that chromatin dominates nuclear mechanics at small extensions,
whereas lamin A/C contributes more strongly as deformation increases, motivating
the use of a large-strain resistance scale as the normalizer in this framework (Hertzog
and Erdel, 2023; Stephens et al., 2017). Curvature itself is workflow-defined, since
some datasets emphasize Gaussian curvature whereas others emphasize mean cur-
vature, so cross-platform comparisons require reporting the curvature definition and
extraction method used.

These lamina signatures warrant cautious interpretation because fluorescence di-
lution can arise from local membrane area expansion and from segmentation or nor-
malization choices, and may not report remodeling alone (Pfeifer et al., 2022). Bio-
chemical differences also matter because lamin B1 is farnesylated and more tightly
membrane-associated, whereas lamin A/C is comparatively dynamic, so similar in-
tensity patterns need not imply identical mechanics (Moir et al., 2000; Nmezi et al.,
2019; Shimi et al., 2008). Axis separability therefore remains a working hypothesis.
Strengthening it would require factorial curvature-by-deformation-rate experiments
across additional lineages and platforms, quantifying both main effects and interac-
tion strength under a fixed analysis pipeline.

LINC assemblies provide a plausible source of coupling between the two axes
because they are modular and differentially anchored, so altering SUN-KASH com-
position can re-route how cytoskeletal loads reach the lamina (Chang et al., 2015),
and the underlying lamin isoform composition modulates the strength of LINC-
dependent nucleocytoskeletal coupling (Vahabikashi et al., 2022). Because effective
envelope loading is composite, LINC perturbations can shift both coordinates in the
same experiment, making diagonal shifts likely in some regimes (Arsenovic et al.,
2016). Disrupting SUN-nesprin coupling reduces nucleocytoskeletal force transmis-
sion and motivates targeted LINC perturbations as practical levers for separability
tests when curvature and deformation-rate proxies are co-measured (Lombardi et al.,
2011). Regulated SUN2 turnover provides an additional route for tuning LINC con-
nectivity in time-resolved perturbation designs (Krshnan et al., 2022).

3.3. Reconciling Apparent Contradictions Across Platforms

Apparent contradictions across platforms may reflect that different assays sam-
ple different combinations of curvature-localized loading and deformation-rate history
within the same geometric-kinetic space, even when nominal constriction sizes are
matched. Three reconciliation hypotheses are proposed below together with obser-
vations that would challenge each one.

*Reconciliation 1. Steep size dependence may reflect heterogeneity in nuclear resistance and relaxation.* Rupture incidence can rise steeply as confinement tightens in representative microfluidic constriction settings, including an approximately exponential dependence on constriction size in a canonical system (Denais et al., 2016). In this framework, the population-level steepness depends on the breadth of single-cell distributions in resistance and relaxation because narrow distributions can yield sharp transitions while broad distributions can yield smoother sigmoids as subpopulations cross risk regions at different operating points. Per-cell resistance and relaxation proxies needed to test this hypothesis can be obtained from time-dependent deformation fits in a microfluidic micropipette format (Davidson et al., 2019). This reconciliation is challenged if broad single-cell distributions in those proxies still yield uniformly sharp rupture transitions under tightly matched deformation histories.

*Reconciliation 2. Memory-like effects may be thresholded and compliance-dependent.* Confinement-associated chromatin changes can persist for days after confined migration through rigid constrictions in a reported system (Hsia et al., 2022; Mukherjee et al., 2020). In a compliant three-dimensional channel system, nuclear deformation was reported to be largely reversible and nuclear stiffness adaptation was not detected on the assay timescale (Stöberl et al., 2024). A proposed reconciliation is a thresholded remodeling hypothesis in which sufficiently severe deformation can trigger calcium-linked chromatin remodeling and nuclear softening that can reset or persist depending on context (Nava et al., 2020; Stephens et al., 2019). This reconciliation is challenged if persistence and drift remain indistinguishable across compliance conditions when geometry and deformation history are matched.

*Reconciliation 3. Cytoskeletal buffering may decouple rupture from bulk stiffness proxies.* A proposed reconciliation is that intermediate-filament-rich perinuclear architecture may redistribute load in a way that dampens local nuclear-surface strain-rate peaks without proportionate changes in bulk stiffness proxies. This reconciliation is challenged if local nuclear-surface strain-rate statistics remain unchanged while rupture-linked readouts shift strongly within the same workflow.

Taken together, these reconciliations suggest that disagreements often reflect
unreported differences in operating region, heterogeneity, deformation history, and
boundary compliance. This motivates the reporting targets summarized in Table 1
and the perturbation tests in the next section.
### 3.4. Testable Predictions

Each prediction below pairs a targeted perturbation with the Table 1 measurement suite to test whether operating points shift in axis-consistent directions. The sharpest stress test is axis-inappropriate motion under matched deformation history. If curvature and deformation-rate trajectories are held fixed, a perturbation expected to mainly alter loading should not appear to act mainly through the rate-relaxation coordinate, and the reverse holds when deformation rate is the intended target.

**Reference falsification designs.** Two designs provide direct single-axis tests. In a fixed-geometry design, identical constrictions can be driven at different entry speeds by tuning driving pressure or chemokinetic conditions with matched curvature trajectories, and in this framework, rupture initiation risk increases with $W_i_{nuc}$ at a similar geometric coordinate. In a matched-kinematics design, entrances with different radii can impose different apex curvature for the same minimum cross-section while entry kinematics are matched, and in this framework, rupture initiation risk increases with the geometric coordinate at fixed $W_i_{nuc}$. Because protrusion growth can be geometry-sensitive in confined migration, entry dynamics may co-vary with geometry in some settings (Flommersfeld et al., 2024). If either design fails to produce axis-consistent ordering under the Table 1 measurements, the two-axis decomposition is incomplete for that lineage and regime.

**LINC perturbation as a geometric-axis-biased test.** Increased nesprin-2G-mediated coupling is expected to increase effective apex loading during entry and shift operating points toward higher $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$ with increased rupture initiation risk under similar kinematics (Davidson et al., 2020). This interpretation is challenged if rupture initiation changes strongly while curvature-localized loading proxies remain unchanged, or if the dominant shift occurs in proxies consistent with a change in $W_i_{\text{nuc}}$ under matched geometry.

**Intermediate filament perturbation as a kinetic-axis-biased test in fast regimes.** If intermediate filaments primarily buffer entry dynamics, vimentin depletion is expected to increase peak nuclear-surface strain rates and shift operating points upward along $W_i_{\text{nuc}}$ under matched constriction geometry (Patteson et al., 2019). This interpretation is challenged if peak local strain-rate statistics remain unchanged while rupture-linked readouts diverge strongly within the same workflow.

**Axis separability as a null hypothesis to test.** Curvature-linked lamin B1 dilution and deformation-rate-dependent lamin A/C dilution motivate modeling curvature and deformation rate as main effects while allowing an interaction term rather than
assuming separability *a priori* (Pfeifer et al., 2022). This interpretation is challenged if curvature and rate terms do not improve rupture-risk ordering beyond constriction size alone in workflows that co-measure curvature, local strain rate, and rupture timing.

*Lamin A/C modulation as a diagonal-shift test.* Increasing lamin A/C is expected to reduce $\sigma_{apex}^{eff}/E_{nuc}$ through higher $E_{nuc}$ while potentially increasing $W_i_{nuc}$ through slower effective relaxation, so sign reversals in rupture initiation risk are expected across assays that occupy different regions of the map (Chen et al., 2018; Davidson et al., 2019; Harada et al., 2014; Lammerding et al., 2006; Swift et al., 2013; Vahabikashi et al., 2022). This interpretation is challenged if lamin A/C shifts only one coordinate consistently across regimes while leaving the other unchanged when both are measured in entry-matched windows.

*Serial confinement as a memory test.* Severe first-pass confinement is expected to shift baseline resistance or relaxation and alter second-pass rupture initiation risk even at matched geometry (Hsia et al., 2022; Nava et al., 2020). Evidence that constricted or pore migration can be followed by DNA damage and downstream state changes supports treating repeated passage as a candidate driver of operating-point drift that depends on both mechanics and repair capacity (Irianto et al., 2017; Xia et al., 2019). This interpretation is challenged if no persistence markers and no detectable drift in $E_{nuc}$ or $\tau_{eff}$ occur under conditions where persistent chromatin-state change is expected (Hsia et al., 2022).

# 4. Translational Implications

Can the two-axis logic generate useful hypotheses beyond biophysics, in contexts such as cancer metastasis, immune trafficking, and fibrosis? This section argues that it can, provided three sequential validation gates are satisfied. Transient nuclear envelope rupture of the primary nucleus during confined migration has been documented in several systems and can cause DNA damage and nuclear stress responses, with downstream consequences shaped by repair and stress-response programs (Denais et al., 2016; Hatch, 2018; Kalukula et al., 2022; Raab et al., 2016). In parallel, micronuclear envelope rupture can provide a route for cytosolic cGAS access to self-DNA and activation of cGAS-STING signaling in some settings (Li and Chen, 2018; Mackenzie et al., 2017).

A practical translational use-case is within-workflow stratification that goes beyond lamin-first stiffness heuristics. Two patient-derived tumor lines with similar lamin A/C abundance can appear mechanically similar by lamin-first stratification
yet differ in curvature generation at entry or in deformation rate relative to relaxation, and would occupy different regions of the two-axis map under matched geometry (Pfeifer et al., 2022). Lineage-specific differences in lamin levels, chromatin organization, and nucleo-cytoskeletal coupling also bias baseline nuclear deformability and stability across cancer, immune, and fibroblast contexts (Kalukula et al., 2022). Each disease-facing hypothesis below is conditional on three gates:

* **Gate A** asks whether rupture initiation occurs at measurable frequency under disease-relevant confinement.

* **Gate B** asks whether both coordinates can be estimated within a single workflow using co-measured geometry and kinematics.

* **Gate C** asks whether coordinate position improves rupture initiation risk ordering beyond constriction size alone under matched boundary conditions.

A minimal platform map aligned to Gates A–C is summarized in Table 2.

## 4.1. *Cancer Metastasis*

Metastatic dissemination requires tumor cells to migrate through dense three-dimensional environments, from basement-membrane openings to stromal collagen networks and endothelial barriers (Davidson et al., 2014; McGregor et al., 2016; Paul et al., 2017; Wolf et al., 2013). In each of these settings the nucleus can become the rate-limiting element for transit. In sufficiently tight confinement, primary-nucleus envelope rupture can occur during nuclear squeezing and can be accompanied by chromatin herniation and DNA damage, with outcomes depending on rapid repair and stress responses (Baird et al., 2026; Chow et al., 2012; Chu et al., 2025; Denais et al., 2016; Gauthier et al., 2021; Irianto et al., 2016; Raab et al., 2016; Xia et al., 2019). Rather than seeking a universal rupture threshold across tumor types, the framework motivates stratifying invasion vulnerabilities by whether rupture initiation risk is dominated by geometric stress focusing or by rate-limited remodeling. This motivation is reinforced by evidence that lamin-B expression scales with tumor growth across cancer types and often predicts poor prognosis (Vashisth et al., 2021), indicating that nuclear envelope composition varies systematically in cancer in ways that would shift baseline nuclear resistance and therefore operating-point position across the two-axis map.
<table><caption>Table 2. Minimal platform map for applying the two-axis framework across Gates A–C.</caption><thead><tr><td>Platform class (work-flow role)</td><td>Gates en-abled</td><td>What it can supply</td><td>Key caveat and minimal mitigation</td><td>References</td></tr></thead><tbody><tr><td>Rigid microconstrictions plus live imaging (core rupture assay)</td><td>A, C</td><td>Rupture reporters, entry kinematics for ˙ε proxies, curvature metrics for the geometric axis when 3D imaging is available</td><td>2D imaging underestimates curvature. Volumetric imaging is strongly recommended when curvature is used and apex patch definition should be reported</td><td>(Denais et al., 2016; Pfeifer et al., 2022)</td></tr><tr><td>Compliant 3D confinement devices (tissue-like generalization and memory)</td><td>A, C under compliant boundaries</td><td>Rupture and kinematics under tunable compliance, repeated passages for operating-point drift and recovery</td><td>Local geometry and compliance vary. Co-report local confinement geometry or calibrated compliance with local kinematics</td><td>(Stöberl et al., 2024)</td></tr><tr><td>Force-probe calibration, microfluidic micropipette aspiration plus AFM with imaging (parameter anchoring)</td><td>B parameter anchoring</td><td>E<sub>nuc</sub>-like resistance and time dependence. Aspiration supports creep-based τ<sub>eff</sub>. AFM plus imaging supports force-shape and constituent dependence</td><td>Fit form and window dependence matter. Report probe geometry, strain window, and fit window or exponent. This class anchors E<sub>nuc</sub> and τ<sub>eff</sub> but does not provide confinement geometry or rupture readouts</td><td>(Davidson et al., 2019; Hobson et al., 2020)</td></tr><tr><td>High-throughput mechanophenotyping microfluidics (triage)</td><td>Pre-gate screening</td><td>Size-deformability distributions across patient-derived samples</td><td>Not rupture-specific and boundary conditions differ from constriction entry. Use to prioritize samples for downstream rupture-capable confinement assays</td><td>(Tse et al., 2013)</td></tr></tbody></table>

*Workflow note.* No single platform class enables all gates. A staged validation workflow could combine triage to identify candidate samples, parameter anchoring to obtain *E*<sub>nuc</sub> and τ<sub>eff</sub>[t<sub>1</sub>, t<sub>2</sub>], and a rupture-capable confinement assay to test Gate C under matched geometry and kinematics, with compliant devices prioritized when tissue-like boundaries or memory effects are central to the question (Suh et al., 2024).
A candidate geometry-dominant cancer phenotype is enhanced LINC-dependent front loading, which is expected to shift operating points toward higher $\sigma_{apex}^{eff}/E_{nuc}$ under matched kinematics and could increase rupture initiation risk in patient-derived tumor cells where this coupling is prominent (Davidson et al., 2020). This supports testing whether nesprin-2G front-to-back polarization correlates with rupture initiation frequency and DNA damage under repeated confinement in a single calibrated workflow (Denais et al., 2016). Protease-dependent matrix remodeling can also enlarge effective paths and reduce constriction severity during invasion, which is expected to reduce geometric stress focusing by altering curvature and contact geometry (Friedl and Wolf, 2003; Wolf et al., 2013).

A complementary, proposed kinetic-dominant phenotype involves buffering of rapid deformation during entry. This buffering module motivates a kinetic-dominant cancer phenotype in which vimentin-rich subpopulations may blunt rapid apex deformation, reducing peak nuclear-surface strain-rate excursions and thereby lowering $Wi_{nuc}$ at comparable geometry (Patteson et al., 2019). Lamin A/C-dependent trade-offs between pore transit and survival further support regime dependence, since increased nuclear resistance can impede passage while also reducing mechanical fragility in some constraints (Harada et al., 2014; Weiss et al., 2022). Conversely, interventions that increase nuclear robustness to reduce rupture-associated damage could impair transit efficiency, so any axis-targeted strategy must be evaluated against both rupture initiation and passage rate within the same workflow. These predictions are most directly testable in patient-derived invasion workflows where rupture reporters are paired with curvature and kinematic proxy extraction in the same assay.

## 4.2. *Immune Cell Trafficking and Adoptive Therapy*

Immune surveillance requires leukocytes to repeatedly navigate tight three-dimensional spaces. Nuclear positioning can bias amoeboid migration toward paths of least resistance, suggesting that confinement is frequent and actively managed rather than passively endured (Lomakin et al., 2020; Renkawitz et al., 2019). *In vivo* evidence further suggests that immune cells can adapt to confined environments by tuning nuclear plasticity, which motivates treating nuclear architecture as an adjustable mechanical constraint in immune trafficking models (Alraies et al., 2024; Karling and Weavers, 2025). Adoptive cell therapies, including CAR T, in solid tumors add a translational constraint because engineered cells must infiltrate stroma-rich tissue while maintaining persistence and effector function in the tumor microenvironment (Martinez and Moon, 2019; Patel et al., 2022; Yong et al., 2017).

In this setting, the two-axis framing suggests that nuclear failure risk during transit may be geometry-dominant when stress is sharply focused at a high-curvature
entry apex, or kinetic-dominant when rapid squeezing outpaces effective remodeling. Curvature-linked lamina dilution together with strain-rate-dependent lamin A/C responses provides mechanistic motivation for treating geometry and rate as distinguishable contributors within a single workflow. Translational use is most actionable once rupture initiation is detectable in the disease-relevant confinement model and both curvature and entry kinematics are quantified in the same assay. Deformation-history matching is particularly relevant in this context given that nuclei can exhibit time-scale-dependent, power-law-like rheology (Dahl et al., 2005).

A proposed kinetic-axis hypothesis is that reducing extreme squeezing episodes or buffering rapid deformation would lower rupture initiation risk when rate-limited remodeling dominates. One candidate route is to enhance path selection and persistence decisions so cells avoid committing to constrictions that impose high instantaneous nuclear strain rates, which is consistent with nucleus-guided path choice in amoeboid migration (Renkawitz et al., 2019). Confinement-dependent energetic costs also bias migration path choice during decision-making (Zanotelli et al., 2019). A second candidate route involves intermediate filament buffering, since load redistribution during rapid entry can reduce peak deformation-rate excursions and lower the rate-relaxation burden in therapeutic immune cells navigating tight stroma (Patteson et al., 2019). A third candidate route involves short-timescale chromatin adaptation, since calcium-dependent softening and recovery could transiently expand effective remodeling capacity during rapid squeezing episodes (Nava et al., 2020).

Mechanical preconditioning is a second, more speculative route that is most sensible as a testable engineering hypothesis rather than a recommended intervention. Chromatin persistence after confinement suggests that controlled *ex vivo* constriction histories could shift baseline operating points in therapeutic immune cells before adoptive transfer (Hsia et al., 2022). Lineage-specific positioning is expected to matter because neutrophils combine lobulated architecture with distinct lamin programs, whereas dendritic cells deploy Arp2/3-dependent perinuclear actin networks during constriction transit (Kalukula et al., 2022; Karling and Weavers, 2025; Thiam et al., 2016). Profiling candidate therapeutic lineages under matched confinement regimes is therefore expected to be more informative than cross-lineage extrapolation.

### 4.3. Fibrosis, Tissue Remodeling, and Validation Infrastructure

Progressive fibrosis involves fibroblasts operating in collagen-rich matrices that stiffen over time, and mechanosensing can reinforce activation and extracellular matrix remodeling through positive-feedback loops (Buxboim et al., 2010; Tschumperlin et al., 2018; Wynn and Ramalingam, 2012). Transient nuclear envelope rupture can occur during migration through sufficiently confining fibrillar collagen in reported sys-
tems, but whether activated, tissue-resident fibroblasts experience measurable rupture initiation during fibrotic matrix navigation *in vivo*, and with what consequences, remains unresolved (Denais et al., 2016). Accordingly, the immediate contribution of the two-axis framing to fibrosis is defining an applicability boundary and a measurement plan rather than advancing an intervention claim. Curvature-localized loading and deformation-rate history remain plausible but not yet calibrated determinants in fibrotic-like workflows.

If rupture initiation is first established under fibrosis-relevant confinement and if curvature and entry kinematics can be quantified together in a single workflow, then matrix and motility perturbations can be interpreted as candidate shifts in geometric stress focusing or rate-limited remodeling rather than as direct therapeutic levers. Collagen crosslinking modulation provides a practical test case. LOX-family activity alters collagen network mechanics and LOX targeting can reduce stiffness in preclinical fibrosis models, so crosslinking perturbations can be evaluated while co-measuring curvature, deformation rate, and rupture reporters (Levental et al., 2009; Tschumperlin et al., 2018). Chromatin persistence after confinement further motivates serial-passage designs in fibrotic-like confinement once baseline rupture initiation is established (Hsia et al., 2022).

Translational validation is framed here as an infrastructure challenge because no single platform simultaneously provides throughput, disease-relevant boundary conditions, and complete coordinate extraction. Accordingly, platform selection is most defensible when it follows the staged logic summarized in Table 2, meaning triage, rupture-capable confinement, and force-probe calibration, with compliant devices prioritized when memory and tissue-like boundaries are central to the question (Davidson et al., 2019; Denais et al., 2016; Stöberl et al., 2024; Tse et al., 2013). Platform choice should therefore be matched to the disease question and the specific coordinates required. More broadly, progress in nuclear mechanobiology will depend on workflows that combine live-cell imaging at high spatiotemporal resolution with genetic perturbation and precise mechanical manipulation (Kalukula et al., 2022).

# 5. Conclusions and Future Directions

In this review, we synthesized observations on nuclear deformation during confined migration into a two-axis framework in which geometric stress focusing and rate-limited remodeling act as distinguishable and interacting contributors to nuclear envelope rupture initiation risk. The framework is implemented using two workflow-defined proxy coordinates ($\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$, $W i_{\text{nuc}}$), together with a regime map, a minimal reporting checklist, and falsifiable perturbation tests. These elements are
intended to support within-workflow ranking and cross-platform calibration rather
than universal thresholds. The framework is most useful when diverse lineages oc-
cupy reproducible regions of operating space and when perturbations shift operating
points in axis-consistent directions under co-measured geometry and kinematics.

5.1. *Framework Deliverables and Validation Priorities*

Three deliverables are needed to advance this framework from a conceptual or-
ganizer to a quantitatively calibrated tool. First, a minimum dataset is required
that includes time-aligned rupture readouts together with co-measured geometry
and kinematics sufficient to compute both coordinates under the Table 1 definitions.

Second, a shared falsification battery is required to test whether axis mappings
are mechanistically interpretable rather than descriptive. The strongest tests use
perturbations expected to primarily change force transmission, buffering, or nuclear
resistance while keeping geometry extraction and kinematic analysis fixed. Repeated
axis-inappropriate shifts under controlled entry histories would indicate that addi-
tional variables dominate in that regime.

Third, reporting standards are essential so that cross-study comparison does not
collapse to constriction size alone. Table 1 defines a minimal reporting unit for
geometry and kinetics, and Table 2 maps how screening, rupture-capable confinement
assays, and force-probe calibration can be combined without mixing non-equivalent
quantities across platforms.

5.2. *Scope Limits, Coupling, and an Implementation Outlook*

This framework is deliberately phenomenological and it trades mechanistic com-
pleteness for cross-platform comparability. Coordinate coupling is expected because
lamin composition, chromatin state, and nucleo-cytoskeletal force transmission can
jointly affect both resistance and remodeling, so separability is a tested property
rather than an assumption. The geometric proxy is least interpretable in regimes
where wall contact, frictional shear, folding, or spatial envelope defects decouple
curvature from the dominant failure pathway, and it should not be interpreted as a
constitutive description at the rupture event itself. The kinetic coordinate is only
comparable when relaxation is defined as an explicitly windowed operational quantity
and reported with its fit form and window.

Rupture initiation risk is not equivalent to net biological outcome. Nuclear en-
velope rupture can be followed by ESCRT-associated repair, and identical loading
histories can yield different net damage when repair kinetics or DNA damage re-
sponses differ across lineages (Denais et al., 2016; Raab et al., 2016; Ventimiglia and
Martin-Serrano, 2016). The coordinate map therefore organizes rupture initiation
risk rather than predicting fate, and studies connecting operating points to func-
tional outcomes should incorporate repair and damage reporters alongside initiation
tracking.

Within these limits, a staged implementation path is practical. Screening can identify conditions where rupture occurs and where entry kinematics differ. Calibration assays can then anchor resistance and relaxation in entry-relevant windows, and confinement workflows that co-measure curvature and strain-rate proxies can test whether axis-based stratification outperforms geometry-only rules. More broadly, the framework addresses a question that extends beyond nuclear mechanics: under what conditions does the mechanical context of a deformation event, including its geometry and deformation kinetics, shape biological outcome as much as the molecular composition of the structure being deformed? The two-axis framing developed here is not a universal predictor of nuclear failure, but it offers a concrete and falsifiable starting point for addressing this question across cell types, confinement regimes, and disease contexts.

Declarations

Data Availability

No new data were generated or analyzed in this review. All information discussed
is available in the cited literature.

Disclosure Statement

The author declares no competing interests and no financial or non-financial
relationships that could be perceived as influencing the content of this review.

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<figure><img src="image_2.png" /><figcaption>**Figure 1.** Curvature-rate operating map for nuclear envelope (NE) rupture initiation (phenomenological). Horizontal axis (log scale) is the geometric coordinate $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$, where $\sigma_{\text{apex}}^{\text{eff}}$ is a curvature-associated apex loading proxy (not a constitutive stress) and $E_{\text{nuc}}$ is a large-strain effective nuclear resistance scale. Vertical axis (log scale) is the kinetic coordinate $W i_{\text{nuc}}$, a windowed rate-relaxation index combining an operational relaxation time $\tau_{\text{eff}}[t_1, t_2]$ with an apex deformation-rate proxy $\dot{\varepsilon}$. Background shading indicates qualitative low/intermediate/high rupture-initiation propensity (green/yellow/red); regime boundaries are illustrative anchors for lineage-and platform-specific calibration and are not universal thresholds. Filled markers show schematic operating tendencies (not measured coordinates); the dashed ellipse denotes expected heterogeneity within mesenchymal cancer populations. Arrows schematize predicted shifts: reduced actomyosin contractility lowers $\sigma_{\text{apex}}^{\text{eff}}/E_{\text{nuc}}$ (leftward), intermediate-filament (IF) reinforcement lowers $W i_{\text{nuc}}$ (downward), and lamin A/C upregulation yields a stiffness-kinetics trade-off (schematic slope -1). Symbols ($*$, $\dagger$) denote literature-inferred or assumption-dependent annotations rather than a single-workflow calibration.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Assay operating envelopes and reporting audit for mapping nuclear confinement experiments onto geometric-kinetic space (schematic synthesis). (A) Assay-class regime envelopes plotted in $\sigma_{apex}^{eff}/E_{nuc}$ versus $W i_{nuc}$ (both axes log scale; coordinates as defined in Sections 2.1–2.2). For pressure-controlled aspiration, $\sigma_{apex}^{eff} \approx \Delta P$. For migration/constriction assays, $\sigma_{apex}^{eff} \approx 2T_{NE} H$ is used only when an effective envelope tension-like prefactor $T_{NE}$ is co-estimated under stated assumptions. Boxes are conservative envelopes propagated from literature-reported parameter ranges and workflow assumptions; they are not rupture thresholds and do not represent single-cell coordinates. Solid versus hatched boxes indicate mappings that are typically co-constrained/derivable versus more assumption-dependent due to incomplete co-reporting. The dashed line marks $W i_{nuc} = 1$ (rate-relaxation parity). (B) Reporting audit heatmap coding each assay as R (reported), D (derivable), or N (not available) for $H$, $\dot{\epsilon}$, $\tau_{eff}$, $E_{nuc}$, loading proxy, and rupture readout; colored squares link rows to the corresponding assay in (A), with solid versus hatched styling mirroring calibration strength.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Lamina dilution “signatures” aligned with the geometric and kinetic axes (schematic, based on Pfeifer et al. 2022). (A) Normalized lamin B1 intensity versus mean curvature *H* (linear axis) for low/medium/high deformation-rate conditions *ε*; near-overlap of curves summarizes a geometry-dominant (curvature-linked) trend with comparatively weak rate sensitivity. (B) Normalized lamin A/C intensity versus *ε* (log scale) for low/medium/high curvature regimes; curve separation with *H* summarizes a kinetic-dominant response in which higher-curvature conditions show earlier onset and larger magnitude of lamin A/C dilution as deformation rate increases. Curves are schematic summaries of reported qualitative dependencies (not fits to a single primary dataset) and are intended to motivate partial axis separability within the two-coordinate framework. Intensity “dilution” should be interpreted cautiously because it can reflect local membrane area expansion, segmentation, and normalization choices in addition to lamina remodeling.</figcaption></figure>