{"id":"7c3d1b23-2235-4393-9167-c4e5ec5b33c2","arxiv_id":"2501.04407","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A coupled reaction-diffusion and elasticity model reproduces stiffness-dependent RhoA signalling and predicts that two-way mechanical-chemical coupling confers homeostatic robustness of cell deformation.","lead":"The authors build a mathematical model of how cells sense and respond to mechanical forces through the RhoA signalling pathway, coupling chemical signals inside the cell to its physical deformation. Their simulations indicate that two-way feedback between signalling and cell stiffness can make cell deformation robust to changes in surrounding stiffness, a behavior called mechanical homeostasis.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The homeostasis plateau is computed with linear elasticity while reported displacements (|u| up to 7 um in a ~13 um cell) violate the small-deformation assumption; the plateau may be an artifact of the linearization.","rationale":"Good-faith reading: the paper extends the RhoA/FAK signalling model of [18] with two-way mechanical coupling and shows a plateau in mean div(u) as a function of substrate stiffness. The load-bearing condition for that claim is not only that Eq. (2) is biologically accurate, but that the equations used to compute the plateau are valid where the plateau is observed. The reported values violate the explicit small-deformation premise of Eq. (3). This is an internal inconsistency: the same manuscript reports |u| up to 7 um for a cell with volume 1193 um^3 and admits the small-strain limitation in the Discussion. Because the plateau is quantified via div(u) and |u|, linear elasticity in an O(1)-strain regime is not a safe basis for the claim. The reader's weakest_assumption focuses on the power-law Ec(phi_a) of Eq. (2); that is a legitimate external-validity concern, but the small-strain issue is more immediate because it affects whether the model's own equations support the conclusion even before biological interpretation. The concrete test is a finite-strain re-simulation, which can be implemented by replacing the linear stress in Eq. (3) with a hyperelastic stress while keeping the coupling terms and parameters unchanged. If the plateau disappears, the paper's central claim is substantially weakened; if it persists, the concern is resolved. The reader's CONDITIONAL verdict already asks for additional support, so this stress-test does not change the verdict; it identifies a specific condition (finite-strain validation) that should be added.","tokens_in":22924,"tokens_out":10013,"duration_ms":102553,"concrete_test":"Compute the maximum Green-Lagrange strain or displacement gradient in the stored solutions of Fig. 3 (e.g., max ||grad u||). If it exceeds roughly 0.1, re-run the same Fig. 3 protocol with a finite-strain hyperelastic constitutive law (neo-Hookean or Saint Venant-Kirchhoff) built from the same Ec(phi_a) in Eq. (2) and the same boundary conditions (4)-(5). If the mean div(u) versus E curve no longer shows a plateau across E = 0.1, 5.7, 7e6 kPa (or shifts by more than 30% at E = 0.1 kPa), the claimed homeostasis is an artifact of the small-strain linearization. If the plateau persists, the concern does not land.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In the section 'Mathematical model for mechanotransduction', the authors state 'we consider small deformations and hence, assume a linear elastic constitutive law'. Equation (3) is therefore the linearized balance of momentum. Yet the Results report maximum displacement magnitudes of 7 um for the 2xD stimulus and 7.5 um for the 3D stimulus (Figs. 1 and 4) on cells with volume |Y|=1193 um^3, i.e. an equivalent spherical diameter of roughly 13 um. A displacement comparable to the cell radius implies O(1) strains, far outside the small-strain regime in which Eq. (3) is a valid approximation. The central claim of mechanical homeostasis is read off from div(u) and |u| in exactly this regime (Fig. 3, Fig. 5, Fig. 7). Finite-strain effects such as geometric stiffening or shape change could modify, or even erase, the plateau that is presented as the main emergent result. The Discussion contains the admission that the linear elastic assumption 'is limiting as it assumes small deformations', but no finite-strain simulation is supplied; the viscoelastic check in S1 Appendix A.7 changes the rheology while retaining linear kinematics. This is an internal gap in the argument for the central claim, not merely a question of parameter fitting.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a reduced bulk-surface reaction-diffusion model for inactive and active FAK and active RhoA, coupled to linear elasticity of the cell. Substrate stiffness activates FAK on the membrane, the cell Young's modulus is made to depend on active FAK concentration through Eq. (2), and the boundary traction depends on active RhoA through Eq. (4). The model is simulated for 2D and 3D stimuli, for axisymmetric and lamellipodium-shaped cells, and the results are used to claim a threshold-like response to substrate stiffness and a robustness of cell deformation to stiffness changes, interpreted as mechanical homeostasis. The paper also presents a bulk-surface finite element method and verifies its convergence on a manufactured solution.","tokens_in":23261,"tokens_out":3700,"duration_ms":38633,"significance":"If the central claim holds, the paper provides a minimal mechanistic explanation of mechanical homeostasis: bidirectional coupling between RhoA signalling and cell mechanics can make cell deformation insensitive to ECM stiffness. The paper has clear strengths: the reduced model is shown to reproduce the qualitative results of the full model of [18]; the numerical scheme is benchmarked on a manufactured solution with the expected orders of convergence; and a parameter sensitivity analysis is provided. However, the main emergent predictions are tied to the assumed power-law stiffness law and to the linear small-strain approximation, so the significance of the homeostasis claim depends on additional validation that the manuscript does not currently provide.","major_comments":[{"comment":"The model is formulated under the explicit assumption of small deformations, leading to the linear elastic equation (3). Yet the results report maximum displacement magnitudes of 7 µm for the 2xD stimulus (Fig. 1) and 7.5 µm for the 3D stimulus (Fig. 4) on a cell with |Y|=1193 µm^3, i.e. an equivalent spherical diameter of roughly 13 µm and radius of roughly 6.5 µm. Displacements comparable to the cell radius imply O(1) strains, far outside the small-strain regime in which Eq. (3) is valid. The central homeostasis claim is read off from div(u) and |u| in exactly this regime (Figs. 3, 5, and 7). The Discussion admits that the linear elastic assumption 'is limiting as it assumes small deformations', and the viscoelastic check in S1 Appendix A.7 retains linear kinematics. A finite-strain computation, or a restriction of the homeostasis claim to genuinely small strains, is needed before the plateau can be regarded as a robust prediction of the model rather than a possible artifact of the linearization.","section":"Mathematical model for mechanotransduction, Eq. (3); Results, Figs. 1 and 4"},{"comment":"The homeostatic plateau is largely a consequence of the assumed constitutive law E_c(phi_a)=k7(1+(k8 phi_a)^p), with k7, k8, and p fitted to results for phi_a in [18] and F-actin in [38]. The threshold-like dependence on substrate stiffness is similarly inherited from the Hill-type terms and parameters taken from [18]. Because these fitted inputs are used to generate the very curves that are then presented as emergent predictions, the claim that homeostasis 'emerges' from the bidirectional coupling is only as strong as the empirical support for Eq. (2). The sensitivity analysis in S1 Appendix A.6 varies the parameters of Eq. (2) by ±10% and ±20%, but it does not test the form of the law itself. The authors should either test alternative functional forms of E_c(phi_a), or present independent data that constrain Eq. (2), before the homeostasis result is presented as a model prediction rather than a restatement of the fitted stiffness law.","section":"Eq. (2), Table 1(b), and S1 Appendix A.6"}],"minor_comments":[{"comment":"There is a typo: 'mechanostranduction' should be 'mechanotransduction'.","section":"Methods, first paragraph"},{"comment":"The caption contains a duplicated phrase: 'simulation results showing rho_a, phi_d, phi_a and |u| simulation results showing phi_a and rho_a for the model...' should be cleaned up.","section":"Results, Fig. 8 caption"},{"comment":"'mechanisms that underlay the mechanical homeostasis' should be 'mechanisms that underlie mechanical homeostasis'.","section":"Introduction, last paragraph"},{"comment":"Reference [43] is cited before [42] in the text; the citation order in the bibliography could be adjusted if the journal requires strict numerical ordering.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The two substantive concerns are both fixable within the manuscript's scope: a finite-strain check or explicit small-strain restriction, and a robustness check on the form of E_c(phi_a). I would not support rejection, but the current manuscript presents the homeostasis plateau as a robust emergent result while the evidence leaves that status uncertain."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the two-way coupling between RhoA/FAK signalling and cell mechanics is a real extension, and the paper does useful things with it. But the stress-test note is correct: reported displacements of 7–7.5 µm in a cell with equivalent radius about 6.6 µm are large deformations, and the linear elasticity the model is built on is not valid there. The homeostasis plateau is read off in exactly that regime, so this is the main soft spot and it is not minor.\n\nWhat the paper does well: it extends the Scott–Rangamani model to include cell elasticity with Young's modulus depending on active FAK and FAK activation depending on stress, in a 3D bulk–surface geometry. The reduced model is checked against the full model and reproduces it qualitatively. The finite element scheme is benchmarked on a manufactured solution with expected convergence orders. There is a sensitivity analysis for the new parameters, and the viscoelastic and nucleus extensions are sensible additions. The authors are upfront about the parameter fitting and about the limitations.\n\nWhere it is soft: the linear-elastic constitutive law is assumed, yet the computed displacements are O(1) compared with the cell radius. The viscoelastic check changes rheology but keeps linear kinematics, so it does not address this. A finite-strain simulation would be needed to know whether the plateau survives geometric stiffening and shape change. Also, k7, k8, and p are fitted to the same [18] data used for comparison, and the threshold response is inherited from the Hill/Michaelis–Menten kinetics, so the quantitative predictions are not independent. No code is shipped, which makes the numerical claims harder to verify.\n\nWho this is for: people modelling cell mechanosensing who want a concrete example of bidirectional coupling. It is a serious paper and deserves a serious referee. I would send it to review, with a request that the authors either provide finite-strain simulations or show the reported deformations are actually small, and that they release the code. If the plateau holds under finite elasticity, the result is worth having; if not, the paper still has value as a model framework.","headline":"Solid two-way coupling model, but the homeostasis plateau is computed in a large-deformation regime the linear elasticity assumption cannot support.","tokens_in":23718,"tokens_out":2778,"would_cite":true,"duration_ms":27086,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["65M60","92C10","35K57","74B05"],"pacs":[],"model":"deepseek-v4-flash","headline":"A two-way RhoA–FAK feedback loop can explain why cells deform similarly on soft and stiff surfaces.","keywords":["mechanotransduction","RhoA signalling","focal adhesion kinase","mechanical homeostasis","reaction-diffusion equations","bulk-surface finite elements","linear elasticity","substrate stiffness"],"falsifier":"Measure, in a single cell type, both active FAK concentration and deformation on substrates spanning 0.1 kPa to 7 GPa. If deformation follows substrate stiffness monotonically instead of plateauing, or if cell stiffness is unchanged when active FAK is elevated, the claimed two-way mechanism is falsified. Pharmacological FAK inhibition should also destroy the plateau if the mechanism is causal.","tokens_in":22732,"feed_emoji":"🧫","tokens_out":6154,"duration_ms":60257,"temperature":0.7,"pith_summary":"This paper tries to establish that mechanical homeostasis—cells deforming by roughly the same amount whether they sit on a soft or a stiff surface—can emerge from a minimal mechanistic model rather than from a tuned control system. The model couples the RhoA signalling pathway to cell elasticity in two directions: mechanical stress activates focal adhesion kinase (FAK), and active FAK increases the cell's Young's modulus. In simulations, this two-way loop makes the magnitude of cell deformation and cell volume change nearly flat across substrate stiffnesses from 0.1 kPa to 7 GPa, while a model with constant cell stiffness shows no such plateau. A sympathetic reader would take the paper to be claiming that the feedback loop, not any single reaction, is the mechanism behind stiffness homeostasis.","feed_headline":"Model shows how RhoA–FAK feedback keeps cell deformation constant","feed_subtitle":"A minimal two-way loop lets cells adjust their own stiffness, matching measured homeostasis.","key_machinery":"The central object is a two-way feedback loop. Stress activates FAK through the term $C_1\\,\\mathrm{tr}(\\sigma)_+\\,\\phi_d$, and the cell's Young's modulus increases with active FAK according to the power law $E_c(\\phi_a)=k_7(1+(k_8\\phi_a)^p)$, where active FAK is used as a proxy for F-actin. This loop is embedded in a bulk-surface reaction-diffusion system for inactive and active FAK in the cytoplasm, active RhoA on the membrane, and a linear elasticity problem whose boundary traction depends on active RhoA. The numerical machinery is a bulk-surface finite element method with semi-implicit time stepping; the power law is the bridge that converts a biochemical signal into a mechanical property, and removing that bridge removes the homeostasis.","core_discovery":"On the paper's own terms, the central discovery is that bidirectional coupling between signalling and cell mechanics is sufficient to reproduce mechanical homeostasis. The authors extend a spatial RhoA signalling model to include linear elastic cell deformation, with the cell's Young's modulus given by $E_c(\\phi_a)=k_7(1+(k_8\\phi_a)^p)$ and with FAK activation driven by the positive part of the stress trace, $C_1\\,\\mathrm{tr}(\\sigma)_+\\,\\phi_d$. When both couplings are present, steady-state cell deformation and $\\mathrm{div}(u)$ become nearly constant over a wide range of ECM stiffnesses, while active FAK and active RhoA still rise in a threshold-like Hill-function manner. This reproduces the qualitative experimental observations of mechanical homeostasis and of threshold-like stiffness responses. The plateau does not occur when the cell is assigned constant stiffness or when stress feedback onto signalling is switched off, so the paper concludes that the bidirectional coupling itself is the load-bearing mechanism.","pith_inferences":["Beyond the paper, the same feedback loop would predict that a cell pre-exposed to a stiff substrate retains a higher Young's modulus and therefore deforms less on a later soft substrate, offering a concrete mechanism for mechanical memory that could be tested by sequential-culture experiments.","Beyond the paper, pharmacological inhibition of FAK or RhoA should erase the plateau: deformation should then scale with substrate stiffness as it does in the constant-stiffness case, providing a direct causal test of the model.","Beyond the paper, the fitted parameters $k_8$ and $p$ could be estimated from combined live imaging of active FAK and atomic force microscopy stiffness maps, turning the fitted constitutive law into a measurable prediction.","Beyond the paper, because the plateau appears only when both couplings are active, one-way stiffness-sensing models may misestimate how cells respond to matrix gradients, especially in slowly varying environments where the bidirectional term dominates."],"forward_implications":["If the central claim is correct, models that treat cell stiffness as a fixed constant will miss the homeostasis plateau; stiffness must be allowed to respond to signalling.","The reduced FAK–RhoA model reproduces the threshold-like dependence of signalling on substrate stiffness seen in experiments, so the threshold response is not an artefact of the full pathway.","Cell shape becomes a control variable: axisymmetric and lamellipodium-shaped cells show different concentrations and different threshold responses, implying that geometry is part of the mechanosensing circuit.","A linear viscoelastic version of the model produces the same qualitative behaviour, so the homeostasis result does not depend on the purely elastic constitutive law.","The framework is designed to be extended to viscoelastic or poroelastic mechanics, nuclear deformation, and spatially varying substrate stiffness."],"supporting_citations":[{"why":"Supplies the full spatial RhoA/YAP/TAZ signalling model, parameter values, and simulation results against which the reduced FAK–RhoA model is validated.","marker":"[18]"},{"why":"Provides experimental elastic behaviour of cross-linked actin networks used to justify and fit the power-law cell stiffness $E_c(\\phi_a)$.","marker":"[38]"},{"why":"Reports the experimental mechanical homeostasis in cells that the coupled model reproduces.","marker":"[28]"},{"why":"Provides the experimental threshold-like dependence of cell responses on substrate stiffness used for comparison.","marker":"[44]"},{"why":"Gives the bulk-surface finite element framework used to discretise the coupled bulk and membrane equations.","marker":"[26]"},{"why":"Supplies a YAP/TAZ mechanosensing model that, with [18], motivates the derivation of the signalling component.","marker":"[24]"}],"fun_headline_variants":["Bidirectional RhoA–mechanics coupling yields cell homeostasis","Two-way RhoA feedback explains constant cell deformation","Model shows RhoA–mechanics loop drives stiffness homeostasis","Mathematical coupling of RhoA and elasticity stabilizes cells"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The homeostasis prediction rests on the assumed law that cell stiffness rises with active FAK according to $E_c(\\phi_a)=k_7(1+(k_8\\phi_a)^p)$, with active FAK standing in for F-actin; if real cells stiffen differently, or if FAK is not a good proxy for F-actin, the plateau could disappear.","fun_headline_variants_meta":{"raw":{"variants":["Bidirectional RhoA–mechanics coupling yields cell homeostasis","Two-way RhoA feedback explains constant cell deformation","Model shows RhoA–mechanics loop drives stiffness homeostasis","Mathematical coupling of RhoA and elasticity stabilizes cells"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000217,"raw_usage":{"total_tokens":1387,"prompt_tokens":845,"completion_tokens":542,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":461,"completion_tokens_details":{"reasoning_tokens":477}},"tokens_in":461,"tokens_out":542,"duration_ms":5626,"temperature":1.0,"reasoning_tokens":477,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:33:43.356071+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure, in a single cell type, both active FAK concentration and deformation on substrates spanning 0.1 kPa to 7 GPa. If deformation follows substrate stiffness monotonically instead of plateauing, or if cell stiffness is unchanged when active FAK is elevated, the claimed two-way mechanism is falsified. Pharmacological FAK inhibition should also destroy the plateau if the mechanism is causal.","supporting_citations":[{"cited_title":"A spatial model of YAP/TAZ signaling reveals how stiffness, dimen- sionality, and shape contribute to emergent outcomes","cited_arxiv_id":null,"evidence_quote":"Supplies the full spatial RhoA/YAP/TAZ signalling model, parameter values, and simulation results against which the reduced FAK–RhoA model is validated."},{"cited_title":"Environmental stiff- ness restores mechanical homeostasis in vimentin-depleted cells","cited_arxiv_id":null,"evidence_quote":"Reports the experimental mechanical homeostasis in cells that the coupled model reproduces."},{"cited_title":"Engineered extracellular matrices with controlled mechanics modulate renal proximal tubular cell epithelialization","cited_arxiv_id":null,"evidence_quote":"Provides the experimental threshold-like dependence of cell responses on substrate stiffness used for comparison."},{"cited_title":"Exploring the influence of cytosolic and mem- brane F AK activation on YAP/TAZ nuclear translocation","cited_arxiv_id":null,"evidence_quote":"Supplies a YAP/TAZ mechanosensing model that, with [18], motivates the derivation of the signalling component."}],"review_version":1}