{"id":"68a0d3f0-0955-4c18-9298-2b98f6bdfe3e","arxiv_id":"2508.17974","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Attractors and repellers of cell flow, measured by finite-time Lyapunov exponents, mark compressive and tensile stress enrichment, packing heterogeneities, and future extrusion sites in MDCK monolayers.","lead":"This preprint reports that Lagrangian coherent structures, mathematical skeletons of collective cell motion, line up with where tissues later build up compressive or tensile stress, and with sites of future cell extrusion. The result suggests cell trajectories alone might be used to infer hidden biomechanical state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"LGR material-point assumption (Eqs. 3–7) is not validated against cell division and extrusion, so high FTLE at extrusion sites and the >10-fold stress-enrichment claim may partly reflect non-material source/sink events rather than coherent flow.","rationale":"The reader identified the material-point assumption as the weakest load-bearing premise, and I agree: every downstream correlation in the strongest claim depends on interpreting high FTLE as coherent material deformation rather than an artifact of discrete cell birth/death events. My critique sharpens the reader's concern by pointing to a specific, unaddressed mechanism — division and extrusion acting as sources and sinks inside the LGR regression window — and to the fact that the paper's own extrusion result makes this contamination especially likely. The reader's verdict of CONDITIONAL is therefore appropriate: the paper should be accepted only if the material-point assumption survives this test and code/data are released. I do not see a reason to move to REJECT without running the check, since the authors did validate LGR against PIV-based FTLE and report robustness across thresholds and perturbations, which are genuine supporting pieces of evidence. The main weakness is not that the correlations are impossible, but that their interpretation as mechanical precursors is unproven until non-material trajectory events are cleanly separated.","tokens_in":13424,"tokens_out":4332,"duration_ms":40935,"concrete_test":"Recompute the LGR-based FTLE fields after excluding from each regression neighborhood all cells that divide, appear, or disappear during the interval [t0, t], using only trajectories that persist for the full interval, then regenerate Fig. 2C and Fig. 5B–E. If the >10-fold stress enrichment and the pre-extrusion bwFTLE elevation persist under this exclusion, the material-point concern is not load-bearing; if they weaken substantially, the reported correlations are contaminated by division/extrusion source-sink artifacts.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires tracked cell trajectories to behave as material trajectories, so the flow map in Eq. 1 and its Jacobian in Eq. 2 are well-defined. In the LGR step, Eq. 7 estimates each incremental deformation gradient by least-squares regression over K_n = 40 neighboring cells within roughly 80 µm. In a dividing, extruding MDCK monolayer the neighbor set is not a fixed material neighborhood: divisions introduce new material points, extrusions remove them, and T1-like rearrangements change adjacency. The paper does not state how trajectories are truncated or excluded at division/extrusion events, nor how the regression handles a neighbor that vanishes or splits mid-interval. A single such event inside the 80 µm regression window appears as an apparent local expansion or contraction, and the least-squares fit in Eq. 7 will absorb it as deformation. This is not a peripheral detail: the extrusion analysis (Fig. 5) specifically treats bwFTLE elevation before extrusion as an attractor signal, but the future loss of a cell creates a local sink-like convergence of neighboring centroids by construction. The same potentially contaminated FTLE fields feed the stress-enrichment statistics (Fig. 2C), the long-term lag analysis (Fig. 4), and the packing correlations. Until the source/sink contribution is separated from genuine advective deformation, the 'precede and drive' wording and the tenfold enrichment magnitudes are not secure.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a framework for inferring mesoscale biomechanical reorganization in MDCK monolayers from Lagrangian coherent structures (LCSs) computed solely from cell trajectories. Using Lagrangian Gradient Regression (LGR) to estimate finite-time Lyapunov exponent (FTLE) fields, the authors report that top-20% attractors (backward FTLE) and repellers (forward FTLE) mark regions of compressive and tensile stress enrichment, respectively, with enrichment magnitudes exceeding tenfold over residual regions. They further report that short-term LCSs are associated with long-term stress enrichment, that the persistence of enrichment is modulated by E-cadherin expression and substrate stiffness, and that backward FTLE is elevated at future cell extrusion sites. A proof-of-concept machine learning model is used to predict stress enrichment maps from FTLE fields. The authors conclude that the hidden 'flow skeleton' precedes and drives long-term intercellular stress reorganization and offers a new route to infer biomechanical metrics from motion data.","tokens_in":13743,"tokens_out":6107,"duration_ms":57456,"significance":"If the central correlations hold, the work offers a practical, purely kinematic route to infer mesoscale biomechanical quantities from cell motion, which is substantially easier to measure than stress via traction force microscopy or fluorescent probes. The paper is notable for its extensive robustness checks: multiple FTLE integration times, threshold variations, five independent experiments, mechanical perturbations, and a comparison against Eulerian metrics. The extrusion analysis is a biologically meaningful endpoint that could extend to tissue homeostasis and disease contexts. The LGR methodology is current and the analysis pipeline is clearly described. However, the central causal claim ('precede and drive') is not supported by the correlational design, and the material-point assumption underlying LGR is not validated against cell division and extrusion, both of which are load-bearing for the paper's main conclusions.","major_comments":[{"comment":"The LGR framework assumes that the K_n nearest neighbors form a fixed material neighborhood over each short subinterval. The manuscript does not state how cell division and extrusion events are handled in the trajectory data or in the local regression. A dividing or extruding cell inside the ~80 µm regression window will appear as an apparent local expansion or contraction, and the least-squares fit in Eq. (7) will absorb that non-material event as deformation. The extrusion analysis in Fig. 5B is particularly exposed: the imminent loss of a cell is itself a sink that will produce elevated bwFTLE by construction. Because the same FTLE fields feed the stress-enrichment statistics (Fig. 2C) and the temporal-lag analysis (Fig. 4), the reported correlations could be contaminated by source/sink artifacts. The authors should either explicitly exclude or mask division/extrusion events in the trajectory data, or provide a sensitivity analysis showing that the results are unchanged when such events are removed.","section":"Extracting Lagrangian Coherent Structures (LCSs) from Sparse Cell Trajectories (Eqs. 3-7)"},{"comment":"The statement that LCSs 'precede and drive long-term intercellular stress reorganization' is stronger than the evidence presented. Fig. 2 compares FTLE and stress enrichment over the same time window (T = Δt), which is a synchronous correlation. Fig. 4 shows that short-term LCSs are correlated with later stress enrichment, but this remains a predictive, not causal, relationship. The E-cadherin and substrate-stiffness perturbations alter the entire mechanical state of the monolayer, so they do not isolate LCSs as the driver. The authors should either soften the causal language to 'predict' or 'are associated with', or provide an intervention that specifically manipulates LCSs while holding other variables fixed.","section":"Abstract and Discussion"},{"comment":"The comparison between LCSs and Eulerian metrics is not matched in temporal processing. The FTLE fields integrate deformation over a time interval T, whereas the Eulerian fields (velocity magnitude, divergence, vorticity) appear to be instantaneous quantities. The claim that Eulerian metrics show 'only subtle relationships' with stress enrichment could reflect this time-window mismatch rather than a fundamental advantage of Lagrangian descriptors. The authors should time-average or time-integrate the Eulerian metrics over the same window T before comparing their association with stress enrichment.","section":"Attractors and Repellers Mark Hotspots for Mechanical Stress Enrichment (Supplementary Fig. S3)"},{"comment":"The central tenfold enrichment claim requires an explicit definition of the stress enrichment metric. The main text only says 'time rate of stress change within a time window Δt' and reports units of Pa·µm/min, but it is not clear whether the enrichment is a spatial gradient, a temporal derivative, or an average change over the window. Without this definition, the reported magnitudes (3.91 Pa·µm/min versus 0.38 Pa·µm/min) cannot be reproduced or interpreted. The authors should provide the exact formula in the main text or a clearly referenced equation in the Supplementary Methods, and state explicitly how regions are pooled across samples and time intervals.","section":"Attractors and Repellers Mark Hotspots for Mechanical Stress Enrichment (Fig. 2C)"}],"minor_comments":[{"comment":"The proof-of-concept ML section reports that predicted maps 'closely matched' experimental measurements, but no quantitative accuracy metric (e.g., R², Pearson correlation) is given in the main text; please add a quantitative measure of prediction quality.","section":"Machine Learning Framework (Supplementary Fig. S7)"},{"comment":"The description of the cluster-tracking method refers to a 'spatial alignment metric' without defining it in the main text; a concise definition or a clear pointer to the Supplementary Methods equation would improve reproducibility.","section":"Clustering Visualization (Fig. 2D)"},{"comment":"The terms 'LCS attractors' and 'LCS repellers' are operationally defined as regions in the top 20% of bwFTLE and fwFTLE, rather than by rigorous ridge extraction of the FTLE field. Please clarify that 'LCS' in this work refers to thresholded FTLE regions, and discuss any implications for comparison with prior LCS studies.","section":"Terminology (Throughout)"},{"comment":"The main text describes the use of Cellpose and Trackmate but does not state how track splits and merges (associated with division and extrusion) are handled in the trajectory linking. A brief statement in the main text or a clear reference to the relevant Supplementary Methods section is needed, given the material-point assumption in Eqs. (3)-(7).","section":"Trajectory Tracking (Methods)"},{"comment":"The definition of the 'residual regions' used as the baseline for the tenfold comparison should be stated explicitly (e.g., the complement of the union of top-20% attracting and repelling regions).","section":"Residual Regions (Fig. 2C)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses an interesting question and contains a substantial amount of experimental and analysis work. However, the causal language in the abstract and discussion is likely to draw criticism from the mechanobiology community, and the lack of explicit handling of division/extrusion events in the LGR step is a serious methodological gap. I recommend that the editor ask for a revised version that either strengthens the causal evidence or tempers the claims, and that includes the requested sensitivity analyses. Making trajectory data and analysis code available would also greatly strengthen reproducibility, given the novelty of the LGR implementation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear X,\n\nThe thing to know: this paper gives the most convincing demonstration I've seen that LCS/FTLE fields computed from sparse cell trajectories track stress enrichment and packing heterogeneities in MDCK monolayers. The link to future extrusion is a nice payoff. But the title and discussion oversell the causal direction: the data are correlational, and the 'precede and drive' wording isn't backed by the analysis. The other real soft spot is the material-point assumption in the LGR step, which the stress-test note flags correctly.\n\nWhat's genuinely new: prior LCS work in cell layers focused on migration fronts and morphogenesis; here they systematically compare attractor/repeller regions against BISM stress enrichment across multiple time windows, perturbations (E-cad knockdown, substrate stiffness), and thresholds. The >10-fold enrichment claim is striking, and the robustness checks (top 30% to 10%, neighborhood size 5–60) are more thorough than most papers of this type. The machine-learning predictor is a stub, but it's honest as a proof of concept. The packing correlations and the junction-dependent lag in stress realignment make sense given what we know about force transmission.\n\nSoft spots, in proportion: (1) The material-point issue is real. LGR assumes the nearest-neighbor set is a fixed material patch over the regression interval. In a dividing/extruding monolayer, divisions and extrusions introduce source/sink effects that the least-squares fit will read as deformation. The paper never states how trajectories are truncated at these events, and the extrusion analysis (Fig. 5) is exactly where you'd expect the artifact to bite: the future loss of a cell creates convergent motion of neighbors by construction. The elevated bwFTLE before extrusion could be partly a kinematic reflection of the upcoming removal, not a 'hidden skeleton' that predicts it. They need a control—e.g., removing the extruding cell from the trajectory set and recomputing, or comparing to a simulation with synthetic division/extrusion. (2) The 'precede' claim is weaker than presented. Fig. 2 uses the same window T = Δt for LCS and stress enrichment; that's a correlation, not a prediction. Fig. 4 does use short LCS intervals against longer enrichment windows, which is better, but the 'drive' language still implies causation from kinematics to stress, whereas both could be driven by a common mechanical process. (3) No code or data. For a methods-heavy paper, that's a big gap. The LGR hyperparameters (K_n, γ, T) are hand-chosen; the robustness checks help, but I couldn't reproduce the exact magnitudes without code.\n\nThe math itself is standard LCS/FTLE, correctly applied. The citation pattern is fair—they cite the LGR method, earlier LCS biology work, and the BISM source. No circularity: stress and motion are independently measured.\n\nWho's it for: anyone working on collective cell migration, monolayer mechanics, or trying to infer stress from kinematics. It deserves a serious referee—the core correlation is likely robust, and the extrusion finding is interesting enough that the material-point artifact needs to be sorted out in the literature, not desk-rejected. I'd send it to review with a request for the trajectory-truncation analysis and a sharper distinction between same-window and lagged correlations.","headline":"Trajectory-only LCS/FTLE analysis gives a striking and mostly convincing correlation with stress enrichment and packing in epithelial monolayers, but the causal 'precede and drive' framing is not supported by the evidence and the material-point assumption in the LGR step needs an explicit artifact check before the extrusion result is secure.","tokens_in":14245,"tokens_out":2598,"would_cite":true,"duration_ms":23490,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Cell trajectories alone can expose where compressive and tensile stress build up in a tissue, because the hidden attractors and repellers of cell flow mark stress hotspots and future extrusion sites.","keywords":["Lagrangian coherent structures","finite-time Lyapunov exponent","collective cell migration","intercellular stress","cell extrusion","cell packing","epithelial monolayers","biomechanical inference"],"falsifier":"Simulate a monolayer with known intercellular stress and frequent cell divisions and extrusions, compute FTLE from the simulated tracks with the same regression settings, and test whether top-20% attractor and repeller regions still align with more-than-tenfold stress enrichment; if the alignment degrades or division/extrusion artifacts dominate, the central claim is wrong.","tokens_in":13244,"feed_emoji":"🔬","tokens_out":6361,"duration_ms":66748,"temperature":0.7,"pith_summary":"The paper claims that the hidden architecture of collective cell motion—attractors and repellers in the Lagrangian flow—marks where compressive and tensile stress accumulate in a cell sheet, and that these structures appear before the stress does. If true, the biomechanical state of a tissue could be read off from ordinary cell trajectories without invasive stress probes. The paper supports this by showing that top-20% attraction and repulsion regions show more than tenfold enrichment of compressive and tensile stress, that the association persists across adhesion and substrate perturbations, that short-term structures track stress reorganization lasting hours, and that attractors mark future cell extrusion sites.","feed_headline":"Cell flows' hidden skeleton reveals where tissue stress builds up","feed_subtitle":"Attractors and repellers computed from cell motion mark 10-fold stress hotspots and foreshadow cell extrusion.","key_machinery":"The central object is the finite-time Lyapunov exponent (FTLE) field: the time-normalized logarithm of the largest singular value of the flow-map Jacobian, computed forward (fwFTLE, repellers) and backward (bwFTLE, attractors) over a time window. Because cell positions are sparse, the flow-map Jacobian is estimated by Lagrangian Gradient Regression—a regularized least-squares fit of the local linearized displacement map over short subintervals, chained across the window—to build the right Cauchy–Green strain tensor $C=(\\nabla F)^\\top \\nabla F$ and extract its largest eigenvalue. That regression-produced deformation field is what converts raw trajectories into the hidden skeleton later correlated with stress enrichment, cell packing, and extrusion.","core_discovery":"The central claim is that in epithelial monolayers, the attractors and repellers of the Lagrangian cell flow are not passive echoes of mechanics but early markers and drivers of stress reorganization: the top 20% backward-FTLE (attracting) regions develop compressive stress enrichment and the top 20% forward-FTLE (repelling) regions develop tensile stress enrichment, with mean amplifications of 3.91 and 3.94 Pa·µm/min versus 0.38 Pa·µm/min in residual regions—more than a tenfold contrast. The association holds across FTLE windows from 30 minutes to 5 hours and under E-cadherin knockdown and substrate-stiffness changes. Short-term (30-minute) FTLE patterns correlate with stress enrichment lasting at least 5 hours, and the temporal lag between coherent motion and stress change grows when cell-cell junctions are weakened. Finally, backward-FTLE fields computed before an extrusion show elevated values at the future extrusion site, with a lead time of roughly 20–30 minutes.","pith_inferences":["The time lag between FTLE patterns and stress enrichment, which lengthens when cell-cell junctions are weakened, could itself be quantified as a non-invasive index of effective intercellular adhesion strength.","The proof-of-concept stress prediction from FTLE fields could likely be extended into a full mapping from trajectory-derived kinematics to stress maps, turning the reported tenfold contrast into a quantitative substitute for stress microscopy.","A direct test using computational epithelial models with known stress fields would independently verify the causal claim that attractors and repellers precede and drive stress reorganization rather than merely correlate with it.","The cited parallel between LCSs and polymeric stress fields suggests the attractor-repeller/stress coupling may generalize to other active and viscoelastic materials, which could be tested in simulation or experiments on non-biological active fluids."],"forward_implications":["Cell trajectories alone could serve as a non-invasive readout of where compressive and tensile stress are building up, reducing the need for force microscopy or fluorescent stress probes.","Short 30-minute trajectory windows predict stress enrichment that persists for hours, giving the method genuine forecasting power for tissue-level mechanical reorganization.","Attracting LCSs mark future cell extrusion sites, so flow kinematics could flag cell-elimination events tens of minutes before they occur.","The framework transfers to systems where individual tracks are unavailable, since trajectories reconstructed from velocity fields yield the same FTLE patterns.","Because the stress associations survive E-cadherin knockout and substrate-stiffness changes, the approach should work across varied mechanical microenvironments."],"supporting_citations":[{"why":"Supplies the definition of FTLE through the right Cauchy–Green strain tensor, which the entire computation is built on.","marker":"[27]"},{"why":"Supplies the Lagrangian Gradient Regression scheme for estimating flow-map Jacobians directly from sparse, noisy trajectory data.","marker":"[33]"},{"why":"Provides the force-inference stress microscopy used to measure intercellular stress and define stress enrichment.","marker":"[7]"},{"why":"Establishes the use of Lagrangian coherent structures in collective tissue flows, which this paper extends to mesoscopic stress correlations.","marker":"[24]"},{"why":"Provides the machine-learning architecture adapted to predict stress enrichment from FTLE input fields.","marker":"[47]"},{"why":"Links cell extrusion to mechanical stress and packing, defining the biological outcome tested against LCS attractors.","marker":"[42]"},{"why":"Provides evidence that stronger cell-cell junctions transmit stress more efficiently, used to interpret the observed delays in stress realignment.","marker":"[57]"}],"fun_headline_variants":["Flow skeleton predicts stress hotspots and cell extrusion","Hidden flow skeleton reveals 10-fold tissue stress buildup","Cell flow attractors mark stress hotspots and extrusion","Flow patterns pinpoint future tissue stress and extrusion"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that tracked cell motion over short windows behaves like material points of a continuous flow, so the local displacement map can be approximated as linear; if cell division, extrusion, or tracking errors break that assumption, the FTLE fields are contaminated by tracking artifacts rather than true coherent motion, and the downstream stress and packing correlations would be compromised.","fun_headline_variants_meta":{"raw":{"variants":["Flow skeleton predicts stress hotspots and cell extrusion","Hidden flow skeleton reveals 10-fold tissue stress buildup","Cell flow attractors mark stress hotspots and extrusion","Flow patterns pinpoint future tissue stress and extrusion"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001104,"raw_usage":{"total_tokens":4606,"prompt_tokens":952,"completion_tokens":3654,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":568,"completion_tokens_details":{"reasoning_tokens":3596}},"tokens_in":568,"tokens_out":3654,"duration_ms":24669,"temperature":1.0,"reasoning_tokens":3596,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:58:03.703637+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a monolayer with known intercellular stress and frequent cell divisions and extrusions, compute FTLE from the simulated tracks with the same regression settings, and test whether top-20% attractor and repeller regions still align with more-than-tenfold stress enrichment; if the alignment degrades or division/extrusion artifacts dominate, the central claim is wrong.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Lagrangian Gradient Regression scheme for estimating flow-map Jacobians directly from sparse, noisy trajectory data."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the machine-learning architecture adapted to predict stress enrichment from FTLE input fields."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Links cell extrusion to mechanical stress and packing, defining the biological outcome tested against LCS attractors."},{"cited_title":"Schoenit, S","cited_arxiv_id":null,"evidence_quote":"Provides evidence that stronger cell-cell junctions transmit stress more efficiently, used to interpret the observed delays in stress realignment."}],"review_version":2}