Chemotaxis of branched cells in complex environments

Antonios Georgantzoglou; Giulia Rinaldi; Ingrid de Vries; Ivanna Williantarra; Jiayi Liu; Jonathan E. Ron; Michael Sixt; Milka Sarris; Nir S. Gov

REVIEW 3 major objections 5 minor 31 references

Chemotaxis of branched cells in complex environments

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A model of branched-cell chemotaxis predicts a speed–accuracy tradeoff and places neutrophils in the fast, less-accurate regime.

desk verdict A solid, honest modeling paper whose central biological claim—neutrophils are fast cells—rests on the same FMI data used to calibrate the model; the speed-accuracy tradeoff itself is a genuine and reproducible model prediction. read the letter →

arxiv 2505.21949 v2 pith:AIX2JVJI submitted 2025-05-28 physics.bio-ph q-bio.CB

Jiayi Liu , Jonathan E. Ron , Giulia Rinaldi , Ivanna Williantarra , Antonios Georgantzoglou , Ingrid de Vries , Michael Sixt , Milka Sarris

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Nir S. Gov

This is my paper · ORCID

classification physics.bio-phq-bio.CB MSC 92C1792C37

keywords chemotaxisbranchedcellmigrationspeed-accuracytradeoffactinpolymerizationdirectionaldecision-makingneutrophilhexagonalnetworkcomputationalmodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper extends a mechanical model of branched cells crawling on a hexagonal network to include chemoattractant gradients, with the chemokine acting as a local amplifier of actin-polymerization activity at each arm tip. It aims to establish a speed–accuracy tradeoff: cells with high baseline actin activity cross junctions faster but make more wrong turns, while slow cells can follow a weak chemoattractant signal accurately. Comparing the model with neutrophils migrating to a laser wound in zebrafish and with cells migrating between pillars, the paper finds that the experimental cells sit in the high-activity, fast, less-accurate regime. If this is right, neutrophil recruitment speed near a wound is bought at the cost of directional accuracy farther away, and efficient long-range recruitment requires additional guidance mechanisms.

What carries the argument

The central object is a branched cell on a hexagonal network, described by coupled variables for each arm: arm length $x_i$, fraction of engaged slip-bond adhesions $n_i$, and local actin treadmilling velocity $v_i$. The chemoattractant enters by increasing the maximal polymerization speed $\alpha$ at each arm tip according to $\alpha(r)=\alpha_0[1+\epsilon(1+C/c_0)c(r)/(c(r)+C)]$, so a gradient biases the competition between arms without any explicit gradient-sensing module. The parameter $\alpha_0$ is the free control knob: below a critical value cells cannot polarize and migrate, while above a higher critical value they get trapped in slow-mode decision events. This machinery produces the tradeoff because faster dynamics make the cell more likely to lose polarity and choose arms based on noise rather than on the weak signal bias.

What would settle it

In the same zebrafish wound assay, measure per-cell speed and wrong-turn rate before and after the chemokine appears: the model predicts a clear negative correlation, with faster cells making more wrong turns, and predicts that drug-treated cells with reduced actin activity become slower but more accurate; observing instead that the fastest cells are also the most accurate would falsify the tradeoff.

Watch

Extended reading notes

Core claim

The paper claims that the chemotactic performance of a branched cell is set by the same directional decision-making machinery that governs its random migration, with the chemokine entering only through a local enhancement of actin-polymerization activity at each arm tip. On a single junction and on a hexagonal network, raising the baseline actin activity $\alpha_0$ makes cells move faster but also makes them choose the wrong arm more often, and at high $\alpha_0$ they can enter slow-mode states with two competing elongated arms. Comparing the model with neutrophils migrating to a laser wound in zebrafish and with cells migrating between pillars, the paper finds that the experimental cells sit in the high-$\alpha_0$ regime. The authors conclude that wild-type neutrophils behave as fast cells that compromise chemotaxis accuracy for arrival speed, a strategy that works because some cells are always close to the wound.

Load-bearing premise

The load-bearing premise is that a chemoattractant gradient influences a branched cell only by locally increasing actin-polymerization activity at each arm tip, with no receptor-binding kinetics, adaptation, or cell-wide gradient comparison, and that the wild-type activity $\alpha_0$ is set by fitting the measured forward-migration-index increase; if real neutrophils sense gradients through additional mechanisms, the prediction that they are fast cells may not transfer.

Editorial extensions

If this is right

Wild-type neutrophils are predicted to prioritize arrival time over directional accuracy, so their recruitment efficiency depends on being densely distributed rather than on each cell navigating perfectly.
Near the wound, where the chemokine signal is strong, high actin activity is the optimal strategy because fast arrival outweighs occasional wrong turns.
Far from the wound, the same fast cells meander and sometimes enter slow-mode traps, so effective long-range recruitment requires signal amplification, for example secondary chemokine secretion by other neutrophils.
Drug-treated cells with reduced actin polymerization or myosin-II activity are predicted to become slower but more accurate, matching the qualitative changes in forward migration index reported for CK666- and blebbistatin-treated cells.
On larger networks, high-activity cells are increasingly slowed by slow-mode events, so the benefit of speed may reverse as tissue geometry becomes more complex.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable extension is to look for the same speed–accuracy tradeoff within a single, genetically identical cell population: individual faster cells should have lower directional persistence and more wrong turns than slower cells.
Because the model treats chemokine sensing only as local actin enhancement, real receptor adaptation or cell-wide gradient comparison could weaken the predicted tradeoff; experiments with cells whose adaptation machinery is perturbed would test this directly.
The mechanism suggests a general design principle for cells moving through crowded geometries: speed and directional accuracy are coupled through decision sampling time, so any intervention that slows a cell may improve its navigation accuracy in complex environments.
On pillar lattices with different spacings, the model appears to predict that denser or more obstructive geometries will increase slow-mode trapping of fast cells, which could be measured as a drop in arrival success at high pillar density.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the speed-accuracy tradeoff is real in the model and is the paper's main contribution. The claim that WT neutrophils sit in the high-alpha0 regime is a calibrated conclusion, not an out-of-sample prediction—the authors say so plainly. That doesn't sink the paper, but it should be labeled as a fit, and the paper would be strengthened by independent constraints on alpha0.

What's new: they take their branched-cell network model and couple it to a chemokine field via local enhancement of actin polymerization at arm tips (Eqs. 1 and 3). The single-junction and network simulations show a speed-accuracy tradeoff that is not put in by hand—it emerges from the stick-slip dynamics and slow-mode events. That's a real mechanistic result, and it's consistent across noise levels and grid sizes. The comparison to the in-vivo neutrophil and in-vitro pillar data captures qualitative features: the post-wound deceleration, reorientation, meandering paths, slow-mode-like events, and the drug-response trends. For a coarse-grained model this is a meaningful degree of contact.

Where it's soft: the load-bearing inference that neutrophils are fast cells comes from calibrating alpha0 to the same FMI increase that is then presented as support. The paper is explicit about the calibration, so it's not hidden, but the conclusion is weaker than the abstract suggests. The FMI increase is a single summary statistic, and alpha0 has at least seven effective parameters around it; no identifiability analysis is given. Simulation statistics in Figs. 2, 3, and S-4 are shown without error bars or bootstrap intervals, so we can't tell how sharp the tradeoff curves really are. No code or trajectory data are shipped, which makes the reproducibility claim hard to check. The drug-treated comparisons are qualitative and use parameter offsets set by hand.

None of these kill the core tradeoff. The central model result is a simulation output, not built into the equations, and it's plausible that fast cells are less accurate. What needs fixing is the evidential claim about real neutrophils: an out-of-sample test, or at least a parameter-identifiability study, is needed before 'neutrophils behave as fast cells' is stated as a conclusion.

Who it's for: people modeling amoeboid/immune cell migration in complex geometries, and experimentalists interested in speed-accuracy tradeoffs in chemotaxis. It deserves a serious referee; I'd send it out with a request for code/data, uncertainty quantification, and an honest reframing of the fast-cell claim as a fit. I'd read it myself, but I'd rewrite the abstract before it goes to press.

Referee Report

3 major / 5 minor

Summary. The manuscript extends a previously developed coarse-grained model of branched-cell migration on hexagonal networks to include chemokine sources. The chemokine acts by locally upregulating the actin polymerization parameter α at arm tips (Eqs. 1 and 3). The model reports a speed-accuracy tradeoff at single junctions and on networks, with an optimal intermediate activity for weak signals. The authors compare the model to in vivo zebrafish neutrophils and in vitro PLB-985 cells, and conclude that neutrophils operate in the high-α0 (fast) regime, sacrificing accuracy for speed.

Significance. If valid, the paper offers a mechanistic explanation for why neutrophils are fast but inaccurate chemotaxers, linking intracellular actin dynamics to tissue-scale recruitment. The speed-accuracy tradeoff is a nontrivial emergent prediction of the model, not imposed by construction. The model reproduces several qualitative features of neutrophil behavior, including the transient slowdown and reorientation after wounding and the occurrence of slow-mode events. The quantitative support for the fast-cell inference, however, rests on a circular calibration and lacks uncertainty quantification.

major comments (3)

[Comparison of the model with the chemotaxis of neutrophils (Fig. 4E-F; SI S-6, S-7)] The conclusion that wild-type neutrophils behave as fast cells is a restatement of the calibration rather than an independent prediction. The paper states that the experimental FMI increase is used 'to calibrate the value of the parameter ´0' and that this increase 'is captured by the model only when we are in the regime of large ´0' (Fig. 4E-F); the simulations in Fig. 4 use ´0=12. The later conclusion that 'the neutrophils correspond to the high-activity cells of our model' is therefore supported by the same observable that fixed the parameter. To break the circularity, the authors should either constrain ´0 using an independent observable (e.g., absolute cell speed, meandering-path frequency, or slow-mode statistics) and then predict the FMI increase out-of-sample, or provide an identifiability analysis showing that the FMI increase uniquely selects the high-´0 regime over the plausible parameter range.
[Comparison of the model with the chemotaxis of neutrophils (Fig. 4C-F; SI S-6, S-7)] The quantitative comparison to experiment is underdetermined. The calibration targets a single summary statistic (the relative FMI increase after BM time), while the model has several free parameters (´0, ϵ, C/c0, y0/yend, d, Ã); no simulation error bars, confidence intervals, or parameter sensitivity analysis are reported. This also applies to the central tradeoff curves in Figs. 2B and 3C, where the non-monotonic features (e.g., the minimum of Tarr in Fig. 3C(i) and the sharp rise in P(wrong) near ´0≈8 in Fig. 2B(i)) could be within noise. Furthermore, the slow-mode comparison in Fig. 5C uses a different parameter set (´0=12.6, d=3.7, Ã=0.6) from the calibration (´0=12, d=3, Ã=0.5), so it is unclear whether the qualitative agreement is robust. Please add error bars and a sensitivity analysis, and demonstrate that the fast-cell interpretation is not an artifact of the chosen parameter point.
[Eqs. (1) and (3); SI S-3] The transfer of the speed-accuracy tradeoff to real neutrophils depends critically on the assumption that chemotaxis is mediated solely by local upregulation of α at each arm tip, with no receptor binding kinetics, adaptation, or cell-wide gradient comparison. While this coarse-graining is a reasonable modeling choice, the paper's claim that the model 'explains the functionality of these immune cells' is stronger than the evidence. I recommend tempering the conclusion or testing whether a different sensing rule (e.g., adding adaptation or a front-back comparison) preserves the predicted tradeoff; such a test would substantially strengthen the biological relevance.

minor comments (5)

[Fig. 4C] The caption contains a typo: 'simlation' should be 'simulation'.
[Fig. 5 caption] The panel labeled '(F)' should likely be '(iii)' for consistency with the (i)-(iii) panels in (C).
[Bullet list on p. 6] In the bullet list, 'Fig. 3D(i)' should probably be 'Fig. 3C(i)' because the arrival-time minimum is shown in Fig. 3C(i), not in the trajectory panel 3D(i).
[SI S-6] The sentence 'The effect of the chemokine on the FMI of the cells is given in Fig. 5E' should refer to Fig. 4E, since Fig. 4E displays the experimental FMI data.
[Comparison of the model with the chemotaxis of neutrophils] The mapping of simulation time to experimental time ('choosing a simulation time interval of ∼ 2.5') is stated without derivation; please provide the calculation or a reference for this conversion.

Circularity Check

2 steps flagged · score 6.0 of 10

The speed-accuracy tradeoff is an emergent simulation result, but the conclusion that neutrophils are fast cells is largely a restatement of the calibration of alpha0 to the experimental FMI increase.

fitted input called prediction [Main text, 'Comparison of the model with the chemotaxis of neutrophils', Fig. 4E-F; SI S-6; Conclusion]
"In Fig. 4E,F, we compare the eﬀects of the chemokine presence on the FMI of the neutrophils [4] with our simulation model. We use this experimental data to calibrate the value of the parameter ´0 in our simulations. The FMI of the wild-type cells is observed to signiﬁcantly increase after the BM time (by ∼ 20% − 30%, Fig. 4E). This behavior is captured by the model only when we are in the regime of large ´0."

The paper's central biological inference, that wild-type neutrophils correspond to the fast, high-alpha0 regime, is not an out-of-sample prediction. The same experimental FMI increase after BM is used both to select alpha0 and as evidence that only large alpha0 reproduces it. The later statement that neutrophils 'behave as fast cells' therefore restates the calibration target. The drug-treated comparison in S-7 likewise fits reduced alpha0 (and k) to the same FMI/length/speed data and then cites the agreement as confirmation.
fitted input called prediction [SI S-7, Fig. S-7C-F]
"In Fig. S-7C,D, we compare the experimental [6] and simulated changes to the FMI for the WT (DMSO) and drug-treated cells. The relative changes are qualitatively captures by the model, especially the increase in FMI due to the chemokine for the WT cells, and the vanishing of this eﬀect upon drug application. This, again, points to the WT cells residing in the high-´0 regime of our model, which is the only regime where we see that the FMI is signiﬁcantly increased by the chemokine gradient."

The drug parameters (alpha0 and k) are chosen to fit the experimental cell length, speed, and FMI data from the drug-treated cells, and then the qualitative agreement is used as evidence that wild-type cells sit in the high-alpha0 regime. Since the model's FMI increase appears only in that regime, the agreement is a byproduct of the fit rather than an independent test.

full rationale

The speed-accuracy tradeoff itself is an emergent output of the stochastic branched-cell equations and is not written into the model: the single-junction and network simulations show Tesc, P(wrong), Lpath, and FMI varying with alpha0 in a nontrivial way. That part of the paper is self-contained and not circular. The circularity concerns the application to neutrophils. The abstract's closing claim, that neutrophils behave as fast cells compromising chemotaxis accuracy, is reached by calibrating alpha0 to the experimental FMI increase after the BM time and then asserting that this behavior occurs only at large alpha0. The FMI increase is thus both the fitting target and the evidence for the high-alpha0 assignment. The supporting observations (meandering trajectories, slow-mode events) are qualitative and are not quantitatively tied to alpha0 with error bars or parameter-identifiability analysis, so they do not break the circularity. Overall, the model's internal tradeoff is independent, but the headline experimental conclusion is partially forced by the calibration, giving a partial circularity score of 6.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The ledger shows that the paper's contribution is a new chemotaxis term added to a pre-existing model with many calibrated parameters. The tradeoff is not an input, but alpha0, the parameter identifying the fast regime, is fitted to the experimental FMI, and the chemokine profiles are chosen by hand. No new physical entities are introduced.

free parameters (7)

alpha0 (baseline actin polymerization activity) = 12.0 for WT comparison; 10.0 for CK-666; 10.0 for blebbistatin; scanned 5.5-10.5
Main control parameter. The WT value is calibrated to the experimental FMI data (Fig. 4E-F, S-7); the fast-cell conclusion depends on placing WT at high alpha0.
epsilon (max chemokine enhancement) = 0.2 in parametric study; 0.1 in experimental comparisons
Chosen by hand; controls strength of signal and affects error rates and arrival times.
C/c0 (chemokine saturation ratio) = 0.01 (strong) and 1 (weak)
Chosen by hand to define strong and weak signal regimes; tradeoff results depend on regime.
y0 (exponential decay length) / yend (linear cutoff) = y0 = 1.5 d; ysource = -yend = 8 d
Chosen; sets spatial scale over which the gradient is felt.
d (hexagonal edge length) = 3, 3.7, 7.5, 9 in different runs
Network length scale; larger d changes slow-mode frequency and arrival time.
noise amplitude Gamma = 0.1, 0.5, 0.6, 1.0, 1.2
Chosen per run; higher noise increases error rates and arrival times (S-4).
adopted model parameters (Table S-1) = c=3.85, D=3.85, k=0.8, fs=5, r=5, eta=20, beta=250
Taken from previous calibration to motile cells [10]; not fit here but set base dynamics.

assumptions (5)

domain assumption A branched cell can be represented as N arms on a hexagonal network with actin flow, slip-bond adhesion, and an advected polarity inhibitor described by Eqs. S-1 to S-5.
This is the authors' own coarse-grained model from prior work; the paper does not re-derive it but uses it as the substrate for chemotaxis.
domain assumption The chemokine signal modulates cell behavior solely by enhancing local actin polymerization speed alpha at each arm tip via Eq. 3, with no receptor dynamics or internal gradient-sensing machinery.
Invoked in Eqs. 1 and 3; this is the load-bearing entry point of the chemical signal. If real cells use other sensing mechanisms, the tradeoff may not transfer.
domain assumption The in-vivo tissue can be approximated by a regular hexagonal lattice with a linear or exponential chemokine profile.
Used for network simulations and the comparison (Eq. 4 and S-7); ignores tissue heterogeneity, cell-cell interactions, and chemokine degradation.
standard math The numerical integration of the stochastic ODEs faithfully samples model behavior over Tmax = 1000.
No convergence analysis or error bars are shown for the simulation statistics; this is a background numerical assumption.
ad hoc to paper The mapping of simulation units to experiment (one cell length in 3 min corresponds to simulation time ~2.5) preserves the dynamics being compared.
Introduced in the experimental comparison section with no independent calibration; used to place simulated speed curves on the experimental time axis.

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Cite this review

Pith. "Pith review of Chemotaxis of branched cells in complex environments." pith.science (2026). https://pith.science/paper/AIX2JVJI

@misc{pith2026250521949,
  author       = {Pith},
  title        = {Pith review of: Chemotaxis of branched cells in complex environments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AIX2JVJI}},
  note         = {Machine review of arXiv:2505.21949}
}

read the original abstract

Cell migration in vivo is often guided by chemical signals. Such chemotaxis, such as performed by immune cells migrating to a wound site, is complicated by the complex geometry inside living tissues. In this study, we extend our theoretical model of branched-cell migration on a network by introducing chemokine sources to explore the cellular response. The model predicts a speed-accuracy tradeoff, whereby slow cells are significantly more accurate and able to follow efficiently a weak chemoattractant signal. We then compare the model's predictions with experimental observations of neutrophils migrating to the site of laser-inflicted wound in a zebrafish larva fin, and migrating in-vitro inside a regular lattice of pillars. We find that the model captures the details of the sub-cellular response to the chemokine gradient, as well as the large-scale migration response. This comparison suggests that the neutrophils behave as fast cells, compromising their chemotaxis accuracy, which explains the functionality of these immune cells.

Figures

Figures reproduced from arXiv: 2505.21949 by the authors.

**Figure 2.** Chemotaxis dynamics over a single-junction with a lo [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Multiple-junction model with a chemokine line source. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Comparisons between the migration dynamics in simulat [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Comparisons between the migration dynamics in simulat [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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