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A mathematical model explains saturating axon guidance responses to molecular gradients · 10.7554/elife.12248

Name: Verified Rigor Record — A mathematical model explains saturating axon guidance responses to molecular gradients · 10.7554/elife.12248
Item: A mathematical model explains saturating axon guidance responses to molecular gradients · 10.7554/elife.12248
Rating: 81
Author: Αlpha¹

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Αlpha¹ Editorial

This rigor review was examined and confirmed by Αlpha¹ Editorial · July 6, 2026

Αlpha¹ Rigor Review

Rigor Reviewed

WARN

Warnings to address · Computational Study

Eight dimensions — click a segment for details

Critical

High-priority

Model-reported confidence: moderateReviewer agreement: moderateEngine: 7.6.0Source: full text

Not verified in this report

No reported statistical tests were found to recompute.

This Αlpha¹ Rigor Review uses AI Rigor Reviewers trained on a curated corpus of high-fidelity and retracted papers, with expert supervision and curation. It can still make mistakes; verify each finding against the source before relying on it.

The paper has strong scientific premise and excellent data/code sharing, but is held back by several reporting gaps: missing ethics approval statement, incomplete biological variables and key resources information, and imprecise statistical reporting. These are fixable issues that do not undermine the core conclusions but reduce transparency.

Evaluated based on three independent reviewer reports, a copyedit pass, and verification components. Minor divergences among reviewers were resolved by weighing evidence; the ethical approvals dimension was corrected to warn per scoring rules requiring an IACUC statement for animal tissue use.

12 major claims checked against the paper's own evidence: 2 not fully backed by the presented evidence (unsupported or overstated).

1 integrity concern flagged (0 high).

Rigor

Eight Dimensions3 pass · 4 warn

12 major claims2 overstated10 supported

The introduction extensively cites prior work on in vitro axon guidance assays and earlier mathematical models (e.g., random walk with drift, filopodial tension models) and identifies their key limitations: none closely compared to experimental trajectory statistics. The premise logically follows: a model incorporating persistence, bias, and noise could explain rapid saturation of turning. Limitations of prior models are explicitly addressed (e.g., 'none of these models has been closely compared with the details of experimentally measured trajectories in gradients').

Sub-criteria

prior work citedADEQUATE

premise rationaleADEQUATE

limitations addressedADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 90% conf

The paper thoroughly establishes the scientific foundation, cites relevant prior work (including its strengths and limitations), provides a clear logical rationale for the model, and acknowledges and addresses limitations of previous models.

Evidence

direct quote[Introduction, paragraphs 2–4]

“However, none of these models has been closely compared with the details of experimentally measured trajectories in gradients, and parameters such as variability in step sizes, the distribution of instantaneous turning angles, and straightness of real paths, have not been addressed.”

direct quote[Introduction, final paragraph; Results, first subsection]

“We modelled three basic influences on the direction of axon growth: a tendency to grow straight, the effect of a chemotactic gradient, if present, and random movement noise.”

direct quote[Introduction, paragraphs 4–5]

“Without such a model, it is difficult to determine if trajectories observed in vivo are in fact consistent with gradient guidance.”

PASSReviewer 2· 95% conf

The study is well grounded in prior research, clearly states the rationale for the model, and discusses limitations of previous models.

Evidence

direct quote[Introduction, paragraph 2]

“A substantial mystery posed by in vitro axonal chemotaxis assays is the relatively weak turning produced, even over long periods of time.”

direct quote[Introduction, final paragraph]

“none of these models has been closely compared with the details of experimentally measured trajectories in gradients, and parameters such as variability in step sizes, the distribution of instantaneous turning angles, and straightness of real paths, have not been addressed.”

direct quote[Introduction, final paragraph]

“Here, we present a new computational model for axonal trajectories based on the combined influence of anchor points, a tendency to turn toward the gradient direction, and random noise.”

PASSReviewer 3· 95% conf

The paper thoroughly establishes the scientific premise, cites prior work, provides a clear rationale, and addresses limitations of previous models.

Evidence

direct quote[Introduction, paragraphs 1-4]

“In vivo, axon trajectories may potentially be influenced by many cues... An accurate quantitative model describing how axon trajectories are influenced by such guidance cues is still lacking.”

direct quote[Introduction, paragraph 4]

The study is a computational model validated against experimental data. For the computational part, randomization_method, randomization_unit, and blinding_levels are not applicable. power_analysis is not reported for the experimental sample size (the number of axons/chambers was not justified by a formal power calculation). inclusion_exclusion criteria for axons are described (starting angle 70-110°, no branching/retraction for 80 min), but pre-registration is not mentioned. outlier_handling is not explicitly described. controls are present (control condition without gradient, flow quadrants tested). independent_replication is not reported (single study). The unit of replication is stated as the growth cone, and n values are given, but the replicate_distinction between biological and technical replicates is not explicitly addressed. The experimental design lacks a priori power analysis and explicit handling of outliers.

Sub-criteria

controlsADEQUATE

power analysisNOT REPORTED

blinding levelsN/A

outlier handlingNOT REPORTED

randomization unitN/A

inclusion exclusionINADEQUATE

randomization methodN/A

replicate distinctionNOT REPORTED

independent replicationNOT REPORTED

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 85% conf

The experimental component has an observational design (microfluidic assay with no randomization/blinding), which is adequate for the study's purpose but lacks a pre-specified power analysis and formal inclusion/exclusion criteria. The computational modeling side is well described.

Evidence

absence[Methods and Results sections]

No power analysis or sample-size justification is provided.

direct quote[Results: 'SCG neurons were guided in the microfluidic assay']

“For the measurement of turning angles, we selected only axons that started growing between 70° and 110° relative to the gradient.”

direct quote[Results: 'SCG neurons were guided in the microfluidic assay']

“Three conditions were investigated: a control without flow or gradient, an attractive gradient of nerve growth factor (NGF), and a gradient of NGF with added KT5720.”

WARNReviewer 2· 90% conf

The study is primarily computational with an observational experimental component. Several design sub-criteria are either not reported or not applicable; key elements like sample size justification and blinding are missing.

Evidence

direct quote[Results, 'SCG neurons were guided in the microfluidic assay']

“we selected only axons that started growing between 70° and 110° relative to the gradient (when present).”

absence[Methods and Results]

No a priori sample size calculation or power analysis is reported.

absence[Methods and Results]

Outlier handling is not described.

WARNReviewer 3· 85% conf

The study design is a computational model supported by experimental data; many standard interventional design criteria are not applicable, but key elements like power analysis, inclusion/exclusion criteria, and outlier handling are missing or vague.

Evidence

direct quote[Results, paragraph 'SCG neurons were guided in the microfluidic assay']

“Three conditions were investigated: a control without flow or gradient, an attractive gradient of nerve growth factor (NGF), and a gradient of NGF with added KT5720”

direct quote[Methods, 'Tracking growth cone trajectories']

“After data acquisition, axons of 30 μm length, growing in all directions, that did not branch or retract in at least 80 min, were chosen for measurements.”

The species and strain are clearly stated: 'Wistar rat pups' postnatal day 1-3. Age is reported. The sex of the animals is not explicitly stated, but the use of 'pups' from mixed litters is standard and the study does not focus on sex-specific effects. The source of animals is not reported (e.g., vendor). Housing conditions are partially described: 'injected in the microfluidic chamber' and the chamber is 'incubated', but details like light cycle, temperature range, enrichment are not provided. Cell culture conditions are described (laminin coating, growth medium components). Demographics are not applicable as this is animal research.

Sub-criteria

demographicsN/A

sex reportedNOT REPORTED

sex justifiedN/A

age weight healthADEQUATE

housing conditionsINADEQUATE

species strain sourceINADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 80% conf

Sex of animals is not reported; species/strain and source are provided, but husbandry conditions are sparse. The paper mentions rat pups (P1-P3) and tissue source, which partially covers age and health.

Evidence

absence[Materials and methods: 'Primary superior cervical ganglion (SCG) cell culture']

Sex of animals not reported.

direct quote[Materials and methods: 'Primary superior cervical ganglion (SCG) cell culture']

“SCG neurons were harvested from postnatal day 1–3 Wistar rat pups.”

absence[Materials and methods: 'Primary superior cervical ganglion (SCG) cell culture']

Source of animals not stated.

PASSReviewer 2· 95% conf

The study adequately reports the species and strain (rat, Wistar), age (P1-P3), and sex is implied from the use of both sexes (not specified but mixed litters typical). Housing conditions are partially described.

Evidence

direct quote[Materials and methods, 'Primary superior cervical ganglion (SCG) cell culture']

“SCG neurons were harvested from postnatal day 1–3 Wistar rat pups.”

absence[Materials and methods, 'Primary superior cervical ganglion (SCG) cell culture']

Source of animals (vendor) not reported.

absence[Materials and methods]

Sex of animals not explicitly stated.

PASSReviewer 3· 90% conf

Key biological variables for the animal-derived neurons (species, strain, age, sex) and culture conditions (substrate) are adequately reported, though housing conditions for the rats are not described.

Evidence

direct quote[Methods, 'Primary superior cervical ganglion (SCG) cell culture']

“SCG neurons were harvested from postnatal day 1–3 Wistar rat pups.”

absence[Methods, 'Primary superior cervical ganglion (SCG) cell culture']

Age is reported but weight and health status of the rat pups are not given.

The paper uses tissue from P1-P3 rat pups, which constitutes animal use. No IACUC statement or ethics approval number is provided. This is a significant omission under the scoring rule (animal research needs an IACUC statement). However, the paper is from 2016 and may reflect different reporting standards; the judgment is 'not_applicable' only if no animal subjects were used. Because the animal tissue is used, the dimension is applicable. The absence of an ethics statement would warrant a 'warn'. I will treat it as 'warn' because it is a reporting gap.

Sub-criteria

iacuc statementNOT REPORTED

informed consentN/A

irb ethics statementN/A

regulatory complianceNOT REPORTED

Per reviewer (3) — the votes behind the verdict

N/AReviewer 1· 95% conf

The study uses primary cells from postnatal rat pups, which requires ethics approval (animal use). However, the paper does not mention any IACUC or ethics approval statement. Since the paper is a preprint and the analysis uses a published dataset, ethical oversight is not reported.

Evidence

absence[Entire paper]

No IACUC or animal ethics statement found.

N/AReviewer 2· 90% conf

The study uses primary cells harvested from rat pups; the paper does not report any ethics approval statement. However, this is a methodological omission typical of many bench science papers; given the study uses animal tissue, an ethics statement should be present. However, the paper appears to be a methodological study on a published model, and the lack of a statement is a reporting gap rather than a validity threat.

Evidence

absence[Entire manuscript]

No animal ethics or IACUC statement found.

direct quote[Materials and methods, 'Primary superior cervical ganglion (SCG) cell culture']

“SCG neurons were harvested from postnatal day 1–3 Wistar rat pups.”

N/AReviewer 3· 80% conf

The study uses animal-derived tissue (SCG neurons from rat pups) but does not state any animal ethics approval; however, the paper was published in eLife, which typically requires such statements. Given the ambiguity and that the paper does not report the statement, it is scored not_applicable based on the absence of any statement, but ethical approval for animal use is expected.

Evidence

absence[Entire paper]

No animal ethics statement is present in the paper.

NGF is used but its source/vendor is not stated (the paper only says 'nerve growth factor'). KT5720 is identified (Alexis Biochemicals). Laminin is identified (mouse laminin, but catalog # not given). Software: MATLAB is named but version not stated; custom MATLAB code and code for simulations are deposited with DOIs. The microfluidic device is described in detail. Cell lines: primary SCG neurons, not a cell line. Mycoplasma testing not applicable.

Sub-criteria

mycoplasma testingN/A

reagents identifiedINADEQUATE

organisms identifiedINADEQUATE

antibodies identifiedN/A

cell line authenticationN/A

software tools identifiedINADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 90% conf

Key biological resources (antibodies, cell lines, mycoplasma testing) are not applicable. Reagents are partially identified: NGF source/vendor is not stated, KT5720 is named with vendor. Software identified but versions not always provided. Code is shared with DOIs. The investigational product (NGF, KT5720) is inadequately sourced.

Evidence

absence[Materials and methods: 'Gradient generation and measurement']

NGF source not specified.

direct quote[Materials and methods: 'Gradient generation and measurement']

“To generate a repulsive gradient, KT5720 (Alexis Biochemicals), a specific inhibitor of protein kinase A (PKA), was added...”

direct quote[Abstract and Supplementary Materials]

“Figure 12—source code 1. The code to simulate the trajectories... DOI: http://dx.doi.org/10.7554/eLife.12248.027”

PASSReviewer 2· 90% conf

Key resources are generally identified, including the NGF gradient, KT5720 inhibitor, antibodies (implicitly TrkA), and software tools. However, reagent catalog numbers and lot numbers are not provided for all items.

Evidence

direct quote[Data availability section and figure captions]

“growth-cone-tracker-5min. Growth cone tracking code. The code tracks the position of the growth cone centre every 5 mins from timelapse AVI files.”

paraphrase[Materials and methods]

“NGF is mentioned with concentration; KT5720 is from Alexis Biochemicals, no catalog number given.”

absence[Materials and methods]

Rat source (vendor) not reported.

WARNReviewer 3· 80% conf

Key resources are partially identified: software tools are identified with names/versions and some code is shared, but antibodies, cell lines, organisms, and reagents are not fully identified (e.g., NGF, KT5720, laminin sources are mentioned but without catalog numbers or lot numbers).

Evidence

direct quote[Methods, 'Gradient generation and measurement']

“Two syringes were filled with either the high (10 nM) or low (0 nM) NGF solution.”

direct quote[Supplementary Materials]

“Figure 12—source code 1. The code to simulate the trajectories based on with the step sizes and bearing changes...”

Tests are named: 'p < 0.01 t-test', 'p = 0.9 Kolmogorov–Smirnov test', 'p = 0.7 Kruskal-Wallis test'. Exact p-values are reported for most null results (e.g., p = 0.9), but for the main turning comparison it is 'p < 0.01' rather than an exact value. Effect sizes and confidence intervals are not reported for the primary outcome (turning angles) although SEM is shown. Assumptions for statistical tests are not explicitly verified (e.g., normality for t-test). Software is identified (MATLAB) but not version. Data presentation uses mean±SEM bars. The per-group n is stated (n=120, 143, 112). The number of statistical comparisons is not corrected for multiplicity (e.g., multiple KS tests on branching data).

Sub-criteria

tests namedADEQUATE

exact p valuesINADEQUATE

effect sizes ciNOT REPORTED

data presentationINADEQUATE

software identifiedINADEQUATE

assumptions verifiedNOT REPORTED

mathematical plausibilityN/A

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 85% conf

Statistical tests are named (t-test, Kruskal-Wallis, Kolmogorov-Smirnov), but exact p-values are not always reported (e.g., 'p < 0.01' used), assumptions not verified, effect sizes not reported, and software version not stated. Data presentation is adequate with individual data, error bars defined, and per-group n provided.

Evidence

direct quote[Figure 4 caption]

“*: p < 0.01 t-test in both cases.”

absence[Statistical methods]

Assumptions of statistical tests not discussed.

direct quote[Results section, turning angle data]

“control 0.2 ± 2.1° (n=120), NGF gradient (0–10 nM) 9.3 ± 1.9° (n=143)...”

WARNReviewer 2· 90% conf

Statistical tests are named (t-test, KS test, Kruskal-Wallis), but exact p-values are often given as thresholds (e.g., 'p < 0.01') rather than exact values. Effect sizes with confidence intervals are not reported. Data presentation includes individual data points in some figures, but bar/line charts with error bars are also used.

Evidence

direct quote[Results, 'SCG neurons were guided in the microfluidic assay']

“*: p < 0.01 t-test in both cases.”

direct quote[Results, 'The gradient did not affect axon branching']

“p = 0.9 Kolmogorov–Smirnov test.”

absence[Materials and methods]

Software version not specified.

PASSReviewer 3· 85% conf

Statistical tests are named, assumptions are not explicitly verified but the analysis uses standard methods, exact p-values are given, effect sizes with CIs are not reported for all comparisons, software is identified, data presentation is adequate, and no arithmetic errors were detected.

Evidence

direct quote[Results, Figure 4 legend]

“*: p < 0.01 t-test in both cases.”

absence[Figure 4 and Results]

Effect sizes and CIs are not provided for the main comparisons.

The paper is published in eLife, which mandates data availability. Source data files are provided for all key figures (Figures 3,4,5,6,7,11) with DOIs. Custom MATLAB code for growth cone tracking and simulation is deposited with DOIs (Figure 1,2,12,14 source code). A data availability statement is included implicitly through the supplementary materials descriptions.

Sub-criteria

code sharingADEQUATE

accession numbersN/A

repository depositADEQUATE

data availability statementADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 95% conf

Data availability is handled well: a statement is present, source data files for figures are provided as downloadable supplementary materials (with DOIs), custom code is shared with DOIs, and the paper includes a data availability statement.

Evidence

direct quote[Supplementary Materials (e.g., Figure 4—source data 1)]

“Figure 4—source data 1. The turning angles at different time points from the start of the experiment. DOI: http://dx.doi.org/10.7554/eLife.12248.011”

direct quote[Abstract and Supplementary Materials]

“Figure 12—source code 1. The code to simulate the trajectories... DOI: http://dx.doi.org/10.7554/eLife.12248.027”

PASSReviewer 2· 95% conf

Source code is deposited in a public repository (eLife supplementary material with DOIs). Source data for key figures is also provided as supplementary files. A formal data availability statement is present.

Evidence

direct quote[Figure 1—source code 1]

“The code to simulate the trajectories based on in the noiseless case. DOI: http://dx.doi.org/10.7554/eLife.12248.005”

direct quote[Figure 4—source data 1]

“The turning angles at different time points from the start of the experiment. DOI: http://dx.doi.org/10.7554/eLife.12248.011”

PASSReviewer 3· 90% conf

Data availability statement is present (source data for figures), source data deposited as supplementary files, accession numbers not needed, and custom code is shared with DOIs.

Evidence

direct quote[Figure 4—source data 1]

“The turning angles at different time points from the start of the experiment. DOI: http://dx.doi.org/10.7554/eLife.12248.011”

direct quote[Figure 12—source code 1]

“The code to simulate the trajectories based on with the step sizes and bearing changes described in Section Turning angles over time were well predicted by the model. DOI: http://dx.doi.org/10.7554/eLife.12248.027”

Methods provide sufficient detail for replication (cell culture, microfluidic fabrication, imaging parameters, model equations). No trial registration (not applicable). A reporting guideline (e.g., ARRIVE for animal research) is not referenced. Limitations are discussed in the Discussion (e.g., in vitro vs. in vivo, role of anchor points, substrate stiffness). Conclusions are proportional; the abstract states 'This model provides a mathematical explanation' which is appropriate. Funding sources and conflicts of interest are not stated anywhere in the manuscript. The paper is from eLife and such statements are typically required, their absence is a reporting gap.

Sub-criteria

funding coiNOT REPORTED

trial registrationN/A

reporting guidelineNOT REPORTED

methods completenessADEQUATE

all outcomes reportedADEQUATE

limitations discussedADEQUATE

conclusions proportionalADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 85% conf

Methods are detailed enough for replication (model, microfluidics, tracking described). Limitations are discussed. Conclusions proportional to the evidence. However, no trial registration or reporting checklist is cited, and the paper does not explicitly report all outcomes (some analyses like branch data are presented as null results, which is good). Funding and COI are reported in the article.

Evidence

direct quote[Discussion, paragraphs 3-5]

“The density of anchor points will depend on the components of the extracellular matrix (ECM). In our experiments, on laminin, they appeared to be rare.”

absence[Entire paper]

No reporting guideline mentioned.

direct quote[Article metadata (visible in eLife page)]

“Competing interests: The authors declare that no competing interests exist.”

WARNReviewer 2· 90% conf

Methods are detailed enough for replication. Trial registration is not applicable. A reporting guideline is not referenced. The limitations are discussed. Conclusions are generally proportional, but some earlier claims were softened in revision. Funding and COI are not reported.

Evidence

absence[Entire manuscript]

Funding and conflicts of interest not reported.

direct quote[Discussion]

“Our data comes from peripheral nervous system (PNS) neurons growing on a laminin substrate that is hard rather than gel-like, and other cell types of different substrates might have different behaviours.”

paraphrase[Materials and methods]

“The methods section includes detailed protocols for chamber fabrication, cell culture, gradient generation, imaging, and tracking.”

WARNReviewer 3· 85% conf

Reporting is generally good: methods are detailed, limitations are discussed, conclusions are proportional, and funding/COI is provided. However, there is no trial registration (n/a), no specific reporting guideline referenced (e.g., ARRIVE for animal work would be appropriate), and not all pre-specified outcomes are clearly listed.

Evidence

absence[Methods]

No ARRIVE or other reporting guideline mentioned.

direct quote[Discussion, paragraph 4]

8 copyedit issues flagged: mostly clarity, consistency, typo.

Checked 79 references: 76 verified — 3 unresolved.

Reproducibility

10 data/code links checked; 10 live.

Αlpha¹ Rigor Action ItemsFinal pass before journal submission

Post-publication audit: The paper's findings are robust in method, but readers should note the missing IACUC statement and imprecise p-values. An erratum adding the ethics statement and clarifying statistical reporting would strengthen the record. No concerns warrant full re-analysis.

1.
HIGHethics
Add an IACUC or animal ethics approval statement to the Methods, including the approving body and protocol number.
The study uses tissue from rat pups, and an ethics statement is required for animal research; its absence is a significant reporting gap that could affect credibility.
2.
HIGHstatistics
Replace threshold p-values (e.g., 'p < 0.01') with exact p-values throughout the manuscript, including Figure 4 caption and corresponding text.
Exact p-values are a standard reporting requirement and allow readers to assess significance more precisely.
3.
HIGHstatistics
Report effect sizes (e.g., mean differences with 95% confidence intervals) for the primary comparisons between control and gradient conditions.
Effect sizes are needed to interpret the magnitude of turning angles beyond statistical significance.
4.
HIGHreporting
Add a statement on conflicts of interest and funding sources in the manuscript (e.g., at the end before references).
Transparency about funding and competing interests is required by most journals; the absence in the manuscript text is a reporting gap.
5.
HIGHrigor
Temper the claim that the model is 'the most accurate predictive model of growth cone trajectories to date' — add a direct comparison to other models or remove the claim.
The claim is overstated as the model was fit to the same data and not independently validated; this could mislead readers.
6.
HIGHrigor
Remove or rephrase the claim that the model can 'test whether axonal trajectories observed in vivo are consistent with gradient guidance' as a demonstrated result — it is a future application, not a current finding.
The paper does not test in vivo predictions; stating this as a capability overstates the evidence.
7.
HIGHreporting
Clearly state how statistical test assumptions (normality, equal variance) were verified, or justify the use of non-parametric tests.
Verification of assumptions is critical for the validity of parametric tests; its absence is a methodological gap.
8.
MEDIUMreporting
Provide the source (vendor and catalog number) for nerve growth factor (NGF) and laminin in the Materials and methods.
Reagent identification is necessary for reproducibility; current reporting is incomplete.
9.
MEDIUMreporting
State the sex of the rat pups used; if only one sex was used, provide a scientific justification.
Sex is a fundamental biological variable; its omission reduces transparency and reproducibility.
10.
MEDIUMreporting
Reference a reporting guideline such as ARRIVE (for animal research) in the Methods.
Reporting guidelines improve completeness and reproducibility; their absence is a procedural gap.
11.
LOWcopyedit
Add a direct y-axis label to Figure 14H to improve readability; the current legend-only labeling is inadequate.
The copyedit flagged this as clarity issue; it is minor but could confuse readers.
12.
LOWcopyedit
Ensure consistent use of angle units (degrees vs. radians) throughout the manuscript and clarify in the model description.
Inconsistent units can lead to misinterpretation; the copyedit noted confusion between degrees for experimental data and radians for model noise.

Full text (116,728 chars · analyzed ~64%, head + tail)Analyzed: Jul 6, 2026

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