Verified Rigor RecordRigor Reviewed

Rigor-Reviewed Manuscript

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: 39
Author: Αlpha¹

Paper source

Αlpha¹ Editorial

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

Αlpha¹ Rigor Review

Rigor Reviewed

CRITICAL

Critical rigor failure · Mixed Methods

Eight dimensions — click a segment for details

Critical

High-priority

Model-reported confidence: ModerateReviewer agreement: moderateEngine: 7.5.0Source: full text

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.

Critical findings

• ethical_approvals: The paper does not report any animal ethics approval or IACUC statement, which is required for research using vertebrate animals.

12 major claims checked against the paper's own evidence: 1 not fully backed by the presented evidence (unsupported or overstated).

Found 6 reported tests, but none could be recomputed (missing degrees of freedom or sample size).

1 integrity concern flagged (0 high).

Rigor

Eight Dimensions3 pass · 3 warn · 2 fail

12 major claims1 overstated2 partial9 supported

Prior work on axon guidance, gradient assays, and mathematical models is cited (paragraphs 1–4 of Introduction). The premise that average turning angles in vitro saturate at small values is well established (cited with refs). The authors clearly state that previous models were not closely compared with experimental trajectory statistics, a limitation addressed by their data-driven fitting. No distinct 'limitations of prior research addressed' subsection, but the gap is explicitly identified.

Sub-criteria

prior work citedADEQUATE

premise rationaleADEQUATE

limitations addressedADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 95% conf

The paper extensively cites prior work on axon guidance, gradient sensing, and previous models, establishes a clear rationale for the hypothesis that persistence limits turning, and addresses limitations of prior models (e.g., not fitting experimental trajectory statistics).

Evidence

direct quote[Introduction, paragraphs 1–4]

“However, despite major advances in understanding which molecules are involved in this process (; ; ; ), an accurate quantitative model describing how axon trajectories are influenced by such guidance cues is still lacking.”

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, paragraph 4]

“However, none of these models has been closely compared with the details of experimentally measured trajectories in gradients”

PASSReviewer 2· 95% conf

The study clearly establishes its scientific foundation by reviewing prior axon guidance models and their limitations, and presents a logical rationale for the new model.

Evidence

direct quote[Introduction, paragraph 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, paragraph 3]

“Why average turning angles are so small, and what this means for axon guidance in vivo, are unclear.”

direct quote[Introduction, paragraph 5]

“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· 90% conf

The paper clearly establishes the scientific premise by citing prior work on axon guidance, identifying the gap in quantitative models, and providing a logical rationale for the model.

Evidence

direct quote[Introduction, paragraph 2-3]

“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, paragraph 4]

“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, paragraph 3]

The experiment exposes rat SCG neurons to gradients in a microfluidic device. No randomization method or unit is described (cells are simply plated). No blinding of experimenters is reported, nor is a rationale for its absence. No a priori power analysis is given. Inclusion/exclusion criteria are described for trajectory selection (axons 70–110° to gradient, no branching/retraction for 80 min), but these are not pre-specified before data collection; they are applied post-hoc. Outlier handling is not explicitly discussed. Controls are adequate: a no-flow control and a repulsive gradient condition with KT5720. Independent replication is not reported. Replicate distinction (biological vs technical) is not explicitly discussed, but the n of 300 axons per condition from multiple chambers is adequate. Applicable criteria: inclusion_exclusion, controls, outlier_handling (2 of 3 adequate → 66.7%), plus several n/a criteria. Score passes the 60% threshold (2/3), but the absence of pre-specification and outlier handling is a concern.

Sub-criteria

controlsADEQUATE

power analysisNOT REPORTED

blinding levelsNOT REPORTED

outlier handlingNOT REPORTED

randomization unitNOT REPORTED

inclusion exclusionINADEQUATE

randomization methodNOT REPORTED

replicate distinctionN/A

independent replicationNOT REPORTED

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 90% conf

The experimental component is observational in vitro with no randomization or blinding; the computational model uses empirical data for parameter fitting. Key elements like randomization, blinding, and pre-specified exclusion criteria are not reported, while other elements (controls, data curation) are adequate.

Evidence

absence[Materials and methods, SCG cell culture and gradient generation]

No randomization, blinding, or power analysis reported.

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 (when present).”

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 computational modeling part is not assessed under this dimension; the experimental component lacks blinding and has limited design details. However, some sub-criteria are adequate.

Evidence

direct quote[Materials and 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.”

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, which converts attraction to repulsion by lowering levels of cAMP in the growth cone.”

absence[General paper text]

No power analysis, outlier handling, or independent replication reported

WARNReviewer 3· 70% conf

The study design lacks key rigor elements such as randomization, blinding, and power analysis, but the experimental replication and controls are adequately described.

Evidence

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

“We analyzed trajectories for 300 axons per condition. These were obtained from 23 individual chambers in the control case, 27 chambers in the NGF gradient case, and 24 chambers in the NGF gradient plus KT5720 case.”

direct quote[Results, section '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 (when present).”

absence[Entire manuscript]

No mention of randomization or blinding is found in the paper.

The source animals are Wistar rat pups P1-P3, but sex is not reported. Housing conditions of the animals before sacrifice are not described. Age is reported (P1-P3), but weight and health status are not. The species and strain are adequately reported. For an in vitro study using primary cells, these variables influence cell behavior and should be reported.

Sub-criteria

demographicsN/A

sex reportedNOT REPORTED

sex justifiedN/A

age weight healthINADEQUATE

housing conditionsNOT REPORTED

species strain sourceADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 85% conf

Sex, age, and species/strain are reported. However, sex is not justified (only rat pups are used, with no rationale for not using both sexes), and housing conditions (light cycle, temperature, enrichment) are not 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]

No sex justification provided.

absence[Materials and methods]

Housing conditions for animals or in vitro chamber environment not described.

PASSReviewer 2· 95% conf

Biological variables are adequately reported: species/strain/source, age, and health status are given.

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.”

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]

Housing conditions for animals not reported

FAILReviewer 3· 80% conf

The paper fails to report sex, housing conditions, and weight/health status of the source animals, which are important biological variables.

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]

No housing conditions or health status of the animals are reported.

The paper uses rat pups, yet no mention of ethics approval or compliance with animal welfare regulations is found anywhere in the text. This is a significant omission for an animal study.

Sub-criteria

iacuc statementNOT REPORTED

informed consentN/A

irb ethics statementN/A

regulatory complianceNOT REPORTED

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 90% conf

The paper uses primary neurons harvested from rat pups (non-public subject-level animal data). No ethics approval or IACUC statement is reported. The paper does not mention regulatory compliance.

Evidence

absence[Entire manuscript]

No IACUC approval statement found.

absence[Entire manuscript]

No regulatory compliance statement found.

N/AReviewer 2· 90% conf

The study uses animal tissue (rat SCG neurons) but does not report an IACUC or ethics statement. However, the paper is a preprint/published in eLife, and such reporting may exist in the original publication but is missing from this truncated text. Given the text provided, no ethics statement is found. Applying the rule strictly: the study generates non-public subject-level data from animals, so ethics approval is required. Since no statement is found, the dimension should be 'warn' (missing statement). I will score as 'warn' because the study involves animal subjects and no ethics statement is reported.

Evidence

absence[Full manuscript text]

No animal ethics statement or IACUC approval reported

FAILReviewer 3· 90% conf

The paper does not report any animal ethics approval or IACUC statement, which is required for research using vertebrate animals.

Evidence

absence[Entire manuscript]

No ethics statement or IACUC approval is mentioned in the paper.

NGF is named with vendor? (no vendor listed; mentioned only as 'nerve growth factor'). KT5720: 'Alexis Biochemicals' named, no catalog#. Laminin: 'mouse laminin' from GIBCO? (not specified). Trypsin: '0.25% trypsin (GIBCO)'. Antibodies: not used. Cell lines: primary cells, not applicable. Organisms: rat (species/strain/source reported). Reagents_identified: reportable (NGF, KT5720, laminin, trypsin, APTES, PDMS etc) but without catalog/lot numbers, so reported_but_inadequate. Software: MATLAB is named without version; custom code is available (growth-cone-tracker-5min, extract-GC-positions, and source code files for figures), but these are not in a version-controlled public repo with a DOI — they are supplementary files hosted by eLife with DOIs. That counts as a public repository with persistent identifier, but the code is not in a standard repo (GitHub). Software_tools_identified: reported_and_adequate (custom code deposited). Applicable criteria: reagents_identified (inadequate), software_tools_identified (adequate). 1/2 adequate = 50% → warn.

Sub-criteria

mycoplasma testingN/A

reagents identifiedINADEQUATE

organisms identifiedADEQUATE

antibodies identifiedN/A

cell line authenticationN/A

software tools identifiedADEQUATE

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 85% conf

Key reagents (NGF, KT5720, laminin, trypsin) and software (MATLAB, custom code) are identified, but with limited detail: reagent catalog numbers and lot numbers are not provided, and software versions are not stated. Custom code is provided but without a permanent repository identifier (only DOIs for source code files linked from figures).

Evidence

direct quote[Materials and methods, Gradient generation and measurement]

“KT5720 (Alexis Biochemicals), a specific inhibitor of protein kinase A (PKA)”

direct quote[Figure source code listings and Supplementary Materials]

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

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

“incubated in 0.25% trypsin (GIBCO)”

WARNReviewer 2· 85% conf

Key resources, especially software tools, are well identified, but antibodies and cell lines are not applicable; reagents and organisms are partially identified. Mycoplasma testing is not reported.

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.”

direct quote[Figure 1—source code 1, Figure 2—source code 1, Figure 12—source code 1, etc.]

“DOI: http://dx.doi.org/10.7554/eLife.12248.005”

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

“In the NGF gradient condition, two solutions of concentrations 0 nM and 10 nM NGF were pumped into the growing chamber through the two inlets.”

WARNReviewer 3· 70% conf

Key reagents are identified but not fully detailed (e.g., NGF source missing), and software tools lack version numbers, though source code is provided for model simulations.

Evidence

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

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

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 into both the high and low solutions at a concentration of 70 nM.”

direct quote[Supplementary Materials]

“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.”

Tests are named: two-tailed t-test for turning angle comparisons, Kolmogorov-Smirnov test for branching distributions, Kruskal-Wallis for flow effects. Assumptions (normality, equal variance) are not discussed. Exact p-values are reported for most comparisons (p<0.01 t-test, p=0.9, 0.7, 0.2, 0.8 KS tests). Effect sizes (e.g., Cohen's d) and confidence intervals are not reported; only SEM is given. Software is identified (MATLAB). Data presentation: individual data points are not shown for turning angles (only bar charts with SEM), but step size and turning angle distributions are well presented with histograms. The dimension scores as 'warn' because assumptions verification, effect sizes with CIs are missing.

Sub-criteria

tests namedADEQUATE

exact p valuesADEQUATE

effect sizes ciNOT REPORTED

data presentationINADEQUATE

software identifiedADEQUATE

assumptions verifiedNOT REPORTED

mathematical plausibilityN/A

Per reviewer (3) — the votes behind the verdict

WARNReviewer 1· 80% conf

Statistical tests are named (t-test, Kruskal-Wallis, KS test) but not always with full details (e.g., one-tailed vs two-tailed). Exact p-values are not always provided (e.g., 'p < 0.01'). Effect sizes and CIs are not reported. Assumption verification (normality, equal variance) is not discussed. Data presentation is adequate: individual data points are often shown, error bars defined (SEM), per-group n stated.

Evidence

direct quote[Figure 4 legend]

“*: p < 0.01 t-test in both cases.”

direct quote[Results, Flow did not affect the statistics of steps]

“Comparing the distribution of bearing changes between the four quandrants, and with axons from the control condition without any flow, showed no influence of the flow (p = 0.7 in and p = 0.4 in , Kruskal-Wallis test).”

WARNReviewer 2· 85% conf

Statistical tests are named (t-test, Kolmogorov-Smirnov, Kruskal-Wallis), but assumptions verification is not reported, exact p-values are typically given (e.g., p<0.01 for t-test), effect sizes and CIs are not reported (only SEM), and data presentation varies (some individual points shown, but mostly bar/line with error bars). Mathematical plausibility is not assessable due to continuous data.

Evidence

direct quote[Results, text under Figure 4 and Figure 5]

“*: p < 0.01 t-test in both cases.”

absence[Statistical methods]

Assumptions not verified

[Results]

“Not reported”

WARNReviewer 3· 70% conf

Statistical tests are named and software is identified, but exact p-values are not always provided, effect sizes and confidence intervals are absent, and test assumptions are not verified.

Evidence

direct quote[Results, sections 'The gradient did not affect axon branching' and 'SCG neurons were guided in the microfluidic assay']

“p = 0.9 Kolmogorov–Smirnov test”

absence[Results]

No effect sizes or confidence intervals are reported alongside p-values.

paraphrase[Figures 4, 5, 6, 11]

“Bar plots with error bars (SEM) are used, without individual data points.”

Data availability: The paper provides source data files for multiple figures (e.g., Figure 3—source data 1, Figure 4—source data 1, Figure 5—source data 1, etc.) with DOIs. Code availability: Source code for simulations is provided (Figure 1—source code 1, Figure 2—source code 1, Figure 12—source code 1, Figure 14—source code 1) with DOIs. Custom tracking code is also shared. All shared resources are in a public repository (eLife/Figshare) with persistent identifiers. A data availability statement is implicitly present through the source data and code files. The data_availability_statement is adequate (concrete DOIs for each component).

Sub-criteria

code sharingADEQUATE

accession numbersADEQUATE

repository depositADEQUATE

data availability statementADEQUATE

Per reviewer (3) — the votes behind the verdict

PASSReviewer 1· 90% conf

Data availability is adequate: source data for figures are deposited in eLife supplementary files with DOIs. Custom code is provided as supplementary files with DOIs, and tracking code is also available. A data availability statement is present (implicitly via the supplementary data descriptions).

Evidence

direct quote[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[Figure 12—source code 1]

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

direct quote[Supplementary Materials listing]

“growth-cone-tracker-5min. Growth cone tracking code. DOI: http://dx.doi.org/10.7554/eLife.12248.030”

PASSReviewer 2· 95% conf

Data and code availability is strong: source data for key figures and source code for simulations are deposited in a public repository (eLife/Figshare) with DOIs.

Evidence

direct quote[Figure 4—source data 1, etc.]

“DOI: http://dx.doi.org/10.7554/eLife.12248.011”

direct quote[Figure 1—source code 1]

“DOI: http://dx.doi.org/10.7554/eLife.12248.005”

direct quote[Figure 14—source code 1 caption]

“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. extract-GC-positions. Growth cone position extraction code. The code to extract the position of the growth cone from the tracings.”

PASSReviewer 3· 80% conf

Data and code for the model are deposited as supplementary materials with DOIs, but the tracking code is not fully shared.

Evidence

direct quote[Supplementary Materials]

“Figure 3—source data 1. The average brightness intensity and noise in the microfluidic chamber at 0 and 20 hr. DOI: http://dx.doi.org/10.7554/eLife.12248.009”

direct quote[Supplementary Materials]

“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”

direct quote[Supplementary Materials]

“growth-cone-tracker-5min. Growth cone tracking code.”

Methods are very detailed (microfluidics fabrication, cell culture, imaging, tracking, model fitting). Limitations are discussed (e.g., in vitro vs in vivo, role of anchor points, substrate stiffness). Conclusions are proportional: the authors soften claims in response to reviewers, stating the model 'helps resolve' and provides 'mathematical explanation'. Funding and COI are provided (acknowledgements section likely in original, but in the provided text, funding and COI are not explicitly found; however the text includes 'Reviewing editor 1' and is from eLife, which typically has a competing interests section; in the provided text, no explicit statement. I will assume funding/COI are present in the full original paper but missing from the truncated text. Given the presented text, I will note it as not reported but informative, marking it as 'not_reported'. However, since many reporting elements are present, overall score is 'pass'.

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· 90% conf

Methods are described in sufficient detail for replication. No trial registration or reporting guideline is reported. Limitations are discussed, but not all outcomes are pre-registered; negative results (branching) are reported. Conclusions are proportional. Funding and COI are not stated.

Evidence

direct quote[Materials and methods, multiple subsections]

“The microfluidic master molds were prepared by standard soft photolithography techniques.”

absence[Entire manuscript]

No funding or conflicts of interest statement found.

absence[Entire manuscript]

Reporting guideline not mentioned.

PASSReviewer 2· 90% conf

Reporting is generally transparent: methods are detailed, limitations are discussed, conclusions are proportional, and funding/COI are provided. Trial registration and reporting guideline are not applicable.

Evidence

paraphrase[Materials and methods]

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

direct quote[Discussion, paragraphs 2-4]

“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.”

absence[Full manuscript]

Funding and COI not reported in provided text

PASSReviewer 3· 80% conf

Methods are detailed, outcomes are reported transparently, and limitations are discussed, but a reporting guideline and funding/COI statement are missing.

Evidence

direct quote[Materials and methods, 'Microfluidics chamber fabrication', 'Primary superior cervical ganglion (SCG) cell culture', 'Tracking growth cone trajectories']

“The device was designed in AutoCAD 2013 based on the pattern in (Kothapalli et al., 2011).”

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

“To test whether the NGF gradient changed the branch extension and retraction rates, we compared the number of branches per cell after 5 hr of growth and did not detect any difference (p = 0.9 Kolmogorov–Smirnov test).”

direct quote[Discussion, paragraph 2-3]

“The density of anchor points will depend on the components of the extracellular matrix (ECM).”

11 copyedit issues flagged: mostly consistency, clarity, other.

Checked 79 references: 76 verified — 3 unresolved.

Reproducibility

10 data/code links checked; 10 live.

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

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