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arxiv: 2411.12123 · v9 · pith:VTRHCFZHnew · submitted 2024-11-18 · 🧬 q-bio.CB · math.DS· q-bio.TO

Optimisation of neoadjuvant pembrolizumab therapy for locally advanced MSI-H/dMMR colorectal cancer using data-driven delay integro-differential equations

Georgio Hawi , Peter S. Kim , Peter P. Lee This is my paper

Pith reviewed 2026-05-23 16:41 UTC · model grok-4.3

classification 🧬 q-bio.CB math.DSq-bio.TO
keywords colorectal cancerpembrolizumabMSI-H/dMMRneoadjuvant therapydelay integro-differential equationsimmune dynamicstumour eradicationmathematical modeling
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The pith

A single medium-to-high dose of pembrolizumab can eradicate tumors in locally advanced MSI-H/dMMR colorectal cancer.

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

The paper constructs a system of delay integro-differential equations that tracks cancer cells, dendritic cells, and CD8+ T cells across the tumor site and tumor-draining lymph node, incorporating checkpoint effects and exhaustion dynamics for the first time in this deterministic setting. Parameters and starting values are taken directly from pharmacokinetic studies, radiographic measurements, and deconvolved RNA-seq profiles from TCGA COADREAD and GSE26571. Optimizing the resulting model for neoadjuvant pembrolizumab shows that one medium-to-high dose achieves tumor clearance while reducing overall drug exposure and toxicity relative to current multi-dose schedules.

Core claim

By modeling immune dynamics with delay integro-differential equations in tumor and lymph node compartments, the authors optimize pembrolizumab dosing and conclude that a single medium-to-high dose may be sufficient for effective tumour eradication while being efficient, safe, and practical in laMCRC patients.

What carries the argument

Delay integro-differential equations tracking DC migration, T cell proliferation, CD8+ T cell exhaustion and reinvigoration in the tumour site and tumour-draining lymph node compartments.

If this is right

  • Current FDA-approved multi-dose regimens for metastatic MSI-H/dMMR CRC can be improved for the locally advanced setting by reducing to a single dose.
  • Mechanistic factors such as T cell reinvigoration rates can be used to predict which patients will respond to neoadjuvant pembrolizumab.
  • Treatment efficiency improves by shortening duration and lowering cumulative toxicity while maintaining tumor eradication.
  • Patient quality of life benefits from fewer infusions without loss of clinical efficacy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same equation framework could be adapted to test dosing schedules for other PD-1 inhibitors in MSI-H tumors outside colorectal cancer.
  • Direct clinical trials in laMCRC patients would provide the decisive test of the single-dose prediction.
  • Adding variables for combination agents such as chemotherapy would allow the model to explore synergistic neoadjuvant strategies.

Load-bearing premise

The parameters and initial conditions derived from pharmacokinetic studies, radiographic data, and deconvolution of TCGA COADREAD and GSE26571 RNA-seq datasets accurately represent the in vivo immune dynamics and drug effects in laMCRC patients.

What would settle it

A clinical observation that tumors persist or recur after administration of a single medium-to-high dose of pembrolizumab to laMCRC patients would falsify the model's optimized dosing result.

Figures

Figures reproduced from arXiv: 2411.12123 by Georgio Hawi, Peter P. Lee, Peter S. Kim.

Figure 1
Figure 1. Figure 1: TCR (top left), efficacy (top right), efficiency (bottom left), and toxicity (bottom right) [PITH_FULL_IMAGE:figures/full_fig_p028_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Time traces of TCR (top left), efficacy (top right), efficiency (bottom left), and toxicity [PITH_FULL_IMAGE:figures/full_fig_p029_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Time traces of V up to 18 weeks from commencement, with no treatment in black, and Treatments 1–6 in blue, red, green, orange, magenta, and grey, respectively. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Time traces of variables in the model, with the units of the variables as in [PITH_FULL_IMAGE:figures/full_fig_p032_4.png] view at source ↗
read the original abstract

Colorectal cancer (CRC) poses a major public health challenge due to its increasing prevalence, particularly among younger populations. Microsatellite instability-high (MSI-H) CRC and deficient mismatch repair (dMMR) CRC constitute 15% of all CRC and exhibit remarkable responsiveness to immunotherapy, especially with PD-1 inhibitors. Despite this, there is a significant need to optimise immunotherapeutic regimens to maximise clinical efficacy and patient quality of life. To address this, we employ a novel framework driven by delay integro-differential equations to model the interactions among cancer cells, immune cells, and immune checkpoints in locally advanced MSI-H/dMMR CRC (laMCRC). Several of these components are being modelled deterministically for the first time in cancer, paving the way for a deeper understanding of the complex underlying immune dynamics. We consider two compartments$\unicode{x2014}$the tumour site and the tumour-draining lymph node (TDLN)$\unicode{x2014}$taking into account phenomena such as DC migration, T cell proliferation, and CD8+ T cell exhaustion and reinvigoration. Parameter values and initial conditions are derived from experimental data, integrating various pharmacokinetic, bioanalytical, and radiographic studies, along with deconvolution of bulk RNA-sequencing data from the TCGA COADREAD and GSE26571 datasets. We finally optimised neoadjuvant treatment with pembrolizumab, a widely used PD-1 inhibitor, to balance efficacy, efficiency, and toxicity in laMCRC patients. We mechanistically analysed factors influencing treatment success and improved upon currently FDA-approved therapeutic regimens for metastatic MSI-H/dMMR CRC, demonstrating that a single medium-to-high dose of pembrolizumab may be sufficient for effective tumour eradication while being efficient, safe, and practical.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a system of delay integro-differential equations (DIDEs) describing interactions among cancer cells, dendritic cells, and CD8+ T cells across tumour and tumour-draining lymph node compartments in locally advanced MSI-H/dMMR colorectal cancer. Parameters and initial conditions are obtained from pharmacokinetic studies, radiographic volumes, and cell-type deconvolution of TCGA COADREAD and GSE26571 RNA-seq data. The model is then used to optimise neoadjuvant pembrolizumab dosing, with the central claim that a single medium-to-high dose suffices for tumour eradication while remaining efficient and safe.

Significance. If the DIDE framework and its parameterisation can be shown to reproduce independent clinical kinetics, the work would supply a mechanistic, data-driven route to regimen optimisation that could reduce treatment burden relative to current FDA-approved schedules. The explicit inclusion of delay-integral terms for DC migration and T-cell reinvigoration is a technical advance over standard ODE models in this setting.

major comments (2)
  1. [Abstract] Abstract (parameter derivation paragraph): all rate constants for DC migration, T-cell proliferation, exhaustion, and reinvigoration, together with compartment initial conditions, are stated to be taken directly from external PK, radiographic, and deconvolution sources; the reported optimum (single medium-to-high dose) is therefore a direct numerical output of these fitted values rather than an independent prediction, creating a circularity that must be addressed by out-of-sample validation against serial biopsy or ctDNA time series.
  2. [Model construction] Model construction (two-compartment DIDE system): the mapping from bulk RNA-seq cell proportions to the delay kernels and integral terms that govern DC trafficking and CD8+ reinvigoration is not shown to be robust under alternative deconvolution methods or under perturbation of the assumed delay distributions; because these kernels determine the location of the optimal dose, their sensitivity must be quantified and reported.
minor comments (2)
  1. Provide the explicit system of DIDEs (including all integral kernels and coupling terms between tumour and TDLN compartments) so that the optimisation procedure can be reproduced.
  2. Report error bars or credible intervals on the optimised dose arising from parameter uncertainty; the current claim of sufficiency for a single dose lacks quantitative bounds.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thorough review and valuable suggestions. Below we provide point-by-point responses to the major comments. We believe these revisions will strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (parameter derivation paragraph): all rate constants for DC migration, T-cell proliferation, exhaustion, and reinvigoration, together with compartment initial conditions, are stated to be taken directly from external PK, radiographic, and deconvolution sources; the reported optimum (single medium-to-high dose) is therefore a direct numerical output of these fitted values rather than an independent prediction, creating a circularity that must be addressed by out-of-sample validation against serial biopsy or ctDNA time series.

    Authors: We clarify that the parameters are sourced from independent external studies and public datasets (PK, radiographic, TCGA COADREAD, GSE26571), and are not tuned to achieve the reported optimum. The single medium-to-high dose sufficiency emerges from the model's mechanistic structure. We agree that out-of-sample validation would be ideal to confirm the prediction. However, the available data do not include serial time-series from the same patients, so such validation is not possible in the current study. In the revised manuscript, we will add an explicit discussion of this limitation and its implications. We have also included additional sensitivity analyses on key parameters to bolster confidence in the results. revision: partial

  2. Referee: [Model construction] Model construction (two-compartment DIDE system): the mapping from bulk RNA-seq cell proportions to the delay kernels and integral terms that govern DC trafficking and CD8+ reinvigoration is not shown to be robust under alternative deconvolution methods or under perturbation of the assumed delay distributions; because these kernels determine the location of the optimal dose, their sensitivity must be quantified and reported.

    Authors: We appreciate this point. The delay kernels were informed by cell proportions from deconvolution of the specified RNA-seq datasets. To address robustness, the revised manuscript will include a new supplementary analysis testing alternative deconvolution methods (such as different algorithms) and perturbations to the delay distributions (varying means and variances by up to 30%). We will report that the optimal dosing regimen remains qualitatively unchanged under these variations, with quantitative details provided. revision: yes

standing simulated objections not resolved
  • Out-of-sample validation with serial biopsy or ctDNA time series data, which is not available in the datasets used and would require new clinical studies.

Circularity Check

0 steps flagged

No circularity: model parameters from external data; optimization is forward simulation

full rationale

The paper constructs a DIDE system whose parameters and initial conditions are taken from independent external sources (pharmacokinetic studies, radiographic data, TCGA COADREAD and GSE26571 deconvolution). The headline result (single medium-to-high pembrolizumab dose suffices) is obtained by numerically optimizing the resulting model; this is a standard forward prediction step, not a reduction of the output to the fitted inputs by construction. No self-citations, self-definitional equations, or renamings of known results are present in the provided text. The derivation chain remains self-contained against the cited external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the accuracy of dozens of rate constants and initial conditions taken from pharmacokinetic, radiographic, and RNA-seq sources; the two-compartment structure and the functional forms of the delay and integral terms are taken as given without independent derivation.

free parameters (2)
  • rate constants for DC migration, T-cell proliferation, exhaustion, and reinvigoration
    Derived from experimental pharmacokinetic, bioanalytical, radiographic studies and deconvolution of TCGA COADREAD and GSE26571 datasets
  • initial conditions for cell populations in tumour and TDLN compartments
    Taken from the same integrated experimental and sequencing data sources
axioms (1)
  • domain assumption The two-compartment (tumour site and tumour-draining lymph node) structure plus delay and integral terms sufficiently capture the relevant immune dynamics
    Invoked in the model construction described in the abstract

pith-pipeline@v0.9.0 · 5876 in / 1469 out tokens · 41204 ms · 2026-05-23T16:41:36.293151+00:00 · methodology

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sensitivity analysis-guided model reduction of a mathematical model of pembrolizumab therapy for de novo metastatic MSI-H/dMMR colorectal cancer

    q-bio.QM 2025-05 conditional novelty 5.0

    Sensitivity analysis using FAST and EFAST reduces a data-driven model of pembrolizumab therapy in de novo metastatic MSI-H/dMMR CRC to two simpler versions that reproduce original trajectories.

Reference graph

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