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arxiv: 2506.09374 · v3 · submitted 2025-06-11 · 🧬 q-bio.QM · physics.data-an· stat.AP· stat.ML

Inherited or produced? Inferring protein production kinetics when protein counts are shaped by a cell's division history

Pedro Pessoa , Juan Andres Martinez , Vincent Vandenbroucke , Frank Delvigne , Steve Press\'e This is my paper

Pith reviewed 2026-05-19 10:30 UTC · model grok-4.3

classification 🧬 q-bio.QM physics.data-anstat.APstat.ML
keywords protein production kineticscell division historyprotein inheritancenormalizing flowsflow cytometryglc3 geneyeast stress responselikelihood approximation
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The pith

Accounting for cell division history shows the glc3 gene is mostly inactive under stress.

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

The paper develops a way to infer protein production rates from snapshot fluorescence data in dividing cells, where measured levels include proteins inherited from mother cells through multiple divisions. Standard likelihood calculations fail because the dependence on division history is non-Markovian and cannot be written in closed form. Conditional normalizing flows are trained on simulated division trajectories to approximate the likelihood of the observed data. Applied to flow cytometry measurements of the glc3 promoter in yeast, the method indicates that the gene is mostly silent during nutrient stress, with activation occurring only briefly and infrequently. This reinterpretation matters because it distinguishes true production kinetics from the confounding effects of population growth and inheritance.

Core claim

When the non-Markovian effects of cell division and protein inheritance are incorporated by training conditional normalizing flows on simulated trajectories, the flow-cytometry fluorescence data for the glc3 promoter are best explained by a model in which the gene is mostly inactive under stress, with only occasional brief activation events rather than widespread low-level expression.

What carries the argument

Conditional normalizing flows trained on simulated cell-division and protein-inheritance trajectories to approximate the otherwise intractable likelihood of observed fluorescence data.

If this is right

  • Flow cytometry snapshots of gene expression in growing populations must be corrected for inherited protein to avoid overestimating active fractions.
  • Normalizing-flow likelihoods enable Bayesian inference for any system whose observations depend on non-Markovian inheritance or division history.
  • Transient glc3 activation implies that glycogen synthesis is tightly regulated and not constitutively on during nutrient limitation.
  • The same simulation-plus-flow approach can be applied to other promoter-reporter strains to extract production rates without requiring continuous observation.

Where Pith is reading between the lines

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

  • Previous studies that interpreted low fluorescence in flow cytometry as low-level steady expression may need reanalysis once division history is included.
  • The method could be combined with lineage-tracing data to test whether the inferred brief activation matches actual on/off switching times.
  • Similar corrections for inheritance would change kinetic parameter estimates in any exponentially growing culture monitored by bulk or snapshot assays.

Load-bearing premise

The simulated cell-division and protein-inheritance trajectories used to train the normalizing flow accurately represent the true biological process.

What would settle it

Time-lapse microscopy of individual yeast lineages that directly measures the frequency and duration of glc3 promoter activation events across multiple generations under the same stress conditions.

Figures

Figures reproduced from arXiv: 2506.09374 by Frank Delvigne, Juan Andres Martinez, Pedro Pessoa, Steve Press\'e, Vincent Vandenbroucke.

Figure 1
Figure 1. Figure 1: Summary of the simulation based inference with likelihood approximation for learning protein count dynamics through flow cytometry. a) Our approach involves developing a system continuously sampling parameters and simulating the dynamics, encompassing the processes underlying both the system’s behavior and the measurement process, to predict the data expected from these parameters. At each new sampling ste… view at source ↗
Figure 1
Figure 1. Figure 1: 2 Methods 2.1 Simulators, latent variables and likelihoods Simulations play a central role across scientific disciplines by enabling researchers to explore how different mechanisms influence observable outcomes. More precisely, a simulator is a computational tool that takes model parameters, denoted by θ, and uses random number generators to sample realization-specific variables, which we collectively deno… view at source ↗
Figure 2
Figure 2. Figure 2: Why the Markovian approach is insufficient to learn protein production counts across cell division. RNA production is often modeled as a birth-death process [28, 36] (simulated in the top left panel), where constant production leads to a Poisson steady-state distribution (top right). While previous literature extend these Markovian models to account for protein production [1–5], marker proteins have lifeti… view at source ↗
Figure 3
Figure 3. Figure 3: Results for Model 1. a) Schematic of the model described in Sec. 3.1. The model involves a single parameter, β, representing the protein production rate. Proteins are diluted during cell division, which occurs at fixed intervals of duration T. b) Neural network approximation of the likelihood (blue) for selected β values, compared to data simulated using these values as ground truth (orange histogram) and … view at source ↗
Figure 4
Figure 4. Figure 4: Results for Model 2. a) Schematic of the model described in Sec. 3.2. We learn the pair of parameters θ = {β, σ} representing the protein production rate and cell division time standard deviation. b) Neural network approximation of the likelihood (blue) for selected θ values, compared to data simulated using these values as ground truth (orange histogram). The neural network accurately captures the likelih… view at source ↗
Figure 5
Figure 5. Figure 5: Results for Model 3. a) Schematic of the model described in Sec. 3.3. Including the budding-type division that is common in S. cerevisiae. We learn the set of parameters θ = {β, σ, λact, λina} representing the protein production rate, cell division time standard deviation, activation rate, and deactivation rate. b) Neural network approximation of the likelihood function for the total flow cytometry intensi… view at source ↗
Figure 6
Figure 6. Figure 6: Inference of protein kinetics from real flow cytometry data. (a) Fluorescence intensity, in arbitrary florescence units, distributions for yeast populations at different dilution rates. Since lower dilution rates correspond to higher nutrient limitation and thus higher stress, the high stress condition (0.12 h −1 ) shows significantly elevated fluorescence compared to the low stress condition (0.23 h −1 ),… view at source ↗
read the original abstract

Inferring protein production kinetics for dividing cells is complicated due to protein inheritance from the mother cell. For instance, fluorescence measurements -- commonly used to assess gene activation -- may reflect not only newly produced proteins but also those inherited through successive cell divisions. In such cases, observed protein levels in any given cell are shaped by its division history. As a case study, we examine activation of the glc3 gene in yeast involved in glycogen synthesis and expressed under nutrient-limiting conditions. We monitor this activity using snapshot fluorescence measurements via flow cytometry, where GFP expression reflects glc3 promoter activity. A na\"ive analysis of flow cytometry data ignoring cell division suggests many cells are active with low expression. Explicitly accounting for the (non-Markovian) effects of cell division and protein inheritance makes it impossible to write down a tractable likelihood -- a key ingredient in physics-inspired inference, defining the probability of observing data given a model. The dependence on a cell's division history breaks the assumptions of standard (Markovian) master equations, rendering traditional likelihood-based approaches inapplicable. Instead, we adapt conditional normalizing flows (a class of neural network models designed to learn probability distributions) to approximate otherwise intractable likelihoods from simulated data. In doing so, we find that glc3 is mostly inactive under stress, showing that while cells occasionally activate the gene, expression is brief and transient.

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 method to infer protein production kinetics from snapshot fluorescence measurements in dividing cells by training conditional normalizing flows on simulated trajectories that incorporate cell division history and protein inheritance. Applied to flow-cytometry data for the glc3 promoter in yeast under nutrient stress, the approach concludes that glc3 is mostly inactive, with only occasional brief and transient activations.

Significance. If the simulation model and normalizing-flow approximation are faithful, the work offers a practical route to likelihood-based inference for non-Markovian processes that are common in growing cell populations, potentially improving the interpretation of static gene-expression data in systems biology. The explicit use of forward simulation to train an approximator for an otherwise intractable likelihood is a clear technical strength.

major comments (2)
  1. [Methods] Methods (simulation model): Division timing, mother-daughter partitioning kernel, and growth-rate variability are selected by the authors without reported quantitative calibration or comparison to experimental division statistics measured under the same stress conditions. Because the normalizing flow is trained exclusively on these simulations, any systematic mismatch propagates directly into the inferred production-rate parameters and the headline claim that glc3 activation is brief and transient.
  2. [Results] Results / Abstract: No validation metrics, error bars, or baseline comparisons are supplied for the normalizing-flow likelihood approximator when applied to real data. Without these, the support for the conclusion that glc3 is mostly inactive remains difficult to assess.
minor comments (2)
  1. [Methods] The notation for the conditional normalizing flow (input/output dimensions, conditioning variables) could be clarified with an explicit diagram or equation set.
  2. [Figures] Figure captions should state the number of simulated trajectories used for training and the precise stress condition (e.g., specific nutrient limitation) to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments, which have helped us identify opportunities to strengthen the presentation and robustness of our work. We address each major comment below and indicate the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Methods] Methods (simulation model): Division timing, mother-daughter partitioning kernel, and growth-rate variability are selected by the authors without reported quantitative calibration or comparison to experimental division statistics measured under the same stress conditions. Because the normalizing flow is trained exclusively on these simulations, any systematic mismatch propagates directly into the inferred production-rate parameters and the headline claim that glc3 activation is brief and transient.

    Authors: We appreciate the referee drawing attention to the need for explicit calibration of the simulation parameters. The division timing, partitioning kernel, and growth-rate variability were chosen from established literature values for budding yeast under nutrient limitation. We agree that a direct quantitative comparison to experimental division statistics under the precise stress conditions of the flow-cytometry experiments would increase confidence. In the revised manuscript we will add a supplementary figure and accompanying text that compares simulated division statistics to published experimental measurements for yeast under comparable nutrient stress, together with a sensitivity analysis demonstrating how plausible variations in these parameters affect the inferred production kinetics. This will clarify the robustness of the conclusion that glc3 activation is brief and transient. revision: partial

  2. Referee: [Results] Results / Abstract: No validation metrics, error bars, or baseline comparisons are supplied for the normalizing-flow likelihood approximator when applied to real data. Without these, the support for the conclusion that glc3 is mostly inactive remains difficult to assess.

    Authors: We acknowledge that additional quantitative checks on the real-data application would aid assessment. The conditional normalizing flow was validated on large held-out synthetic datasets generated from the forward model, where ground-truth parameters are known; these tests showed accurate recovery of production-rate parameters and faithful approximation of the intractable likelihood. For the experimental flow-cytometry data we already include a consistency check by comparing the observed fluorescence distribution to forward simulations under the inferred parameters. In revision we will augment the Results section with explicit validation metrics (including log-likelihood on a held-out subset of real measurements and variability across independently trained flows), error bars derived from the flow ensemble, and a baseline comparison against inference performed while ignoring division history. These additions will provide clearer quantitative support for the claim that glc3 is mostly inactive. revision: yes

Circularity Check

0 steps flagged

No significant circularity; simulation-based inference is independent of target data

full rationale

The paper constructs an explicit forward model of cell division, protein inheritance, and production, generates simulated trajectories from it, trains a conditional normalizing flow to approximate the resulting likelihood, and applies the trained approximator to real flow-cytometry observations to infer production-rate parameters. This chain does not reduce any claimed result to its inputs by construction: the simulation parameters are chosen independently of the experimental measurements, the normalizing-flow training is a standard density-estimation step on synthetic data, and the final inference step operates on held-out real data. No self-definitional equations, fitted-input predictions, or load-bearing self-citations appear in the derivation. The central claim that glc3 is mostly inactive follows from the data-driven posterior rather than tautological re-expression of the simulation assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate specific free parameters or axioms; the approach rests on an explicit but unspecified model of cell division timing and protein partitioning.

axioms (1)
  • domain assumption Cell division history and protein inheritance follow a non-Markovian process that can be simulated forward in time.
    Invoked to justify why standard master equations are inapplicable and why simulation plus normalizing flows are required.

pith-pipeline@v0.9.0 · 5804 in / 1148 out tokens · 56093 ms · 2026-05-19T10:30:06.290299+00:00 · methodology

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