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

arXiv: https://arxiv.org/abs/2506.09374 · HTML: https://mlsanity.com/paper/2506.09374/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 91 references that are in the map.
- First posted on arXiv 11 Jun 2025.

## Builds on (most cited first, 19 of 19)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Cognitive computational neuroscience](https://mlsanity.com/paper/1807.11819/) (2018)
- [Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective](https://mlsanity.com/paper/2308.14085/) (2023)
- [Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability](https://mlsanity.com/paper/2310.13402/) (2023)
- [Unifying Simulation and Inference with Normalizing Flows](https://mlsanity.com/paper/2404.18992/) (2024)
- [Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve](https://mlsanity.com/paper/2501.08288/) (2025)
- [Approximation and inference methods for stochastic biochemical kinetics - a tutorial review](https://mlsanity.com/paper/1608.06582/) (2016)

## Abstract (arXiv)

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.