Stochastic branching-diffusion models for gene expression
Bibliographic record
Abstract
A challenge to both understanding and modeling biochemical networks is integrating the effects of diffusion and stochasticity. Here, we use the theory of branching processes to give exact analytical expressions for the mean and variance of protein numbers as a function of time and position in a spatial version of an established model of gene expression. We show that both the mean and the magnitude of fluctuations are determined by the protein's Kuramoto length--the typical distance a protein diffuses over its lifetime--and find that the covariance between local concentrations of proteins often increases if there are substantial bursts of synthesis during translation. Using high-throughput data, we estimate that the Kuramoto length of cytoplasmic proteins in budding yeast to be an order of magnitude larger than the cell diameter, implying that many such proteins should have an approximately uniform concentration. For constitutively expressed proteins that live substantially longer than their mRNA, we give an exact expression for the deviation of their local fluctuations from Poisson fluctuations. If the Kuramoto length of mRNA is sufficiently small, we predict that such local fluctuations become approximately Poisson in bacteria in much of the cell, unless translational bursting is exceptionally strong. Our results therefore demonstrate that diffusion can act to both increase and decrease the complexity of fluctuations in biochemical networks.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".