Threshold-crossing time statistics for gene expression in growing cells
Many intracellular events are triggered by attaining critical concentrations of their corresponding regulatory proteins. How cells ensure precision in the timing of the protein accumulation is a fundamental problem, and contrasting predictions of different models can help us understand the mech...
| Autores principales: | , , , |
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| Formato: | article |
| Lenguaje: | Inglés |
| Publicado: |
Cold Sprimg Harbor Laboratory (CSH)
2024
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| Materias: | |
| Acceso en línea: | https://www.biorxiv.org/content/10.1101/2022.06.09.494908v1 http://hdl.handle.net/20.500.12324/39919 https://doi.org/10.1101/2022.06.09.494908 |
| Sumario: | Many intracellular events are triggered by attaining
critical concentrations of their corresponding regulatory
proteins. How cells ensure precision in the timing of the protein
accumulation is a fundamental problem, and contrasting
predictions of different models can help us understand the
mechanisms involved in such processes. Here, we formulate
the timing of protein threshold-crossing as a first passage
time (FPT) problem focusing on how the mean FPT and
its fluctuations depend on the threshold protein concentration.
First, we model the protein-crossing dynamics from the
perspective of three classical models of gene expression that
do not explicitly accounts for cell growth but consider the
dilution as equivalent to degradation: (birth-death process,
discrete birth with continuous deterministic degradation, and
Fokker-Planck approximation). We compare the resulting FPT
statistics with a fourth model proposed by us (growing cell)
that comprises size-dependent expression in an exponentially
growing cell. When proteins accumulate in growing cells, their
concentration reaches a steady value.We observe that if dilution
by cell growth is modeled as degradation, cells can reach
concentrations higher than this steady-state level at a finite
time. In the growing cell model, on the other hand, the FPT
moments diverge if the threshold is higher than the steady-state
level. This effect can be interpreted as a transition between
noisy dynamics when cells are small to an almost deterministic
behavior when cells grow enough. We finally study the mean
FPT that optimizes the timing precision. The growing cell model
predicts a higher optimal FPT and less variability than the
classical models. |
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