Slowest first passage times, redundancy, and menopause timing

Area of Science:

• Mathematical Biology
• Stochastic Processes
• Extreme Value Theory

Background:

• Biological events often depend on a 'searcher' locating a 'target,' quantified by first passage time (FPT).
• In systems with multiple searchers, the time taken by the slowest searcher(s) is a critical timescale.
• This slowest FPT is relevant to processes like ovarian aging and cell signaling reliability.

Purpose of the Study:

• To derive rigorous approximations for the full probability distribution and moments of slowest first passage times (FPTs).
• To apply these mathematical findings to biological models, specifically ovarian aging and menopause timing.
• To investigate the role of slowest FPTs in biological redundancy and cellular stimulus localization.

Main Methods:

• Utilized extreme value theory and asymptotic analysis to approximate slowest FPT distributions.
• Developed general mathematical results applicable to various stochastic search models.
• Conducted numerical simulations to validate approximations across different numbers of searchers.

Main Results:

• Obtained accurate approximations for the probability distribution and moments of slowest FPTs.
• Demonstrated the applicability of these approximations even with fewer searchers than theoretically assumed.
• Revealed the significance of slowest FPTs in understanding redundancy in biological systems, using ovarian aging as a model.

Conclusions:

• The developed mathematical framework provides robust tools for analyzing slowest FPTs in biological systems.
• Slowest FPTs play a key role in biological redundancy and timing-dependent events.
• The theory is applicable to diverse stochastic search scenarios, including diffusive, subdiffusive, and mortal searchers.