Stochastic shielding and edge importance for Markov chains with timescale separation.

Area of Science:

• Computational Neuroscience
• Biophysics
• Mathematical Biology

Background:

• Nerve cell electrical impulses (spikes) arise from ion channel dynamics.
• Stochastic models capture ion channel gating but require computationally intensive simulations.
• Previous work introduced a fast approximation method (stochastic shielding) for these simulations.

Purpose of the Study:

• To extend the mathematical analysis of stochastic shielding to arbitrary discrete population models.
• To develop a method for ranking the contribution of individual transitions (edges) to ion channel noise variance.
• To investigate the phenomenon of 'edge importance reversal' where non-conducting state transitions dominate noise.

Main Methods:

• Analysis of stationary variance decomposition for first-order kinetic models.
• Application of the stochastic shielding approximation.
• Exhaustive investigation of edge importance in simplified 3-state models.

Main Results:

• A decomposition method quantifies the contribution of each transition to the total variance of ion channel occupancy.
• Most transitions between open and closed states contribute most to variance, but exceptions exist.
• Edge importance reversal occurs when transitions between closed states dominate variance, particularly under specific rate and occupancy conditions.

Conclusions:

• The developed decomposition method provides insights into the sources of noise in ion channel gating.
• Edge importance reversal highlights the significant role of 'hidden' transitions in dictating current fluctuations.
• Understanding these noise sources is crucial for accurate modeling of neuronal excitability and function.