Why Biological Systems Suddenly Change State: An Intuitive Guide to Freidlin–Wentzell Theory

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  Stochasticity is ubiquitous in biology and neuroscience, manifesting in various forms, including ion channel noise, synaptic variability, gene regulatory fluctuations, noisy population dynamics, and more. Many biological systems spend long periods in a stable “state” and only rarely transition to another state due to noise. For instance, a neuron typically remains inactive but may occasionally trigger a spontaneous spike. Similarly, a gene can switch from the OFF state to the ON state due to rare bursts of transcription factors. Cells can also transition out of metabolic or epigenetic states, populations might shift between different ecological equilibria, and a viral infection can fluctuate between phases of control and uncontrollability. Freidlin–Wentzell theory provides a mathematically rigorous framework to study these phenomena when noise is small but nonzero . It tells you, firstly, h ow likely rare transitions are,    secondly,   h ow fast they occ...
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Relationship between the modified Rankin Scale and the Barthel Index in the process of functional recovery after stroke

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The modified Rankin Scale (mRS) and the Barthel Index (BI) are the most  
common clinimetrical instruments for measuring disability after stroke. 

 This study [here] investigated the relationship between the BI and the 

 mRS at multiple time points after stroke. 

The BI, which is a widely used instrument for longitudinal follow-up post-

 stroke, was used as  reference to determine the effect of time on the 

 sensitivity of the mRS in differentiating  functional recovery. 
Methods: Ninety-two patients with first stroke and hemispheric brain 

 lesion were evaluated using the BI and mRS at 10 days, 3 and 6 months. 

 The Kruskal-Wallis test was applied to examine median differences in BI 

 among the mRS levels at 10 days, 3 and 6 months with Dunn's correction 

 for multigroup comparison. The Mann and Whitney test was used to 

 compare median differences in BI scores between two aggregations of 

 mRS grades (mRS=0-2, mRS=3-5) at the same time periods after 

 stroke. 
Results: BI score distribution amongst mRS grades overlapped at 10 

 days, differentiating only between extreme grades (no disability vs severe 

 disability). At 3 months, independent patients with slight disability could be 

 distinguished from dependent patients with marked disability. At 6 

 months, grade 2 and 3 overlapped no more, differentiating independence 

 (class 0-2) from dependence (class 3-5). The largest transition to an 

 independent functional status occurred from grade 4, at 3 months.
Conclusion: Maximum sensitivity of mRS in differentiating functional 

 recovery is reached at six months post-stroke.



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