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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Cerebral Circulation Time is Prolonged and Not Correlated with EDSS in Multiple Sclerosis Patients

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Literature has suggested that changes in brain flow circulation occur in patients with multiple sclerosis. 

 In this study, digital subtraction angiography (DSA) was used to measure the absolute CCT value in MS patients and to correlate its value to age at disease onset and duration, and to expand disability status scale (EDSS). 

 DSA assessment was performed on eighty MS patients and on a control group of forty-four age-matched patients. CCT in MS and control groups was calculated by analyzing the angiographic images. Lesion and brain volumes were calculated in a representative group of MS patients. Statistical correlations among CCT and disease duration, age at disease onset, lesion load, brain volumes and EDSS were considered. 

 A significant difference between CCT in MS patients (mean = 4.9s; sd = 1.27s) and control group (mean = 2.8s; sd = 0.51s) was demonstrated. No significant statistical correlation was found between CCT and the other parameters in all MS patients. 

 Significantly increased CCT value in MS patients suggests the presence of microvascular dysfunctions, which do not depend on clinical and MRI findings. Hemodynamic changes may not be exclusively the result of a late chronic inflammatory process.

Figure. DSA examination: antero-posterior lateral views of color-coded right carotid artery of control (panels a, b) and MS patients (panels c, d).

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