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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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R function conf_int_Accuracy

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  R function conf_int_Accuracy <- function(GMTobs, s, nDays = 2, nAnalysts = 2, nPlates = 2, nReplicates = 3, FoldDilution = 2, Threshold = 1, alpha = 0.05) {   # INPUT:   # GMTobs: vector of observed geometric means at each fold dilution   # s: vector of the standard deviations of the log-transformed replicates   # nDays: number of experimental days (default = 2)   # nAnalysts: number of analysts performing the tests in validation (default = 2)   # nPlates: number of plates used per analyst per day (default = 2)   # nReplicates: number of measurements that each analyst performs per plate per day   # FoldDilution: step of the serial dilution (default = 2)   # Threshold: critical threshold of the log-difference between the observed and the true mean (default=1)   # alpha: significance level (default=0.05)   #   # OUTPUT:   # vector of Relative Accuracy calculated at each fold dilution and its confidence interval. In...
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Quantifying a biossay: confidence interval of the accuracy

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A bioassay validation is a set of procedures that ensure the precision and accuracy of the test results. Precision refers to the proximity of results to each other, and accuracy is the proximity of measurements results to the true value. Here we want to focus on the accuracy and the building of a confidence interval around it.   Let's design the validation experiments with three possible sources of variability, day, analyst, and plate having nd levels, na levels, and np levels, respectively. Each analyst performs nm measurements per plate per day on each sample. The samples will be serially diluted by a factor of two, resulting in dl dilution levels from 1/1 to 1/(2^(dl-1)). So, the total number of measurements, N, for each dilution level will N=nd*na*np*nm.   To calculate the accuracy , A, we can follow the FDA recommendation [1] of comparing the mean of the measured values with the "true" value, and define accuracy as that is the ratio between the observed geometric m...
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Understanding Anaerobic Threshold (VT2) and VO2 Max in Endurance Training

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  Introduction: The Science Behind Ventilatory Thresholds VT1 vs. VT2: Defining Energy Transitions p (Aerobic Threshold) : The transition from lipid metawwwpp (fat-burning) to a mixed metabolism, where both carbohydrates and fats fuel muscle activity. V0T2 (Anaerobic Threshold) : The point where the  shifts to a predominantly carbohydrate-based wmetabolism , leading to rapid lactate waccumpulation and increased reliance on anaerobic energy pathways. www w In p VT1 and VT2 Wwww ewAgep & Sex Younger athletes generally exhibit higher VT2 values , while aging naturally reduces aerobicw capacity. Men tend to have a higher VO2 Max due to greater lung capacity and muscle mass, but women can achieve similar endurance levels through optimized training. Body Composition & Health Status High body fat percentage may reduce VT2 efficiency, as excess weight increases ...
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Owen's Function: A Simple Solution to Complex Problems

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Definition   If you are interested in statistics or probability, you may have encountered the Owen's function , a special function that arises in various applications involving bivariate normal distributions. Let’s explain what Owen's function is, how it is defined and notated, and why it is useful.  The Owen's function is defined as follows: for any real numbers h and a, Owen's function T(h,a) is given by T ( h , a ) = 1 2 π · ∫ 0 a exp ( - h 2 2 · ( 1 ...
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Cell Count Analysis with cycleTrendR

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  1. Introduction Long‑term monitoring of adherent cell cultures (e.g., Vero, MDCK) is central to vaccine development, viral propagation, and QC workflows in CRO environments. Standard analyses typically focus on short‑term growth metrics such as doubling time, confluence progression, and endpoint viability. While informative, these metrics overlook slow drifts, cyclic environmental influences, and structural transitions that emerge over multi‑day or multi‑week monitoring. Operational routines (e.g., weekly medium changes), environmental oscillations (e.g., daily temperature cycles), and metabolic rhythms can introduce periodic components into cell‑density trajectories. These patterns are rarely analyzed explicitly, despite their potential impact on viral yield, infection kinetics, and batch‑to‑batch reproducibility. This post demonstrates how cycleTrendR can extract long‑term trends, dominant cycles, and structural transitions from a realistically simulated adherent cell‑co...
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