Fluorescence Fluctuation Spectroscopy Linear Regression Analysis
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Solution Overview
Problem
Current fluorescence fluctuation spectroscopy methods, such as FIDA and PCH, face challenges in intuitively predicting photon counting histograms, are non-intuitive, and struggle with complex applications due to non-linear models and assumptions that violate triplet state populations and molecular diffusion, limiting their ability to accurately determine molecular concentrations and brightness.
Innovation Solution
The method introduces the concept of effective volume and single particle distribution, characterized by Veff and P1(n), which provides a robust and intuitive approach to determine molecular concentrations, independent of spatial boundaries and diffusion, allowing for the characterization of molecules in various environments and conditions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If FIDA or PCH methods are used to determine molecular concentrations, then measurement can be performed, but the models are highly non-linear and the determination of parameters is complicated
Solution Approach 1:
The patent transforms the highly non-linear parameter determination problem into a linear regression problem by changing the mathematical representation. Instead of directly fitting non-linear parameters, the method uses a linear combination of basis functions that can be solved through standard linear regression techniques, dramatically simplifying the computational complexity while maintaining measurement precision.
Solution Approach 2:
The patent introduces an intermediary mathematical framework that bridges the gap between the raw photon counting data and the molecular concentration parameters. By using a linear basis function expansion as an intermediary step, the complex non-linear relationship is decomposed into manageable linear components that can be systematically solved.
2Measurement precision
If standard FFS methods are used, then photon counting distribution can be analyzed, but the spatial brightness function assumption violates triplet state populations for different species
Solution Approach 1:
The patent segments the spatial brightness function into multiple independent basis functions rather than assuming a single unified spatial distribution. This segmentation allows each species to have its own effective spatial profile, accommodating different triplet state populations and relaxation dynamics without requiring them to share a common spatial brightness function.
Solution Approach 2:
The patent introduces dynamic flexibility by allowing the spatial brightness function to vary independently for different molecular species. Instead of a static assumption that all species share the same spatial profile, the method dynamically adapts the spatial characteristics to match the specific photophysical properties of each species, including their unique triplet state behaviors.
3Productivity
If FIDA is used for high throughput screening, then analysis speed is improved, but the generating function approach makes the theoretical model not intuitive and extension to complex applications difficult
Solution Approach 1:
The patent uses a linear basis function expansion that copies and combines simple, well-understood spatial profiles to construct the overall brightness distribution. This approach replaces the abstract generating function mathematics with a more intuitive linear combination of familiar spatial patterns, making the model both computationally efficient and conceptually accessible.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables fast and precise determination of molecular concentrations, is robust against noise and diffusion, and can be applied to complex environments like flows and micro-structures, providing a more profound physical insight and improved accuracy compared to existing methods.
Implementation Method 1
molecules of interest and ignore any background noise produced e.g. by the detector hardware or scattered light
Implementation Method 2
Photons emitted from molecules in a small observation volume V hit a detector for photons
Data Source
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AI summary
A method of determining characteristic properties of a sample containing particles of single species which emit, scatter and/or reflect photons in an predetermined observation volume including the steps of : 1) registering and counting the number n i