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In the study of amyloid fiber formation, the fiber length distribution playsa central role. From this microscopic distribution, all macroscopic statisticalquantities, like the fiber number concentration P(t) and mass concentrationM(t), can be easily achieved. However the inverse problem is usuallynon-trivial. In this paper, a practical method is introduced to show how toreconstruct the fiber length distribution function based on the knowledge ofP(t) and M(t). Compared to directly solving mass-action equations, our methodspeeds up the calculation by at least ten thousand times (from days toseconds). And the accuracy is also quite satisfactory. Furthermore our methodprovides an interesting linkage between the fluorescence imaging and moredetailed TEM studies, which may inspire wider applications in this field.

Link the Fluorescence and TEM Studies on Amyloid Fiber Formation -- To  Reconstruct the Fiber Length Distribution Based on the Knowledge of Moments  Evolution