During the application of mass-action equation models to the study of amyloid fiber formation, time-consuming numerical calculations constitute a major bottleneck when no analytical solution is available. To conquer this difficulty, here an alternative efficient method is introduced for the fragmentation-only model. It includes two basic steps: (1) simulate close-formed time-evolution equations for the number concentration ( ) P t derived from the moment-closure method; (2) reconstruct the detailed fiber length distribution based on the knowledge of moments obtained in the first step. Compared to direct solution, current method speeds up the calculation by at least ten thousand times. The accuracy is also quite satastifactory if suitable forms of approximate distribution fucntion is taken. Further application to PI 264 -b-PFS 48 micelles study performed by Guerin et al. confirms our method is very promising for the real-time analysis of the experimental data on fiber fragmentation.Keywords: amyloid fiber, length-dependent fragmentation, moment closure, fiber length distribution, inverse problem INTRODUCTIONThe linear aggregation of soluble peptides and proteins into insoluble amyloid fibrils is a typical self-assembling phenomenon of bio-macromolecules[1], and is closely related to many well-known human neurodegenerative diseases [2]. Thus to uncover the mechanisms of amyloid fiber formation, will not only have great theoretical values, but also shed light on the medical diagnosis and treatment of amyloidosis [3].In the past decades, related to this hot topic, many efforts have been dedicated to quantify the effects of primary nucleation and elongation [4,5]. While fragmentation [6] and other processes, like fiber surface facilitated nucleation [7], lateral thickening [8] and etc., have received far less attention.However as we know, single filament becomes mechanically unstable and tend to break when its length exceeds certain values [9]. Even for bundled fibrils in vivo, fragmentation is unavoidable in the presence of mechanical stress, thermal motion, or chaperones such as Hsp104, which has a known ability to fragment fibril samples [10]. Actually as a special kind of secondary nucleation, fragmentation can effectively accelerate the fiber formation process by providing new seeds [11], affect the scaling relations between kinetic quantities (like the lag-time and maximum fiber growth rate) and protein concentration (from critical-nucleus-size dependent to independent) [12], alter the detailed fiber length distribution from exponentially decaying to bell-shape-like [13], and even enhance the toxicity of fibril samples to disrupt membranes and to reduce cell viability [14].To quantify the key role of fragmentation played during the formation of breakable amyloid fiber, various experiments, like the shear flow [15,16] and sonication studies [17,18], are designed. However to interpret the experimental results, especially to provide a quantitative relationship between the observed data and their underlyin...

A novel data-based machine learning algorithm for predicting amyloid aggregation rates is reported in this paper. Based on a highly nonlinear projection from 16 intrinsic features of a protein and 4 extrinsic features of the environment to the protein aggregation rate, a feedforward fully connected neural network (FCN) with one hidden layer is trained on a dataset composed of 21 different kinds of amyloid proteins and tested on 4 rest proteins. FCN shows a much better performance than traditional algorithms, such as multivariable linear regression and support vector regression, with an average accuracy higher than 90%. Furthermore, by the correlation analysis and the principal component analysis, seven key features, folding energy, HP patterns for helix, sheet and helices cross membrane, pH, ionic strength, and protein concentration, are shown to constitute a minimum feature set for characterizing the amyloid aggregation kinetics.