Estimation from moments measurements for amyloid depolymerisation

Abstract

Estimating reaction rates and size distributions of protein polymers is an important step for understanding the mechanisms of protein misfolding and aggregation, a key feature for amyloid diseases. This study aims at setting this framework problem when the experimental measurements consist in the time-dynamics of a moment of the population (i.e. for instance the total polymerised mass, as in Thioflavine T measurements, or the second moment measured by Static Light Scattering). We propose a general methodology, and we solve the problem theoretically and numerically in the case of a depolymerising system. We then apply our method to experimental data of degrading oligomers, and conclude that smaller aggregates of ovPrP protein should be more stable than larger ones. This has an important biological implication, since it is commonly admitted that small oligomers constitute the most cytotoxic species during prion misfolding process.

Analytic Philosophy for Biomedical Research: The Imperative of Applying Yesterday’s Timeless Messages to Today’s Impasses

“…For some examples, see refs [45][46][47][48][49][50][51] 7. The phrase "philosophical biology", or "philosophical science" in general, would have seemed pleonastic to the scientists of the Enlightenment and later periods, but today this pleonasm may be necessary8 Any point, however absurd or incorrect, could theoretically be debatable or arguable, and if this becomes the basis of a philosophical and scientific investigation, there would be no room for true progress9 From the Greek elegkhos "refutation"…”

The mechanism of monomer transfer between two structurally distinct PrP oligomers

“…We call W the estimation of the observation noise covariance and , , , P θ the initial uncertainty covariance of the model parameters. Here, we decide to only rely on the SLS data—the observation operator being the second moment as in [17]—during the estimation. The SEC data are then used to validate the resulting estimations.…”

A bi-monomeric, nonlinear Becker–Döring-type system to capture oscillatory aggregation kinetics in prion dynamics

“…Under assumption (39), this series with coefficients i j=1 α j has a strictly positive convergence radius R and since we are looking for steady states in 1 1 , we consider here only z < R. Moreover, the equations for v and w as well as the mass and polymer conservation laws yield the relations:…”

“…Turning back to the experiments as shown in Figure 1, it also appears that much remains to be done before reaching a fully quantitative model: integrating the proposed reaction scheme in a more complete model, where "usual" reactions (like linear depolymerisation) would be the dominant reactions, governing the slow dynamics of the reactions, and these ones local corrections; experimental evidence and quantitative comparison, for instance through data assimilation strategies in the spirit of [1,2].…”