Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.

Data Mining Crystallization Kinetics

<p>Population balance model is a valuable modelling tool which facilitates the optimization and understanding of crystallization processes. However, in order to use this tool, it is necessary to have previous knowledge of the crystallization kinetics, specifically crystal growth and nucleation. The majority of approaches to achieve proper estimations of kinetic parameters required experimental data. Across time, a vast literature about the estimation of kinetic parameters and population balances have been published. Considering the availability of data, this work built a database with information on solute, solvent, kinetic expression, parameters, crystallization method and seeding. Correlations were assessed and clusters structures identified by hierarchical clustering analysis. The final database contains 336 data of kinetic parameters from 185 different sources. The data were analysed using kinetic parameters of the most common expressions. Subsequently, clusters were identified for each kinetic model. With these clusters, classification random forest models were made using solute descriptors, seeding, solvent, and crystallization methods as classifiers. Random forest models had an overall classification accuracy higher than 70% whereby they were useful to provide rough estimates of kinetic parameters, although these methods have some limitations.</p>

Data Mining Crystallization Kinetics

<p>Population balance model is a valuable modelling tool which facilitates the optimization and understanding of crystallization processes. However, in order to use this tool, it is necessary to have previous knowledge of the crystallization kinetics, specifically crystal growth and nucleation. The majority of approaches to achieve proper estimations of kinetic parameters required experimental data. Across time, a vast literature about the estimation of kinetic parameters and population balances have been published. Considering the availability of data, this work built a database with information on solute, solvent, kinetic expression, parameters, crystallization method and seeding. Correlations were assessed and clusters structures identified by hierarchical clustering analysis. The final database contains 336 data of kinetic parameters from 185 different sources. The data were analysed using kinetic parameters of the most common expressions. Subsequently, clusters were identified for each kinetic model. With these clusters, classification random forest models were made using solute descriptors, seeding, solvent, and crystallization methods as classifiers. Random forest models had an overall classification accuracy higher than 70% whereby they were useful to provide rough estimates of kinetic parameters, although these methods have some limitations.</p>

Solution Polymerization of Acrylic Acid Initiated by Redox Couple Na-PS/Na-MBS: Kinetic Model and Transition to Continuous Process

This work aims at modeling in detail the polymerization of non-ionized acrylic acid in aqueous solution. The population balances required to evaluate the main average properties of molecular weight were solved by the method of moments. The polymerization process considered is initiated by a persulfate/metabisulfate redox couple and, in particular, the kinetic scheme considers the possible formation of mid-chain radicals and transfer reactions. The proposed model is validated using experimental data collected in a laboratory-scale discontinuous reactor. The developed kinetic model is then used to intensify the discontinuous process by shifting it to a continuous one based on a tubular reactor with intermediate feeds. One of the experimental runs is selected to show how the proposed model can be used to assess the transition from batch to continuous process and allow faster scale-up to industrial scale using a literature approach.