Experimental analysis and modelling of in vitro HUVECs proliferation in the presence of various types of drugs

Structured population balances to support microalgae-based processes: Review of the state-of-art and perspectives analysis

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

Cell-size distribution in epithelial tissue formation and homeostasis

How cell growth and proliferation are orchestrated in living tissues to achieve a given biological function is a central problem in biology. During development, tissue regeneration and homeostasis, cell proliferation must be coordinated by spatial cues in order for cells to attain the correct size and shape. Biological tissues also feature a notable homogeneity of cell size, which, in specific cases, represents a physiological need. Here, we study the temporal evolution of the cell-size distribution by applying the theory of kinetic fragmentation to tissue development and homeostasis. Our theory predicts self-similar probability density function (PDF) of cell size and explains how division times and redistribution ensure cell size homogeneity across the tissue. Theoretical predictions and numerical simulations of confluent non-homeostatic tissue cultures show that cell size distribution is self-similar. Our experimental data confirm predictions and reveal that, as assumed in the theory, cell division times scale like a power-law of the cell size. We find that in homeostatic conditions there is a stationary distribution with lognormal tails, consistently with our experimental data. Our theoretical predictions and numerical simulations show that the shape of the PDF depends on how the space inherited by apoptotic cells is redistributed and that apoptotic cell rates might also depend on size.

Numerical rate function determination in partial differential equations modeling cell population dynamics

This paper introduces a method to solve the inverse problem of determining an unknown rate function in a partial differential equation (PDE) based on discrete measurements of the modeled quantity. The focus is put on a size-structured population balance equation (PBE) predicting the evolution of the number distribution of a single cell population as a function of the size variable. Since the inverse problem at hand is ill-posed, an adequate regularization scheme is required to avoid amplification of measurement errors in the solution method. The technique developed in this work to determine a rate function in a PBE is based on the approximate inverse method, a pointwise regularization scheme, which employs two key ideas. Firstly, the mollification in the directions of time and size variables are separated. Secondly, instable numerical data derivatives are circumvented by shifting the differentiation to an analytically given function. To examine the performance of the introduced scheme, adapted test scenarios have been designed with different levels of data disturbance simulating the model and measurement errors in practice. The success of the method is substantiated by visualizing the results of these numerical experiments.