Modeling of reaction-diffusion transport into a core-shell geometry

Modulating Nucleus Oxygen Concentration by Altering Intramembrane Cholesterol Levels: Creating Hypoxic Nucleus in Oxic Conditions

We propose a novel mechanism by which cancer cells can modulate the oxygen concentration within the nucleus, potentially creating low nuclear oxygen conditions without the need of an hypoxic micro-environment and suited for allowing cancer cells to resist chemo- and radio-therapy. The cells ability to alter intra-cellular oxygen conditions depends on the amount of cholesterol present within the cellular membranes, where high levels of cholesterol can yield rigid membranes that slow oxygen diffusion. The proposed mechanism centers on the competition between (1) the diffusion of oxygen within the cell and across cellular membranes that replenishes any consumed oxygen and (2) the consumption of oxygen in the mitochondria, peroxisomes, endoplasmic reticulum (ER), etc. The novelty of our work centers around the assumption that the cholesterol content of a membrane can affect the oxygen diffusion across the membrane, reducing the cell ability to replenish the oxygen consumed within the cell. For these conditions, the effective diffusion rate of oxygen becomes of the same order as the oxygen consumption rate, allowing the cell to reduce the oxygen concentration of the nucleus, with implications to the Warburg Effect. The cellular and nucleus oxygen content is indirectly evaluated experimentally for bladder (T24) cancer cells and during the cell cycle, where the cells are initially synchronized using hydroxeaurea (HU) at the late G1-phase/early S-phase. The analysis of cellular and nucleus oxygen concentration during cell cycle is performed via (i) RT-qPCR gene analysis of hypoxia inducible transcription factors (HIF) and prolyl hydroxylases (PHD) and (ii) radiation clonogenic assay every 2 h, after release from synchronization. The HIF/PHD genes allowed us to correlate cellular oxygen with oxygen concentration in the nucleus that is obtained from the cells radiation response, where the amount DNA damage due to radiation is directly related to the amount of oxygen present in the nucleus. We demonstrate that during the S-phase cells can become hypoxic in the late S-phase/early G2-phase and therefore the radiation resistance increases 2- to 3-fold.

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether these data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second, we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods, we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.

Diffusion in heterogeneous discs and spheres: New closed-form expressions for exit times and homogenization formulas

Mathematical models of diffusive transport underpin our understanding of chemical, biochemical, and biological transport phenomena. Analysis of such models often focuses on relatively simple geometries and deals with diffusion through highly idealized homogeneous media. In contrast, practical applications of diffusive transport theory inevitably involve dealing with more complicated geometries as well as dealing with heterogeneous media. One of the most fundamental properties of diffusive transport is the concept of mean particle lifetime or mean exit time, which are particular applications of the concept of first passage time and provide the mean time required for a diffusing particle to reach an absorbing boundary. Most formal analysis of mean particle lifetime applies to relatively simple geometries, often with homogeneous (spatially invariant) material properties. In this work, we present a general framework that provides exact mathematical insight into the mean particle lifetime, and higher moments of particle lifetime, for point particles diffusing in heterogeneous discs and spheres with radial symmetry. Our analysis applies to geometries with an arbitrary number and arrangement of distinct layers, where transport in each layer is characterized by a distinct diffusivity. We obtain exact closed-form expressions for the mean particle lifetime for a diffusing particle released at an arbitrary location, and we generalize these results to give exact, closed-form expressions for any higher-order moment of particle lifetime for a range of different boundary conditions. Finally, using these results, we construct new homogenization formulas that provide an accurate simplified description of diffusion through heterogeneous discs and spheres.

Quantitative Analysis of the Correlation between Cell Size and Cellular Uptake of Particles

The size of a cell is central to many functions, including cellular communication and exchange of materials with the environment. This modeling and experimental study focused on understanding how the size of a cell determines its ability to uptake nanometer-scale extracellular materials from the environment. Several mechanisms in the cell plasma membrane mediate cellular uptake of nutrients, biomolecules, and particles. These mechanisms involve recognition and internalization of the extracellular molecules via endocytic components, such as clathrin-coated pits, vacuoles, and micropinocytic vesicles. Because the demand for an external resource could be different for cells of different sizes, the collective actions of these various endocytic routes should also vary based on the cell size. Here, using a reaction-diffusion model, we analyze single-cell data to interrogate the one/one mapping between the size of the MDA-MB 231 breast cancer cells and their ability to uptake nanoparticles. Our analysis indicates that under both reaction- and diffusion-controlled regimes, cellular uptake follows a linear relationship with the cell radius. Furthermore, this linear dependency is insensitive to particle size variation within 20-200 nm range. This result is counterintuitive because the general perception is that cellular uptake is proportional to the cell volume (mass) or surface area and hence follow a cubic or square relationship with the cell radius. A further analysis using our model reveals a potential mechanism underlying this linear relationship.

Generation of Human Stem Cell-Derived Pancreatic Organoids (POs) for Regenerative Medicine

Insulin-dependent diabetes mellitus or type 1 diabetes mellitus (T1DM) is an auto-immune condition characterized by the loss of pancreatic β-cells. The curative approach for highly selected patients is the pancreas or the pancreatic islet transplantation. Nevertheless, these options are limited by a growing shortage of donor organs and by the requirement of immunosuppression.Xenotransplantation of porcine islets has been extensively investigated. Nevertheless, the strong xenoimmunity and the risk of transmission of porcine endogenous retroviruses, have limited their application in clinic. Generation of β-like cells from stem cells is one of the most promising strategies in regenerative medicine. Embryonic, and more recently, adult stem cells are currently the most promising cell sources exploited to generate functional β-cells in vitro. A number of studies demonstrated that stem cells could generate functional pancreatic organoids (POs), able to restore normoglycemia when implanted in different preclinical diabetic models. Nevertheless, a gradual loss of function and cell dead are commonly detected when POs are transplanted in immunocompetent animals. So far, the main issue to be solved is the post-transplanted islet loss, due to the host immune attack. To avoid this hurdle, nanotechnology has provided a number of polymers currently under investigation for islet micro and macro-encapsulation. These new approaches, besides conferring PO immune protection, are able to supply oxygen and nutrients and to preserve PO morphology and long-term viability.Herein, we summarize the current knowledge on bioengineered POs and the stem cell differentiation platforms. We also discuss the in vitro strategies used to generate functional POs, and the protocols currently used to confer immune-protection against the host immune attack (micro- and macro-encapsulation). In addition, the most relevant ongoing clinical trials, and the most relevant hurdles met to move towards clinical application are revised.