Modeling the interaction of polymeric nanoparticles functionalized with cell penetrating peptides at the nano-bio interface.

The interaction of nanoparticles with Caco-2 monolayers in cell culture underpins our predictions of the uptake of nanoformulations in vivo for drug delivery. Cell-penetrating peptides (CPP), such as oligoarginine, are currently of interest to enhance cellular uptake of bioactives and nanoparticles. This paper assesses the cellular association of poly(ethyl-cyanoacrylate) nanoparticles functionalized with di-arginine-histidine (RRH) in a Caco-2 cell model. We applied a computational model of particokinetics, In vitro Sedimentation, Diffusion and Dosimetry (ISDD) to predict the accumulation of nanoparticles on the cell surface. An important finding is that the proportion of nanoparticles associated with cells was less than 5 %. This has important implications for interpreting nanoparticle uptake in vitro. RRH-decoration does not appear to alter nanoparticle deposition, but increases association of nanoparticles with Caco-2 cells. Immediate deposition of nanoparticles on the cell surface was apparent and similar between formulations, but underestimated by the ISDD model. Key to understanding the nano-bio interface for drug delivery, nanoparticles that reach the cells were not necessarily absorbed by them, but can become detached. This variable of nanoparticle release from cells was incorporated into a new mathematical model presented here.

Accounting for unintended binding events in the analysis of quartz crystal microbalance kinetic data.

Previous methods for analyzing protein-ligand binding events using the quartz crystal microbalance with dissipation monitoring (QCM-D) fail to account for unintended binding that inevitably occurs during surface measurements and obscure kinetic information. In this article, we present a system of differential equations that accounts for both reversible and irreversible unintended interactions. This model is tested on three protein-ligand systems, each of which has different features, to establish the feasibility of using the QCM-D for protein binding analysis. Based on this analysis, we were able to obtain kinetic information for the intended interaction that is consistent with those obtained in literature via bulk-phase methods. In the appendix, we include a method for decoupling these from the intended binding events and extracting relevant affinity information.

Best practices in mathematical modeling.

Mathematical modeling is a vehicle that allows for explanation and prediction of natural phenomena. In this chapter we present guidelines and best practices for developing and implementing mathematical models, using cancer growth, chemotherapy, and immunotherapy modeling as examples.

Team research at the biology-mathematics interface: project management perspectives.

The success of interdisciplinary research teams depends largely upon skills related to team performance. We evaluated student and team performance for undergraduate biology and mathematics students who participated in summer research projects conducted in off-campus laboratories. The student teams were composed of a student with a mathematics background and an experimentally oriented biology student. The team mentors typically ranked the students' performance very good to excellent over a range of attributes that included creativity and ability to conduct independent research. However, the research teams experienced problems meeting prespecified deadlines due to poor time and project management skills. Because time and project management skills can be readily taught and moreover typically reflect good research practices, simple modifications should be made to undergraduate curricula so that the promise of initiatives, such as MATH-BIO 2010, can be implemented.

A validated mathematical model of cell-mediated immune response to tumor growth.

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions describing tumor-immune growth, response, and interaction rates, as well as associated variables, are developed using a least-squares method combined with a numerical differential equations solver. Parameter estimates and model validations use data from published mouse and human studies. Specifically, CD8+ T-tumor and NK-tumor lysis data from chromium release assays as well as in vivo tumor growth data are used. A variable sensitivity analysis is done on the model. The new functional forms developed show that there is a clear distinction between the dynamics of NK and CD8+ T cells. Simulations of tumor growth using different levels of immune stimulating ligands, effector cells, and tumor challenge are able to reproduce data from the published studies. A sensitivity analysis reveals that the variable to which the model is most sensitive is patient specific, and can be measured with a chromium release assay. The variable sensitivity analysis suggests that the model can predict which patients may positively respond to treatment. Computer simulations highlight the importance of CD8+ T-cell activation in cancer therapy.