Quantitative analyses of EGFR localization and trafficking dynamics in the follicular epithelium.

To bridge the gap between qualitative and quantitative analyses of the epidermal growth factor receptor (EGFR) in tissues, we generated an sfGFP-tagged EGF receptor (EGFR-sfGFP) in Drosophila The homozygous fly appears similar to wild type with EGFR expression and activation patterns that are consistent with previous reports in the ovary, early embryo, and imaginal discs. Using ELISA, we quantified an average of 1100, 6200 and 2500 receptors per follicle cell (FC) at stages 8/9, 10 and ≥11 of oogenesis, respectively. Interestingly, the spatial localization of the EGFR to the apical side of the FCs at early stages depended on the TGFα-like ligand Gurken. At later stages, EGFR localized to basolateral positions of the FCs. Finally, we followed the endosomal localization of EGFR in the FCs. The EGFR colocalized with the late endosome, but no significant colocalization of the receptor was found with the early endosome. The EGFR-sfGFP fly is an exciting new resource for studying cellular localization and regulation of EGFR in tissues.

Determination of the optimal therapeutic protocols in cancer immunotherapy.

Cancer immunotherapy aims at eliciting an immune system response against the tumor. However, it is often characterized by toxic side-effects. Limiting the tumor growth and, concurrently, avoiding the toxicity of a drug, is the problem of protocol design. We formulate this question as an optimization problem and derive an algorithm for its solution. Unlike the standard optimal control approach, the algorithm simulates impulse-like drug administrations. It relies on an exact computation of the gradient of the cost function with respect to any protocol by means of the variational equations, that can be solved in parallel with the system. In comparison with previous versions of this method [F. Castiglione, B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bull. Math. Biol. 68 (2006) 255-274; B. Piccoli, F. Castiglione, Optimal vaccine scheduling in cancer immunotherapy, Physica A. 370 (2) (2007) 672-680], we optimize both the timing and the dosage of each administration and introduce a penalty term to avoid clustering of subsequent injections, a requirement consistent with the clinical practice. In addition, we implement the optimization scheme to simulate the case of multi-therapies. The procedure works for any ODE system describing the pharmacokinetics and pharmacodynamics of an arbitrary number of therapeutic agents. In this work, it was tested for a well known model of the tumor-immune system interaction [D. Kirschner, J.C. Panetta, Modeling immunotherapy of tumor-immune interaction, J. Math. Biol. 37 (1998) 235-252]. Exploring three immunotherapeutic scenarios (CTL therapy, IL-2 therapy and combined therapy), we display the stability and efficacy of the optimization method, obtaining protocols that are successful compromises between various clinical requirements.

Optimal control in a model of dendritic cell transfection cancer immunotherapy.

We construct a population dynamics model of the competition among immune system cells and generic tumor cells. Then, we apply the theory of optimal control to find the optimal schedule of injection of autologous dendritic cells used as immunotherapeutic agent. The optimization method works for a general ODE system and can be applied to find the optimal schedule in a variety of medical treatments that have been described by a mathematical model.