Deterministic mathematical modelling for cancer chronotherapeutics: cell population dynamics and treatment optimisation

Chronotherapeutics has been designed and used for more than twenty years as an effective treatment against cancer by a few teams around the world, among whom one of the first is Francis Lévi's at Paul-Brousse hospital (Villejuif, France), in application of circadian clock physiology to determine best infusion times within the 24-hour span for anticancer drug delivery. Mathematical models have been called in the last ten years to give a rational basis to such optimised treatments, for use in the laboratory and ultimately in the clinic. While actual clinical applications of the theoretical optimisation principles found have remained elusive so far to improve chronotherapeutic treatments in use, mathematical models provide proofs of concepts and tracks to be explored experimentally, to progress from theory to bedside. Starting from a simple ordinary differential equation model that allowed setting and numerically solving a drug delivery optimisation problem with toxicity constraints, this modelling enterprise has been extended to represent the division cycle in proliferating cell populations with different molecular targets, to allow for the representation of anticancer drug combinations that are used in clinical oncology. The main point to be made precise in such a therapeutic optimisation problem is to establish, here in the frame of circadian chronobiology, physiologically based differences between healthy and cancer cell populations in their responses to drugs. To this aim, clear biological evidence at the molecular level is still lacking, so that, starting from indirect observations at the experimental and clinical levels and from theoretical considerations on the model, speculations have been made, that will be exposed in this review of cancer chronotherapeutics models with the corresponding optimisation problems and their numerical solutions, to represent these differences between the two cell populations, with regard to circadian clock control

Functional activity of GSSM™ and reassembled combination antibody variants

() The top 10 antibody variants from the GSSM™ as determined by functional spike ELISA normalized to the relative expression of the antibody variant. The specific activity for each antibody was normalized to the wild-type (WT) control antibody (WT: chimeric antibody, 4049Fab14). () Purified antibody candidates from (A) tested in the plaque reduction neutralization test (PRNT). The number of plaques resulting in 50 and 80% neutralization is noted. Statistical analysis at the approximate WT antibody concentration for 80% neutralization (0.78 µg/ml) indicates better neutralization (i.e. fewer plaques) for 51E7 and 52G3 ( < 0.02 and < 0.03, respectively). () Top 10 antibody variants from the combination library (containing the best GSSM™ mutants placed in the best framework backbones) determined as described in (A). () Purified antibody candidates from (C) tested in the PRNT. Data was not collected for one of the 10 variants. Statistical analysis at the WT antibody concentration for 80% neutralization (1.56 µg/ml) indicates better neutralization (i.e. fewer plaques) for several antibodies (i.e. < 0.02 for 2978/15, 2992/15, 2978/10, 2702/10; < 0.03 for 2703/10; < 0.04 for 2703/15 and < 0.05 for 2699/10). Duplicates of each variant were assayed in the ELISA and PRNT experiments.<p><b>Copyright information:</b></p><p>Taken from "Rapid discovery and optimization of therapeutic antibodies against emerging infectious diseases"</p><p></p><p>Protein Engineering, Design and Selection 2008;21(8):495-505.</p><p>Published online 13 May 2008</p><p>PMCID:PMC2461042.</p><p>© 2008 The Author(s)</p

Functional activity of human framework reassembly (HuFR™) antibody variants

() The top 10 antibody variants from the heavy chain library as determined by functional spike ELISA normalized to the relative expression of antibody variant. The specific activity for each antibody was further normalized to the wild-type (WT) control antibody (i.e. WT: chimeric antibody, 4049Fab14). () The top 10 antibody variants from the light chain library determined as described in (A). Numbers within bars indicate the corresponding heavy chains. () Purified antibody candidates were tested in the plaque reduction neutralization test (PRNT). The number of plaques resulting in 50 and 80% neutralization is noted. Statistical analysis at the approximate WT antibody concentration for 80% neutralization (0.78 µg/ml) indicates better neutralization (i.e. fewer plaques) for 61G4 ( < 0.04). Duplicates of each variant were assayed in the ELISA and PRNT experiments.<p><b>Copyright information:</b></p><p>Taken from "Rapid discovery and optimization of therapeutic antibodies against emerging infectious diseases"</p><p></p><p>Protein Engineering, Design and Selection 2008;21(8):495-505.</p><p>Published online 13 May 2008</p><p>PMCID:PMC2461042.</p><p>© 2008 The Author(s)</p

Representative ELISA data of SARS-CoV-reactive Fabs isolated by DNA display

() Zinc finger-Fab fusion proteins analyzed in an ELISA using the spike protein as a capture reagent on 48 wells of a 96-well Maxisorp plates. Bovine serum albumin coated on the remaining 48 wells was used to determine specificity of binding. () Relative specific activity is the functional activity from Fig. A normalized to the amount of fusion protein determined using an ELISA measuring relative expression levels.<p><b>Copyright information:</b></p><p>Taken from "Rapid discovery and optimization of therapeutic antibodies against emerging infectious diseases"</p><p></p><p>Protein Engineering, Design and Selection 2008;21(8):495-505.</p><p>Published online 13 May 2008</p><p>PMCID:PMC2461042.</p><p>© 2008 The Author(s)</p