Mathematical characterization of population dynamics in breast cancer cells treated with doxorubicin.

The development of chemoresistance remains a significant cause of treatment failure in breast cancer. We posit that a mathematical understanding of chemoresistance could assist in developing successful treatment strategies. Towards that end, we have developed a model that describes the cytotoxic effects of the standard chemotherapeutic drug doxorubicin on the MCF-7 breast cancer cell line. We assume that treatment with doxorubicin induces a compartmentalization of the breast cancer cell population into surviving cells, which continue proliferating after treatment, and irreversibly damaged cells, which gradually transition from proliferating to treatment-induced death. The model is fit to experimental data including variations in drug concentration, inter-treatment interval, and number of doses. Our model recapitulates tumor cell dynamics in all these scenarios (as quantified by the concordance correlation coefficient, CCC > 0.95). In particular, superior tumor control is observed with higher doxorubicin concentrations, shorter inter-treatment intervals, and a higher number of doses (p < 0.05). Longer inter-treatment intervals require adapting the model parameterization after each doxorubicin dose, suggesting the promotion of chemoresistance. Additionally, we propose promising empirical formulas to describe the variation of model parameters as functions of doxorubicin concentration (CCC > 0.78). Thus, we conclude that our mathematical model could deepen our understanding of the cytotoxic effects of doxorubicin and could be used to explore practical drug regimens achieving optimal tumor control.

Leadership and governance-what is needed to deliver the Aotearoa New Zealand health reforms.

Nil.

Doctors as leaders and governors.

Doctors working in healthcare are operating in complex adaptive systems that are unpredictable and have complex problems requiring new and unique skills. The Medical Council of New Zealand has specified a scope of practice for doctors involved in health system leadership, and there are several programmes of study that exist in Aotearoa New Zealand (Aotearoa NZ) to gain skills in this domain. It is crucial at this time of change that we understand why doctors as leaders and governors improve outcomes, the importance of training future medical leaders and how we validate these skills as well as the environment in which they operate. As we begin to reorganise our health system, the question we ask is when will we organise our system to recognise, develop and value these skills?

Quantification of long-term doxorubicin response dynamics in breast cancer cell lines to direct treatment schedules.

While acquired chemoresistance is recognized as a key challenge to treating many types of cancer, the dynamics with which drug sensitivity changes after exposure are poorly characterized. Most chemotherapeutic regimens call for repeated dosing at regular intervals, and if drug sensitivity changes on a similar time scale then the treatment interval could be optimized to improve treatment performance. Theoretical work suggests that such optimal schedules exist, but experimental confirmation has been obstructed by the difficulty of deconvolving the simultaneous processes of death, adaptation, and regrowth taking place in cancer cell populations. Here we present a method of optimizing drug schedules in vitro through iterative application of experimentally calibrated models, and demonstrate its ability to characterize dynamic changes in sensitivity to the chemotherapeutic doxorubicin in three breast cancer cell lines subjected to treatment schedules varying in concentration, interval between pulse treatments, and number of sequential pulse treatments. Cell populations are monitored longitudinally through automated imaging for 600-800 hours, and this data is used to calibrate a family of cancer growth models, each consisting of a system of ordinary differential equations, derived from the bi-exponential model which characterizes resistant and sensitive subpopulations. We identify a model incorporating both a period of growth arrest in surviving cells and a delay in the death of chemosensitive cells which outperforms the original bi-exponential growth model in Akaike Information Criterion based model selection, and use the calibrated model to quantify the performance of each drug schedule. We find that the inter-treatment interval is a key variable in determining the performance of sequential dosing schedules and identify an optimal retreatment time for each cell line which extends regrowth time by 40%-239%, demonstrating that the time scale of changes in chemosensitivity following doxorubicin exposure allows optimization of drug scheduling by varying this inter-treatment interval.

CD4 T-cell immune stimulation of HER2 + breast cancer cells alters response to trastuzumab in vitro.

INTRODUCTION: The HER2 + tumor immune microenvironment is composed of macrophages, natural killer cells, and tumor infiltrating lymphocytes, which produce pro-inflammatory cytokines. Determining the effect of T-cells on HER2 + cancer cells during therapy could guide immunogenic therapies that trigger antibody-dependent cellular cytotoxicity. This study utilized longitudinal in vitro time-resolved microscopy to measure T-cell influence on trastuzumab in HER2 + breast cancer. METHODS: Fluorescently-labeled breast cancer cells (BT474, SKBR3, MDA-MB-453, and MDA-MB-231) were co-cultured with CD4 + T-cells (Jurkat cell line) and longitudinally imaged to quantify cancer cell viability when treated with or without trastuzumab (10, 25, 50 and 100 µg/mL). The presence and timing of T-cell co-culturing was manipulated to determine immune stimulation of trastuzumab-treated HER2 + breast cancer. HER2 and TNF-α expression were evaluated with western blot and ELISA, respectively. Significance was calculated using a two-tailed parametric t-test. RESULTS: The viability of HER2 + cancer cells significantly decreased when exposed to 25 µg/mL trastuzumab and T-cells, compared to cancer cells exposed to trastuzumab without T-cells (p = 0.01). The presence of T-cells significantly increased TNF-α expression in trastuzumab-treated cancer cells (p = 0.02). Conversely, cancer cells treated with TNF-α and trastuzumab had a similar decrease in viability as trastuzumab-treated cancer cells co-cultured with T-cells (p = 0.32). CONCLUSIONS: The presence of T-cells significantly increases the efficacy of targeted therapies and suggests trastuzumab may trigger immune mediated cytotoxicity. Increased TNF-α receptor expression suggest cytokines may interact with trastuzumab to create a state of enhanced response to therapy in HER2 + breast cancer, which has potential to reducing tumor burden.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect.

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

A multi-state model of chemoresistance to characterize phenotypic dynamics in breast cancer.

The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models' ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model's ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.

Spatial assembly and RNA binding stoichiometry of a LINE-1 protein essential for retrotransposition.

LINE-1, or L1, is a highly successful retrotransposon in mammals, comprising 17% and 19% of the human and mouse genomes, respectively. L1 retrotransposition and hence amplification requires the protein products of its two open reading frames, ORF1 and ORF2. The sequence of the ORF1 protein (ORF1p) is not related to any protein with known function. ORF1p has RNA binding and nucleic acid chaperone activities that are both required for retrotransposition. Earlier studies have shown that ORF1p forms a homotrimer with an asymmetric dumbbell shape, in which a rod separates a large end from a small end. Here, we determine the topological arrangement of monomers within the homotrimer by comparing atomic force microscopy (AFM) images of the full ORF1p with those of truncations containing just the N or C-terminal regions. In addition, AFM images of ORF1p bound to RNA at high protein/RNA molar ratios show that ORF1p can form tightly packed clusters on RNA, with binding occurring at the C-terminal domain. The number of bound ORF1p trimers increases with increasing length of the RNA, revealing that the binding site size is about 50 nt, a value confirmed by nitrocellulose filter binding under stoichiometric conditions. These results are consistent with a role for ORF1p during L1 retrotransposition that includes both coating the RNA and acting as a nucleic acid chaperone. Furthermore, these in vitro L1 ribonucleoprotein particles provide insight into the structure of the L1 retrotransposition intermediate.

Free and total cefazolin plasma and interstitial fluid concentrations at steady state during continuous infusion.

Free and total concentrations of cefazolin were compared in plasma and interstitial fluid during continuous intravenous infusion therapy. Seven patients, median age 53 (25-74) years, were administered a constant infusion of cefazolin at a mean (+/-S.D.) dose of 3.5 g (+/-1.1) per 24 h for > or = 5 days. Four blisters were induced on the forearm of each patient for sampling of interstitial fluid. Free concentrations in plasma and interstitial fluid were similar, and correlated better than total concentrations (r(2) = 0.82, P = 0.005 versus r(2) = 0.54, P = 0.056). In all patients, the free concentrations in the interstitial fluid were at least two-fold the MIC(90) for Staphylococcus aureus.