Mathematical modeling to distinguish cell cycle arrest and cell killing in chemotherapeutic concentration response curves

Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures

Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.

Towards better combination regimens of cytarabine and FLT3 inhibitors in acute myeloid leukemia

BACKGROUND

AML patients with FLT3/ITD mutations have poor response to cytarabine-based chemotherapy. FLT3 inhibitors (FLT3i) may resensitize cells to cytarabine (CYT). Improving treatment outcome of this combination may benefit from a mechanistic extrapolation approach from in vitro data.

METHODS

The effects of CYT and several FLT3i on cell proliferation and cell cycle kinetics were examined in AML cell lines. The effect of FLT3i (quizartinib, midostaurin, sorafenib) on cell proliferation and cell cycle kinetics was assessed in AML cell lines with differing FLT3 status; HEL (negligible expression of wild-type FLT3), EOL1 (wild-type FLT3), MV4-11 (FLT3-ITD resulting in constitutively active isoform). Semi-mechanistic cell cycle models for CYT and FLT3i were developed. Clinical CYT and quizartinib pharmacokinetic dosage regimens were modeled. Survival of AML patients was described via a hazard model. Simulations exploring different CYT/quizartinib regimens were conducted with the goal of improving treatment outcome.

RESULTS

FLT3 status was associated with sensitivity to CYT (HEL cells most sensitive > EOL1 > MV4-11 cells). This order of sensitivity is reversed for FLT3i. Cytarabine induced apoptosis in the S-phase while all FLT3i induced apoptosis and cell cycle arrest at G1 phase. Simulations of candidate clinical regimens predict better cell kill upon adding quizartinib simultaneously with or immediately after CYT exposure. Overall survival was predicted to be significantly better with quizartinib 200 mg administered every 48 h vs every 24 h in patients with FLT3 aberrations.

CONCLUSION

Simultaneous administration of quizartinib and CYT every other day is a promising combination regimen for AML patients with FLT3 mutations.

Crosstalk between M2 macrophages and glioma stem cells

PURPOSE

Given its extremely poor prognosis, there is a pressing need for an improved understanding of the biology of glioblastoma multiforme (GBM), including the roles of tumor subpopulations that may contribute to their growth rate and therapy resistance. The most malignant phenotypes of GBM have been ascribed to the presence of subpopulations of cancer stem cells (CSCs), which are resistant to chemotherapeutic drugs and ionizing radiation and which promote invasiveness and metastasis. The mechanisms by which the CSC state is obtained and by which it promotes tumor maintenance are only beginning to emerge. We hypothesize that M2 polarized macrophages may affect CSC phenotypes via cell-cell communication.

METHODS

We investigated the interplay between glioma CSCs and macrophages via co-culture. The invasiveness of CSCs in the absence and presence of macrophages was assessed using collagen degradation and Transwell migration assays. The role of STAT3 as a CSC phenotypic mediator was assessed using siRNA-mediated gene silencing.

RESULTS

We found that the levels of a M2 macrophage-specific secreted cytokine, TGF-β1, were elevated in the presence of CSCs, regardless of whether the cells were plated as contacting or non-contacting co-cultures. In addition, we found that the co-culture resulted in enhanced expression of M2 markers in macrophages that were previously polarized to the M1 phenotype. siRNA-mediated STAT3 silencing was found to reduce the chemo-responsiveness and migratory abilities of the CSCs. Combination treatment of STAT3 siRNA and DNA alkylating agents was found to further abrogate CSC functions.

CONCLUSIONS

Our data indicate that the co-culture of CSCs and macrophages results in bi-directional signaling that alters the phenotypes of both cell types. These results provide an explanation for recently observed effects of macrophages on GBM tumor cell growth, motility and therapeutic resistance, and suggest potential therapeutic strategies to disrupt the CSC phenotype by impairing its communication with macrophages.

Pharmacodynamic Modeling of Cell Cycle Effects for Gemcitabine and Trabectedin Combinations in Pancreatic Cancer Cells

Combinations of gemcitabine and trabectedin exert modest synergistic cytotoxic effects on two pancreatic cancer cell lines. Here, systems pharmacodynamic (PD) models that integrate cellular response data and extend a prototype model framework were developed to characterize dynamic changes in cell cycle phases of cancer cell subpopulations in response to gemcitabine and trabectedin as single agents and in combination. Extensive experimental data were obtained for two pancreatic cancer cell lines (MiaPaCa-2 and BxPC-3), including cell proliferation rates over 0-120 h of drug exposure, and the fraction of cells in different cell cycle phases or apoptosis. Cell cycle analysis demonstrated that gemcitabine induced cell cycle arrest in S phase, and trabectedin induced transient cell cycle arrest in S phase that progressed to G₂/M phase. Over time, cells in the control group accumulated in G₀/G₁ phase. Systems cell cycle models were developed based on observed mechanisms and were used to characterize both cell proliferation and cell numbers in the sub G₁, G₀/G₁, S, and G₂/M phases in the control and drug-treated groups. The proposed mathematical models captured well both single and joint effects of gemcitabine and trabectedin. Interaction parameters were applied to quantify unexplainable drug-drug interaction effects on cell cycle arrest in S phase and in inducing apoptosis. The developed models were able to identify and quantify the different underlying interactions between gemcitabine and trabectedin, and captured well our large datasets in the dimensions of time, drug concentrations, and cellular subpopulations.

Assessment of non-linear combination effect terms for drug-drug interactions

Drugs interact with their targets in different ways. A diversity of modeling approaches exists to describe the combination effects of two drugs. We investigate several combination effect terms (CET) regarding their underlying mechanism based on drug-receptor binding kinetics, empirical and statistical summation principles and indirect response models. A list with properties is provided and the interrelationship of the CETs is analyzed. A method is presented to calculate the optimal drug concentration pair to produce the half-maximal combination effect. This work provides a comprehensive overview of typically applied CETs and should shed light into the question as to which CET is appropriate for application in pharmacokinetic/pharmacodynamic models to describe a specific drug-drug interaction mechanism.

Mixture dynamics: Combination therapy in oncology

In recent years combination therapies have become increasingly popular in most therapeutic areas. We present a qualitative and quantitative approach and elucidate some of the challenges and solutions to a more optimal therapy. For tumor growth this involves the study of semi-mechanistic cell-growth/kill models with multiple sites of action. We introduce such models and analyze their dynamic properties using simulations and mathematical analysis. This is done for two specific case studies, one involving a single compound and one a combination of two compounds. We generalize the notion of Tumor Static Concentration to cases when two compounds are involved and develop a graphical method for determining the optimal combination of the two compounds, using ideas akin to those used in studies employing isobolograms. In studying the dynamics of the second case study we focus, not only on the different concentrations, but also on the different dosing regimens and pharmacokinetics of the two compounds.

Application of Pharmacokinetic-Pharmacodynamic Modeling and Simulation for Antibody-Drug Conjugate Development

Characterization and prediction of the pharmacokinetics (PK) and pharmacodynamics (PD) of Antibody-Drug Conjugates (ADCs) is challenging, since it requires simultaneous quantitative understanding about the PK-PD properties of three different molecular species i.e., the monoclonal antibody, the drug, and the conjugate. Mathematical modeling and simulation provides an excellent tool to overcome these challenges, as it can simultaneously integrate the PK-PD of ADCs and their components in a quantitative manner. Additionally, the computational PK-PD models can also serve as a cornerstone for the model-based drug development and preclinical-to-clinical translation of ADCs. To provide an overview of this subject matter, this manuscript reviews the PK-PD models applicable to ADCs. Additionally, the usage of these models during different drug development stages (i.e., discovery, preclinical development, and clinical development) is also emphasized. The importance of PK-PD modeling and simulation in making rationale go/no-go decisions throughout the drug development process is also highlighted. There is an array of PK-PD models available, ranging from the systems models specifically developed for ADCs to the empirical models applicable to all chemotherapeutic agents, which one can employ for ADCs. The decision about which model to choose depends on the questions to be answered, time at hand, and resources available.

Exposure time independent summary statistics for assessment of drug dependent cell line growth inhibition

Background

In vitro generated dose-response curves of human cancer cell lines are widely used to develop new therapeutics. The curves are summarised by simplified statistics that ignore the conventionally used dose-response curves’ dependency on drug exposure time and growth kinetics. This may lead to suboptimal exploitation of data and biased conclusions on the potential of the drug in question. Therefore we set out to improve the dose-response assessments by eliminating the impact of time dependency.

Results

First, a mathematical model for drug induced cell growth inhibition was formulated and used to derive novel dose-response curves and improved summary statistics that are independent of time under the proposed model. Next, a statistical analysis workflow for estimating the improved statistics was suggested consisting of 1) nonlinear regression models for estimation of cell counts and doubling times, 2) isotonic regression for modelling the suggested dose-response curves, and 3) resampling based method for assessing variation of the novel summary statistics. We document that conventionally used summary statistics for dose-response experiments depend on time so that fast growing cell lines compared to slowly growing ones are considered overly sensitive. The adequacy of the mathematical model is tested for doxorubicin and found to fit real data to an acceptable degree. Dose-response data from the NCI60 drug screen were used to illustrate the time dependency and demonstrate an adjustment correcting for it. The applicability of the workflow was illustrated by simulation and application on a doxorubicin growth inhibition screen. The simulations show that under the proposed mathematical model the suggested statistical workflow results in unbiased estimates of the time independent summary statistics. Variance estimates of the novel summary statistics are used to conclude that the doxorubicin screen covers a significant diverse range of responses ensuring it is useful for biological interpretations.

Conclusion

Time independent summary statistics may aid the understanding of drugs’ action mechanism on tumour cells and potentially renew previous drug sensitivity evaluation studies.

Pharmacodynamic modeling of cell cycle and apoptotic effects of gemcitabine on pancreatic adenocarcinoma cells

PURPOSE

The standard of care for treating patients with pancreatic adenocarcinomas includes gemcitabine (2',2'-difluorodeoxycytidine). Gemcitabine primarily elicits its response by stalling the DNA replication forks of cells in the S phase of the cell cycle. To provide a quantitative framework for characterizing the cell cycle and apoptotic effects of gemcitabine, we developed a pharmacodynamic model in which the activation of cell cycle checkpoints or cell death is dependent on gemcitabine exposure.

METHODS

Three pancreatic adenocarcinoma cell lines (AsPC-1, BxPC-3, and MiaPaca-2) were exposed to varying concentrations (0-100,000 ng/mL) of gemcitabine over a period of 96 h in order to quantify proliferation kinetics and cell distributions among the cell cycle phases. The model assumes that the drug can inhibit cycle-phase transitioning in each of the 3 phases (G1, S, and G2/M) and can cause apoptosis of cells in G1 and G2/M phases. Fitting was performed using the ADAPT5 program.

RESULTS

The time course of gemcitabine effects was well described by the model, and parameters were estimated with good precision. Model predictions and experimental data show that gemcitabine induces cell cycle arrest in the S phase at low concentrations, whereas higher concentrations induce arrest in all cell cycle phases. Furthermore, apoptotic effects of gemcitabine appear to be minimal and take place at later time points.

CONCLUSION

The pharmacodynamic model developed provides a quantitative, mechanistic interpretation of gemcitabine efficacy in 3 pancreatic cancer cell lines, and provides useful insights for rational selection of chemotherapeutic agents for combination therapy.