# Different Calculation Strategies Are Congruent in Determining Chemotherapy Resistance of Brain Tumors In Vitro

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## Abstract

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## 1. Introduction

^{®}assay. The presented results are an interdisciplinary compendium of state-of-the-art disease modeling, state-of-the-art laboratory procedures, and innovative statistical modeling to investigate a biotechnological and socio-economical relevant challenge.

## 2. Materials and Methods

#### 2.1. Mathematical Background

#### 2.2. Cell Models and Experimental Setup

^{®}CX, Sigma-Aldrich, St Louis, MO, USA) and neural stem cells (H9-Derived, Gibco) were used as healthy controls to evaluate the toxicity of the drugs. Additionally, we also tested the inhibition efficiency using three different normal adult human dermal fibroblasts (NHDF-Ad, Lonza, Basel, Switzerland). Effects on cell growth were assessed 72 h after substance exposure using the CellTiterGlow

^{®}assay (Promega, Madison, WI, USA). All procedures were in consent with the local ethical commission oversights.

#### 2.3. Fitting the Curves

#### 2.4. Quantifying the Drug Effect

## 3. Results

## 4. Discussion

#### Limitations

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GI${}_{50}$ | concentration required for 50% inhibition of growth |

PoD | point-of-departure |

AUC | area under the curve |

IC${}_{50}$ | inhibitory concentration 50% |

CI | confidence interval |

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**Figure 1.**(

**a**) Graphical representation of the parameters of the Hill equation: ${A}_{0}$: the curve upper bound; ${b}_{\infty}$: the curve lower bound, as a fraction of ${A}_{0}$; ${\mathit{logIC}}_{50}$: the logarithm of the substance concentration at the inflection point of the curve, $I{C}_{50}$; $\beta $: the parameter controlling the slope of the curve. Note that GI${}_{50}$ is not itself a parameter of the curve; it is the point at which the curve falls to 50% of its maximum value, ${A}_{0}$. (

**b**) Definition of the point-of-departure (PoD), based on the confidence band of the curve. The existence of a drug effect can be established with 95% confidence at the lowest concentration at which the Hill curve’s confidence interval (CI, red) does not overlap with the 95% CI at $\mathit{logC}=0$ (green).

**Figure 2.**The function used to transform the data and its effect on the Hill curve: (

**a**) For low values, close to zero, the inverse softplus function (solid, red) approximates the logarithm (dashed, green). For high values, it approaches the identity line, $y=x$ (dotted, blue). (

**b**) Where the logistic (Hill) function (dashed, red) has high values, the inverse softplus (solid, blue) leaves it almost unchanged. At low values, where the logistic function becomes close to a falling exponential, the inverse softplus transforms it to an almost straight line.

**Figure 3.**Different cell lines have different growth patterns, and after 72 h of incubation, their numbers differ significantly at every drug concentration. Curves differing only in the amplitude parameter ${A}_{0}$ and sharing the remaining three parameters, ${b}_{\infty}$, $\mathit{logC}$, and $\beta $, were fitted to the empirical data. The different amplitudes were later used for normalizing the curves.

**Figure 5.**(

**a**) Correlation between the AUC and GI${}_{50}$ (dots, solid line) and between the AUC and PoD (crosses, dashed line). The three measures can be used more-or-less interchangeably for detecting substance effect. (

**b**) Correlation between GI${}_{50}$ and PoD. When both values could be computed (i.e., neither was infinite), they were very similar. Note, however, that PoD also depends on the experimental setup (see Discussion below).

**Figure 6.**(

**a**) If a drug failed to reach GI${}_{50}$, the AUC had a significantly higher value. (

**b**) The same behavior, only with slightly lower AUC values, was observed when using PoD as the criterion for the effect. (

**c**) Correlation between the rankings by GI${}_{50}$ and by PoD. For the top 20 substances (lower left corner in the figure), there is little difference between the two criteria.

**Figure 7.**(

**a**) Bortezomib showed an effect very early, at concentrations for which there were no measurements, so the confidence band was very wide. (

**b**) Itraconazole did not have an effect, and the numeric algorithm failed to fit a logistic curve to the empirical data.

**Figure 8.**(

**a**) Rigosertib sodium leveled off shortly after reaching GI${}_{50}$. (

**b**) Vinflunine tartrate leveled off before reaching GI${}_{50}$.

Substance | Rank (GI${}_{50}$) | Tox@GI${}_{50}$ | Rank (PoD) | Tox@PoD | Rank (AUC) |
---|---|---|---|---|---|

Itraconazole | 1 | 0.000 | 64 | inf | 10 |

Bortezomib | 2 | 0.411 | 63 | inf | 1 |

Actinomycin D | 3 | 0.596 | 1 | 0.636 | 6 |

Dinaciclib | 4 | 0.586 | 2 | 0.641 | 8 |

Staurosporine | 5 | 0.472 | 4 | 0.654 | 2 |

Ganetespib | 6 | 0.566 | 3 | 0.600 | 3 |

Romidepsin | 7 | 0.000 | 12 | 0.005 | 7 |

MLN9708 | 8 | inf | 5 | inf | 4 |

Carfilzomib | 9 | 0.930 | 6 | 0.930 | 5 |

Homoharringtonine | 10 | 0.659 | 7 | 0.696 | 9 |

PF-04691502 | 11 | 0.345 | 8 | 0.329 | 14 |

BAY80-6946 | 12 | inf | 9 | inf | 13 |

INK128 | 13 | inf | 28 | inf | 12 |

Obatoclax | 14 | 0.534 | 10 | 0.434 | 11 |

Panobinostat | 15 | 0.658 | 11 | 0.639 | 16 |

Auranofin | 16 | inf | 13 | inf | 15 |

17-AAG | 17 | inf | 14 | inf | 17 |

Idarubicin hydrochloride | 18 | 0.834 | 16 | 0.790 | 19 |

Fludarabine phosphate | 19 | 0.000 | 22 | 0.000 | 24 |

Daunorubicin hydrochloride | 20 | 0.710 | 17 | 0.675 | 20 |

Substance | Rank (PoD) | Tox@PoD | Rank (GI${}_{50}$) | Tox@GI${}_{50}$ | Rank (AUC) |
---|---|---|---|---|---|

Actinomycin D | 1 | 0.636 | 3 | 0.596 | 6 |

Dinaciclib | 2 | 0.641 | 4 | 0.586 | 8 |

Ganetespib | 3 | 0.600 | 6 | 0.566 | 3 |

Staurosporine | 4 | 0.654 | 5 | 0.472 | 2 |

MLN9708 | 5 | inf | 8 | inf | 4 |

Carfilzomib | 6 | 0.930 | 9 | 0.930 | 5 |

Homoharringtonine | 7 | 0.696 | 10 | 0.659 | 9 |

PF-04691502 | 8 | 0.329 | 11 | 0.345 | 14 |

BAY 80-6946 | 9 | inf | 12 | inf | 13 |

Obatoclax | 10 | 0.434 | 14 | 0.534 | 11 |

Panobinostat | 11 | 0.639 | 15 | 0.658 | 16 |

Romidepsin | 12 | 0.005 | 7 | 0.000 | 7 |

Auranofin | 13 | inf | 16 | inf | 15 |

17-AAG | 14 | inf | 17 | inf | 17 |

Rigosertib sodium | 15 | 0.477 | 24 | 0.477 | 25 |

Idarubicin hydrochloride | 16 | 0.790 | 18 | 0.834 | 19 |

Daunorubicin hydrochloride | 17 | 0.675 | 20 | 0.710 | 20 |

Vinflunine tartrate | 18 | 0.404 | 97 | inf | 63 |

Doxorubicin hydrochloride | 19 | 0.735 | 21 | 0.736 | 23 |

Ponatinib | 20 | 0.854 | 23 | 0.894 | 21 |

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**MDPI and ACS Style**

Fischer, I.; Nickel, A.-C.; Qin, N.; Taban, K.; Pauck, D.; Steiger, H.-J.; Kamp, M.; Muhammad, S.; Hänggi, D.; Fritsche, E.;
et al. Different Calculation Strategies Are Congruent in Determining Chemotherapy Resistance of Brain Tumors In Vitro. *Cells* **2020**, *9*, 2689.
https://doi.org/10.3390/cells9122689

**AMA Style**

Fischer I, Nickel A-C, Qin N, Taban K, Pauck D, Steiger H-J, Kamp M, Muhammad S, Hänggi D, Fritsche E,
et al. Different Calculation Strategies Are Congruent in Determining Chemotherapy Resistance of Brain Tumors In Vitro. *Cells*. 2020; 9(12):2689.
https://doi.org/10.3390/cells9122689

**Chicago/Turabian Style**

Fischer, Igor, Ann-Christin Nickel, Nan Qin, Kübra Taban, David Pauck, Hans-Jakob Steiger, Marcel Kamp, Sajjad Muhammad, Daniel Hänggi, Ellen Fritsche,
and et al. 2020. "Different Calculation Strategies Are Congruent in Determining Chemotherapy Resistance of Brain Tumors In Vitro" *Cells* 9, no. 12: 2689.
https://doi.org/10.3390/cells9122689