The IC-50-time evolution is a new model to improve drug responses consistency of large scale studies [version 1; peer review: awaiting peer review]

Abstract Abstract: Large-scale studies combining hundreds of cancer cell lines and many cancer drugs, with their promises and challenges, represent a new development in the in vitro screening of cancer drugs. However, drugs sensitivity results of the same cancer cell lines exposed to the same cancer drugs generated different IC50s by these studies as noticed by Haibe-Kains B et al (1). These inconsistencies are due to many factors: the experimental conditions and the use of the Four Parameter Logistic (4PL) regression model to analyze drugs sensitivity results. A new model based on the Levasseur LM et al model, the Gompertzian growth model of in vitro monolayer culture, and the IC-50 time course evolution is more appropriate to improve the accuracy of these large scale studies.

In addition, the examination of the previous studies [2][3][4] and other large-scale studies, [6][7][8][9][10][11][12] especially their experimental protocols validate Haibe-Kains B et al concerns and predicts coming ones. The whole high throughput screening idea of exposing large panels of cancer cell lines to anticancer drugs and the viability results (symbolized by the classical IC-50s), when combined with the availability of many data bases (DNA, mRNA, proteomics, miRNA etc.) can identify novel biomarkers suitable for diagnosis and treatment. This endeavor has many challenges to overcome to be successful. This type of studies is only possible in vitro. In order to investigate the reasons of inconsistency let's examine the specifics: parameters of in vitro cell culture, drug exposure timing, the IC-50 as an essential factor of drugs potency and usefulness.
II. Experimental in vitro cell culture conditions 1. Cell densities A quick survey of the cell densities used in these studies 2,3,6-12 shows three figures. First, a fixed cell seeding number going from 250 2 to 500 11 cells per well. Second, a range variation between low and high cell densities depending on cell lines doubling time: 5000-40,000 for the NCI60/DTP screen, 12 300-3600, 7 and 1,000-15,000. 9 Third, cell density expressed as cellular confluence degree: 70% 3 and 80%. 8 In addition, the microplates 'size used in these studies have between 96, 384 and 1536 wells with a reaction volume (which contain cells, media, serum and drugs) respectively 100μl, 20μl and 5μl. The combination of these experimental conditions cannot guarantee for one cancer cell line to grow and respond to the same drug the same way in different studies. The growth inhibitory effects of anticancer drugs depend on cell density used as shown in multiple studies, 13,[136][137][138][139][140][141][142] this being a main cause of inconsistency in viability results between the mentioned large-scale studies.
2. Duration of cell exposure to drugs It has been known since the early days of cancer chemotherapy that cytotoxicity of anticancer drugs depends on drugs concentration and exposure time. 14,15 For the large scale studies the drug exposure time is variable: 48h for JFCR screen 6 and NCI60/DT screen, 12 72h for CGP, 3 72-84h for CCLE, 2 and 72h-168h until cell reach 80% confluent. 8 For the fourother large-scale studies the exposure is 72h but cell densities are not the same. If the cell doubling time is included, which just for the NCI60/DT screen is between 17.4h (colon HCT-116) and 79.4h (lung HOP-92) cancer cell lines, 16 some cell lines have some growth while others didn't grow at all in the drug exposure time allowed. The same cell line used in the previous studies cannot exhibit the same viability and the IC-50 for every drug. Up to this point the basic parameters of in vitro cancer cell culture (cell density whether expressed as cell seeding number or degree of confluence, cell doubling time and drug exposure time) are not harmonized at all between the different large-scale studies. 17 III. The limitations of the Hill model 1. Time factor The viability results in the large-scale studies are processed with the four-parameter logistic (4PL) regression derived from the Hill function, 18,19 so are determined the IC-50s and Hill coefficient. The 4PL is practical in fitting the doseresponse curves and deliver the IC-50 that characterized every drug and determine its future as an anticancer drug. However, the Hill model from its inception in 1910, does not include the factor time in anticancer drugs cytotoxicity. It was Fritz Haber 143 and others, [144][145][146][147][148] being out of cancer research field, to link a toxicant concentration and exposure time of an organism to evaluate the resulting toxicity. The Haber's law is expressed as C x t = k 143 where C is the lethal concentration of the toxicant; t, the exposure time and k, a constant. The Haber's law did generate many variants as reviewed by Connell et al. 145 In the cancer research field, it was Osawa et al 20 who showed that anticancer drug cytotoxicity is (C x T) dependent, C being the concentration and T the time. Then Adams et al 21 extended it to C n x T = k, where n is the concentration coefficient and k is the drug exposure constant. All this body of research brings the concept of "dose-time response curves", 148 totally different from the concept "dose response curves" mentioned by a lot of cancer research papers and especially the large-scale studies. 2,3,6-12 Levasseur LM et al 15 combined cytotoxicity with the Hill model and established a modified Hill model, IC n x xT= k. in which IC x is the amount of inhibition, the equivalent of the IC-50. This is a new "paradigm to facilitate the quantitative assessment of the growth-inhibitory effect of anticancer agents as a function of concentration and exposure time". 15 In addition, the Levasseur LM et al model linked drug exposure time to the IC-50 by this equation IC50 = (k/T) 1/n . 22 This shows clearly that in the large-scale studies 2,3,6-12 there is no connection between the IC50 and the exposure time to drugs, thus the inconsistency noticed by Haibe-Kains B et al 1 and Reinhold et al. 5 In these large-scale studies, there is a kind of tacit assumption the IC-50 is constant over the time exposure of cancer cells to cancer drugs. I will prove in this review such statement is incorrect.

Inflection point
The S shaped dose response curve fitted with the Hill model has only one inflection point and therefore a unique IC-50 taken at one-time point. Prinz et al 23 inspecting the NCI60/DT results analyzed with the Hill model, noticed that some results do not fit in it because of the complexity of their dose-response curves. Levasseur LM et al 15 noticed that the "double or triple Hill roller coaster concentration-effect curve" can be explained by the coexistence of two populations of cells with different sensitivities (IC-50a and IC-50b) to drugs, by the target's multiplicity for the same drug, 22 and the allosteric nature of the drug-target interaction. 23 DiVeroli et al 24 point to the multiphasic dose-response curves also referred to as hormesis. Hormesis is a non-monotonic/biphasic dose response, with specific dose response patterns coming in many shapes 25,26 : U, inverted U, J and bell shapes. 152,153 This has been reported with 138 cancer cell lines treated by over 120 drugs. 27,28 As a solution to this problem Di Veroli et al developped an algorithm referred to as Dr Fit.

Cellular heterogeneity
It is another hurdle to the Hill model used to determine drugs IC-50s and can explain the inconsistency between the IC50s noticed by Haibe-Kains B et al, 1 Baggerly KA et al, 4 Reinhold WC et al, 5 Levasseur LM et al, 15 DiVeroli et al, 24 Calabrese et al 28 and Rashkov et al. 29 The issue is how to explain the heterogeneity of cancer cell lines used in vitro and considered homogenous cell lines and checked thoroughly as such? 2,3 IV. The Gompertzian growth of cancer cells in vitro 1. The Gompertzian model Since the Norton et al 1976 landmark paper 30 tumor growth has two phases, an initial avascular exponential phase followed by the retardation or decremented exponential phase due to feedback inhibition. It fits well with the Gompertzian model. 31 The growth type of cancer cells cultured in vitro as a monolayer or spheroids was not addressed by Haibe-Kains et al 1 and also by all the commentaries 32-38 related to Haibe-Kains et al concerns. It should be considered one of the hallmarks of cancer whether in in vitro or in vivo clinical studies 39 since it will have a huge impact in the selection of future cancer drugs. According to results obtained by three research groups, Drasdo et al, 40 Demicheli et al 41,42 and Poplawski et al 43 cancer cells cultured in vitro, as monolayers or spheroids, or in vivo (injected into mice to induce tumors) have the same Gompertzian growth type. For in vitro spheroids and tumors induced in mice there is always a central necrotic zone (due the difficulty of internal cancer cells to have access to oxygen and other nutrients) surrounded by a growing outer layer of cancer cells. Cancer cell growth in two dimensional (2D) monolayers have similar situation in spite of equal accessibility of all cell in 2D to oxygen and nutrients. In both cases, 2D and 3D, the growth is limited to the outer layer as shown by Bru et al. 44 In monolayers, internal cancer cells, squeezed by other surrounding cells, survive by two mechanisms: size reduction divisions 45 and quiescence. 46 Therefore in vitro monolayers of cancer cells although derived from the same cell line are heterogeneous in their behavior and respond differently to anticancer drugs. The Gompertzian growth type of in vitro cancer cells monolayers are well explained by the "two compartment of cell population growth". 47,48 This cellular heterogeneity had been already mentioned previously by Levasseur LM et al 15 and Rashkov et al. 29

One time point IC-50
The Gompertzian growth of cancer cells in vitro had been neglected by the all the large-scale studies and that has serious consequences on the sampling of IC50s at only one time point from 48h to 156h. 2,3,[6][7][8][9][10][11][12] The dual effect of doubling times diversity and the Gompertzian growth type of these cells applied to large number of cancer cells (60 for the NCI-60 to a thousand and even more), is the main reason of inconsistency of the IC-50s between the different large-scale studies. The same cell line won't have the same growth level since the sampling of the IC-50 at different times points in these different large-scale studies.

Dose dense chemotherapy
The Gompertzian growth type of human tumors has led to the introduction of the dose dense chemotherapy protocols. 49,50 Tumor growth is faster for small size tumors than for large size ones. Cancer cells cultured in vitro exhibit the same phenomenon, in the beginning the growth is exponential and after it slows down. Therefore, the IC-50 should be evaluated at different time points especially at an early time point.

4.
In vitro self-seeding Human tumors are characterized by metastasis due to self-seeding. 51 There is no metastasis in vitro, but a similar phenomenon is operating since cancer cells are heterogeneous in their growth (a growing population and a quiescent population) and their response to drugs. Once some cancer cells are killed the quiescent cells start growing because there is more space and nutrient available.

2D vs 3D debate
In vitro 2D monolayers of cancer cells does not reproduce the complexity of in vivo mice or human 3D tumors. The stromal reaction, vascular networks, the immune system are missing in vitro. 52,53 In addition, the failure to reproduce in vivo the in vitro results obtained with 2D cultures, the 3D cultures became the solution to bridge the gap in this 2D vs 3D debate. However, the Gompertzian growth of cancer cells cultured in 2D or 3D formats, in both cases there is a heterogeneous population of cancer cells, thus in both cases cellular dynamics are similar. Unfortunately, many studies using 3D cell culture systems in vitro, time exposure of cancer cells to drugs is variable: 24h, 54 48h, 55 72h 56 and 168h. 57,58 This fact limits the capacity of the 3D spheroids model to improve the accuracy of the 2D monolayers in vitro screening of cancer drugs.
V. The IC-50 time course evolution model After analysis of the multiple sources of inconsistencies of IC-50s between large scale studies, I would like to propose the following model.

The evaluation of drugs IC50 at multiple time points
As above mentioned the large-scale studies the IC-50s were evaluated at only one time point between 48h and 168h. 2,3,6-12 The drugs IC-50s were supposed to be constant over time regardless of the chosen time point. This is not always true.

At least three times points are necessary
Early time points (2-3h, 24h) are necessary for drugs high doses supposed to kill all cells. This will show how much time is necessary for high doses need to kill all cells, and that depend on cancer cell line (it depends on the doubling time and the genetic makeup). Some drugs have a toxic effect in just 2-3 hours. 54 Late time points are necessary for medium and low doses. In addition, drugs 'killing mechanisms, whether cell cycle dependent like paclitaxel or independent like carboplatin, whether by apoptosis or necrosis, the influence of all these factors cannot be explored by one time point drugs IC50s.

The IC50 time evolution model
It reflects the cellular phenomenology which is Gompertzian for in vitro monolayers and spheroids. The current largescale studies using in vitro monolayers are completely disconnected from the reality of cellular dynamic evolution. The same problem exists with the in vitro spheroids. Thus, the 2D vs 3D debate aimed at replacing in vitro monolayers with spheroids should include the new model exposed here for a better accuracy of drugs IC-50s measurement over time.
2. Type 2 (Cases 236-249) is characterized by an IC-50 increase over time ( The second can be explained by the killing of the bulk of cancer cells in the first phase and the takeover by a resistant clone like cancer stem cells in the second phase. It is an in vitro self-seeding mechanism. 51 Type 3 shows the advantage of the multiple IC-50 time points and its farreaching capacity to explore the complex behavior of cancer cells. This a clear demonstration that cancer cells monolayer is heterogeneous and respond differently to cancer drugs. In addition, the IC-50 taken in different time points between the large-scale studies will lead to dramatic inconsistency.

Type 4
Is an Arabic eight-digit Λ or the Greek lambda Λ letter shaped curve also characterized by two phases in the interaction between cancer cells and drugs [64][65][66] (Table 4 and Figure 1d).

Type 5
Is characterized by a constant IC50 over time (Table 4 and Figure 1e). I found only one case [24h, 48h and 72h for Case 291]. The proteasome inhibitor Bortezomib killing mechanism is not cell cycle dependent.
6. Is there a relationship between cancer drugs molecular targets and their IC-50 Time Evolution Type (TET)? As Table 5 shows, it is difficult to find a clear pattern for cancer drugs TET. Etoposide which targets DNA Topoisomerase II kills seven cancer cell lines with IC-50 TET 1. Cisplatin kills six cell lines with TET 1 and kills PC-3 cell line with different TET in two different papers: TET3 113 and TET4. 114 Resveratrol's molecular target still unknown, it kills six cancer cell lines with TET1. Paclitaxel which targets microtubules kills cancer cells with TET1, 3 and 4. Bortezomib which targets the proteasome system kills cancer cells with TET 1 and 5. Further studies are necessary to explore this relationship, if there is any, between cancer drugs and their IC-50 TET.
7. Is there a relationship between cancer cell lines and cancer drugs IC-50 Time Evolution Type (TET)?
As shown in Table 6 it is hard to find a general pattern. Cancer cell line A549 exposed to 10 drugs respond with the same IC-50 TET1 as reported by different papers. 60,92,94,96 Cancer cell line MDA-MB-231 exposed to 9 different drugs respond with the same TET1 as reported by 8 different papers. 54,70,72,95,102,105,106 and 120 Cancer cell line MCF-7 has a mixed response to drugs but responds with IC-50 TET1 to 12 drugs as reported by 9 papers. 54,70,72,95,102,105,106 and 120 Cancer cell line HCT-116 has a mixed response to drugs but responds with IC-50 TET1 to 7 drugs as reported by 5 papers. 61,67,98,100 and 112 Cancer cell line HeLa has a mixed response to drugs but responds with IC-50 TET1 to 5 drugs as reported by 4 papers. 61,87,111 and 123 Cancer cell line HT-29 has a mixed response to drugs but responds with IC-50 TET1 to 5 drugs as reported by 5 papers. 61,67,98,109 and 115 As shown in Table 6 a variety of cancer cells (K-562, MCF-7,  UACC-903, HL-60, HCT-116, LnCap, HeLa, T47D, A-375, HT-29, SW872 and PC-3) have a mixed response of IC-50 TET 1,2,3,4 and 5 to many cancer drugs. The good thing is that the response of each cancer cell line is reported by several research groups in the world. That is proof of validity, the strength and the usefulness of the IC-50-time evolution model compared to the one time point IC-50, aka 4PL model based on the Hill equation.

VII. Conclusions
The in vitro testing of cancer drugs remains a necessary step in their evaluation. To solve the inconsistencies of the drugs IC-50s between large scale studies several attempts 24,37,79-83 failed. It is my opinion that the in vitro assessment of drugs is still a necessary step before going to in vivo mice studies and human clinical trials. Considering the failure of many drugs at the end, and the billions of dollars to support that, it is necessary to strengthen the prediction power of in vitro studies by considering a better understanding of cancer cells behavior in microplates. It is tempting to use high capacity microplates in which the reaction volume can be as small as 5μl and the number of cells is in the hundreds, making any statistical analysis futile. The automation of the process imposing an arbitrary one time point IC-50 regardless of the diversity of hundreds cancer cells doubling times provides this technology euphoria but does not advance cancer research field nor it improves patient's life. The growth of cancer cells in vitro as it is in vivo is not a continuous growth. Jacques Monod used to say "the dream of a bacteria is to become two bacteria". Cancer cells have another dream referred to as the "Gompertzian model". This model applied in vivo has dramatically improved cancer treatment, the same model governs cancer cells growth in microplates whether in 2D or 3D formats. As I explained the meaning of different IC-50-time evolution Types 1-5, the effects of cancer drugs on cancer cells is time dependent. It was Fritz Haber who noticed that a low dose applied at long time has the same effect as a high dose applied at a short time. The Hill model short of the time factor is the main source of our problems with the in vitro screening of cancer drugs. 84 We need to go beyond the Hill model and embrace the IC-50-time course evolution already predicted by Levasseur LM et al modified Hill model, 15 the Gompertzian growth type of in vitro, 30,40-43 the heterogeneous nature of in vitro monolayers 47 and microspheres, and the hormesis phenomenon. [25][26][27][28][29] This new model, still a work in progress, connects the IC50 time evolution to in vitro cellular monolayer dynamics: cancer cells exposed to killing drugs do not respond as individual cells but as group of cells governed by quorum sensing. 85,86 In addition, the results gathered in 80 papers validate the new model I am presenting.

Declarations
Data availability: No data are associated with this article.