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 – 142} this being a main cause of inconsistency in viability results between the mentioned large-scale studies.

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 four-other 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

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 dose-response 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 – 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.

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.

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}

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

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 – 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.

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.

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.

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.

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.

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.

Current experimental protocols in the large-scale studies and a lot of small-scale studies use one cell set and expose cancer cells to increasing drug doses for a unique period of time going from 48h to 168h, and after determine the IC-50. The new protocol recommends multiple sets, every set specific for a drug exposure time: from 2-3h, 24h, 48h, 72h and even further if the doubling time is long. For every time point, there is an IC-50, thus an IC-50-time course because drugs IC-50s are variable over time. The inconsistency of the drugs IC-50s noticed by Haibe-Kains et al ¹ is due to the difference in cell drugs exposure times. ^{2 , 3}

It reflects the cellular phenomenology which is Gompertzian for in vitro monolayers and spheroids. The current large-scale 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.

(Cases 1-235) is characterized by an IC-50 decrease over time ( Table 1 and Figure 1a). There are several choices of time points: [24h, 48h and 72h for Cases 1-185], [3h, 24h and 120h for Cases 186-190], [2h, 24h, and 48h for Cases 191-194], [48h, 72h, and 120h for Cases 195-206], [24h, 48h, 72h and 96h for Cases 207-215], [24h, 48h,72h and 120h for Cases 216-222], [24h, and 48h for Cases 223-233], and [48h and 72h for Cases 234-235]. The IC-50 decrease is dramatic in many Cases (3, 4, 13, 14, 21, 24-27, 65, 67, 75, 79, 111, 112, 114, 116, 123, 151, 163, 165, 170, 171, 173, 197, 199, 200, 201, 201, 206 and 210). The IC-50 decrease over time depends on the cell lines and drugs. This shows that one IC-50 taken at one time point is misleading in its value and can explain the inconsistency noticed by Haibe-Kains et al, ¹ Baggerly et al ⁴ and Reinhold et al. ⁵ The increase of sensitivity of cancer cells to drugs, missing with the 4PL model based on one time point IC-50, is consistent with Haber’s law of increase of drug toxicity with time.

(Cases 236-249) is characterized by an IC-50 increase over time ( Table 2 and Figure 1b). There are several choices of time points: [24h, 48h and 72h for Cases 236-245], [2h, 24h and 48h for Case 246], [48h and 72h for Cases 247-248], and [24h, 48h and 72h for Case 249]. This IC-50 increase can be dramatic as in Cases 243-245 and 248. This IC-50 increase over time is not predicted by the Haber’s law and the 4PL model. It is only described by the multiple time points IC-50 introduced by this paper. It shows how cancer cells drug resistance is evidenced in vitro over a short period of time and shows the usefulness of the multiple IC-50-time points model.

(Cases 250-279) is a V shaped curve characterized by two phases in the interaction between cancer cells and drugs, a decrease phase of the IC-50 followed by an increase of the IC-50 over time ( Table 3 and Figure 1c). There are several choices of time points: [24h, 48h and 72h for Cases 250-268], [4h, 24h and 48h for Cases 269-272], [2h, 24h and 48h for Case 273], [24h, 48h and 72h for Cases 274-276], [24h, 72h and 120h for Case 277] and [3h, 48h and 72h for Cases 278-279]. Type 3 is not predicted by the Haber’s law and the 4PL model. This type shows how complex the interaction between cancer cells and drugs can be. In this type we are in vitro out of reach of the immune system and whatever a living organism can do to stop the growth of cancer cells. There are two possible interpretations. The first is based on what have been said before, that not all cancer cells in vitro are growing according the Gompertzian model. The IC-50 decrease phase is the killing of growing cells in vitro, and the IC-50 increase phase shows the resistance of non-growing quiescent cancer cells. After all the majority of cancer drugs are targeting growing cells. 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 far-reaching 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.

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 – 66} ( Table 4 and Figure 1d). There are several choices of time points: [24h, 48h and 72h for Cases 280-288], [3h, 24h and 120h for Case 289], [12h, 24h, 48h and 72h for Case 290]. This Type in addition of showing the heterogeneity of cancer in vitro (growing cells vs quiescent cells), demonstrates in IC-50 increasing phase cancer cells resistance, then suddenly in the IC-50 decreasing phase the resistance collapse. So, any IC-50 taken at the time point corresponding to the apex of the Λ is seriously misleading. This type of situation is not predicted by the Haber’s law or the 4PL model.

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.

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.

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.