# TP53 and the Ultimate Biological Optimization Steps of Curative Radiation Oncology

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

_{n}, σ

_{h}, and σ

_{i}. These are the key events induced by radiation for the induction of nonhomologous end-joining and homologous recombination repair pathways and direct inactivation, and for simplicity, in Figure 2 (cf also Section 2.4 Figure), they are denoted as n, h, and i, respectively. Interestingly, this ability to quantify apoptosis has helped us to identify the early low-dose hypersensitivity (LDHS) and low-dose apoptosis (LDA) of most normal tissues but also tumor tissues with intact TP53 and ATM genes [2]. This important mechanism, probably developed by the survival advantage of the species, ensures minimal risk for severe mutations before the DNA repair system is fully functional after about ½ to 1 Gy (cf. Figure 1 and Figure 2 and [1,2,3,4,5]). As a compensating measure, the apoptosis-inducing caspase3 remarkably “remembers” this low-dose apoptotic cell loss and starts cellular repopulation to re-establish homeostasis in the tissues after being irradiated. This useful mechanism in normal tissue is a well-known problem after suboptimal radiation therapy as it can cause accelerated tumor cell repopulation at the end of a noncurative treatment [6]. A clear curative intent is probably the principal way to avoid this tumor-reactivating mechanism. The above studies also identified that the most effective HDA is induced through Ser 46 phosphorylation, i.e., via ATM and p38K at dual double-strand breaks (DDSBs) generated by the lowest LET ions, largely as they have the highest fluence of secondary δ-electrons generated by the primary ion fluence per unit dose [1,2]. With a very high LET (of carbon ions and others), the apoptosis and senescence will instead also be high in the normal tissues in the entrance region of the beam, which is undesirable from a complication-free cure point of view, even if hypoxic tumor-cell inactivation may be marginally improved by such a process [1] (Figure 22), [7,8,9].

## 2. TP53 and Cell Survival and Apoptosis at Low and High Doses and LETs

#### 2.1. TP53 Damage Response

#### 2.2. Cell Survival

^{5+}[2] (Figures 7, 9, 10 and 12)), and a clear but small LDHS was observed [24] mainly due to the early dual NHEJ only and HR misrepair (5% at 0.5 Gy, calculated [2] (Figures 7, 8 and 9b)). The 31% value was not just LDA but mainly serine-46-induced HDA. So, even if there is a weak low-LET ion LDHS and LDA, it is most likely not sufficient to establish a real light ion fractionation window with carbon ions but surely with the entrance plateau and fragmentation tail of low-LET lithium ions (in Figure 1 [2,7], in Figure 2 [2,20] (with

^{60}Co) and Figure 4 (with mut p53-reactivated)), as well as for lowest-LET boron ions and

^{60}Co in Section 2.6. The Bragg peak should always be reserved for target tissues. Thus, HDA is very valuable [25], and even more so, the often associated senescence [1,2,26,27,28], also described in Figure 1, since it does not cause later problems with caspase-3 [6]. To further elucidate the development of the shapes of the cell survival curve, some key steps are summarized in Figure 2, considering the normal lung epithelial cell data [1,2,20]. During the 1940s to 1960s, the logarithmic linear model (Ln) was established, with a back extrapolated (slope D

_{0}) initial cell number (n) larger than 1 to account for cellular division and repair during irradiation. Alternatively, the so-called quasi-threshold dose (Dq) was also used to indicate that the linear extrapolation seemed to start from a dose that was wasted due to tumor cell repopulation and repair. Clearly, this was a rather crude way to describe the early cell survival that often was of low clinical importance at the time but not really today [4]. From the late 1960s, the still currently dominating linear quadratic model could better describe the slight curvature of the quasi-linear high-dose cell survival by its α and β factors of most tumors but did not account so well for the low- and high-dose survival, at least for most normal tissues, as seen in Figure 2. It also misses a true repair term, as a high repair requires a high β, but that means less survival since the term is negative, so α needs to be reduced to better describe the survival, which may only work in a small-dose region and α loses its original meaning. This illogical effect, and the fact that it gives a poor description of LDHS normal tissue survival, has misled two generations of radiation biologists to trust it rather uncritically. The beauty of the third repairable–conditionally repairable (RCR) model is that it is very simple and describes what occurs at large to the cells using Poisson statistics with a simple exponential term for missed cells and a linear exponential term for the correctly repaired fraction of sublethal hit cells. Thus, it is a logical continuation of the Ln expression, as seen in Figure 2 and [29]. It therefore can describe the LDHS quite well and solves the repair and overkill problem at high doses seen with the LQ model. The repairable–homologically repairable formulation (RHR) goes a few steps further by accounting for the two major DNA repair pathways, as mentioned above, and their associated misrepair processes, as seen in the lower right corner of Figure 2. This model can therefore handle, e.g., cell lines with mutant and/or knocked-out repair genes, high and low LETs, and apoptosis induction [1,2]. It is thus extremely important to consider the significant differences between the cell survival of most tumors and generally LDHS normal tissues when designing optimal radiation therapy protocols. It is unfortunate that the bulk of established tumor cell lines mostly suffer from TP53 and associated mutations, so they can easily grow in the lab and lead to the assumption that all cell lines have LQ-like shoulders, almost making the LQ model a dogmatic model of true cell survival. In fact, it is most likely that all intact normal tissues have wild-type TP53 and ATM genes, and thus are linked to LDHS and LDA, as recently indicated [1,2,4], and it is probably an inherited growth advantage to avoid cancerous transformations after low-level genetic damage that may not be correctly repaired. The intriguing reason why it went undetected for such a long time is that too few studies were conducted on live normal tissues at low doses and with sufficient accuracy (until Joiner [30]), but also because the associated accelerated repopulation via caspase-3 tries to compensate for LDA and LDHS at the end of irradiation to re-establish tissue homeostasis [6]. A relative apoptotic effectiveness (RAE) value of about 3.4 has been noted for low-LET boron ions around 40 eV/nm, whereas the peak relative biological effectiveness (RBE) was found to be about 3.5 but closer to an LET of about 160 eV/nm, as seen in Figure 3 (cf also Section 2.6 Figure).

#### 2.3. Apoptosis Induction

^{60}Co, almost all misrepair processes contribute via NHEJ that now dominate cell repair (see [2] for more details). It is indeed seen that low-LET ions produce the highest LDA and HDA per unit dose since the fluence and the number of ions are reduced by half each time the LET is doubled, and so is the apoptosis, as described in more detail in [2] (Figures 7, 9, 10 and 12). The upper right corner of Figure 3 includes the theoretical expression for apoptosis induction showing the increase by lowering the LET by its last 1/LET term that breaks down when the LET is too low, so no apoptosis can be induced. From Figure 3, it is seen that lower LETs (≈20 eV/nm) are preferable to optimize tumor apoptosis and senescence simultaneously, as they are also lowered in normal tissues, and this may generally be better than optimizing the total relative biological effectiveness (RBE) in the tumor and consequently maximizing the hypoxic cell kill. However, unfortunately, this is associated with adverse effects on normal tissue damage in front of and behind the tumor [1,2,9,11], which poses clinical challenges when using Neon ions [31] but also to some extent Carbon ions. The optimal therapeutic choice may also depend on the use of adjuvant therapies, e.g., to enhance antitumor immune reactions or ROS effects [2].

#### 2.4. Reactivation of Mutant TP53

^{60}Co γ-rays is shown in detail in Figure 4, indicating full survival. The curves with PRIMA-1 are here shown as solid lines, and the plain SCLC cell line U1690 without PRIMA-1 are shown as dashed lines, with arrows indicating the change in survival by the presence of PRIMA-1 during irradiation. At higher doses, the relative survival loss is quite large (almost 27% at 4 Gy, see Figure 4). Therefore, there would be a clinical advantage of using high doses per fraction with PRIMA-1. There is an increased HR repair alone (f

_{h}by almost 50%) but also to fix NHEJ misrepair (l is more than doubled), indicating that the HR pathway is largely improved through p53 reactivation, partly increasing the very low-dose apoptosis [2]. The recovery of the HR pathway with PRIMA-1 is more than tenfold increased below 0.15 Gy, sixfold at about ½ Gy (LDA), fourfold at 1 Gy, and more than doubled at high doses (HDA) with PRIMA-1. Due to the wide therapeutic effect spectrum of the active component MQ of APR 246 and PRIMA-1 [2,32], both on reactive oxygen species (ROS), inhibiting the enzyme thioredoxin reductase 1 and thioredoxin and decreasing cellular glutathione levels and increasing apoptosis, it is difficult to say exactly what caused the increase in HDA apoptosis by ≈15% in the current study. Even if PRIMA-1 increased the HR only, and its repair of NHEJ misrepair, this probably occurred due to improved HR initiation via TP53, there are also indications that apoptosis could be caused by direct mitochondrial effects or via caspase-3, and the cell cycle block via p21 is not generally restored either [33,34]. This latter fact may even be an advantage for cancer treatment as tumor cells will continue cycling and incorporate damaged DNA in their genomes without repair, and they may finally end up in a mitotic catastrophe situation like in classical radiation therapy. The first very interesting cell culture study of using APR 246 on colorectal cancer combined with radiation was recently published, and mut TP53 showed almost wt TP53 response with 5 μM APR 246, whereas TP53 Null cells were only half as responsive [35] generally consistent with Figure 4. At 7.5 μM, the mut cell line was even more responsive than the wt, which should be a valuable treatment property. In a tumor growth assay, 20 μM APR 246 and 6 Gy both halved the mut xenograft size, whereas the combination brought it down to ≈1/5, but wt showed only a 30% APR 246 reduction, and null and mut cells were similar [35]. Interesting Venn diagrams of significantly enriched pathways and genes for combined and radiation-alone treatments were also included for wt, mut, and TP53 null cells.

#### 2.5. The Fractionation Window

#### 2.6. Secondary Cancer Induction

#### 2.7. Simplistic Clinical Example

^{30}≈ 0.000023 accumulated normal tissue survival reduction (Figure 2) whereas RHR would lead to a 0.5

^{15}≈ 0.000031 or preferably 0.65

^{18}≈ 0.00046, i.e., ≈20-fold better normal tissue survival, thus very likely increasing the complication-free cure. Interestingly, a somewhat similar thinking was recently presented by Yarnold and coworkers [41]. There are therefore definitely many reasons to re-evaluate the time–dose fractionation along the current ideas and those presented in a previous study on DNA repair ([1] (Figure 21); see also the Graphical Abstract) to really introduce a major paradigm shift in curative radiation therapy thinking as suggested in the Section 5.

## 3. Influence of Microdosimetric Beam Characteristics on the Dose–Response Relation of Tumors and Normal Tissues

#### 3.1. The Dose–Response Relation

_{B}(D) = e

^{−N0 · }

^{S}

^{(D)}= e

^{−N0 · e−D/D0}

_{0}is the initial clonogen number, S(D) is the relative clonogen survival after dose D, and D

_{0}is the exponential slope defined in Figure 2. As dose D is increased, the number of remaining clonogens is reduced until at high doses, the number of surviving clonogens tends to zero, and the cure probability approaches unity along a sigmoidal curve, as shown in Equation (1) and Figure 7. The curve shape is reminiscent of the cumulative distribution function of a random variable, which, by definition, also starts from zero, finally reaching one or 100% when all random events have been counted. Interestingly, the curve shape is rather well described (within a few %) using the cumulative generalized gamma distribution, but even more exactly using the perhaps more well-known extreme value distribution, which is known to describe the distribution of outliers of random processes, whereas the rest of the distribution is approximately normal distributed.

^{−e(μ−D)/ν}= e

^{−e(D0∗}

^{lnN0−D)/D0,}

_{0}lnN

_{0}and the “radiation resistance” ν = D

_{0}can be identified in Equation (2). More precisely, the true mean value is actually $\overline{D}$ = μ + ν ∗ γ = D

_{0}(lnN

_{0}+ γ), the median value is D

_{50}= μ − ν ln(ln2) = D

_{0}ln(N

_{0}/ln2), the Variance is V = σ

_{D}

^{2}= π

^{2}D

_{0}

^{2}/6, and finally, the relative standard deviation is σ

_{D}/ $\overline{D}$= π /$(\sqrt{6}$ (μ/ν + γ)) = π /$(\sqrt{6}$(lnN

_{0}+ γ)). These are important parameters from a microdosimetric point of view (in all these equations, γ ≈ Euler’s gamma constant, not γ

_{C}). For a common tumor size of N

_{0}= 10

^{7}clonogens, the relative standard deviation is σ

_{D}/ $\overline{D}$≈ 0.0768, so only about 7.7%, resulting in a relatively steep tumor control curve that is rather sensitive to microscopic dose fluctuations. This is partly due to its high Kurtosis = 5.4 independent of μ and ν as well as N

_{0}and D

_{0}, and so is the skewness≈1.1395, explaining the steeper rise in the tumor control curve at low doses and the shallower extended shoulder at high doses, which makes it generally quite hard to achieve 100% perfect tumor cure.

#### 3.2. The Dose–Response Steepness

_{C}, which is defined as

_{C}%) for 1% increase in the delivered dose ([42], γ

_{C}is not γ!). The absolute steepness of the dose–response relationship has its maximum exactly at D

_{max}= D

_{0}ln N

_{0}with γ

_{C}= ln N

_{0}/e. Since D also increases at this point, the true γ

_{max}will be at a slightly higher dose $\widehat{D}$ ≈ D

_{0}(ln N

_{0}+ 1/ln N

_{0}) and thus

_{max}≈ (ln N

_{0}+ 1/ln N

_{0})/e,

_{0}= 10

^{7}), the normalized steepness (γ

_{max}≈ 5.94) further supports the high statistical steepness observed above (see the table in Figure 7). The sharp dose–response and small relative standard deviation make the tumor cure curve quite dependent on dosimetric uncertainties. These uncertainties include both macroscopic dose variations due to imperfect beam homogeneity and the strong microscopic dose heterogeneity in light ions, which is often unavoidable, especially with the heavier ions from carbon and upwards ([43], see also [44] (Figure 3). Although it is a clear figure, it does not even show the therapeutically important ½ MGy doses in 10 nm sites of ions and their δ-electron cores [14] and the DDSBs at e

^{−}track ends [1] due to a too-large pixel size). The recent high-resolution electron microscopic data with Ku70 binding 6 nm gold nanoparticles to detect DSBs have effectively demonstrated the common occurrence of DDSBs. For 2 MeV/u carbon ions, out of 113 DSBs, 69 were single DSBs, 22 were detected as DDSBs, 18 as triple DSBs, and 4 as quadruple DSBs [45] (Figures 2, 4 and 14). Altogether, ≈40% were of DDSB or higher complexity, most likely on the periphery of nucleosomes, where the two DNA strands are only ≈1 nm apart, with a high risk of severe misrepair at close to MGy doses in 5–10 nm δ e

^{−}track end volumes [1] (Figures 2, 13 and 14). Interestingly, DDSBs are the most lethal cellular event for all radiations, and they are about 3 times more common in ion than in electron and photon beams [1], causing an RBE of ≈3. Of the simple ordinary DSBs, 99.2% (if not all) are effectively repaired via the NHEJ and HR pathways (Figure 1 and Figure 2 and [1,2,14]).

#### 3.3. Microdosimetric Heterogeneity Effects on the Dose–Response

^{−}curve in Figure 7. The effect of the microdosimetric relative standard deviation σ

_{D}/$\overline{D}$ on the slope γ

_{C}of the dose–response relation was pointed out many years ago by approximating the tumor control curve, Equation (1), using a simple error function [46,47]. In Figure 7, this is improved upon by using the full extreme value distribution according to Equation (2), now convolved with the microdosimetric relative standard deviations for e

^{−}and X-rays, H

^{+}, He

^{2+}, Li

^{3+}, B

^{5+}, C

^{6+}, and n and Ne

^{10+}with σ

_{D}/$=0$.7%, 1.8%, 3%, 4%, 5%, 7%, and 15%, respectively for an 8 μm diameter cell nuclei (see [46] (Figure 10) and [47] (Figure 15)). The significant reduction in the γ

_{C}value is clearly seen in Figure 8, as the microdosimetric relative standard deviation increases with increasing atomic weight, LET, and RBE. This problem has been well known for neutron therapy, where the relative standard deviation is almost as high as for carbon and neon ions (Figure 7) partly due to the high LET and low therapeutic dose (≈20 Gy). The interesting clinical neutron and photon dose–response dataset of Lionel Cohen [48] also supports this fact, as was later analyzed quantitatively and showed a reduction in the dose–response steepness by about 50% for neutrons, compared with photons [49]. This is in good agreement with the present data calculated in the tabular portion of Figure 7.

#### 3.4. Treatment Optimization

_{C}value reduction will still limit this positive influence (see the tabulation in Figure 7; more details are provided in a recent review [54] (Figure 8.5n, 8.10, 8.23c)).

_{B}≈ e

^{−5*0.5^5}see Equation (1) and Figure 2) or one 3 Gy ion fraction at RBE ≈ 3.3, providing ≈ 61% tumor cure (→P

_{B}≈ e

^{−5*0.1}with C

^{6+}survival data [1] (Figures 16 and 19)). For completeness, the Poisson probability of surviving clonogenic tumor cells after ion irradiation is quite accurately provided using the probability of no cell-nuclear (=0) hits:

_{n}(0) = = e

^{−σ n}

^{Φ}= e

^{−σ n}

^{D}

^{ρ}/L

_{Δ},

_{n}Φ, by definition, is the Poisson mean lethal hit number per cell of cross-section; σ

_{n}≈πρ

^{2}= π 4

^{2}μm

^{2}≈ 50 μm

^{2}at a fluence Φ = D/L

_{Δ}/ρ; and L

_{Δ}/ρ is the restricted mass stopping power of the ions [1]. With appropriate units, this is $3$.14(eVnm

^{−1}/Gy)∗D/L

_{Δ}/ρ, which for 2 MeV/u carbon ions of LET ≈ 214 eVnm

^{−1}, and a dose of 3 Gy gives $\overline{\nu}$ ≈ 4.4 and P

_{n}(0) ≈ 1.22%, so more than 1% of the cells are not hit at this dose. Therefore, it is important to switch to a low-LET modality such as photons or high-energy electrons (or even protons) during the last week of treatment, with the lowest possible microdosimetric relative standard deviation in dose delivery. With a high LET, not only is the dose mostly concentrated on the ion tracks surrounded by microscopic cold regions (Figure 8), but also the absorbed dose is about 3 times lower, reducing the number of DSBs by a factor of ≈3 and further increasing the microscopic dose nonuniformity.

#### 3.5. Optimal Use of Low-LET Beams

## 4. Consideration of Low-Dose Hypersensitivity and Apoptosis and Photons, Electrons, and Light Ions in Radiation Therapy Optimization

- The peak absorbed dose to critical normal tissues with adverse reactions, when quasi-uniformly irradiated (organs at risk), should preferably be in the range of 1.8–2.3 Gy/Fraction and of the lowest possible LET and biological effectiveness (Figure 5). Interestingly, this is the dose and LET range that maximizes the LDHS-related normal tissue tolerance with wt TP53, as seen in Figure 1, Figure 2, Figure 4 and Figure 6 [1,2,29,46,54]. A full minimization of the total risk for complications would naturally be preferred or preferably a full so-called P
_{++}optimization strategy approach combining 1. here with 2. and 4. below [60]. - In order to make the treatment as curative as possible, it is desirable that the mean dose to the tumor (internal target volume [36]) is as high as possible to ensure a true complication-free cure (P
_{+}) and perfect clonogenic tumor cell eradication. Interestingly, this can be achieved quite accurately today via advanced biologically optimized intensity-modulated radiation therapy from a few inversely planned beam directions [38,50,54,60]. This will work well even for intact TP53 and ATM pathway tumors (Figure 6 and [2] (Figure 7)) since a simple LQ-type calculation may be far from optimal. - To further minimize normal tissue damage as far as possible, it is desirable to introduce an optimal weekly dose fractionation schedule where the DNA repair of normal tissues is really taken into account to minimize their injury. Up to about 50% higher tumor doses should optimally be delivered Monday morning, Wednesday midday, Friday evening, and the last evening of treatment, to use the weekend and end of therapy for maximal normal tissue recovery (see the dashed line in the Graphical Abstract, [1] (Figure 21) and [61]) and preferably still staying below the 2.3 Gy/Fr to organs at risk. This will especially optimize the weekly HR recovery towards ≈72+ h since NHEJ achieves it quite well in the 24+ h from day to day, as shown in the lower right part of the Graphical Abstract. This fractionation advantage works well for low-LET radiations but also for the lightest ions with mainly a low LET in normal tissues.
- For elderly patients, a larger number of optimized beam portals may be ideal, whereas younger patients may benefit from fewer beams (<5) and low-to-medium LET ions (see [5]) to reduce the risk for secondary cancers in extended low-dose regions (1–6 Gy total dose; see Figure 6 and [39,40]). These volumes should therefore be reduced as far as possible using sharp penumbras simultaneously as the complication-free cure (P
^{+}) or preferably the P^{++}optimization strategy (P^{+}followed by a constrained injury relaxation) are the key objectives of the treatment [60] (Figure 22). - To further increase the biologically effective tumor dose delivery, a few light ion beam portals should be used preferably in the range from helium to boron ions only with their Bragg peaks located in the gross tumor volume, to keep the LET low (<10 eV/nm) and the dose within 1.8–2.3 Gy/fraction in organs at risk [1] (Figure 22). Organs at risk have to be passed through with beams to reach the target volume, and with the lightest ions (He-B), this can be carried out using a fairly low LET (<10 eV/nm). To maximize the complication-free cure, it is best to switch to electrons or photons in the last 10–15 GyE, and for bulky tumors, possibly a light ion concomitant gross tumor boost should be used in the last 5 GyE before the final plain 10 GyE low-LET round-up (Figure 8, Figure 9 and Figure 10; [47,54]).
- The influence of tumor vasculature heterogeneity on the distribution of hypoxia was carefully calculated for key tumor types and showed good agreement with clinically measured Eppendorf distributions of hypoxia [62,63,64,65]. This clinically very useful dataset for treating common hypoxic tumors with low LET later showed that the optimal LET for treating them is only as low as 25 eV/nm [46,47,54,65]. This is in good agreement with the optimal LET window of 15–55 eV/nm [1,31,54], so it also can cover other types of tumor heterogeneity and radiation resistance using helium to boron ions.
- For the multitude of radiation-resistant TP53 and/or ATM-mutated tumors that are often a severe clinical problem, the interesting p53 reactivating PRIMA-1 and APR-246 pharmaca may be useful to increase tumor cell apoptosis and further augment the radiation-induced reactive oxygen species effects in the high-dose tumor volume. Interestingly, PRIMA-1 and APR-246 promote the normal function of a missense mutant p53 protein-increasing LDA and HDA apoptosis in the tumor as well as senescence (Figure 4; [2,7,26,27,28,35]). Among other effects, as shown in Figure 4, it inhibits the enzyme thioredoxin reductase 1 and thioredoxin and decreases cellular glutathione levels, which is especially valuable with low-LET radiations, when the lightest ions are not available [2] (Figure 17).

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AT | Ataxia telangiectasia cell line |

ATM | Ataxia telangiectasia-mutated |

CDN1 | One-dimensional closest distance norm |

CHK2 | Checkpoint kinase 2 |

DDSB | Dual double-strand break |

DSB | Double-strand break |

DYRK2 | Dual-specificity tyrosine-regulated kinase 2 |

GSH | Glutathione |

HDA | High-dose apoptosis |

HR | Homologous recombination |

LDA | Low-dose apoptosis |

LDHS | Low-dose hypersensitivity |

LET | Linear energy transfer |

LQ | Linear quadratic |

Mut | Mutant type |

NHEJ | Nonhomologous end-joining |

p | Phosphorylated |

RBE | Relative biological effectiveness |

RCR | Repairable–conditionally repairable model |

RHR | Repairable–homologically repairable formulation |

Trx1 | Thioredoxin reductase 1 |

wt | Wild type |

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**Figure 1.**The complex response of the TP53 gene (upper third) to mild and severe genetic stress largely determines the cellular response to radiation [1,2,3,4,5,10,11,12]. Mild stress phosphorylates the serine 15 and 20 sites on p53 via ATM and CHK2, resulting in cell cycle block and DNA repair. This results in LDHS in normal tissues, but generally not in tumors, often with a mutant TP53 gene (as seen in the cell-survival insert (simplified middle third)). Local high doses or high ionization densities resulting in DDSBs (dual double-strand breaks [1,13,14]) increase the severity of the damage, also phosphorylating the serine 46 site, e.g., via p38K or ATM, and a high-dose apoptotic (HDA) response may be triggered. Lithium ions allow for unique therapeutic use by inducing a massive apoptotic–senescent tumor cell response, mainly within the Bragg peak (σ

_{h}homologically repairable damage and σi direct inactivation cross-sections [1,2]). However, in front of and beyond the Bragg peak, the LET is low, and rapidly and easily repairable nonhomological damage is mainly induced (lower third, σ

_{n}cross-section [1], [2] (Figure 8), [7,8]). The upper third shows the inner workings of p53 in its complex downstream pathways (cf. [15] (Figure 1)).

**Figure 2.**The development of models defining the shape of the cell survival curve during the last ≈ hundred years, from the linear exponential model with back extrapolated effective initial cell number (n, Ln) to the currently dominating linear quadratic formula (LQ), which does not even accurately account for cell repair as Ln does. The more recent repairable–conditionally repairable model handles the cellular repair considerably better and separates it from un-hit survival, whereas the most recent repairable–homologically repairable (RHR) formulation further accounts separately for nonhomologous and homologous recombination repair, as shown in the lower right corner, and can estimate the apoptotic fraction and individual repair processes (cf. [2] (Figures 4 and 6)). The least damage per unit dose is obtained between 1.8 and 2.3 Gy/Fr, as indicated by the fine dotted blue line with the shallowest slope possible through the unit survival point. For further details see [14] (Figure 4).

**Figure 3.**Comparison of the induced apoptosis (programmed cell death shown with solid lines and experimental dots) and the clonogenic survival measured by the RBE (pale-shaded dashed areas) as a function of increasing LET values. The induction of apoptotic cell kill depending on the status of the p53 pathway of the cells is also shown. When some part of the p53 pathway is mutant, A

_{Fr}is reduced to about half its value for normal wt p53 and non-AT cell lines that are intact on the ATM gene upstream of p53. Interestingly, the A

_{Fr}peaks occur at lower LET values than the RBE peaks due to the higher flux density of ions and apoptotic events per unit-absorbed dose. KI is Karolinska Institutet Stockholm Sweden, and NRIS is National Institute of Radiological Sciences, Chiba, Japan, and the table is used for extrapolation to lithium ions and discussed in the text.

**Figure 4.**Increased LDA and HDA via mutant TP53 reactivation. The change in fractional cell survival, S(D), and major DNA repair processes with PRIMA-1 (solid lines) and without (dotted lines) for U1690 SCLC cells with mutant TP53 irradiated using 60Co γ-rays are shown. Arrows indicate the change after adding 5 μM PRIMA-1 for 14 h (10 h before to 4 h post-irradiation). Even if the apoptotic survival change is small, about 7% at low doses (LDA) and up to 15% at high doses (HDA), there are large changes in the reparability of radiation damage with PRIMA-1 added, as seen in the HR-only repair (

**f**≈ +50%) and the HR repair of NHEJ misrepair (

_{h}**l**≈ +100%) and sum of all repair terms that even compensate somewhat for the increased apoptosis via the reactivated mutant p53. The shaded low-dose area between the calculated apoptotic cell survival and measured clonogenic survival is due to apoptotic loss before the full activation of p53 at serine 15 and 20 via the checkpoint kinases ATM and Chk2 (cf. Figure 1 and [1,2,3]). The high-dose loss in cell survival is most likely due to PRIMA-1-induced augmented toxicity through the increasing associated ROS production (PRIMA-1 inhibits the enzyme thioredoxin reductase 1 and thioredoxin and decreases cellular glutathione levels), and increasing HDA and senescence [2,21,22,23]. The mean error μ and standard deviation σ are also shown all below ≈1% but obviously much higher in some of the individual components (≈10%). The volume of data that can be estimated using the new, more flexible, and thus probably more accurate, cell survival and DNA repair formulation is striking. Updated from [2] (Figure 6) with LDA and HDA and the effects of ROS. CDN1: one-dimensional closest distance norm (not least square, see [1]). The original U1690 SCLC cell survival data were provided by Margareta Edgren at KI 2003, and the new RHR formulation significantly helped the interpretation of the wide range of effects of PRIMA-1 (f, g, k, l are repair fractions in which HR fixes various NHEJ misrepair and damage, as indirectly explained in this Figure, f

_{h}plain HR, and f

_{n}plain NHEJ; see [2,14] for further details).

**Figure 5.**The effect of varying the doses per fraction on normal tissue damage is illustrated based on the experimental survival data in Figure 2 for lung epithelial cells. The low-dose hypersensitivity of most normal tissues establishes a therapeutic fractionation window of opportunity to cure cancer with minimal normal tissue damage. The new cell survival models discussed here can fine-tune the dose range to 1.8–2.3 Gy, as shown here for the lungs, a common organ at risk in the thorax region.

**Figure 6.**The secondary cancer induction probability as a function of the dose delivered to normal tissues. At low doses, the risk of inducing a mutation is small, whereas at high doses, the probability of generating a mutation is higher, but so is the probability of eliminating it via treatment. The risk is highest in normal tissues between 1 and 4 Gy, so this volume in patients should really be minimal. The LDA and LDHS of this TP53 intact cell line are clear from the curve shape for the two lowest LET beams. Interestingly, the risk is the smallest for the lowest-LET boron ions due to their high LDA and HDA. The upper shaded area is due to nonapoptotic misrepair for 40 eV/nm

^{10}B ions. CDN1: the one-dimensional closest distance norm (not least square; for details, see [1]).

**Figure 7.**Description of the shape of the tumor control probability curve for a uniform cell line with different radiation modalities as a function of the absorbed dose (upper scale) and approximately normalized to the 50% tumor control dose (≈dose equivalent, lower scale, dashed lines) to more clearly see the effect on the γ

_{C}value as the microdosimetric relative standard deviation increases with the LET. Not only are the hot spots often in the form of dual double-strand breaks (DDSBs, Figure 1; [1] (Figures 2 and 16)) and cold regions become more extreme with increasing LET, but also the RBE increases, thus reducing the total dose about threefold with carbon, neutron, and neon, increasing the relative standard deviation, and reducing the γ

_{C}value more than desirable. For mixed high- and low-LET treatments such as neon ions + e

^{−}, a Gy-equivalent upper scale is needed in units: GyE.

**Figure 8.**The adverse effect of a too-high LET on the complication-free cure reduces the tumor cure and simultaneously increases normal tissue injury (dashed lines, solid lines: [41,42] (Figure 4)). Interestingly, there is a cost-efficient clinical solution to this problem by switching to electrons, photons, or even protons during the last week of treatment. This will lead to a steeper tumor response [1] (Figures 20 and 22), [7,28], generating a higher complication-free cure, all at a lower delivered dose equivalent (see Figure 7 for Ne + e

^{−}) and reduced risk of damaging normal tissues, as demonstrated here. P($\overline{D}$) is the probability of tumor control or normal tissue damage as a function of the mean tumor dose.

**Figure 9.**The optimal shape of the dose profile in the penumbra and setup margin region at the periphery of the internal target volume, assuming a microscopic invasive tumor of Gaussian spread (pink-shaded). Toward the end of the treatment, there are very few clonogenic tumor cells in this volume, and the probability that any of them is hypoxic is very small, even throughout the treatment, so there is no real need to use a high LET in this region (see also the periphery shown in Figure 10). It still needs a fairly high dose via low LET as the response is logarithmic (≈75–80% of D

_{max}) and much less if it initially received a high dose of ion therapy. P

^{+}is the probability of a complication-free cure (Figure 8).

**Figure 10.**The projection of a 4D space–time internal target volume on a 2D flat surface shows the need for low-LET electrons or photons to round up an optimally performed light ion treatment. A 3D cube in 2D is two squares with all corners connected and a 4D cube in 3D is two 3D cubes with all their cubical corners connected, in this case with the blue fourth dimension time arrows. The periphery of the 4D internal target volume including the initial setup margin (pale pink; see Figure 9) and the few remaining gross tumor clonogenic cells (green volume) will substantially benefit from the last 10–15 GyE being delivered with minimal LET and microdosimetric variance of electron or photon beams. Interestingly, both the few remaining clonogenic tumor cells in the gross tumor and the setup margin are best eliminated with an optimized 15 GyE low-LET treatment round-up, and for bulky tumors, the first 5 GyE of those may include a concomitant higher-LET gross tumor boost [50].

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Brahme, A.
TP53 and the Ultimate Biological Optimization Steps of Curative Radiation Oncology. *Cancers* **2023**, *15*, 4286.
https://doi.org/10.3390/cancers15174286

**AMA Style**

Brahme A.
TP53 and the Ultimate Biological Optimization Steps of Curative Radiation Oncology. *Cancers*. 2023; 15(17):4286.
https://doi.org/10.3390/cancers15174286

**Chicago/Turabian Style**

Brahme, Anders.
2023. "TP53 and the Ultimate Biological Optimization Steps of Curative Radiation Oncology" *Cancers* 15, no. 17: 4286.
https://doi.org/10.3390/cancers15174286