Clifford W Fong
email: cwfong@internode.on.net

Keywords: cucurbiturils, molecular containers, cyclodextrins, cucurbiturils, tumour concurrent chemotherapy and radiotherapy, hypoxic drug delivery, anti-cancer, Abbreviations Tirapazamine TPZ , cyclodextrins CD, [γ]cyclodextrin [ Lowest unoccupied molecular orbital LUMO, natural bond orbitals NBO, Adiabatic electron affinity AEA in eV, extracellular matrix

The potential use of cucurbiturils and cyclodextrins to facilitate delivery and anti-neoplastic potentiation of tirapazamine and cisplatin with concurrent radiotherapy in tumours -A quantum mechanical study

Clifford W Fong

To cite this version:

Clifford W Fong. The potential use of cucurbiturils and cyclodextrins to facilitate delivery and antineoplastic potentiation of tirapazamine and cisplatin with concurrent radiotherapy in tumours -A quantum mechanical study.

Introduction

Clinical results with tirapazamine, cisplatin and radiotherapy

It is well known that there is a strong link between tumour hypoxia and malignancy progression. [START_REF] Osinsky | Tumor hypoxia and malignant progression[END_REF] [START_REF] Osinsky | Tumor hypoxia and malignant progression[END_REF]] Tirapazamine (TPZ) can significantly enhance the antitumour effect of radiotherapy and chemotherapy, particularly platinum-based drugs and taxanes, in both murine and human xenograft models. However phase I, II, III, IV clinical trials with TPZ in combination with cisplatin (CisPt) and radiotherapy have proved less than conclusive. TPZ/CisPt/chemoradiotherapy was not superior to CisPt/chemoradiotherapy in either progression-free survival or overall survival against locally advanced cervical cancer, although a definitive conclusion was possibly limited by a statistically inadequate number of outcome events. [START_REF] Disilvestro | Phase III Randomized Trial of Weekly Cisplatin and Irradiation Versus Cisplatin and Tirapazamine and Irradiation in Stages IB2, IIA, IIB, IIIB, and IVA Cervical Carcinoma Limited to the Pelvis: A Gynecologic Oncology Group Study[END_REF][DiSilvestro 2014] Pre-clinical studies had shown that the tumourspecific potentiation of cisplatin cytotoxicity was the result of an interaction between TPZ and CisPt at the cellular level that requires the low oxygen levels typical of those in solid tumours. A synergy between TPZ and CisPt particularly in the treatment of non-small cell lung cancer was found. [START_REF] Gatzemeier | Tirapazamine-cisplatin: the synergy[END_REF] [START_REF] Gatzemeier | Tirapazamine-cisplatin: the synergy[END_REF]] The cytotoxicity of TPZ results from bioreduction of TPZ to produce radical species that caused DNA damage. [START_REF] Kovacs | Cisplatin antitumour potentiation by tirapazamine results from a hypoxia-dependent cellular sensitization to cisplatin[END_REF][ [START_REF] Kovacs | Cisplatin antitumour potentiation by tirapazamine results from a hypoxia-dependent cellular sensitization to cisplatin[END_REF]] The mechanism of the interaction amongst TPZ, CisPt and radiotherapy was thought to be the potentiation of CisPt-induced DNA interstrand cross-links, possibly as a result of a diminished or delayed repair of these lesions. Whether the activity of tirapazamine in clinical trials is related to its hypoxic selectivity or to sensitization of CisPt is not definitely known. [START_REF] Disilvestro | Phase III Randomized Trial of Weekly Cisplatin and Irradiation Versus Cisplatin and Tirapazamine and Irradiation in Stages IB2, IIA, IIB, IIIB, and IVA Cervical Carcinoma Limited to the Pelvis: A Gynecologic Oncology Group Study[END_REF][START_REF] Green | Hypoxic cell sensitization in chemoradiation for cervical cancer[END_REF][DiSilvestro 2014, [START_REF] Green | Hypoxic cell sensitization in chemoradiation for cervical cancer[END_REF]] Combined TPZ/CisPt cytotoxicity was schedule dependent clinically. [START_REF] Kovacs | Cisplatin antitumour potentiation by tirapazamine results from a hypoxia-dependent cellular sensitization to cisplatin[END_REF] [START_REF] Kovacs | Cisplatin antitumour potentiation by tirapazamine results from a hypoxia-dependent cellular sensitization to cisplatin[END_REF]] A 2008 individual patient meta-analysis of combined CisPt/radiotherapy showed an absolute risk reduction of death of 6% and a 7% reduction in distant metastases. [START_REF] Green | Hypoxic cell sensitization in chemoradiation for cervical cancer[END_REF] Green 2016] Hypoxia is also known to increase resistance to CisPt in ovarian cancer lines. [START_REF] Mcevoy | Identifying novel hypoxia-associated markers of chemoresistance in ovarian cancer[END_REF][McEvoy 2015] However, free radical induced DNA damage is enhanced in the presence of oxygen by about three times more than under anoxic conditions (OER=oxygen enhancement ratio=3). That is under anaerobic conditions, the radiation dose must be increased by a factor of 3 to achieve the same degree of cytotoxicity that occurs under oxygenated conditions. The timescale of oxygen effect is related to the lifetime of the induced free radical lesions within the cell. Free radical scavengers such as various biological thiols reduce the lives of free radical species, such as the Pt radicals. [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF][von Sonntag 2006] The electron-affinic oxygen chemical process of fixation of radical damage to DNA is thought to be only fully counteracted for oxygen levels below about 0.01% [START_REF] Pettersen | Targeting tumour hypoxia to prevent cancer metastasis. From biology, biosensing and technology to drug development: the METOXIA consortium[END_REF] [START_REF] Pettersen | Targeting tumour hypoxia to prevent cancer metastasis. From biology, biosensing and technology to drug development: the METOXIA consortium[END_REF]] which may affect various studies of the influence of hypoxia on cancer cell line sensitivity. For example, it has been shown that CisPt and TPZ (which was more sensitive than cisplatin) were more effective in anoxic (0.1% oxygen) or hypoxic (1.0% oxygen) environments than a number of other anti-cancer drugs in 5 cell lines. [START_REF] Strese | Effects of hypoxia on human cancer cell line chemosensitivity[END_REF] [START_REF] Strese | Effects of hypoxia on human cancer cell line chemosensitivity[END_REF]] Tirapazamine Tirapazamine (TPZ) has a high specificity for hypoxic cells at clinically relevant partial oxygen pressures over a broad oxygen concentration range. TPZ is a prodrug that is bioactivated in hypoxic conditions via one-electron reduction (NADPH:CYP450 reductase) as shown in Figure 1. Labelling experiments with anaerobic supercoiled plasmid DNA, NADPH, and cytochrome P450 reductase showed that the bioreductively activated hypoxiaselective DNA-strand cleavage caused by TPZ (1,2,4-benzotriazine 1,4-dioxide) is consistent with the hydroxyl radical being the main cause of DNA damage. [START_REF] Shen | Isotopic labeling experiments that elucidate the mechanism of DNA strand cleavage by the hypoxia-selective antitumor agent 1,2,4-benzotriazine 1,4-di-N-oxide[END_REF] [START_REF] Shen | Isotopic labeling experiments that elucidate the mechanism of DNA strand cleavage by the hypoxia-selective antitumor agent 1,2,4-benzotriazine 1,4-di-N-oxide[END_REF] The fate of this TPZ free radical is dependent upon the level of oxygen, and in hypoxia, the free radical spontaneously decays, generating hydroxyl radicals HO• that abstracts hydrogen from DNA causing single-and double-strand breaks. The one electron reduction of TPZ by the NADPH/CP450 couple under acidic conditions leads to an intermediate free radical species TPZ• which can produce hydroxyl radicals. The pH of tumours is typically 6.5-6.9 in the extracellular maxtrix (ECM), and close to neutral 7.2-7.4 within cancerous cells. [START_REF] Estrella | Acidity Generated by the Tumor Microenvironment Drives Local Invasion[END_REF][START_REF] Sluis | In vivo imaging of extracellular pH using 1 H MRSI[END_REF][START_REF] Zhang | Tumor pH and its measurement[END_REF][Estrella 2013, Sluis 1999, Zhang 2010] Oxygen inhibits the metabolic activation of TPZ and the free radical species undergoes rapid back oxidation to the prodrug with the release of the less toxic superoxide anion species. [START_REF] Denny | Tirapazamine: a bioreductive anticancer drug that exploits tumour hypoxia[END_REF] [START_REF] Denny | Tirapazamine: a bioreductive anticancer drug that exploits tumour hypoxia[END_REF]] The different pH and oxygen environments in the ECM compared to those within the cancerous cells in the tumour contribute to a reduction of TPZ being available to enter cancerous cells, so protecting the TPZ within cyclodextrin CD or cucurbituril CB molecular containers would facilitate a higher TPZ payload being deliverable inside cells. The mechanisms by which bare TPZ and TPZ@CB or TPZ@CD can enter cells are unknown, but macrophages and endocytosis mechanisms have been documented for CD and CB inclusion complexes. [START_REF] Hettiarachchi | Toxicology and Drug Delivery by Cucurbit[n]uril Type Molecular Containers[END_REF][START_REF] Tanaka | Tumor targeting based on the effect of enhanced permeability and retention (EPR) and the mechanism of receptor-mediated endocytosis (RME)[END_REF][START_REF] Garmann | Cellular accumulation and cytotoxicity of macromolecular platinum complexes in cisplatin-resistant tumor cells[END_REF][START_REF] Kim | Regulating exocytosis of nanoparticles via host-guest chemistry[END_REF][ [START_REF] Hettiarachchi | Toxicology and Drug Delivery by Cucurbit[n]uril Type Molecular Containers[END_REF][START_REF] Tanaka | Tumor targeting based on the effect of enhanced permeability and retention (EPR) and the mechanism of receptor-mediated endocytosis (RME)[END_REF][START_REF] Garmann | Cellular accumulation and cytotoxicity of macromolecular platinum complexes in cisplatin-resistant tumor cells[END_REF][START_REF] Kim | Regulating exocytosis of nanoparticles via host-guest chemistry[END_REF]] It has been shown that extravascular penetration of TPZ in multicellular cultures to peripheral cells existing at low oxygen tension is limited by the metabolism of TPZ by more proximal cells existing at moderate oxygen tension. TPZ reached only 10% of the blood concentration at cells most peripheral to blood vessels and is only cytotoxic to cells located within ∼75μm of blood vessels. [START_REF] Kyle | Measurement of delivery and metabolism of tirapazamine to tumour tissue using the multilayered cell culture model[END_REF][ [START_REF] Kyle | Measurement of delivery and metabolism of tirapazamine to tumour tissue using the multilayered cell culture model[END_REF] It has been found [START_REF] Evans | Tirapazamine Is Metabolized to Its DNA-damaging Radical by Intranuclear Enzymes[END_REF] [START_REF] Evans | Tirapazamine Is Metabolized to Its DNA-damaging Radical by Intranuclear Enzymes[END_REF]] that TPZ radicals that are formed outside nuclei do not contribute to intranuclear DNA damage, and essentially all of the DNA damage from TPZ results from radicals generated within the nucleus. About 80% of the drug metabolism that occurs in the cytoplasm does not contribute to the activity of TPZ in killing hypoxic cells. We have recently developed a model of the cytotoxic behaviour of TPZ and a number of TPZ analogues: extravascular tumour diffusion is governed by the desolvation, lipophilicity, dipole moment and molecular volume, whilst hypoxic assays and aerobic properties are determined by desolvation, lipophilicity, dipole moment and electron affinity. The cytotoxic dependency on electron affinity is consistent with radical mechanisms. [START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Fong | Platinum anti-cancer drugs: Free radical mechanism of Pt-DNA adduct formation and anti-neoplastic effect[END_REF][START_REF] Fong | Platinum based radiochemotherapies: free radical mechanisms and radiotherapy sensitizers[END_REF][START_REF] Fong | The extravascular penetration of tirapazamine into tumours: a predictive model of the transport and efficacy of hypoxia specific cytotoxic analogues and the potential use of cucurbiturils to facilitate delivery[END_REF][ Fong 2016Fong ,2017] ] Cisplatin Cisplatin (CisPt) is a widely used chemotherapy drug used to treat testicular, cervical, germ cell, ovarian, bladder, head and neck, and non-small cell lung cancer. Radiation therapy is also used in conjunction with cisplatin for treating cervical, bladder, and head and neck cancers. Comparisons of concurrent chemotherapy and radiation with radiation alone in cervical cancer treatments have shown that chemoradiation reduces the risk of death by 30-50% [START_REF] Koivusalo | Chemoradiation of cervical cancer cells: targeting human papillomavirus E6 and p53 leads to either augmented or attenuated apoptosis depending on the platinum carrier ligand[END_REF][ [START_REF] Koivusalo | Chemoradiation of cervical cancer cells: targeting human papillomavirus E6 and p53 leads to either augmented or attenuated apoptosis depending on the platinum carrier ligand[END_REF]]. Similarly trials have show an overall survival advantage of 30% for cisplatin-based chemotherapy given concurrently with radiation therapy [START_REF] Berclaz | Long-term followup of concurrent radiotherapy and chemotherapy for locally advanced cervical cancer: 12-Year survival after radiochemotherapy[END_REF] [START_REF] Berclaz | Long-term followup of concurrent radiotherapy and chemotherapy for locally advanced cervical cancer: 12-Year survival after radiochemotherapy[END_REF]]. It is thought that the molecular mechanism involves the induction of strand breaks by the ionizing radiation adds to platinum crosslinks and interferes with DNA repair processes. The molecular mechanism of this synergistic interaction between cisplatin and ionizing radiation has been investigated. The cisplatin-ionizing radiation synergistic interaction requires the DNA-dependent protein kinase-dependent nonhomologous end joining catalysed repair of DNA double-strand breaks, and the presence of a cisplatin lesion on the DNA blocks this pathway. [26][Broeckman 2005] The efficacy of various radiosensitizers on Pt based cervical cancer treatments has been reviewed. [START_REF] Candelaria | Radiosensitizers in cervical cancer. Cisplatin and beyond[END_REF] [START_REF] Candelaria | Radiosensitizers in cervical cancer. Cisplatin and beyond[END_REF]] In one study, with cisplatin or Lipoplatin (a liposomal cisplatin), followed by irradiation, it was observed that drug concentrations higher than IC50 were found to be synergistic, but concentrations lower than the IC50 were antagonistic, indicating a schedule dependence of the synergism of platinum-based drugs and radiation which has important implications for drug and radiation time administration in the clinic. [START_REF] Tippayamontri | Synergism in Concomitant Chemoradiotherapy of Cisplatin and Oxaliplatin and their Liposomal Formulation in the Human Colorectal Cancer HCT116 Model[END_REF] [START_REF] Tippayamontri | Synergism in Concomitant Chemoradiotherapy of Cisplatin and Oxaliplatin and their Liposomal Formulation in the Human Colorectal Cancer HCT116 Model[END_REF] We have recently shown that the inclusion complexes formed from CisPt and cucurbit [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]uril, {CisPt@ [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB} and cyclodextrins {CisPt@[γ]CD or {CisPt@HPBCD}, can be sources of Pt based free radicals such as (H 3 N) 2 PtCl• and (H 3 N) 2 Pt•• species in water within a radiation environment which can produce hydrated electrons. Also we have shown that free radicals formed from cisplatin, carboplatin and oxaliplatin may be involved in Pt-DNA adduct formation and the anti-neoplastic effect (as well as the commonly accepted nucleophilicelectrophilic effect of Pt-DNA adduct formation). [START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Fong | Platinum anti-cancer drugs: Free radical mechanism of Pt-DNA adduct formation and anti-neoplastic effect[END_REF][START_REF] Fong | Platinum based radiochemotherapies: free radical mechanisms and radiotherapy sensitizers[END_REF][START_REF] Fong | Cisplatin cyclodextrin complexes as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][ Fong 2016Fong , 2017] ] Cisplatin electrophilic reaction with DNA: is the most widely accepted mechanism of the anti-neoplastic and anti-cancer efficacy of cisplatin and related Pt based analogues. Cisplatin free radical reaction with DNA or non-DNA targets: It has been recently shown that cisplatin and its analogues may also exert its anti-neoplastic chemotherapeutic effect via free radicals. [Fong 2016,17] The source of free radicals e• may come from enzymatic bioreductive processes or in a chemoradiation environment from radiation induced hydrated electrons, or other free radicals in the cell nucleus.

(
(H 3 N) 2 PtCl 2 + e• (H 3 N) 2 Pt• (H 2 O)Cl + Cl• (H 3 N) 2 Pt•• (H 2 O) 2 + Cl• (H 3 N) 2 Pt• (H 2 O)Cl or (H 3 N) 2 Pt

Synergistic interaction between chemotherapy and radiotherapy

Seiwert has reviewed the likely multiple mechanisms that contribute to concurrent chemotherapy and radiotherapy efficacy and potentiation against tumours. Radioresistance also occurs through multiple mechanism, including hypoxia. There is evidence that the synergistic effect of radiotherapy using cisplatin with other chemotherapeutic drugs involves free radical Pt intermediates that increase cytotoxicity. CisPt is also reported to be active against well oxygenated as well as hypoxic cells. [32][Seiwert 2007] However as discussed above, cisplatin can be cytotoxic via two pathways, via electrophilic and free radical pathways, the latter particularly so in radiotherapy. The effect of the tumour microenviroment and its effect on radical species produced during radiation is well known. [START_REF] Yoshimura | Microenvironment and Radiation Therapy[END_REF][Yoshimura 2013] Early clinical trials of concurrent CisPt/TPZ/radiotherapy showed synergistic results over and above the separate treatments, but later trials were less clear. [START_REF] Disilvestro | Phase III Randomized Trial of Weekly Cisplatin and Irradiation Versus Cisplatin and Tirapazamine and Irradiation in Stages IB2, IIA, IIB, IIIB, and IVA Cervical Carcinoma Limited to the Pelvis: A Gynecologic Oncology Group Study[END_REF][DiSilvestro 2014]

The effect of radiation on hypoxic cytotoxins in tumours is known. [34][Stratford 2003] The potentiation (enhancement) ratio, increases with dose fractionation (a greater potentiation with fractionated irradiation than with single doses), but the opposite occurs with hypoxic cell radiosensitizers because of reoxygenation between doses (the enhancement ratio decreases with increasing number of fractions). The reoxygenation/rehypoxiation of hypoxic cytotoxins between doses is the major reason for their theoretical superiority over hypoxic radiosensitizers. TPZ is effective with single doses of radiation as well as fractionated radiation. Radiochemotherapy techniques can target solid tumours quite accurately, hence increasing the concentrations of hydrated electrons in the tumour itself.

It is clear that drugs like TPZ with multiple modalities in a hypoxic-oxic radiation environment will depend on the behaviour of the free radicals species and their consequent cytotoxicities, particularly when combined with other free radical species derived from CisPt.

We have previously shown that inclusion of CisPt and TPZ in CBs or CDs may enhance the efficacy of drug delivery to tumour targets. However the possible potentiation of CisPt and TPZ when delivered via the CisPt@CB/CD and TPZ@CB/CD inclusion complexes might occur concurrently with radiotherapy which can produce hydrated electrons in the tumour environment.

Molecular containers as drug delivery agents with concurrent drug potentiation with radiotherapy

Macrocyclic molecular containers such as cucurbit[n]urils (CB[n]), n-cyclodextrins (CD) and calix[n]arenes have been used to enhance delivery and efficacy of platin-based drugs.

[30][Apps 2015] Cyclodextrins (CDs) have been widely used in the pharmaceutical and food industries as solubilising agents, as well as active pharmaceutical ingredients. [START_REF] Di Cagno | The Potential of Cyclodextrins as Novel Active Pharmaceutical Ingredients: A Short Overview[END_REF][START_REF] Gidwani | A Comprehensive Review on Cyclodextrin-Based Carriers for Delivery of Chemotherapeutic Cytotoxic Anticancer Drugs[END_REF][di Cagno 2017, Gidwani 2015] Cyclodextrin are commonly used to pharmaceutically enhance the solubility, stability, reduction of side effects, bioavailability and delivery of various drugs. They are also used as delivery vehicles for anti-cancer drugs. [START_REF] Gidwani | A Comprehensive Review on Cyclodextrin-Based Carriers for Delivery of Chemotherapeutic Cytotoxic Anticancer Drugs[END_REF][START_REF] Malanga | Back to the Future: A New Look at Hydroxypropyl Beta-Cyclodextrins[END_REF][Gidwani 2015, Malanga 2016] A cisplatin/hydroxypropyl--cyclodextrin complex {CisPt@HPBCD} has been characterized. [START_REF] Balaji | Synthesis and characterization studies of cisplatin/hydroxypropyl--cyclodextrin complex[END_REF][ [START_REF] Balaji | Synthesis and characterization studies of cisplatin/hydroxypropyl--cyclodextrin complex[END_REF]]

Cucurbit[n]urils (CB[n]
) is another family of macrocycles that can improve drug delivery by encapsulation of drugs within the CB [START_REF] Mcevoy | Identifying novel hypoxia-associated markers of chemoresistance in ovarian cancer[END_REF], [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB or CB [START_REF] Pettersen | Targeting tumour hypoxia to prevent cancer metastasis. From biology, biosensing and technology to drug development: the METOXIA consortium[END_REF] molecular containers, resulting in enhanced chemical and physical stability, improve drug solubility and controlled drug release. [START_REF] Hettiarachchi | Toxicology and Drug Delivery by Cucurbit[n]uril Type Molecular Containers[END_REF][START_REF] Walker | The potential of cucurbit[n]urils in drug delivery[END_REF][START_REF] Wheate | Cucurbit[n]urils as excipients in pharmaceutical dosage forms[END_REF] We have previously shown that CisPt@CB, Cispt@CD, TPZ@CB and TPZ@CD inclusion complexes when subject to electron attachment show significant potentiation of the guest CisPt and TPZ moieties within the host macrocycles. In the case of CisPt this is manifested in elongation of the Pt---Cl bonds upon electron attachment to the inclusion complex (with a large increase in the adiabatic electron affinity, AEA) and enhanced binding energy between the CisPt and the host macrocycle. The behaviour of a guest CisPt in a macrocycle is very similar to the free radical behaviour of bare CisPt in water when an electron is attached, but with a noted enhancement for the formation of Pt free radical species. Similar behaviour is seen with TPZ inclusion complexes when subject to electron attachment in water, with a resultant large AEA and increased binding affinity. A linear correlation has been observed between the electron affinity of 15 analogs of 2-and 5-nitroimadazoles and 5-nitrofurons and the hypoxic toxicity towards Chinese hamster V79 cells, with the more electron-affinic drugs having the higher toxicity. [START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Stratford | Combining Bioreductive Drugs and Radiation for the Treatment of Solid Tumors[END_REF][START_REF] Fong | Cisplatin cyclodextrin complexes as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Fong | The extravascular penetration of tirapazamine into tumours: a predictive model of the transport and efficacy of hypoxia specific cytotoxic analogues and the potential use of cucurbiturils to facilitate delivery[END_REF] The enhanced permeability and retention effect (EPR) is a well documented mechanism that enhances the anti-tumour effect of large drugs (> 40k Da) as a result of defective lymphatic flow and leaky tumour blood vessels. [START_REF] Fang | The EPR effect: Unique features of tumor blood vessels for drug delivery, factors involved, and limitations and augmentation of the effect[END_REF][ [START_REF] Fang | The EPR effect: Unique features of tumor blood vessels for drug delivery, factors involved, and limitations and augmentation of the effect[END_REF]] Carcinogenesis induced by pathogenic infection and inflammation may proceed through the generation free radicals or oxidative stress, particularly in hypoxic tumour tissue, and may augment the EPR.

[44][Maeda 2013] Encapsulating CisPt with high molecular weight lipophilic polymeric materials (eg Lipoplatin) has been one approach to improving the anti-cancer delivery and efficacy of CisPt.

Ternary complexes of drug@CB and drug@CD complexes have been documented. CDs are known to form ternary complexes with human serum albumin (HSA), [β]CD has the greater ability to decrease the aggregation of HSA and the results indicated that the inhibition order is [START_REF] Oftadeh | Investigation of the Effects of Various Cyclodextrins on the Stabilisation of Human Serum Albumin by a Spectroscopic Method[END_REF][START_REF] Ghosh | Interaction of cyclodextrins with human and bovine serum albumins: a combined spectroscopic and computational investigation[END_REF][Oftadeh 2015, [START_REF] Ghosh | Interaction of cyclodextrins with human and bovine serum albumins: a combined spectroscopic and computational investigation[END_REF]]. CB inclusion complexes are also known to form 1:1 ternary complexes with the HSA surface. [START_REF] Li | Interactions of cucurbit[6,7]urils with human serum albumin and their effects on zaltoprofen transportation[END_REF][ Li 2016] The presence of a high molecular weight ternary complexes such as CisPt@CD@HSA or CisPt@CB@HSA (or TPZ@CD@HSA or TPZ@CB@HSA) increases the likelihood of the EPR effect being operative in tumours. CBs and CB inclusion complexes are known to be efficiently internalized by macrophages, indicating that inclusion of anti-neoplastic drugs in CBs can be effectively delivered to carcinoma cells, since macrophages are particularly active in inflamed and cancerous tissue. [START_REF] Hettiarachchi | Toxicology and Drug Delivery by Cucurbit[n]uril Type Molecular Containers[END_REF][Hettiarachchi 2010]

[γ]CD < [α]CD < [β]CD.
The delivery of cisplatin (and most other conventional anti-cancer drugs) to its tumour cellular targets is known to be poor, with damage to healthy tissue producing unwanted side effects, which limit dosage and efficacy. One day after CisPt administration, about 65-98% of the platinum is (mainly blood serum) protein bound, resulting in deactivation of the drug and possibly causing some of the severe side effects such as nephrotoxicity. It is estimated that only about 1 % of the administered CisPt reacts with nuclear DNA to form Pt-DNA adducts inside the cell which induce tumour cell death. [START_REF] Fong | Molecular Mechanisms of Cellular Transport, Resistance and Cytotoxic Side Effects of Platinum and Adjuvant Anti-cancer Drugs -A Molecular Orbital Study[END_REF][Fong 2015] Improved delivery techniques such as incorporation of CisPt prodrug nanoparticles have shown that concentration of released CisPt prodrugs upon acidification that reached the tumours was seven times higher than normal when released CisPt is delivered in the usual intravenous way, achieving a 95 percent growth inhibition in tests on multicellular spheroids derived from human pancreatic cancer cells (compared to 10 percent using conventional administration).

[

49][Li 2016]

Reduced cellular uptake is a well-known resistance mechanism of cisplatin. Efforts to overcome resistance by increased endocytotic cellular uptake accumulation of macromolecular platinum complexes in cisplatin-resistant ovarian cancer A2780 cells has been demonstrated using macromolecular prodrugs Pt-albumin and Pt-polyethylene glycol complexes. [START_REF] Garmann | Cellular accumulation and cytotoxicity of macromolecular platinum complexes in cisplatin-resistant tumor cells[END_REF] [START_REF] Garmann | Cellular accumulation and cytotoxicity of macromolecular platinum complexes in cisplatin-resistant tumor cells[END_REF]] Tumour cells often exhibit high endocytotic rates due to an increased requirements for proteins as nutrients in the fast growing tumour cells. [START_REF] Sinn | Design of compounds having an enhanced tumour uptake, using serum albumin as a carrier, Part I[END_REF][START_REF] Stehle | Plasma protein (albumin) catabolism by the tumor itself-implications for tumor metabolism and the genesis of cachexia[END_REF][START_REF] Tanaka | Tumor targeting based on the effect of enhanced permeability and retention (EPR) and the mechanism of receptor-mediated endocytosis (RME)[END_REF][START_REF] Kim | Regulating exocytosis of nanoparticles via host-guest chemistry[END_REF] [Sinn1990, [START_REF] Stehle | Plasma protein (albumin) catabolism by the tumor itself-implications for tumor metabolism and the genesis of cachexia[END_REF][START_REF] Tanaka | Tumor targeting based on the effect of enhanced permeability and retention (EPR) and the mechanism of receptor-mediated endocytosis (RME)[END_REF][START_REF] Kim | Regulating exocytosis of nanoparticles via host-guest chemistry[END_REF]].

Although not a molecular container, transferring conjugates can also act as drug delivery agents. A TPZ@transferrin conjugate co-administered with cisplatin resulted in a substantially higher cytotoxicity of tumour cells than the combination of TPZ and cisplatin.

The synergistic anti-tumour inhibition rate of the TPZ@transferrin and cisplatin combination showed an enhancement of 53%. The intravenous accumulation of the TPZ@transferrin complex into tumour-bearing mice was 2.3 fold higher than that of the unmodified TPZ.

[51][Wu 2012] It has also been shown that poly(acrylic acid) nanogels can encapsulate and co-deliver doxorubicin and cisplatin together into MCF-7/ADR tumour cells at higher levels than the separate agents with a synergistic cell killing effect of 0.84. [START_REF] Wu | Enhanced antitumor efficacy of cisplatin by tirapazamine-transferrin conjugate[END_REF][ [START_REF] Wu | Synergistic Cisplatin/Doxorubicin Combination Chemotherapy for Multidrug-Resistant Cancer via Polymeric Nanogels Targeting Delivery[END_REF]]

It can be concluded that many molecular containers such as CB and CD inclusion complexes, high molecular conjugates and encapsulated nanostructures or macromolecular complexes can effectively deliver their drug payloads to the cytosol of tumour cells via macrophages or endocytosis. The EPR effect also enhances payload delivery of these species by increased retention and concentration in the extracellular matrix of solid tumours. The CB and CD containers may also increase the survivability of the inclusion payloads TPZ and CisPt in the blood stream before they reach their tumour target.

Study objective:

To examine the possible increased efficacy and increased deliverable concentration of CisPt and TPZ as anti-neoplastic agents in tumours when delivered by CD and CB molecular containers. To examine the possibility that increased synergism occurs when both agents are delivered by molecular containers which increase potentiation of either or both agents in the extracellular matrix of tumours.

Results

Potentiation of TPZ and CisPt in CB and CD inclusion complexes upon electron attachment

Molecular containers such as CD or CB are known to confer enhanced drug delivery characteristics and reduced side effects for included drugs. However the possibility that these inclusion complexes may also show enhanced electron attachment abilities as well could lead to enhanced anti-tumour properties in a localized radiochemical environment.

Electron affinity is widely acknowledged as the major determinant of radiosensitivity of various anti-cancer drugs. [START_REF] Seiwert | The concurrent chemoradiation paradigm -general principles[END_REF][START_REF] Stratford | Combining Bioreductive Drugs and Radiation for the Treatment of Solid Tumors[END_REF][START_REF] Wardman | Chemical radiosensitizers for use in radiotherapy[END_REF][ Seiwert 2006[START_REF] Stratford | Combining Bioreductive Drugs and Radiation for the Treatment of Solid Tumors[END_REF][START_REF] Wardman | Chemical radiosensitizers for use in radiotherapy[END_REF]] The higher the electron affinity the more easily a species can accept electrons. The adiabatic electron affinity AEA is taken to be a direct measure of the potentiation of CisPt and TPZ to be sensitized by hydrated electrons in a radiochemical environment within a tumour environment. [START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Fong | Platinum anti-cancer drugs: Free radical mechanism of Pt-DNA adduct formation and anti-neoplastic effect[END_REF][START_REF] Fong | Platinum based radiochemotherapies: free radical mechanisms and radiotherapy sensitizers[END_REF][START_REF] Fong | The extravascular penetration of tirapazamine into tumours: a predictive model of the transport and efficacy of hypoxia specific cytotoxic analogues and the potential use of cucurbiturils to facilitate delivery[END_REF][START_REF] Fang | The EPR effect: Unique features of tumor blood vessels for drug delivery, factors involved, and limitations and augmentation of the effect[END_REF][ Fong 2016Fong , 2017] ] In particular, inclusion of these anti-neoplastic agents within a macrocyclic CB or CD molecular container can lead to enhanced activation of these agents over those of the free species as judged by the higher AEA values or increasing AEA values as multiple electrons can be attached to the inclusion complexes.

The For the CisPt complexes, the potentiation is most clearly in the relative elongation of the Pt---Cl bond in particular compared to the bare CisPt• species. These potentiations can be clearly seen in the Table for the two different configurations of the {CisPt@CB [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]} complex which show 1, 2 and 3 electron attachments with increasing values of AEA and increasing elongations of the Pt---Cl and Pt---N bonds. The localized NBO highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO show where the electron is predominantly localized (HOMO) and where the next electron will be attached (LUMO) in the inclusion complex. The configuration of the CisPt moiety with respect to the CB or CD macrocycle has a variable influence on the AEA, but the induced changes to the Pt---Cl and Pt---N bond length as electrons are attached are significant, showing a strong interaction between the CisPt and [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB moieties as electrons are attached.

In terms of the efficiency of capture of hydrated electrons by the CD or CB complexes of CisPt or TPZ, these complexes represent a larger cross sectional target than the bare CisPt or TPZ species and the macrocycles have multiple attachment sites such as the CB carbonyl groups or CD hydroxyl groups. The localized HOMO and LUMO reside on the Pt atom for the {CisPt@CD} and {CisPt@CD}• complexes, but for the {CisPt@CB} the HOMO and LUMO reside on the CB. For the {CisPt@CB}• and {CisPt@CB}•• the HOMO resides on the Pt and the LUMO resides on the CB. In other words the electron affinic ability of the CB macrocycle of the inclusion complexes is greater than that of the corresponding CD macrocycle in the inclusion complexes.

For the {TPZ@[7]CB} the HOMO and LUMO resides on the TPZ, which differs from the {CisPt@[7]CB} complex, and for the {TPZ@[7]CB}• and {TPZ@[7]CB}•• the HOMO resides on the TPZ and the LUMO resides on the [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB moiety. Again like the CisPt complexes, the [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB moiety has an enhanced electron affinic capacity. The enhanced electron affinity of TPZ will increase the formation of the HO• radical which is known to be the anti-neoplastic agent (see Figure 1).

The CisPt@CD complexes generally show much larger potentiations of the CisPt moiety upon electron attachment than the corresponding [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB complexes, indicating a potentially stronger radiochemical anti-neoplastic effect. The binding (as reflected in the binding energies) of the CD complexes of TPZ and CisPt are generally weaker for the CD complexes compared to the [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB complexes, indicating that these species can release the potentiated TPZ and CisPt moieties more easily than the [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB complex, hence allowing possible tailoring of anti-neoplastic regimes or protocols.

The CB macrocycle can also stabilize TPZ when complexed via hydrogen bonding via the carbonyl groups as seen in the {TPZ@[7]CBHBOND}• complex, where a 2.31 Å H-bond between [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]CB-C=O----H-N(H) of TPZ. This requires the normal "closed" portal where the carbonyl groups face inwards towards the cavity, allowing hydrogen bonding with the amino group of TPZ. (see Figure 10)

Besides the potentiation of TPZ or CisPt when included in {TPZ@CD}• or {CisPt@CB}• and related radical species, a critical feature is the dynamic nature of inclusion complexes in solution. The following dynamic equilibria exist (using {TPZ@CB}• as an example):

{TPZ@CB} ⇄ TPZ + CB {TPZ@CB} + e• closed {TPZ@CB}• ⇄ open {TPZ@CB}• ⇄ TPZ• + CB closed {TPZ@CB}• + e• closed {TPZ@CB}•• closed {TPZ@CB}•• ⇄ open {TPZ@CB}•• ⇄ TPZ•• + CB
The behaviour is an example of thermodynamic stability of the complexes (as represented by the stability measures or binding energies of the complexes) versus kinetic control of the above equilibria where radical TPZ payloads are released under certain conditions dictated by the properties of the cytoplasm of the tumour cells. These aspects include pH (particularly for TPZ where the bioreduction is acid catalysed, see Figure 1), oxygen concentration, presence of protein species, ions, radical scavengers such as biological thiols etc. [START_REF] Rieth | Controlling the dynamics of molecular encapsulation and gating[END_REF][Reith 2011] has discussed gated molecular encapsulation, i.e., trapping and releasing of guest molecules at rates that are controlled by conformational changes in the host's structure. NMR studies have shown a slow exchange between internally bound CisPt and free CisPt from the {CisPt@[7]CB} complex. [START_REF] Wheate | Cucurbit[n]uril binding of platinum anticancer complexes[END_REF][START_REF] Jeon | Novel molecular drug carrier: encapsulation of oxaliplatin in cucurbit[7]uril and its effects on stability and reactivity of the drug[END_REF][START_REF] Plumb | Cucurbit[7]uril encapsulated cisplatin overcomes cisplatin resistance via a pharmacokinetic effect[END_REF] Analogous kinetic release behaviour of CisPt in the CisPt@HPBCD can also be observed. The most stable configuration of CisPt@HPBCD is shown in Figure 4 which shows a non symmetrical CD structure with the CisPt located towards the opening with 4 hydroxypropyl group, and a lower opening partly closed by one of the 3 lower hydroxypropyls. A series of time dependent calculations were made of several configurations, starting with CisPt located at the centroid position of the HPBCD and fully relaxing or optimising the inclusion structure in water. It was found that movement of CisPt away from the centroid position towards the edge of the HPBCD macrocycle stabilized the complex: for example movement of the CisPt from 3.525Å to 3.60Å away from the centroid position stabilized the complex by ΔG -20.1 kcal/mol, with small changes in Pt-Cl out and Pt-Cl in bond lengths of 1.5 and 2.2%.

Conclusions

It has been shown that CisPt and TPZ can form stable inclusion complexes with the CD and CB macrocyclic molecular containers. These complexes are predicted to undergo multiple electron attachments which can potentiate the guest TPZ and CisPt species forming radical species such as TPZ•, TPZ••, TPZ••• and CisPt•, CisPt•• and CisPt••• etc which can be released from their molecular containers in an aqueous environment. Inclusion of CisPt and TPZ in CD and CB molecular containers are also expected to confer reduced side effects and enhanced delivery and retention in tumours.

It is predicted that these finding may have relevance to the recent clinical trials where TPZ/CisPt/radiotherapy combinatorial anti-cancer regimes have been extensively examined with less than definitive outcomes.

Based on the well known radical mechanism of radiotherapy/CisPt therapy where hydrated electrons produced by radiotherapy are known to potentiate CisPt, and the known radical mechanism of the anti-cancer properties of TPZ, it is suggested that the use of {TPZ@CD} and {TPZ@CB} coupled with the {CisPt@CD} and {CisPt@CB} inclusion complexes in a radiotherapeutic environment may offer significant enhancements in TPZ and CisPt payload delivery to tumours, as well as enhanced potentiation of radical species of TPZ and CisPt at tumour sites. Since the CD complexes appear to release the guest TPZ and CisPt radical species more easily than the corresponding CB complexes, there is potential for a mixed mode application using both CD and CB complexes to alter the delivery timing schedules for optimized efficacy.

There is also substantial literature evidence that suggests TPZ and CisPt inclusion complexes may also show a enhanced permeation and retention effect in tumours which could increase payload delivery into tumours.

Experimental

All calculations were carried out using the Gaussian 09 package. Energy optimisations were at the DFT/B3LYP/6-31+G(d,p) (6d, 7f) level of theory for all atoms for non inclusion complexes. Selected optimisations at the DFT/B3LYP/6-311+G(d,p) (6d, 7f) level of theory gave very similar results to those at the lower level. Optimized structures were checked to ensure energy minima were located, with no negative frequencies. Energy calculations were conducted at the DFT/B3LYP/6-311+G(d,p) (6d, 7f) level of theory with optimised geometries in water, using the IEFPCM/SMD solvent model. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6 -1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions. [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF]] The 6-31G** basis set has been used to calculate absolute free energies of solvation and compare these data with experimental results for more than 500 neutral and charged compounds. The calculated values were in good agreement with experimental results across a wide range of compounds. [START_REF] Rayne | Accuracy of computational solvation free energies for neutral and ionic compounds: Dependence on level of theory and solvent model[END_REF][START_REF] Rizzo | Estimation of Absolute Free Energies of Hydration Using Continuum Methods: Accuracy of Partial Charge Models and Optimization of Nonpolar Contributions[END_REF][ [START_REF] Rayne | Accuracy of computational solvation free energies for neutral and ionic compounds: Dependence on level of theory and solvent model[END_REF][START_REF] Rizzo | Estimation of Absolute Free Energies of Hydration Using Continuum Methods: Accuracy of Partial Charge Models and Optimization of Nonpolar Contributions[END_REF]] Adding diffuse functions to the 6-31G* basis set (ie 6-31+G**) had no significant effect on the solvation energies with a difference of less than 1% observed in solvents, which is within the literature error range for the IEFPCM/SMD solvent model. HOMO and LUMO calculations included both delocalized and localized orbitals (NBO).

Adiabatic electron affinities (AEA) in eV in water were calculated by the SCF difference between the optimised neutral and optimised radical species method as previously described. [START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Fong | Cisplatin cyclodextrin complexes as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][Fong 2016] It has been shown that the B3LYP/6-31G++(d,p) and B3LYP/6-311G++(d,p) combinations give accurate electron affinities when tested against a large range of molecules, atoms, ions and radicals with an absolute maximum error of 0.2 eV. [START_REF] Rienstra-Kiracofe | Atomic and molecular electron affinities: Photoelectron experiments and theoretical computations[END_REF][START_REF] Peverati | The quest for a universal density functional: the accuracy of density functionals across a broad spectrum of databases in chemistry and physics[END_REF][START_REF] Riley | Critical Assessment of the Performance of Density Functional Methods for Several Atomic and Molecular Properties[END_REF][Rienstra-Kiracofe 2002, Peverati 2014, [START_REF] Riley | Critical Assessment of the Performance of Density Functional Methods for Several Atomic and Molecular Properties[END_REF] For the TPZ and CisPt inclusion complexes with CB and CD, energy optimisations were done at the DFT/B3LYP/3-21G level of theory, and using a two layer ONIOM model, at the 6-31+G(d,p) and 6-311++G(d,p) levels for the high level CisPt and TPZ moieties, and using the UFF force field or semi-empirical PM6 at the low level. Energy calculations were done at the DFT/B3LYP/6-311+G(d,p) level of theory. The wB97XD functional was also used for optimization and thermodynamic calculations. This functional is a long range corrected hybrid with damped dispersion correction which gives good results with non-covalent and covalent systems and have been shown to give quite accurate results when compared to experimental data. Energy optimisations for the inclusion complexes of CisPt were also done at the DFT/B3LYP/LANL2DZ, and DFT/B3LYP/3-21G level of theory for all atoms except for Pt where the relativistic ECP SDD Stuttgart-Dresden basis set for transition metals was used. Optimisations were also conducted using a two layer ONIOM model, at the LANL2DZ, 6-31+G(d,p) and 6-311+G(d,p) levels for the high level moiety, and using the UFF force field or semi-empirical PM6 at the low level. High computational accuracy for the inclusion complexes is not the aim of this study as small changes in optimised configurational structures of the inclusion complexes and functionals gave slightly different AEA values (0.5 to 1.0eV), particularly for CisPt@[n]CB complexes, but the AEA values always reflected significant bond elongations of the Pt---Cl bond as shown in the Table . For the {TPZ@[7]CB}• the AEA water values were 11.2-12.2eV, 8.5% variation between B3LYP and wB97XD functionals. For {TPZ@BHCD}• the AEA water values were 12.8-13.6eV, a 6.1% variation between B3LYP and wB97XD functionals.

The free energy of formation of the inclusion complexes ΔG Form,Complex,Sol in a particular solvent (water) is calculated from the thermodynamic cycle at standard conditions, T = 298.15 K and P = 1 atm: ΔG Form,Complex,Sol = ΔG Form,Complex,Gas + ΔG Solv,Complex -ΔG Solv,CB/CD -ΔG Solv,TPZ/CisPt where ΔG form,Gas is the free energy of formation of the complex in the gas phase, and ΔG solv is the free energy of solvation. The ΔG Form,Complex,Solv are corrected for the BSSE (basis set supposition error) using the counterpoise method for full QM calculations, but are not necessary when using the ONIOM method employed in this study. The CPCM solvation model was used for most calculations, but some computations used the SMD model which gave similar results to the CPCM model. Thermochemical analysis of inclusion complexes were also conducted at the DFT/wB97XD/6-31+G(d,p) level of theory to test for significant dispersion effects, [START_REF] Waller | Investigating inclusion complexes using quantum chemical methods[END_REF] [START_REF] Waller | Investigating inclusion complexes using quantum chemical methods[END_REF]] whereas the DFT/B3LYP/6-31+G(d,p) level may be more appropriate for testing for induction (from the permanent dipoles) mixed with dispersion. [START_REF] Roy | Comparison of some dispersion-corrected and traditional functional with CCSD(T) and MP2 ab initio methods: Dispersion, induction, and basis set superposition error[END_REF][Roy 2012] There were small variations between ΔG Form,Complex,Sol calculations using the B3LYP and wB97XD functionals which did not materially affect the outcomes of whether the various inclusion complexes were deemed to be stable in water.

Free energy calculations of inclusion complexes were conducted at the wB97XD/6-31G++(d,p)/UFF/QEq/EE and B3LYP/6-31G++(d,p)/UFF/QEq/EE ONIOM levels, both of which gave similar results. Electronic embedding incorporates the partial charges of the MM(UFF) region into the quantum mechanical Hamiltonian. This technique provides a better description of the electrostatic interaction between the QM and MM regions (as it is treated at the QM level) and allows the QM wavefunction to be polarized.

The absolute potential of the aqueous standard hydrogen electrode is generally taken to be either 4.28V or 4.44V, which are derived from values of ΔGS * (H + ) of -1112.5 and -1098.9 kJ mol -1 respectively. The value of 4.44 V includes an estimate of the contribution due to the surface potential of water. However since the total charge is conserved in a reaction, the contribution due to the surface potential cancels out in a chemically balanced chemical reaction that occurs in a single phase. The SMD model uses a ΔGS * (H + ) of -1112.5 kJ mol -1 and SHE value of 4.28 V. [69,[START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF][Ho 2016, [START_REF] Marenich | Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions[END_REF] We have previously shown a very strong linear relationship between adiabatic electron affinity in water (AEA in eV) and the experimental E(1) in V determined by pulse radiolysis for 30 TPZ analogues with an intercept of 4.25 V, very close to the theoretical value of 4.28 V. The electrochemical reduction potential of TPZ is -0.45V (SHE at pH 7.0) [START_REF] Ik Priyadarsini | The One-Electron Reduction Potential of 3Amino1, 2, 4-benzotriazine 1, 4-dioxide (Tirapazamine): A Hypoxia-Selective Bioreductive Drug[END_REF][Priyadarsini 1999] which is converts to 3.83eV against the SHE value of 4.28V for the SMD solvation model. The calculated AEA for TPZ in water is this study is 3.7eV. It is clear that DFT AEA calculations using the SMD water solvation model are good proxies for aqueous reduction potentials. [START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][START_REF] Fong | Cisplatin cyclodextrin complexes as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][Fong 2017] Romalho 2004 [START_REF] Ramalho | Theoretical study of adiabatic and vertical electron affinity of radiosensitizers in solution part 2: analogues of tirapazamine[END_REF] has examined five 8-substituted TPZ analogues and found that B3LYP/6-311++G(d,p) AEA calculations in water were in good agreement with experimental reduction potentials.

To test the accuracy of the calculations and computational methods, the ΔG form,Complex,Water of 1:1 inclusion complex formed between ibuprofen and [β]cyclodextrin, ibuprofen@[β]cyclodextrin was calculated to be -4.1 kcal/mol for the configuration shown in Figure 12. The experimental Gibbs free energy for the formation of the 1:1 inclusion complex, ibuprofen@[β]cyclodextrin in Tris-HCl buffer solutions (pH = 7.0) has been determined by isothermal titration calorimetry (-5.6 kcal/mol), and by spectrophotometric, titration and phase solubility analyses to average -5.4 kcal/mol (6 experimental values). [START_REF] Xing | Isothermal titration calorimetry and theoretical studies on host-guest interaction of ibuprofen with α-, β-and γ-cyclodextrin[END_REF][START_REF] Manzoori | Spectrofluorimetric study of host-guest complexation of ibuprofen with beta-cyclodextrin and its analytical application[END_REF][START_REF] Wang | Comparison of Three Molecular Simulation Approaches for Cyclodextrin-Ibuprofen Complexation[END_REF][ [START_REF] Xing | Isothermal titration calorimetry and theoretical studies on host-guest interaction of ibuprofen with α-, β-and γ-cyclodextrin[END_REF][START_REF] Manzoori | Spectrofluorimetric study of host-guest complexation of ibuprofen with beta-cyclodextrin and its analytical application[END_REF][START_REF] Wang | Comparison of Three Molecular Simulation Approaches for Cyclodextrin-Ibuprofen Complexation[END_REF]] The agreement is close considering the experimental result is the average of a number of configurations, whereas the configuration shown in Figure 12 is only one stable configuration of many possibilities, (it is not possible to calculate all possible stable configurations) but the displayed configuration is most likely very similar to the dominant configuration, considering the close agreement between the calculated and experimental values. Other tested configurations with the carboxyl group located near the smaller opening of [β]cyclodextrin were unstable, compared to the configuration shown in Figure 12 which has the carboxyl group located near the larger opening. It is noted that MM/PBSA/GBSA method [START_REF] Fujisawa | Interaction Energy Analysis for Drug-Cyclodextrin Inclusion Complexes in Aqueous Solutions[END_REF][START_REF] Núñez-Agüero | Chiral discrimination of ibuprofen isomers in beta-cyclodextrin inclusion complexes: Experimental (NMR) and theoretical (MD, MM/GBSA) studies[END_REF] HOMO on Pt, LUMO on CB [START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF] {CisPt@[7]CB}

{CisPt@[7]CB} A {CisPt@[7]CB•} A {CisPt@[7]CB••} A {CisPt@[7]CB]•••} A -25 -

[

  Hettiarachchi 2010,Walker 2011, Wheate 2016] Figure 2 schematically illustrates the drug delivery process where molecular containers are involved.

Figure 1 .

 1 Figure 1. Mechanism of anti-cancer behaviour of Tirapazamine TPZ.

Figure 2 .

 2 Figure 2. Schematic representation of delivery and concurrent radiotherapy of (a) TPZ and CisPt CD and CB inclusion complexes, and (b) TPZ and CisPt to tumour cells

  [START_REF] Wheate | Cucurbit[n]uril binding of platinum anticancer complexes[END_REF][START_REF] Jeon | Novel molecular drug carrier: encapsulation of oxaliplatin in cucurbit[7]uril and its effects on stability and reactivity of the drug[END_REF][START_REF] Plumb | Cucurbit[7]uril encapsulated cisplatin overcomes cisplatin resistance via a pharmacokinetic effect[END_REF] The "open" portal {TPZ@[7]CBOPEN}• (AEA 3.5eV) and "open" portal {TPZ@[7]CBOPEN}•• species (AEA 5.2eV) can be observed in time dependent optimizations (relaxations) of these species and the latter is shown in Figure11. The AEA of {TPZ@[7]CBOPEN}• 3.5eV compares to the AEA of TPZ• in the free state (3.65eV) , indicating the kinetic release of TPZ• from the {TPZ@[7]CBOPEN}• complex would occur. Similarly release of TPZ•• from {TPZ@[7]CBOPEN}•• complex can also occur.

Fig 5

 5 Fig 5(a), (b)HOMO & LUMO on CB[START_REF] Von Sonntag | Free-Radical-Induced DNA Damage and Its Repair: A Chemical Perspective[END_REF]

Figure 7 {TPZ

 7 Figure 7

  Figure 8 HOMO & LUMO on TPZ

Figure 3 (

 3 Figure 3(b) CisPt•@[γ]CD• dianion complex in water, Pt---Cl out (Pt---Cl bond pointing outwards) bond length 2.71Å, Pt---Cl in (Pt---Cl bond pointing inwards) 2.41Å, Pt---N out 2.31Å, Pt---N in 2.14Å. The larger outer rim of the truncated cone of the CD faces downwards in the figure.

Figure 4 (Figure 4 (Figure 5 Figure 6 .Figure 7 (Figure 7 (Figure 8 (Figure 8 (Figure 9 .Figure 10 (Figure 11 .Figure 12 .

 445677889101112 Figure 4(a) CisPt@HPBCD complex in water, Pt---Cl out (Pt---Cl bond pointing outwards) bond length 2.31Å, Pt---Cl in (Pt---Cl bond pointing inwards) 2.28Å, Pt---N out 2.08Å, Pt---N in 2.07Å

  Tableshowsthe AEA values of the free CisPt and TPZ in water, and various CB or CD inclusion complexes of these agents. For CisPt inclusion complexes, electron attachment always results in changes to the CisPt moiety mainly an increase in Pt---Cl bond length, which has been previously shown to be a precursor to the formation of the radical species, such as (H 3 N) 2 Pt• (H 2 O)Cl, (H 3 N) 2 Pt•• (H 2 O) 2 and Cl•.[START_REF] Fong | Platinum anti-cancer drugs: Free radical mechanism of Pt-DNA adduct formation and anti-neoplastic effect[END_REF][START_REF] Fong | Platinum based radiochemotherapies: free radical mechanisms and radiotherapy sensitizers[END_REF] [Fong 2016] The physically larger macrocycles CB or CD also can act as larger electron targets which have multiple sites of electron attachment which can potentiate the included CisPt by a Marcus type inner sphere electron transfer[START_REF] Fong | Cucurbiturils as potential free radical chemoradiosensitizers for enhanced cisplatin treatment of cancers: A quantum mechanical study[END_REF][Fong 2017]. A measure of potentiation of the included CisPt or TPZ in CD or CB inclusion complexes is taken to be the enhancement of the AEA of the inclusion complexes compared to the bare CisPt or TPZ, or for CisPt complexes, the relative elongation of the Pt---Cl bond compared to the bare CisPt• species. The Table shows the P(1) and P(2) measures of relative potentiation of the AEA and Pt---Cl bond elongation in CisPt complexes compared to bare CisPt in water. P(3) is a measure of potentiation of the AEA in TPZ complexes relative to bare TPZ in water.

Table of binding energies, adiabatic electron affinities (AEA), CisPt bond lengths of selected {CisPt@[n]CD}, {CisPt@[n]CB}, {TPZ@[n]CD}, and {TPZ@[n]CB} complexes Species and inclusion complexes in water

  [START_REF] Fujisawa | Interaction Energy Analysis for Drug-Cyclodextrin Inclusion Complexes in Aqueous Solutions[END_REF], Nunez-Aguero 2006] gave much poorer agreements with experimental values, the best being binding energies about three times more than the experimental value.[START_REF] Núñez-Agüero | Chiral discrimination of ibuprofen isomers in beta-cyclodextrin inclusion complexes: Experimental (NMR) and theoretical (MD, MM/GBSA) studies[END_REF][Nunez-Aguero 2006] It has been shown that the MM/PBSA and MM/GBSA methods do not yield accurate ligand binding affinities, and are only useful for early drug screening or docking studies.[77] [Geneheden 2015]

		Binding Energy kcal/mol	Pt---Cl a bond length	Pt---Cl b bond length	Pt---N a bond length	Pt---N b bond length	AEA eV	Potent-iation	Figure reference & NBO locations
			Å	Å	Å	Å
	CisPt	NA	2.38	2.38	2.08	2.08
	CisPt•	NA	4.62	2.39	2.28	2.11	2.8
	{CisPt@[γ]CD}	-69 to -	2.40	2.36	2.07	2.06			Fig 3(a)
	Configuration 1	73
	{CisPt•@[γ]CD•} Configuration 1	0 to -3	2.71	2.41	2.31	2.14	5.8	1.2 (P2) 2.1(P1)	Fig 3(b)
	{CisPt@[γ]CD} Configuration 2	-29	2.32	2.32	2.10	2.10			HOMO on Pt LUMO on Pt
	{CisPt••@[γ]CD••}		4.07	2.38	3.35	2.11	9.4	3.4 (P1) 1.7 (P2)
	{CisPt@[β]CD}		2.31	2.30	2.02	2.00			HOMO on Pt LUMO on Pt
	{CisPt•@[β]CD•}	-65	2.46	2.42	2.17	2.12	2.2	0.8 (P1) 1.1 (P2)	HOMO on Pt LUMO on Pt
	{CisPt@HPBCD}	-54	2.31	2.28	2.08	2.07			Fig 4(a) HOMO on Pt
									LUMO on Pt
	{CisPt•@HPBCD•} 0 to -5	2.69	2.47	2.38	2.18	5.3-6.1	2.1 (P1) 1.1 (P2)	Fig 4(b) HOMO on Pt LUMO on Pt
	{CisPt@[7]CB}		2.42	2.42	2.06	2.06
	{CisPt•@[7]CB} (e• attached to Pt)		2.57	2.58	2.22	2.22	1.9	0.7 (P1) 1.1 (P2)