A Metabolic Theory of Cell Survival Curves

Orr, J. S.; Hope, C S; Wakerley, Sheila E; Stark, Jeremy M.

doi:10.1088/0031-9155/11/1/309

Cited by 18 publications

(2 citation statements)

References 11 publications

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“…Staying still within chemical kinetics, one of the alternatives to the IMM model is to conceive the damage repair as being mediated by the so-called pool repair molecules from the cell environment [56,[115][116][117][118][119][120]. To proceed, let the set of quan- Pool substances p can be both repair molecules and lesions.…”

Section: Cell Repair By Pool Repair Molecules From the Cell Environmentmentioning

confidence: 99%

The Euler T and Lambert W functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells

Belkić

2018

J Math Chem

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Recently, the Euler T and Lambert W transcendental functions found useful applications in cellular radiobiology. Specifically, these functions appeared in mathematical modeling of cell survival after irradiation using the formalism of chemical kinetics. An example is a mechanistic inclusion of cell repair through enzyme catalysis in the Michaelis-Menten formalism, where the concentration of radiation lesions is given by the Lambert function. This function also appears in cell surviving fractions in an alternative aspect of chemical kinetics when lesion repair is carried out by the so-called pool repair molecules without passing through enzyme catalysis. Moreover, even with no reference to chemical kinetics at all, both the Lambert and Euler functions emerge in the framework of the cell repair dynamics described by delayed differential equations. The Euler function is also encountered within the cell blocking mechanism of damage repair in analogy with the counting coincidence correction for the dead time of the radiation detecting instruments. Presently, we analyze the overall usefulness of the Lambert and Euler functions in radiotherapy with a goal of motivating a further exploration of this analytical methodology in mechanistic radiobiological models for cell survival. The main reason for pursuing this pathway is in its unified mechanistic concept of cell surviving fractions valid at all doses from low through intermediate to high radiation exposures. With this advance, no artificial cut-off doses are needed any longer for empirical connections of the intermediate and high dose regimens in mathematical modelings. This is particularly important in radiotherapy because the clinically most frequently used linear-quadratic model is inadequate at high doses. High doses are of main relevance to stereotactic radiotherapy for treatment of localized tumors by efficaciously administering relatively large doses per fraction in a small number of fractions within only a few days. Such a non-conventional treatment schedule is advantageous both for the patient and hospitals' cost effectiveness, especially relative to conventional radiotherapy, which uses small doses (2 Gy) per fraction within a month long period.

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Section: Cell Repair By Pool Repair Molecules From the Cell Environmentmentioning

confidence: 99%

The Euler T and Lambert W functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells

Belkić

2018

J Math Chem

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“…Split-dose recovery has been described in several cell systems and is at least partly due to the repair of single and double stranded DNA breaks (Elkind and Sutton 1959; Elkind et al 1967; Hall 2000; Utsumi and Elkine 2001). Other hypotheses such as repair pool replenishment have been suggested (Orr et al 1966a; Orr et al 1966b; Malone et al 1971; Laurie et al 1972; Malone et al 1972; Orr 1984). Inducible defenses such as those seen in classical adaptive response experiments have been suggested to be involved in split dose recovery as well (Seymour and Mothersill 1989; Mothersill and Seymour 1993).…”

Section: Introductionmentioning

confidence: 99%

Investigation of Non-Linear Adaptive Responses and Split Dose Recovery Induced by Ionizing Radiation in Three Human Epithelial Derived Cell Lines

Ryan¹,

Seymour²,

Mothersill³

2009

Dose-Response

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Two almost completely exclusive fields in radiobiology deal with splitting doses of radiation and comparing the effect to a similar total dose given in one exposure. In radiotherapy, dose "fractionation" is used to "spare" normal tissue and in the low dose field, the adaptive response is well documented as a phenomenon where a small "priming" dose administered before the larger "challenge" dose reduces the effect of the large dose. There have been very few studies where these fields overlap, thus it is not possible to ascertain whether common or distinct mechanisms underlie both phenomena but this is certainly an interesting question and relevant to our understanding of high and low dose radiobiology. This paper presents data for three human cell lines with varying p53 status and radiation responses, treated at a range of times between first and second dose and for 3 different first doses (0.1, 0.5 and 2Gy). The data show that time between doses is critical. Protective (adaptive) effects were seen in each cell line but most prominently in the malignant HT 29 cell line. Surprisingly none of the cell lines showed pronounced split dose recovery. This suggests different mechanisms may underlie the two phenomena.

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Actions of radiation on living cells in the “post-bystander” era

Mothersill

Seymour

Experientia Supplementum

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A Metabolic Theory of Cell Survival Curves

Abstract: A metabolic theory of cell survival after irradiation is presented and developed in the form of a mathematical model. The parameters which fit the model t o some published experimental data are given. The effects on survival of environmental changes are considered in terms of the model.

Cited by 18 publications

References 11 publications

The Euler T and Lambert W functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells

The Euler T and Lambert W functions in mechanistic radiobiological models with chemical kinetics for repair of irradiated cells

Investigation of Non-Linear Adaptive Responses and Split Dose Recovery Induced by Ionizing Radiation in Three Human Epithelial Derived Cell Lines

Actions of radiation on living cells in the “post-bystander” era

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