The Lethal and Potentially Lethal Model — A Review and Recent Development

Abstract

The Lethal and Potentially Lethal (LPL) Model [1] is a kinetic model of cell killing based on the following basic assumptions:

• 1. The damage caused by ionizing radiation at the molecular level that eventually leads to cell death can be separated into two broad classes: that which has the potential of being lethal but also can be repaired correctly and that which is lethal ab initio and cannot be repaired correctly. The molecular lesions causing these types of damage are called potentially lethal and lethal lesions respectively. They are tentatively being identified with DNA double strand breaks of different severity.

• 2. Two fates other than (viable) repair are possible for the potentially lethal lesions: (a) they can interact with one another to form a lethal lesion (this is called binary misrepair) or (b) they can be fixed (i.e., made lethal) by such events as progression of the cell through specific points in the cell cycle or the addition of a repair inhibiting drug (this is called linear fixation). It might be remarked here that both the present model and the RMR model [2,3] share this assumption. The idea of misrepair was initially applied by Lea and Catcheside [4] to describe the formation of chromosome aberrations in tradescantia and has been invoked in various models of cell killing [2,3,5,6,7,8,9].

• 3. The potentially lethal lesions can be further subdivided into subclasses which depend on their characteristic repair times. Two subclasses have been identified and discussed by Iliakis [10], one with a half-time for repair of 10–15 minutes [11,12] and one with a half-time for repair of 1–2 hours [13]. In what follows, the short-lived lesions are assumed to last too short a time to be able to interact with each other. They, in fact, usually repair unnoticed and it requires a drastic change in the cellular milieu such as the addition of NaC1 to provide hypertonicity for the damage to be expressed. Although the identity of these two types of lesions is presently unknown, one suggestion is that the fast component comprises double strand breaks that occur in DNA which is bound to nucleosomes and the slow component comprises double strand breaks that occur in the linker DNA.

• 4. In the dose range of interest (i.e., less than 20 Gy), all types of the biologically important lesions are produced linearly with dose. The rates of production per unit dose are η_L and η_PL for the lethal and potentially lethal lesions, respectively.

• 5. The repair rate constants for the slowly and rapidly repairing subclasses of potentially lethal lesions are ε_PL and ε′_PL, respectively. The slowly repairing lesions can interact with each other at a rate ε_2PL producing binary misrepaired lesions. The rapidly repairing component is not normally expressed and will not be considered in the following treatment.