TITLE:
The Relative Biologic Effectiveness versus Linear Energy Transfer Curve as a Cell Trait
AUTHORS:
Quoc T. Luu, Paul DuChateau
KEYWORDS:
RBE-LET Curve; Cell Trait; Systems Biology; Fourier Analysis; Stochastic Differential Equation
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11C,
October
29,
2013
ABSTRACT:
The magnitude of biological response varies with different radiation types. Using Linear Energy Transfer (LET) to differentiate types of incident radiation beam, the Relative Biologic Effectiveness (RBE) as a function of LET (RBE-LET) was found to have a characteristic shape with a peak around LET values 100 - 200 eV/nm. This general feature is believed to be a property of the incident beam. Our systems engineering model, however, suggests that the shape of the RBE-LET curve is a cell trait, a property of the cell. Like any other trait, phenotypic variations result from interactions of the genes and their context. State-space block diagram of the differential equation model suggests the genes are those in the DNA double strand break (dsb) repair pathway; and the context is cellular stress responsing to DNA damage by both external stimuli and internal redox state. At a deeper level, the block diagram suggests cell using mathematical calculations in its decision-making when facing a stress signal. The MRN protein complex, in particular, may perform addition to count the degree of DNA twisting for the homeostatic regulation of DNA supercoiling. The ATM protein may act as a feedback amplifier.