2009, 6(3): 591-602. doi: 10.3934/mbe.2009.6.591

The relative biologic effectiveness versus linear energy transfer curve as an output-input relation for linear cellular systems


Department of Radiation Oncology, Stanford University, Stanford, CA 94305, United States


Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States

Received  September 2008 Revised  December 2008 Published  June 2009

Experiments have established that different radiation types have different magnitudes of biological response. When biological response is defined in terms of the Relative Biologic Effectiveness (RBE) and different radiation type is characterized by Linear Energy Transfer (LET), the plot of the RBE versus LET (RBE-LET) curve shows RBE to increase with increasing LET, to reach a maximum, and to decrease with further increasing LET. Perhaps due to the descriptive nature of biology, most quantitative models for the RBE-LET curve ignore the reality of the underlying molecular biology. On the other hand, the molecular basis for the RBE-LET curve is not completely known despite recent efforts.
   Here we introduce a differential equation formulation for a signal-and-system model that sees cells as systems, different radiation types as input, and cellular responses as output. Because of scant knowledge of the underlying biochemical network, the current version is necessarily a work in progress. It explains the RBE-LET curve using not just input parameters but also systems internal state parameters. These systems internal state parameters represent parts of a biochemical network within a cell. Although multiple biochemical parts may well be involved, the shape of the RBE-LET curve is reproduced when only three system parameters are related to three biochemical parts: the molecular machinery for DNA double strand break repair; the molecular pathways for handling oxidative stress; and the radiolytic products of the cellular water.
   Despite being a simplified ''toy model,'' changes in the systems state parameters lead to model curves that are refutable in a modern molecular biology laboratory. As the parts in the biochemical network of the radiation response are being further elucidated, this model can incorporate new systems state parameters to allow a more accurate fit.
Citation: Quoc T. Luu, Paul DuChateau. The relative biologic effectiveness versus linear energy transfer curve as an output-input relation for linear cellular systems. Mathematical Biosciences & Engineering, 2009, 6 (3) : 591-602. doi: 10.3934/mbe.2009.6.591

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