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A model of the formation of particle tracks in emulsion has been extended through the use of biological target theory to formulate a theory of the response of biological cells and molecules of biological importance to irradiation with energetic heavy ions. For this purpose the response to γ rays is represented by the single-hit, multi-target model with parameters m and D0, while additional parameters κ (or a0) and σ0 are required to represent the size of internal cellular targets and the effective cross-sectional area of the cell nucleus, respectively, for heavy-ion bombardments. For one-or-more-hit detectors, only the first three of these parameters are required and m = 1. For cells m is typically 2 or more. The model is developed from the concept that response to secondary electrons follows the same functional form for γ rays and for the 6 rays surrounding an ion's path. Originally applied to dry enzymes and viruses in 1967, the model of the one-hit detector has been extended to emulsions, to other physical and chemical detectors, to single- and double-strand breaks in DNA in EO buffer and to three E. coli strains. The two-hit response has been observed for "track core" effects in radiation chemistry, for supralinearity in thermoluminescent dosimeters and for desensitized nuclear emulsions, where hit numbers up to 6 have been observed. In its extension to biological cells, additional concepts are required relating to the character of the track, namely the grain-count and track-width regimes, and to the ability of multi-target systems to acquire damage from intertrack δ rays (called gamma kill) as well as from intratrack δ rays (called ion kill). The model has been applied to some 40 sets of radiobiological data obtained from γ, track-segment heavy-ion and neutron irradiations. Here we elaborate on the meaning of these concepts, tabulate the cellular parameters, and display their systematic behavior and the relationships among them. In particular the parameter κ, which serves to determine the location in of the maximum value of the RBE, shows little variation among cell types, while Do, which describes the response to y rays and σ0, which appears to indicate the target size, varies over many orders of magnitude.