To account for particle interactions in the extracellular (physical) environment, information from the cell-level Monte Carlo damage simulation (MCDS) for DNA double strand break (DSB) induction has been integrated into the general purpose Monte Carlo N-particle (MCNP) radiation transport code system. The effort to integrate these models is motivated by the need for a computationally efficient model to accurately predict particle relative biological effectiveness (RBE) in cell cultures and in vivo. To illustrate the approach and highlight the impact of the larger scale physical environment (e.g. establishing charged particle equilibrium), we examined the RBE for DSB induction (RBEDSB) of x-rays, (137)Cs γ-rays, neutrons and light ions relative to γ-rays from (60)Co in monolayer cell cultures at various depths in water. Under normoxic conditions, we found that (137)Cs γ-rays are about 1.7% more effective at creating DSB than γ-rays from (60)Co (RBEDSB = 1.017) whereas 60-250 kV x-rays are 1.1 to 1.25 times more efficient at creating DSB than (60)Co. Under anoxic conditions, kV x-rays may have an RBEDSB up to 1.51 times as large as (60)Co γ-rays. Fission neutrons passing through monolayer cell cultures have an RBEDSB that ranges from 2.6 to 3.0 in normoxic cells, but may be as large as 9.93 for anoxic cells. For proton pencil beams, Monte Carlo simulations suggest an RBEDSB of about 1.2 at the tip of the Bragg peak and up to 1.6 a few mm beyond the Bragg peak. Bragg peak RBEDSB increases with decreasing oxygen concentration, which may create opportunities to apply proton dose painting to help address tumor hypoxia. Modeling of the particle RBE for DSB induction across multiple physical and biological scales has the potential to aid in the interpretation of laboratory experiments and provide useful information to advance the safety and effectiveness of hadron therapy in the treatment of cancer.