Expression of tumor suppressor p53 is regulated at multiple levels, disruption of which often leads to cancer. We have adopted an approach combining computational systems modeling with experimental validation to elucidate the translation regulatory network that controls p53 expression post DNA damage. The RNA-binding protein HuR activates p53 mRNA translation in response to UVC-induced DNA damage in breast carcinoma cells. p53 and HuR levels show pulsatile change post UV irradiation. The computed model fitted with the observed pulse of p53 and HuR only when hypothetical regulators of synthesis and degradation of HuR were incorporated. miR-125b, a UV-responsive microRNA, was found to represses the translation of HuR mRNA. Furthermore, UV irradiation triggered proteasomal degradation of HuR mediated by an E3-ubiquitin ligase tripartite motif-containing 21 (TRIM21). The integrated action of miR-125b and TRIM21 constitutes an intricate control system that regulates pulsatile expression of HuR and p53 and determines cell viability in response to DNA damage.