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Transcription factor-DNA interactions play a central role in transcriptional control. These bindings are stochastic processes and regulated by the nucleosomes in vivo. However, current models tend to neglect the nucleosomes and regard the binding as a set of binary cases. A computational model is presented here to address the issues. It integrates TF bindings to nucleosomal and naked DNA in a quantitative manner and results in continuous binding probabilities along the genome. The predictive ability of the model was applied to rationalize the binding data for the TFs considered, which made improvements over those models disregarding the nucleosomes.