Recent experiments have revealed that some transcription factors (TFs) can bind to and affect the stability of nucleosomes. Here we use coarse-grained molecular dynamics simulations to study the nucleosome-binding of two TFs, Sox2 and Oct4. Our simulations show that Sox2 energetically selects DNA motifs exquisitely phasing outward, or entropically binds to the dyad, where more possible rotational positions exist. We also find that the two domains of Oct4 can bind on the acidic patch or the two parallel gyres of nucleosomal DNA. By simulating multiple TFs binding on nucleosome, we find a DNA allosteric mechanism, by which the binding of one Sox2 can change the rotational position of DNA and affect the binding probability of the second approaching Sox2 or Oct4.