Biomolecular cooperativity is of great scientific interest due to its role in biological processes. Two transcription factors (TFs), Oct-4 and Sox-2, are crucial in transcriptional regulation of embryonic stem cells. In this paper, we analyze how Oct-1 (a similar POU factor) and Sox-2, interact cooperatively at their enhancer binding sites in collective motions. Normal mode analysis (NMA) is implemented to study the collective motions of two complexes with each involving these TFs and an enhancer. The special structure of Oct proteins is analyzed comprehensively, after which each Oct/Sox group is reassembled into two protein pairs. We subsequently propose a segmentation idea to extract the most correlated segments in each pair, using correlations of motion magnitude curves. The median analysis on these correlation values shows the intimacy of subunit POUS (Oct-1) and Sox-2. Using those larger-than-median correlation values, we conduct statistical studies and propose several protein-protein cooperative modes (S and D) coupled with their subtypes. Additional filters are applied and similar results are obtained. A supplementary study on the rotation angle curves reaches an agreement with these modes. Overall, these proposed cooperative modes provide useful information for us to understand the complicated interaction mechanism in the POU/HMG/DNA complexes. 1. Introduction Embryonic stem cells (ES cells) possess the pluripotency of differentiating into all the three germ layers (endoderm, mesoderm, and ectoderm), which correspond to hundreds of cell types. These pluripotent stem cells are transcriptionally regulated by a number of transcription factors (TFs) [1]. A specific TF called Oct-4, belonging to the POU class of homeodomain proteins, is regarded as a necessity for maintaining the undifferentiated state of embryonic ES cells. Generally, Oct-4 interacts with other TFs as a group to affect the gene expression of mouse ES cells in early embryo development [2], and Oct-4 coupled with its cofactor Sox-2 (HMG-box domain) is at the center of this group. Botquin and Nishimoto have both proven the cooperative effects of Oct-4 and Sox-2 on the expression of several genes in mouse embryonic ES cells [3, 4]. Dailey and Basilico further bring forward the idea that the interaction within the POU/HMG group, especially for groups composed of Oct and Sox proteins, at DNA binding sites is a fundamental mechanism for transcriptional regulation in early embryo development [5]. At the early stage of transcription, TFs bind to specific regulatory DNA regions to
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