“Stripe” transcription factors provide accessibility to regulatory DNA in mammalian genomes_2

Single molecule raw data is visualized with ImageJ software. Further analysis is required for the trajectory generation, residence time and mean square displacement (MSD) of single molecules. To generate the trajectories in Figure 7A and S7A, single molecules are localized and tracked using SLIMfast and evalSPT, implementing the Multiple-Target-Tracing algorithm for localizing and tracking single molecules. Single molecules are first localized with 2D Gaussian fitting subject to a log-likelihood ratio test with a localization error. A maximal expected diffusion constant was set to connect localizations between consecutive frames. To perform the residence time analysis for Figure 7B,C,D and Figure S7C,D, the dwell time was obtained by calculating the ensemble distribution of bound times for Smad3 and Smad7 in different cells from each biological replicate and corrected by dividing the exponential component estimated in the H2B dwell time distribution analysis (S(t)=e^γt S_E (t), where S(t) corresponds to the survival distribution after photobleaching correction. To perform the MSD analysis in Figure S7B, Perturbation Expectation Maximation (pEM) together with Bayesian Inference Criterion (BIC) was used to classify the trajectories of the protein into the least number of diffusive modes (sub-diffusion, diffusion and super-diffusion). The number of reinitializations were set up to 10, number of perturbations to 50, maximum number of iterations to 10000, convergence criteria for change in log-likelihood to 1e-7 and the number of features of the covariance matrix to 3. The posterior probability weighted MSD for each diffusive state was computed. To calculate the diffusion coefficient (D) for a diffusive state (Brownian motion), the variance of the instantaneous velocity vector v was related to the diffusion coefficient as 〈v^2 〉=4D/∆t , ∆t is the acquisition interval and D is the diffusion coefficient of the particle.单分子原始数据通过ImageJ软件完成可视化。针对单分子的轨迹生成、停留时间以及均方位移（mean square displacement, MSD），需开展进一步分析。 为生成图7A与补充图S7A中的轨迹，我们采用SLIMfast与evalSPT工具，通过多目标追踪（Multiple-Target-Tracing）算法完成单分子的定位与追踪。单分子首先通过二维高斯拟合进行定位，并结合对数似然比检验以控制定位误差。我们设定了最大预期扩散系数，用于连接连续帧间的定位结果。 针对图7B、C、D及补充图S7C、D开展停留时间分析时，我们通过计算各生物学重复中不同细胞内Smad3与Smad7的结合时间整体分布，得到停留时长，并通过除以H2B停留时间分布分析中估算的指数分量完成校正，校正公式为S(t)=e^γt S_E(t)，其中S(t)代表经光漂白校正后的存活分布。 针对补充图S7B开展均方位移分析时，我们使用扰动期望最大化（Perturbation Expectation Maximation, pEM）与贝叶斯信息准则（Bayesian Inference Criterion, BIC），将蛋白质轨迹分类为最少数量的扩散模式：亚扩散（sub-diffusion）、扩散（diffusion）与超扩散（super-diffusion）。我们将重初始化次数设为10次，扰动次数设为50次，最大迭代次数设为10000次，对数似然变化的收敛阈值设为1e-7，并将协方差矩阵的特征数设为3。随后计算了各扩散状态下经后验概率加权的均方位移。为计算某一扩散状态（布朗运动，Brownian motion）下的扩散系数D，我们将瞬时速度矢量v的方差与扩散系数建立关联，公式为⟨v²⟩=4D/Δt，其中Δt为采集间隔，D为粒子的扩散系数。