Bridging-Induced Phase Separation and Loop Extrusion Drive Noise in Chromatin Transcription

TL;DR

Bridging-Induced Phase Separation and Loop Extrusion Drive Noise in Chromatin Transcription investigates how 3D chromatin organization shapes transcriptional noise using a coarse-grained polymer model with transcription units, multivalent transcription factors, and loop extrusion by cohesin-like complexes. Transcriptional activity is quantified by the fraction of time a TU is engaged, and intrinsic noise arises from BIPS-driven TU clustering, while extrinsic noise stems from stochastic loop extrusion across cells; noise is tunable via TU spacing and TF valency, with mean expression largely unaffected by LE. The work provides mechanistic predictions for single-cell assays and offers a framework linking chromatin patterning and loop architecture to transcriptional plasticity and evolution, including implications for younger genes. Overall, it demonstrates that 3D genome organization imposes distinct, testable contributions to transcriptional variability through intrinsic clustering and extrinsic loop-network diversity, guiding future experimental investigations.

Abstract

Transcriptional noise, or heterogeneity, is important in cellular development and in disease. The molecular mechanisms driving it are, however, elusive and ill-understood. Here, we use computer simulations to explore the role of 3D chromatin structure in driving transcriptional noise. We study a simple polymer model where proteins - modeling complexes of transcription factors and polymerases - bind multivalently to transcription units - modeling regulatory elements such as promoters and enhancers. We also include cohesin-like factors which extrude chromatin loops that are important for the physiological folding of chromosomes. We find that transcription factor binding creates spatiotemporal patterning and a highly variable correlation time in transcriptional dynamics, providing a mechanism for intrinsic noise within a single cell. Instead, loop extrusion contributes to extrinsic noise, as the stochastic nature of this process leads to different networks of cohesin loops in different cells in our simulations. Our results could be tested with single-cell experiments and provide a pathway to understanding the principles underlying transcriptional plasticity in vivo.

Figures (10)

• Figure 1: Polymer modeling of 3D chromatin structure and transcription. (a) Schematics of the simulation model. A chromatin fiber is modeled as a bead-and-spring chain, with certain beads denoted as TUs, separated by distance $d_{\text{TU}}$, with high affinity to TFs, which can switch between a binding (ON) and a non-binding state (OFF). (b) Chromatin loops in the simulation are driven by chromatin-TF bridges or loop extrusion (the latter are modeled by springs, mimicking cohesin complexes). (c) Simulation snapshots with TFs and cohesin loops. (d) Schematics showing how a prediction of transcriptional dynamics of each TU (blue segment) is extracted from the simulation. By measuring the fraction of time $\phi_i$ a TU is transcribed in simulation run $i$ ($i = 1,\dots,N_{\text{sim}}$; middle), we obtain a distribution of transcriptional activities, and quantify both the average transcriptional activity $\mu$ and noise $\sigma$ of that TU (right). (e) Distributions of transcriptional activities for TUs as predicted by sampling the baseline binomial model (left). By varying TF number $N_{\text{TF}}$, we can vary $\mu$ and build a "boomerang plot", showing how $\sigma$ changes with $\mu$ (right).
• Figure 2: Linear separation between TUs regulates transcriptional noise. (a) Boomerang plots for TU spacing $d_{\text{TU}}$ from $10$ to $200$ kbp (top) and the maximum transcriptional noise $\sigma(\phi)$ as a function of $d_{\text{TU}}$ (bottom). Each boomerang is obtained by varying $N_{\text{TF}}$ from $5$ to $200$, and we fit the curve $\sigma(\mu) = \frac{A_{\sigma}\mu^{\alpha}(1-\mu)^{\beta}}{\nu^{\alpha}(1-\nu)^{\beta}}$, with $\nu = \frac{\alpha}{\alpha+\beta}$, to guide the eye across different boomerangs and to extract the maximum noise [i.e., $\text{max}[\sigma(\phi)] = A_{\sigma}$]. The dashed boomerang corresponds to the binomial model, and in all cases we use $M = 101$; note that changing $M$ or total simulation time would scale all boomerang plots by the same factor. (b) Similar to (a), but showing boomerangs for patchy TFs with limited valency $N_{\text{patch}}$ (top) and their maximal noise (bottom), with $d_{\text{TU}} = 30$ kbp (see SM for the values of $N_{\text{TF}}$). The blue boomerang is for the case with non-patchy TFs (i.e., $N_{\text{patch}} = \infty$). Snapshots show the geometry of the chromatin-binding patches (cyan beads) on TFs. (c) Standard deviation of the fraction of time $f_{\text{clust}}$ a TU is in a cluster with other TUs as a function of activity $\mu(\phi)$ for different $d_{\text{TU}}$ (top) and their maxima (bottom). Error bars representing the standard error on the mean (from averaging over TUs) are shown for both axes in all boomerangs but are smaller than the data points (same for most of subsequent boomerang plots).
• Figure 3: Chromatin loops driven by loop-extruding factors enhance transcriptional noise. (a) Transcription boomerangs corresponding to cases with and without cohesin loops ($+$/$-$LE, respectively), and the case with loops placed at the same locations across all simulations [$+$LE (same loops)]. We vary $N_{\text{TF}}$ from $5$ to $100$, and for LE, we set the number of extruders $N_{\text{ex}} = 40$ and loop size parameter $\lambda_{\text{ex}} = 150$ kbp. (b) Scatterplots comparing the transcriptional activity $\mu$ (top) and noise $\sigma$ (bottom) of individual TUs between the cases with and without LE. While the data points remain close to the diagonal for $\mu$, suggesting LE has little impact on activity, they are in the lower triangle for $\sigma$, indicating that noise is higher with LE. (c) and (d) Phase diagrams showing how $\lambda_{\text{ex}}$ and $N_{\text{ex}}$ modulate (c) transcriptional noise $\sigma(\phi)$ and (d) the fluctuations in clustering $\sigma(f_{\text{clust}})$. Here $N_{\text{TF}} = 50$, and the gray crossover line indicates the midpoint between the minimum fluctuation in the case without extruders and the maximum fluctuation across all parameter points. $N_{\text{TU}} = 40$ and $d_{\text{TU}} = 30$ kbp for all plots.
• Figure S1: Modeling TFs as patchy rigid bodies to limit their valency in chromatin binding. (a) Schematics of the modified TFs. The cyan patches on a TF are attracted to TUs when the TF is switched on, and the orange core bead interacts repulsively with the TU. (b) The geometry and relative orientation of the chromatin-binding patches on a TF as the number of patches $N_{\text{patch}}$ increases from $1$ to $4$. (c) Simulation snapshots illustrating that each patch on a TF can typically bind to a single bead (left) or two consecutive beads (right). (d) Comparing the unbinding rates $k_{\text{unbind}}$ from chromatin for a non-patchy and a single-patch TF when varying the energy of the respective potentials (i.e., $U_{\text{LJ/cut}}$ for non-patchy and $U_{\text{patch}}$ for patchy TFs). (e) A plot showing the fraction of TFs which form clusters $\psi_c$ as a function of $N_{\text{patch}}$ (note that $N_{\text{patch}} = \infty$ corresponds to the non-patchy case). The line connecting the data points is drawn to guide the eye. Insets show representative snapshots of the system for the one-patch and four-patch cases. In all patchy-TF simulations we consider $d_{\text{TU}} = 30$ kbp and $N_{\text{TU}} = 30$.
• Figure S2: Temporal correlation in transcriptional activity of TUs. (a) Transcription boomerangs for different TU spacings $d_{\text{TU}}$ as shown in Fig. \ref{['fig:TU_noise']}(a). (b)--(d) Kymographs showing the transcription status $s_i$ [i.e., ON ($+1$) or OFF ($-1$)] of each TU over time for cases with low activity $\mu \sim 0.1$ [points marked by circles in (a); left] and intermediate activity $\mu \sim 0.6$ [points marked by squares; right], for (b) $d_{\text{TU}} = 100$ kbp and (c) $d_{\text{TU}} = 10$ kbp, and for (d) the binomial model (i.e., a sequence of Bernoulli trials), where we consider the same as the number of sampling events ($M = 101$) as in the other cases (i.e., the time interval between frame/event is $10^3\tau$). (e) The autocorrelation $\chi(t) = \tilde{\chi}(t)/\tilde{\chi}(0)$ in transcription [see Eq. \ref{['eqn:auto_corr']}] for the points considered in (b)--(d). The dashed line indicates the threshold ($\chi^* = 0.5$) we use for defining the correlation time $\tau_s$. (f) Measured $\tau_s$ as a function of $\mu$ for different $d_{\text{TU}}$ (top). As with transcription boomerangs, we fit the curve $\tau_s(\mu) = \frac{A_{\tau_s}\mu^{\alpha}(1-\mu)^{\beta}}{\nu^{\alpha}(1-\nu)^{\beta}}$, with $\nu = \frac{\alpha}{\alpha+\beta}$, to guide the eye and extract the maximum correlation time [i.e., $\text{max}(\tau_s) = A_{\tau_s}$], which we plot as a function of $d_{\text{TU}}$ in the bottom panel. Error bars representing the standard error on the mean (from averaging over all TUs) are shown for both axes in all boomerangs, but are smaller than the data points.