Konda V. the fractal dimension of the polymer and is determined by the balance of the free energy of polymer-polymer and polymer-solvent interactions. of an unconstrained free polymer may range from = 5/3 for an excluded volume polymer to = 2 for an ideal chain polymer in theta solvent and to = 3 for a completely space-filling polymer. A polymer with a uniform chain structure throughout would form a single fractal domain name with determined by the properties of the chain and the solvent. Chromatin, on the other hand, is usually a heterogeneous polymer with variable post-translational histone modifications and DNA methylation patterns. This leads to differential interactions between the heterogeneous chromatin subunits and results in chromatin compartmentalization, potentially as a result of liquid-liquid phase separation (within a given chromatin domain name or compartment. Electron microscopy and super-resolution imaging studies have exhibited the presence of spatially segregated supranucleosomal nanoscale packing domains with a variable size distribution in 3D space ((Fig. 1, F and G), and genomic size ((e.g., grouped by their initial expression or associated gene ontologies) would respond to changes in average measurable physical conditions. Specifically, we study how average nuclear crowding density (?in,0), average chromatin packing scaling (for a gene of length is the radius of the conversation volume for a single base pair and is approximated from previous MC simulations of crowding effects (and ?in,0, and is further influenced by length of the gene. The transcription rate ? itself is usually assumed to depend on molecular features and on local crowding density ?in. We calculate all expression rates under the assumption that molecular features remain constant throughout the population, with physiologically relevant values used in previous MC and BD crowding simulations (table S1) (as on gene expression, we calculated the sensitivity of gene expression as a function of as predicted by the CPMC model. Sensitivity (Se) is the measurement of how a dependent variable (i.e., gene expression) will change as a function of a perturbation to an independent variable (i.e., is the initial average expression rate of the group of genes sharing comparable molecular features and gene length are not considered to alter the degradation rate of mRNA. Thus, sensitivity should be directly related to the number of transcripts produced for any group of genes in the nucleus. To solve Eq. 4, we used a Taylor series approximation of around ?in,0 is a nonmonotonic function of ?in due to the competing effects of crowding on depletion interactions and molecular diffusion, and 2-Atractylenolide quantifies gene expression as a function of crowding within a transcriptional conversation volume. Expression rate = 22.6 nM/s is derived from a steady-state solution of rate equations that model transcription and whose crowding-dependent rates were determined from BD and MC simulations as described previously (can be simulated by varying any or several of the components of as a function of may depend on which component of is being varied, i.e., depends on primarily through (Fig. 2, A and B) (was calculated by first averaging values from PWS measurements within each cell nucleus and then averaging these measurements over the entire cell population for each treatment condition. Using ChromEM, average chromatin density was measured within each nucleus with ~3-nm resolution. As ?in,0 represents the crowding contributions from both chromatin and mobile crowders within the nucleus, we added to our ChromEM measurements an additional 5% contribution from unbound macromolecules (as described in Materials and Methods). In addition, we ECT2 used publicly available DNA sequencing information to obtain gene length and high-throughput chromatin conformation (Hi-C) capture data to approximate scaled between 2.56 and 2.66 for control (A) and 12-hour dexamethasone (DXM)Ctreated lung adenocarcinoma A549 cells (B). Brighter red corresponds to higher chromatin 2-Atractylenolide packing scaling. (C and D) Representative heat maps of CVC values from analysis of ChromEM images of cell nuclei from A549 cells (C) and human fibroblasts BJ (D). Representative magnified regions from each nucleus demonstrate an average CVC of 0.35 in A549 cells compared to 0.30 in BJ cells, which represents the chromatin contribution to the average crowding volume fraction in,0. (E to J) Comparison between the CPMC model (solid lines) and experimentally measured (points) sensitivity of gene expression to an incremental change in chromatin packing scaling (Se, axis) as a function of initial gene expression (axis). (E) Cells with chromatin with a higher initial [wild-type (WT) HT-29 cells] have a bidirectional Se curve that becomes attenuated if were induced by cell 2-Atractylenolide treatment with 10% FBS, 100 nM EGF, and 100 nM PMA. The CPMC model was able to explain 86% of the variance of the experimental data for WT HT-29 cells and 51%.