Department of Mathematics and Statistics, Boston University, Boston, MA, USA,
Bull Math Biol. 2013 Nov;75(11):2093-117. doi: 10.1007/s11538-013-9883-9. Epub 2013 Aug 17.
In this work, we examine how volume exclusion caused by regions of high chromatin density might influence the time required for proteins to find specific DNA binding sites. The spatial variation of chromatin density within mouse olfactory sensory neurons is determined from soft X-ray tomography reconstructions of five nuclei. We show that there is a division of the nuclear space into regions of low-density euchromatin and high-density heterochromatin. Volume exclusion experienced by a diffusing protein caused by this varying density of chromatin is modeled by a repulsive potential. The value of the potential at a given point in space is chosen to be proportional to the density of chromatin at that location. The constant of proportionality, called the volume exclusivity, provides a model parameter that determines the strength of volume exclusion. Numerical simulations demonstrate that the mean time for a protein to locate a binding site localized in euchromatin is minimized for a finite, nonzero volume exclusivity. For binding sites in heterochromatin, the mean time is minimized when the volume exclusivity is zero (the protein experiences no volume exclusion). An analytical theory is developed to explain these results. The theory suggests that for binding sites in euchromatin there is an optimal level of volume exclusivity that balances a reduction in the volume searched in finding the binding site, with the height of effective potential barriers the protein must cross during the search process.
在这项工作中，我们研究了由于高染色质密度区域引起的体积排除如何影响蛋白质找到特定 DNA 结合位点所需的时间。通过对五个核的软 X 射线断层重建，确定了小鼠嗅觉感觉神经元内染色质密度的空间变化。我们表明，核空间分为低密度常染色质和高密度异染色质区域。由这种染色质密度变化引起的扩散蛋白所经历的体积排除通过排斥势来建模。在给定空间点的势能值选择为该位置处染色质密度的比例。比例常数称为体积排他性，提供了确定体积排除强度的模型参数。数值模拟表明，对于有限的非零体积排他性，蛋白质定位位于常染色质中的结合位点的平均时间最小化。对于异染色质中的结合位点，当体积排他性为零时（蛋白质不经历体积排除），平均时间最小化。提出了一种分析理论来解释这些结果。该理论表明，对于常染色质中的结合位点，存在一个最佳的体积排他性水平，该水平平衡了在寻找结合位点时减少搜索的体积，以及蛋白质在搜索过程中必须穿过的有效势垒的高度。
