Design principles of transcription factors with intrinsically disordered regions

TL;DR

Key design principles of the Intrinsically Disordered Region related to TF binding affinity and search time are revealed and it is demonstrated that the IDR significantly enhances both of these aspects.

Abstract

Transcription Factors (TFs) are proteins crucial for regulating gene expression. Effective regulation requires the TFs to rapidly bind to their correct target, enabling the cell to respond efficiently to stimuli such as nutrient availability or the presence of toxins. However, the search process is hindered by slow diffusive movement and the presence of `false' targets --DNA segments that are similar to the true target. In eukaryotic cells, most TFs contain an Intrinsically Disordered Region (IDR), which is commonly assumed to behave as a long, flexible polymeric tail composed of hundreds of amino acids. Recent experimental findings indicate that the IDR of certain TFs plays a pivotal role in the search process. However, the principles underlying the IDR's role remain unclear. Here, we reveal key design principles of the IDR related to TF binding affinity and search time. Our results demonstrate that the IDR significantly enhances both of these aspects. Furthermore, our model shows good agreement with experimental results, and we propose further experiments to validate the model's predictions.

Figures (15)

• Figure 1: Model illustration of a TF with the IDR and its search process.a, Illustration of a TF locating its target site (highlighted in orange) on the DNA strand (depicted as a green curve). Surrounding the target is a region of length $L$, where the TF's IDR interacts with the DNA. The TF performs 3D diffusion until it encounters and binds to this "antenna" region. b, Illustration of a TF that includes an IDR composed of AAs. On the right: a model of the TF, a polymer chain, comprising of a single binding site on the DNA Binding Domain (DBD), and multiple binding sites on the IDR (also known as short linear motifsJonas2025). c, Once bound to the antenna, the TF performs effective 1D diffusion until it reaches its target. The 1D diffusion is via the binding and unbinding of sites along the IDR, a process we coin "octopusing". $V_1$ is the targets' volume, $d$ the separation, and $E_B$ the binding energy per binding site, where each site corresponds to a short linear motif.
• Figure 2: Design principles across various parameters: $l_0/d$, $n_b$, $n_t$, and $E_B$.a, Plots of $Q\!\equiv\! P_{\rm TF}/P_{\rm simple}$ varying with $l_0/d$ are shown for several combinations of $n_t$ and $n_b$ for typical values of the relevant quantities: the nucleus volume is $\!1 {\rm \mu m}^3$, $E_{\rm DBD}\!=\!15$, $E_B\!=\!10$, $V_{1}\!=\!(0.34{\rm nm})^{3}$, and $d\!=\!\sqrt{50}\cdot0.34 {\rm nm}$. b, A heatmap of $Q$ vs. $n_{b}$ and $n_t$ at $E_B\!=\!10$ and $d\!=\!l_0$. c, Contour lines at different $E_B$ at $P_{\rm TF}\!=\!0.9$. Blue hexagrams represent the design principle $n_b^*=n_t^*$, with the black dashed line as a visual guide. The inset shows the dependence of $n_b^*$ on energy. d, $Q$ for varying $E_{B}$ at $d\!=\!l_0$ for several $n_b\!=\!n_t$. The vertical line represents $E_{\rm th}$ as determined by equation \ref{['eq:E_TH']}, the solid curves illustrate the approximation of $Q$ obtained from equation \ref{['eq:Q']}, and the horizontal line indicates where $P_{\rm TF}\!=\!1$.
• Figure 3: Mean search time varying with the antenna length $L$. $t_{\rm total}$, $t_{\rm 3D}$ and $t_{\rm 1D}$ vs. $L$ at $E_B^*$ and $\tilde{n}^*$. The solid curves correspond to $t_{\rm total}$ , $t_{\rm 3D}$ and $t_{\rm 1D}$ in equation (\ref{['Eq_time']}). Inset: probability density function (pdf) exponentially decays at large $t$. ${\rm pdf}\approx \exp(-t/t_{\rm total})/t_{\rm total}$ (black solid line). The unit $t_0$ represents the time for one AA to diffuse $1\rm bp$. $a\!=\!0.5\rm bp$, $d\!=\!10\rm bp$, and $l_0\!=\!5\rm bp$.
• Figure 4: a, Relative binding probability varies with the truncation length of the IDR, which quantitatively agrees with the experimental data in Ref. Naama20, where we only vary $E_{\rm DBD}$ (binding energy of DBD) to ensure that the maximal value reaches 1 at zero truncation length. Antenna length $L=1000\rm nm$, $E_{\rm DBD}\!=\!22$ and $E_B\!=\!11$. Other parameters are set the same as in Fig. 2. b, The search time estimated by our model (from Eq. (\ref{['Eq_time']}) and divided by a TF copy number of $100$) is quantitatively comparable with the experimental results Larson2011, as guided by the shaded area. c, The on-rate $k_{\rm on}=t_{\rm total}/V_c$ and off-rate $k_{\rm off}=(1-P_{\rm TF})/(P_{\rm TF} t_{\rm total})$ varying with the IDR length, indicating that $k_D\equiv k_{\rm off}/k_{\rm on}$ ranges from $0.01$ to $10$ nM, with its variation primarily dominated by the off-rate.
• Figure S1: $f(r,l_0)$ aligns well with Eq. [\ref{['eq:f_rl0']}] (solid curves) for moderate $m$ at various $b_0$. Inset: $a_{\rm eff}^2/a_0^2$ vs. $b_0/a_0$ from Eq. [\ref{['eq:f_pred']}]. (b) Eq. [\ref{['eq:f_rl0']}] serves as a good approximation (solid lines) even at small $m$.