Physics of Living Systems

Design principles of transcription factors with intrinsically disordered regions

Wencheng Ji author has email address
Ori Hachmo
Naama Barkai
Ariel Amir author has email address

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, United States
Department of Molecular Genetics, Weizmann Institute of Science, Rehovot, Israel

https://doi.org/10.7554/eLife.104956.1

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Figures and data

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. 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”.

Design principles across various parameters: l₀/d, n_b, n_t, and E_B.
a, Plots of Q = P_TF/P_simple varying with l₀/d are shown for several combinations of n_t and n_b for typical values of the relevant quantities: the nucleus volume is 1μm³, E_DBD = 15, E_B = 10, V₁ = (0.34nm)³, and . b, A heatmap of Q vs. n_b and n_t at E_B = 10 and d = l₀. c, Contour lines at different E_B at P_TF = 0.9. Blue hexagrams represent the design principle , with the black dashed line as a visual guide. The inset shows the dependence of on energy. d, Q for varying E_B at d = l₀ for several n_b = n_t. The vertical line represents E_th as determined by equation (4), the solid curves illustrate the approximation of Q obtained from equation (3), and the horizontal line indicates where P_TF = 1.

Design principles across various parameters: l₀/d, n_b, n_t, and E_B.
a, Plots of Q = P_TF/P_simple varying with l₀/d are shown for several combinations of n_t and n_b for typical values of the relevant quantities: the nucleus volume is 1μm³, E_DBD = 15, E_B = 10, V₁ = (0.34nm)³, and . b, A heatmap of Q vs. n_b and n_t at E_B = 10 and d = l₀. c, Contour lines at different E_B at P_TF = 0.9. Blue hexagrams represent the design principle , with the black dashed line as a visual guide. The inset shows the dependence of on energy. d, Q for varying E_B at d = l₀ for several n_b = n_t. The vertical line represents E_th as determined by equation (4), the solid curves illustrate the approximation of Q obtained from equation (3), and the horizontal line indicates where P_TF = 1.

Mean search time varying with the antenna length L.
t_total, t_3D and t_1D vs. L at and ñ^*. The solid curves correspond to t_total , t_3D and t_1D in equation (5). Inset: probability density function (pdf) exponentially decays at large t. pdf ≈ exp(-t/t_total)/t_total (black solid line). The unit t₀ represents the time for one AA to diffuse 1bp. a = 0.5bp, d= 10bp, and l₀ = 5bp.

Mean search time varying with the antenna length L.
t_total, t_3D and t_1D vs. L at and ñ^*. The solid curves correspond to t_total , t_3D and t_1D in equation (5). Inset: probability density function (pdf) exponentially decays at large t. pdf ≈ exp(-t/t_total)/t_total (black solid line). The unit t₀ represents the time for one AA to diffuse 1bp. a = 0.5bp, d= 10bp, and l₀ = 5bp.

(a) Relative binding probability varies with the truncation length of the IDR, which quantitatively agrees with the experimental data in Ref. [12], where we only vary E_DBD (binding energy of DBD) to ensure that the maximal value reaches 1 at zero truncation length. Antenna length L = 1000nm, E_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. (5)) is quantitatively comparable with the experimental results, as guided by the shaded area. (c) The on-rate k_on = t_total/V_c and off-rate k_off = (1 − P_TF) / (P_TFt_total) varying with the IDR length, indicating that k_D = k_off/k_on ranges from 0.01 to 10 nM, with its variation primarily dominated by the off-rate.

f(r, l₀) aligns well with Eq. [S1] (solid curves) for moderate m at various b₀. Inset: vs. b₀/a₀ from Eq. [S3]. (b) Eq. [S1] serves as a good approximation (solid lines) even at small m.

f(r, l₀) aligns well with Eq. [S1] (solid curves) for moderate m at various b₀. Inset: vs. b₀/a₀ from Eq. [S3]. (b) Eq. [S1] serves as a good approximation (solid lines) even at small m.

A diagram of the bound configurations at n = 3.

Maximal Q is observed at l₀ ~d for all combinations of n_b and n_t.

(a) P_TF varying with n_b at n_t = 12. P_TF initially increases rapidly, until eventually saturating. (b) P_TF varies non-monotonically with n_t. P_TF slightly decreases with increasing n_t at n_t > n_b. Three examples at n_b = 7, 8, 9 are displayed. P_TF is denoted by pentagrams at n_t = n_b.

Contour lines at P_TF =0.9 and P_TF =0.5 on the plane defined by the number of binding sites, n_b, and the number of binding targets, n_t.
The black dashed line is added to guide the relationship n_b = n_t.

Plots of the affinity enhancement, quantified by the ratio Q = P_TF/P_simple, for the case where IDR sites as well as their targets are randomly positioned on the IDR and DNA, respectively.
See the analogous Figure 2 in the main text for the case of homogeneously distributed IDR sites and targets. (a) Q is maximal when l₀ ~ d (shaded region) for different values of n_t = n_b. The average distance between IDR sites is l₀ , and the average distance between IDR targets is d. (b) A heatmap of Q at E_B = 10 and l₀ =d. (c) Contour lines at different E_B at P_TF = 0.5 exhibit an approximate symmetrical L-shape, which indicates , as shown by the red triangles. decreases with increasing E_B. (d) Q varies with E_B for several different constants of n_t = n_b. The characteristic energy E_th, as predicted by Eq. [5] in the main text, corresponds to the region where a notable increase is observed.

Plots of the affinity enhancement, quantified by the ratio Q = P_TF/P_simple, for the case where IDR sites as well as their targets are randomly positioned on the IDR and DNA, respectively.
See the analogous Figure 2 in the main text for the case of homogeneously distributed IDR sites and targets. (a) Q is maximal when l₀ ~ d (shaded region) for different values of n_t = n_b. The average distance between IDR sites is l₀ , and the average distance between IDR targets is d. (b) A heatmap of Q at E_B = 10 and l₀ =d. (c) Contour lines at different E_B at P_TF = 0.5 exhibit an approximate symmetrical L-shape, which indicates , as shown by the red triangles. decreases with increasing E_B. (d) Q varies with E_B for several different constants of n_t = n_b. The characteristic energy E_th, as predicted by Eq. [5] in the main text, corresponds to the region where a notable increase is observed.

(a) A trajectory (red) of TF in the cell nucleus (light blue). r_DNA is the average distance of the TF to the antenna, and X_c is the position of the center of mass along the antenna direction. The trajectory is displayed with a time interval of 10⁶t₀. (b) The average number of rounds the TF hits the antenna, n_hits, before reaching the DBD target. The optimal mean total search time is obtained at L^* = 300bp.

(a) t_total, t_3D, and t_1D vs. E_B at fixed L* and . The red solid line is the prediction of t_3D from Eq. [5], and the blue line (also in the inset) is the exponential fit for t_1D. The black curve in the inset is the number of rounds the TF hits the antenna, n_hits, vs. E_B. (b) t_total, t_3D, and t_1D vs. at fixed L* and . The red and blue solid lines represent the predictions of t_3D and t_1D from Eq. [5], respectively. n_hits varying with is shown in the inset.

(a) t_total, t_3D, and t_1D vs. E_B at fixed L* and . The red solid line is the prediction of t_3D from Eq. [5], and the blue line (also in the inset) is the exponential fit for t_1D. The black curve in the inset is the number of rounds the TF hits the antenna, n_hits, vs. E_B. (b) t_total, t_3D, and t_1D vs. at fixed L* and . The red and blue solid lines represent the predictions of t_3D and t_1D from Eq. [5], respectively. n_hits varying with is shown in the inset.

Left: an example of the target configuration (the antenna) generated by the worm-like chain model, where L = 300bp, d = 10bp, and the persistence length also equals 10bp. Right: Mean total search times weakly vary with persistence length when targets are generated using the worm-like chain model. The values are represented by the black dots, with parameters set to E_B = 11, L = 300 bp, and = 4. For each persistence length, we obtained ten mean total search times by considering ten different target configurations. The mean total search times do not exhibit significant differences compared to that for targets arranged linearly (indicated by the horizontal orange line).

Left: an example of the target configuration (the antenna) generated by the worm-like chain model, where L = 300bp, d = 10bp, and the persistence length also equals 10bp. Right: Mean total search times weakly vary with persistence length when targets are generated using the worm-like chain model. The values are represented by the black dots, with parameters set to E_B = 11, L = 300 bp, and = 4. For each persistence length, we obtained ten mean total search times by considering ten different target configurations. The mean total search times do not exhibit significant differences compared to that for targets arranged linearly (indicated by the horizontal orange line).

(a) Configuration of DNA (in red) at v = 0.008 with a complex structure and a trajectory of TF (in black). A TF acts as a point searcher that diffuses in 3D space and becomes trapped once it hits the DNA, which is 1nm wide. It detaches at a rate of . (b) MSD at different E_nonsp.

(a) Configuration of DNA (in red) at v = 0.008 with a complex structure and a trajectory of TF (in black). A TF acts as a point searcher that diffuses in 3D space and becomes trapped once it hits the DNA, which is 1nm wide. It detaches at a rate of . (b) MSD at different E_nonsp.

(a) W_n,n+1 (or W_n,n-1) denoted by “on” (or “off”) varies with n for E_B = 6 and = 12. Inset: Mean square displacement (MSD) suggests diffusive motion, as indicated by the dashed line following MSD ∝ t. (b) Steady probability distribution of bound sites.

(a) W_n,n+1 (or W_n,n-1) denoted by “on” (or “off”) varies with n for E_B = 6 and = 12. Inset: Mean square displacement (MSD) suggests diffusive motion, as indicated by the dashed line following MSD ∝ t. (b) Steady probability distribution of bound sites.

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