Intrinsic limits to gene regulation by global crosstalk

Abstract

Gene regulation relies on the specificity of transcription factor (TF)-DNA interactions. Limited specificity may lead to crosstalk: a regulatory state in which a gene is either incorrectly activated due to noncognate TF-DNA interactions or remains erroneously inactive. As each TF can have numerous interactions with noncognate cis-regulatory elements, crosstalk is inherently a global problem, yet has previously not been studied as such. We construct a theoretical framework to analyse the effects of global crosstalk on gene regulation. We find that crosstalk presents a significant challenge for organisms with low-specificity TFs, such as metazoans. Crosstalk is not easily mitigated by known regulatory schemes acting at equilibrium, including variants of cooperativity and combinatorial regulation. Our results suggest that crosstalk imposes a previously unexplored global constraint on the functioning and evolution of regulatory networks, which is qualitatively distinct from the known constraints that act at the level of individual gene regulatory elements.

Figure 1. Crosstalk in gene regulation.

(a) A TF preferentially binds to its cognate binding site, but can also bind non-cognate sites, potentially causing crosstalk—an erroneous activation or repression of a gene. (b) In a global setting where many TFs regulate many genes, the number of possible non-cognate interactions grows quickly with the number of TFs; in addition, it may become difficult to keep TF recognition sequences sufficiently distinct from each other. (c) Cells respond to changing environments by attempting to activate subsets of their genes. In this example, the total number of genes is M=4 and different environments (here, 6 in total) call for activation of different subsets with Q=2 genes. To control the expression in every environment, TFs for Q required genes are present, whereas the TFs for the remaining M−Q genes are absent. Because of crosstalk, TFs can bind non-cognate sites, generating a pattern of gene expression that can differ from the one required.

Figure 2. Binding site similarity S and number of genes M are basic determinants of crosstalk.

(a) Binding site similarity, , determines the likelihood that a TF will bind non-cognate sites, if recognition sequences are of length L and the energy per mismatch is . A schematic diagram of sequence space packing by different TFs: sequences (dots) in a coloured circle are likely to be bound by the TF whose consensus is the circle's centre star. Smaller L contracts the sequence space and makes crosstalk (circle overlap) more likely (larger S); crosstalk is increased (larger S) also by smaller , which expands the circle radius. (b) Typical values for the number of genes, M, and binding site similarity, , across different taxa, estimated from genomic databases. For each organism, we find a distribution of S over its reported TFs (dots=median of the distribution, black bars=±1-quartile range; see Supplementary Note 2 for details).

Figure 3. Basic model with one activator binding site per gene exhibits three distinct regulatory regimes.

(a) Each binding site can be in either of the three possible states with different corresponding energies: bound by a cognate factor (E=0, green molecule), bound by a non-cognate factor with d-mismatches (, here a blue molecule with d=2), or unbound (E=E_a, pink molecule). The table shows which of these states lead to transcription and which of these outcomes is considered as crosstalk when the cognate TF is present and the gene is required to be active (left), or if it is absent and the gene is required to be inactive (right). (b) Minimal crosstalk X*, shown in colour, as a function of the number of coactivated genes Q and binding site similarity, S. Three different regulatory regimes are separated by black and white boundary lines (analytical expressions in Supplementary Note 1), identical between b and c. Dotted lines refer to the ‘baseline parameters' (Q=2,500, M=5,000, log(S)=−10.5—represents L=10, with d_min=2) that we use in all subsequent figures if not specified differently. (c) Optimal TF concentration, C*, that minimizes the crosstalk, relative to C₁, the optimal concentration at baseline parameters. For high binding site similarity (large S), the crosstalk is minimized at C*=0 (white region, I: ‘no regulation regime'). For Q→M and intermediate S, the crosstalk is minimized at C*→∞ (black region, II: ‘constitutive regime'). In a large, biologically plausible intermediate regime, crosstalk is minimized at a finite non-zero TF concentration (colour, III: ‘regulation regime').

Figure 4. Cooperative regulation reduces crosstalk and the required optimal TF concentration.

(a) Cognate binding configurations (non-cognate not shown) for two sites of length L leading to transcription (green check) or not (red cross); doubly occupied promoter gains a cooperative energy Δ. Transcription proceeds only when the proximal (rightmost) site is occupied. (b) Difference in minimal crosstalk, shown in colour, between the cooperative model and the basic model of Fig. 3, , for cooperative interaction strength Δ=10. Cooperativity significantly reduces crosstalk (blue; at baseline parameters shown with white dashed lines, here versus X*=0.23 in the basic model) and shrinks the ‘no regulation' (C*=0) regime. (c) Minimal crosstalk error, X*, versus binding site length L for different values of cooperative energy Δ shows that strong cooperativity can decrease the crosstalk beyond the basic model with binding site of length 2L (red). (d) Optimal TF concentration, C*, required to minimize crosstalk, decreases with increasing cooperativity Δ for all L and is consistently below the single-site basic model with site length of either L (black) or even 2L (red). Circles denote transition to the ‘no regulation' (C*=0) regime at low L (large S), showing that cooperativity extends the ‘regulation regime.' In c,d, we convert S values to the equivalent binding site lengths L using the random sequence model.

Figure 5. Combinatorial regulation by activators and repressors yields marginal improvements in crosstalk error.

(a) Separate (left) or overlapping (right) binding sites for activators A and repressors R. A subset of binding configurations for cognate regulators is shown; transcription proceeds (green) only when the A site is bound by the cognate activator and the R site is unbound. (b,c) Difference (shown in colour) between minimal crosstalk achievable with activator–repressor regulation and the basic model of Fig. 3. With optimal value for the affinity of repressor sites (E_r) selected in both cases, a small overall improvement in crosstalk error is seen in b and a larger improvement, but localized to log S≲−10, in c. At baseline parameters (white dashed lines), X*=0.2 for the non-overlapping case, X*=0.15 for the overlapping case and X*=0.23 in the basic model. (d) Dependence of the crosstalk on the repressor binding affinity E_r (activator affinity fixed at E_a=15). When E_r>E_a, the crosstalk quickly increases: instead of helping prevent erroneous activation, repressors themselves bind too frequently in noncognate configurations, aggravating the crosstalk. For non-overlapping sites scenario, E_r<<E_a is optimal, whereas in the overlapping sites case, E_r=E_a is optimal. (e) Dependence of crosstalk on the total concentration, C, of transcription factors, for non-overlapping sites case (orange-brown curves representing different E_r, as indicated) and overlapping sites case (green curves representing different E_r as indicated). The total concentration is optimally split between activators and repressors for each C, and is reported relative to the optimal concentration C₁ of the basic model.