Figure 3. Definition of the outside distance, D<sub>out</sub>, as the sum of the distances from each of the two protein binding sites to their corresponding.

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Figure 3. Definition of the outside distance, D<sub>out</sub>, as the sum of the distances from each of the two protein binding sites to their corresponding ends in units of nt. Black dots represent bases and the two blocks represent the protein binding sites with footprint length l (in this figure l = 4 nt). In our numerical calculation we restrict ourselves to the symmetric case n<sub>1</sub> = n<sub>2</sub> and use a footprint size of l = 6 nt. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 2. The four possible RNA–protein complexes to consider Figure 2. The four possible RNA–protein complexes to consider. Lines are RNA backbones and dots are bases. Transparent and black blocks represent the unoccupied and occupied protein binding sites, respectively. Only the bases that are not in the occupied binding regions participate in base pairing. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 1. An example of structure-mediated cooperativity, where open boxes indicate unoccupied protein binding sites and filled boxes indicate occupied protein binding sites. G is the free energy of the RNA–protein complex in each step, G<sub>0</sub> is the free energy of the RNA secondary structure alone, ΔG<sub>s</sub> is the free energy associated with breaking the base pairs in the stem containing the two protein binding sites, c<sub>1</sub>, c<sub>2</sub>, K<sub>D, 1</sub> and K<sub>D, 2</sub> are the concentrations and dissociation constants of the first and the second protein, respectively, R is the gas constant and T is the temperature in kelvin. (a) To have the first protein bind to bases in a stem of the structure in the absence of the second protein, the stem has to be broken, resulting in a free energy difference of ΔG<sub>0 → 1</sub> = ΔG<sub>s</sub> − RTln (c<sub>1</sub>/K<sub>D, 1</sub>). (b) Once the second protein is bound to the opposing bases in the stem, the first protein can directly bind to its binding site without the loss of free energy by breaking additional base pairs, yielding ΔG<sub>2 → 12</sub> = −RTln (c<sub>1</sub>/K<sub>D, 1</sub>) < ΔG<sub>0 → 1</sub>. Thus, in this case the two proteins exhibit positive cooperativity. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 4. The mean (circles) and standard deviation (diamonds) of the cooperativity free energy ΔΔG of 2282 human sequences, as a function of the outside distance D<sub>out</sub> between the two protein binding sites. The mean of the cooperativity free energy ΔΔG is close to zero for all outside distances, while its standard deviation is on the order of or greater than the thermal energy scale of RT =0.6 kcal/mol. The dashed vertical lines label two different outside distances D<sub>out</sub> for which the whole distribution of the cooperativity free energies is compared in Figure 5. The maximum of the standard deviation of the cooperativity free energy occurs at D<sub>out</sub> = 8 nt. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 11. The number of microRNA–mRNA binding pairs, for which the strongest cooperativity with respect to a binding site in the 5′UTR corresponds to a given value of ΔΔG<sub>max</sub>, in bins of 0.2 kcal/mol. While the number distribution of human binding pairs does not show significant differences compared to randomly shuffled binding pairs for most values of ΔΔG<sub>max</sub>, a peak at ΔΔG<sub>max</sub> ≈ −3.8 kcal/mol suggests that there is a group of human sequences with strongly negative cooperativities between the 3′UTR-bound microRNA and putative 5′UTR-bound proteins. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 5. The number of mRNA molecules with respect to given cooperativity free energies ΔΔG (in bin sizes of 0.2 kcal/mol) at outside distances between the protein binding sites of D<sub>out</sub> = 8 (solid line) and D<sub>out</sub> = 150 (dashed line). The inset shows the same data on a logarithmic scale. The two distributions are both centered at 0. The distribution for D<sub>out</sub> = 8 (when the protein binding sites are close to their respective ends of the molecule) extends much wider than that for D<sub>out</sub> = 150 when the protein binding sites are further away from the ends of the molecule. Vertical black dashed and dash-dotted lines label |ΔΔG| = RT and |ΔΔG| = 2 RT, respectively. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 6. The number of mRNA sequences with biochemically relevant protein binding cooperativity among the 2282 investigated human mRNA sequences. The two data sets correspond to |ΔΔG|/RT > 1 (circles) and |ΔΔG|/RT > 2 (diamonds). The data show that at any given distance D<sub>out</sub> a significant fraction of molecules has a significant cooperativity free energy. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 8. The fractions of sequences that have |ΔΔG(D<sub>out</sub>)| > 2RT in different sequence ensembles: natural human mRNAs (circles), dinucleotide-shuffled human sequences (diamonds), sequences with randomized UTRs (crosses) and natural C. elegans mRNAs (squares). All four ensembles show maxima of the fraction at small D<sub>out</sub>. However, their distance dependences are different. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 9. The standard deviations of the cooperativity free energy ΔΔG of 2282 human mRNAs and 1377 CDS-replaced sequences. The two standard deviations are very similar to each other, implying that the cooperativity depends on UTRs instead of CDSs. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 10. The cooperativity free energy of four randomly selected mRNA molecules longer than 2000 nt as a function of outside distance ΔΔG(D<sub>out</sub>). Horizontal lines label the scales of ±RT and ±2RT. For all four molecules, ΔΔG exceeds these energy scales and thus develops significant cooperativity at specific values of the outside distance D<sub>out</sub>. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 12. Cooperativities along artificial evolutionary trajectories starting from five human sequences seeking to maximize the cooperativity free energy. Compared to the cooperativities in natural human sequences, which are on the order of RT, the artificial sequences generated by mutations support much stronger cooperativities of |ΔΔG| > 10RT. The original sequences for initiating the evolutions are (from top to bottom at the final evolutionary step of 1000): NM_001272086, NM_001244390, NM_001104548, NM_022645 and NM_006308. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Figure 7. The standard deviations of the cooperativity free energy ΔΔG for different mRNA ensembles including 2282 sequences each, as functions of the distance D<sub>out</sub> between the protein binding sites. Statistics of four sequence ensembles are shown: natural human mRNAs (circles), dinucleotide-shuffled human sequences (diamonds), sequences with randomized UTRs (crosses) and natural C. elegans mRNAs (squares). All four sequence ensembles have standard deviations on the order of or greater than the thermal energy scale of RT =0.6 kcal/mol, implying that a biologically relevant ΔΔG is a general property for mRNA sequence ensembles. However, different sequence ensembles show different statistical characteristics. From: RNA structure generates natural cooperativity between single-stranded RNA binding proteins targeting 5′ and 3′UTRs Nucleic Acids Res. 2014;43(2):1160-1169. doi:10.1093/nar/gku1320 Nucleic Acids Res | © The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com