“…For proper estimates of the parameters in the formulas, we used some sequences of known pseudoknots that are evidenced by experiments and/or phylogenetic comparisons, assuming that the free energies of these pseudoknots are lower than those of corresponding hairpins formed by the pseudoknot stems+ As seen in Table 1, these H-pseudoknots cover rather broad ranges of loop and stem sizes+ The majority of pseudoknots, available for analysis, are found in viral RNAs (ten Dam et al+, 1990;Deiman & Pleij, 1997) and representative structures are shown in Figure 2+ The large group of well-documented H-pseudoknots are found at the very 39 ends of plant viral RNAs (tymoviruses and tobamoviruses) as parts of tRNA-like structures (for review, see, e+g+, Mans et al+, 1991)+ These pseudoknots seem to have minimal loop sizes and show little variation in stem lengths, with a stem S1 of 3 bp and S2 of 4 bp in tobamoviruses and 5-6 bp in tymoviruses (Fig+ 2A)+ Upstream of the tRNA-like structure in tobamoviruses, a conserved structure of three consecutive pseudoknots is located (Fig+ 2B), which seems to be very important in regulation of viral multiplication and mRNA translation (van Belkum et al+, 1985;Leathers et al+, 1993)+ Those three pseudoknots or only two are duplicated in some tobamoviruses and satellite tobacco mosaic virus, sometimes with a considerable sequence variation (Gultyaev et al+, 1994)+ Similar pseudoknot stalks are conserved in some hordei-, furoand tobraviruses and satellite tobacco necrosis viruses STNV-1 and STNV-2 (Pleij et al+, 1986;Danthinne et al+, 1991;Solovyev et al+, 1996;Koenig et al+, 1998), with different numbers of pseudoknots (Table 1)+ The biggest variation in the sizes of pseudoknot loops and stems is observed in the sites of pseudoknot-dependent ribosomal frameshift and readthrough (ten Dam et al+, 1990;Brierley et al+, 1991;Chamorro et al+, 1992;Garcia et al+, 1993;Kujawa et al+, 1993;Wills et al+, 1994)+ Although large pseudoknot loops, like those found in frameshift sites of coronaviruses (Fig+ 2E), may have an interior structure, we included them in our analysis to test the performance of logarithmic extrapolation+ For each analyzed pseudoknot, the condition of lower free energy than that of either of two hairpins formed separately by stems S1 or S2 (Fig+ 1) leads to the requirement that the sum of loop energies be less than some computable value+ In these calculations, possible coaxial stacking on stems adjacent to the pseudoknots, as in 39-terminal tRNA-like structures or pseudoknot stalks (Fig+ 2A,B), was also taken into account+ Possible extensions of stems, when they are formed separately, were also considered+ Also, in case of...…”