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Synopsis
A theoretical model to determine the probability of loop formation, based on an elaborated form of the Jacobson-Stockmayer theory of cyclization equilibria, has been developed and used on RNA chains of homogeneous puckering and lengths up to F' residues. The probability Qx(q,yo,co) of occurrence of hairpin loops of a particular chain x is given by Qx(q,yo,co) = [ W(q)6r] [2rq(y0)6y] [Eq,,,(co)6c] where W(q) is the three-dimensional density distribution function of end-to-end vectors r centered about the ideal loop closure position q; r,(yo) is an angular correlation factor that restricts the orientation of terminal bonds (i.e., bond x and bond 1) in the loop to a specified value A0 = cos-l(y0) when r adopts a value within a range 6r from position q; and E,,,,(EO) is the probability that c falls within 6c of โฌ0 when r and y assume the values denoted by the respective subscripts. The parameter E is related to the angle between a hypothetical bond ( x + 1) and bond 1. In these calculations, E,,,,(co) was set equal to 1. For randomly coiling models previously developed to reproduce polynucleotide unperturbed dimensions, loop closure probability is maximized with chains of length 22 residues. Larger hairpin loops of 24-25 residues, also favored in C3'-endo random coils of this type, are potential models of tRNA unfolding. W(q) is a stronger determinant of loop closure than r,(-yO). The angular correlation effect is most noticeable at chain lengths 22 and 23 where Sr,(yo) deviates from unity.