Generalization of the One-Dimensional Ising Model Applicable to Helix Transitions in Nucleic Acids and Proteins

Abstract

The exact treatment of the Ising model for an infinite, one‐dimensional system has been generalized to make it applicable to the helix transition in synthetic polynucleotides, DNA, synthetic polypeptides, and proteins. The particular advantages of the present treatment are flexibility and generality: the free energies of sequences of similar units of any size can be assigned arbitrary values in the final equations; also ``mismatching'' between the two strands in a double helix is allowed for. Anderson's general theory of collision line broadening has been applied to H₂O–N₂ encounters. The only attractive force was assumed to be that between the H₂O dipole, μ=1.87×10^—18 esu, and the N₂ quadrupole, q_N2, an adjustable parameter. A second adjustable parameter, b_m, the distance of closest approach, includes the effects of all other forces. The IBM 704 was used in the calculation. Effects of varying the parameters were noted for a number of lines, and in the final calculation, which yielded the widths of all significant type B transitions up to J″=13, parameters q_N2=2.62×10^—26 esu and b_m=3.2 A which give an exact fit of the observed width of the microwave line 6_—5—5_—1, were adopted. The temperature dependence of the line width over the range 220–2400°K, and the effects of vibration‐rotation interactions were also calculated. At 300°K widths vary from 0.11115 cm^—1 atmos for 1₁—1_—1 to 0.03200 cm^—1 atoms^—1 for 14_—13—13_—13, there being a general decrease in width with increasing J, and at a given J, decreasing width with increasing τ.