An in vivo approach to tRNA identity

A leucine-inserting tRNA has been transformed into a serine-inserting tRNA by changing 12 nucleotides. Only 8 of the 12 changes are required to effect the conversion of the leucine tRNA to serine tRNA identity. The 8 essential changes reside in basepair 11-24 in the D stem, basepairs 3-70, 2-71 and nucleotides 72 and 73, all of the acceptor stem.

Functional amber suppressor tRNA genes were generated for 14 species of tRNA in E. coli, and their amino acid specificities determined. The suppressors can be classified into three groups, based upon their specificities. Class I suppressors, tRNA^(Ala2)_(CUA), tRNA^(GlyU)_(CUA), tRNA^(HisA)_(CUA), tRNA^(Lys)_(CUA), and tRNA^(ProH)_(CUA), inserted the predicted amino acid. The Class II suppressors, tRNA^(GluA)_(CUA) , tRNA^(GlyT)_(CUA), and tRNA^(Ile1)_(CUA) were either partially or predominantly mischarged by the glutamine aminoacyl tRNA synthetase (AAS). The Class III suppressors, tRNA^(Arg)_(CUA), tRNA^(AspM)_(CUA), tRNA^(Ile2)_(CUA), tRNA^(Thr2)_(CUA), tRNA^(Met(m))_(CUA) and tRNA^(Val)_(CUA) inserted predominantly lysine.

Symmetric representation of an integral domain over a subdomain

Let F(θ) be a separable extension of degree n of a field F. Let Δ and D be integral domains with quotient fields F(θ) and F respectively. Assume that Δ ᴝ D. A mapping φ of Δ into the n x n D matrices is called a Δ/D rep if (i) it is a ring isomorphism and (ii) it maps d onto dI_n whenever d ϵ D. If the matrices are also symmetric, φ is a Δ/D symrep.

Every Δ/D rep can be extended uniquely to an F(θ)/F rep. This extension is completely determined by the image of θ. Two Δ/D reps are called equivalent if the images of θ differ by a D unimodular similarity. There is a one-to-one correspondence between classes of Δ/D reps and classes of Δ ideals having an n element basis over D.

The condition that a given Δ/D rep class contain a Δ/D symrep can be phrased in various ways. Using these formulations it is possible to (i) bound the number of symreps in a given class, (ii) count the number of symreps if F is finite, (iii) establish the existence of an F(θ)/F symrep when n is odd, F is an algebraic number field, and F(θ) is totally real if F is formally real (for n = 3 see Sapiro, “Characteristic polynomials of symmetric matrices” Sibirsk. Mat. Ž. 3 (1962) pp. 280-291), and (iv) study the case D = Z, the integers (see Taussky, “On matrix classes corresponding to an ideal and its inverse” Illinois J. Math. 1 (1957) pp. 108-113 and Faddeev, “On the characteristic equations of rational symmetric matrices” Dokl. Akad. Nauk SSSR 58 (1947) pp. 753-754).

The case D = Z and n = 2 is studied in detail. Let Δ’ be an integral domain also having quotient field F(θ) and such that Δ’ ᴝ Δ. Let φ be a Δ/Z symrep. A method is given for finding a Δ’/Z symrep ʘ such that the Δ’ ideal class corresponding to the class of ʘ is an extension to Δ’ of the Δ ideal class corresponding to the class of φ. The problem of finding all Δ/Z symreps equivalent to a given one is studied.