Amplification of the DFR1 gene in Saccaromyces cerevisiae

A new system was employed to study amplification of t,he DHF'R gene DFB,1 ) in Sa<,:;charoillYCB§. .Q~~Yi...S!i<;1~. . This system consists of a series of yeast strains containing a casset,te which encodes t he yeast, D..ERl gene ttghtly linked tjO a f usion of the yeast 1EU2. regulat,ory region wi tJ1 the LAQZ str ctural gene from E. cO.1-1 (,) . M. Clement , unpubl i,::;hed) . Th's casset;t e was shown t.o be integrat,ed int o a unj que chromosomal l ocati on in each strain . Yeast cells were se l ected for MTX-resistance and overproduction of ~ galac t osi d se ( B-gal ). Since the inserted DF'Rl and ~ACZ genes are independently regulated, it was thought that cel l s with this phenotype probably contain e d ampl if ications of the cassette. A lar ge variat ion in the f requn y o f MTX-resistance was found between the di ff e r ent str ains. These freqlen c ~ es r anged from about 2 x 10 - 7 fo r a population of cells containing the cassette integrated at, the BI J2.l gene in t,he middle of the long arm of chromosome V, to about 5 x 10-4 for a strain with the cassette i nserted in the r DNA cluster Abo It 85% of the MTX- res i stcmt iso l ates examined showed enhanced B·-gal act i v ity rel a t ive t o the parental strain . For the ma jorit y of strains, the mean B- gal activity in drug-r sistant clones was about 3 times that o f the parent following a single se l ect i on step . I n con t r ast, primary MTX-resistant derivat~ves of cells with the cassette inserted 3 at the rDNA cluster showed inc r eases in B- gal activity ranging from 9 - 14 f old r elative to the parent. Analysis of the latte r s train by Southe rn hybr idization indicated that the cassette was inde e d amplified several fold in MTX-re sistant derivatives. A sing l e strain, in which the cassette was inserted at the !lEA;], loc u.s , was used to examine in more detai 1 , the parameters affecting DFRl gene amplificat~ion in yeast . The mean B- gal activity in drug-resistant derivatives of this strain could be increased from 3 to 6 or 7 fold relative to the parent, by stepwise sel ection using increasing MTX concentrations. B-gal overproduction was found to be un stable in all primary and highly -resistant isolates examined. There was no indication, h owever, of a decrease i n growth r a t e in MTX-res i s tant cells which overproduced B - gal.

Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.