Hyers–Ulam stability of functional equations with a square-symmetric operation

The stability of the functional equation f(x ○ y) = H(f(x), f(y)) (x, y ∈ S) is investigated, where H is a homogeneous function and ○ is a square-symmetric operation on the set S. The results presented include and generalize the classical theorem of Hyers obtained in 1941 on the stability of the Cauchy functional equation.

Random circular permutation of genes and expressed polypeptide chains: application of the method to the catalytic chains of aspartate transcarbamoylase.

Recent studies on proteins whose N and C termini are in close proximity have demonstrated that folding of polypeptide chains and assembly of oligomers can be accomplished with circularly permuted chains. As yet no methodical study has been conducted to determine how extensively new termini can be introduced and where such termini cannot be tolerated. We have devised a procedure to generate random circular permutations of the catalytic chains of Escherichia coli aspartate transcarbamoylase (ATCase; EC 2.1.3.2) and to select clones that produce active or stable holoenzyme containing permuted chains. A tandem gene construct was made, based on the desired linkage between amino acid residues in the C- and N-terminal regions of the polypeptide chain, and this DNA was treated with a suitable restriction enzyme to yield a fragment containing the rearranged coding sequence for the chain. Circularization achieved with DNA ligase, followed by linearization at random with DNase I, and incorporation of the linearized, repaired, blunt-ended, rearranged genes into a suitable plasmid permitted the expression of randomly permuted polypeptide chains. The plasmid with appropriate stop codons also contained pyrI, the gene encoding the regulatory chain of ATCase. Colonies expressing detectable amounts of ATCase-like molecules containing permuted catalytic chains were identified by an immunoblot technique or by their ability to grow in the absence of pyrimidines in the growth medium. Sequencing of positive clones revealed a variety of novel circular permutations. Some had N and C termini within helices of the wild-type enzyme as well as deletions and insertions. Permutations were concentrated in the C-terminal domain and only few were detected in the N-terminal domain. The technique, which is adaptable generally to proteins whose N and C termini are near each other, can be of value in relating in vivo folding of nascent, growing polypeptide chains to in vitro renaturation of complete chains and determining the role of protein sequence in folding kinetics.

Introduction of asymmetry in the naturally symmetric restriction endonuclease EcoRV to investigate intersubunit communication in the homodimeric protein.

Type II restriction endonucleases are dimers of two identical subunits that together form one binding site for the double-stranded DNA substrate. Cleavage within the palindromic recognition site occurs in the two strands of the duplex in a concerted manner, due to the action of two catalytic centers, one per subunit. To investigate how the two identical subunits of the restriction endonuclease EcoRV cooperate in binding and cleaving their substrate, heterodimeric versions of EcoRV with different amino acid substitutions in the two subunits were constructed. For this purpose, the ecorV gene was fused to the coding region for the glutathione-binding domain of the glutathione S-transferase and a His6-tag, respectively. Upon cotransformation of Escherichia coli cells with both gene fusions stable homo- and heterodimers of the EcoRV variants are produced, which can be separated and purified to homogeneity by affinity chromatography over Ni-nitrilotriacetic acid and glutathione columns. A steady-state kinetic analysis shows that the activity of a heterodimeric variant with one inactive catalytic center is decreased by 2-fold, demonstrating that the two catalytic centers operate independently from each other. In contrast, heterodimeric variants with a defect in one DNA-binding site have a 30- to 50-fold lower activity, indicating that the two subunits of EcoRV cooperate in the recognition of the palindromic DNA sequence. By combining a subunit with an inactive catalytic center with a subunit with a defect in the DNA-binding site, EcoRV heterodimers were produced that only nick DNA specifically within the EcoRV recognition sequence.

The protein-folding activity of chaperonins correlates with the symmetric GroEL14(GroES7)2 heterooligomer.

Chaperonins GroEL and GroES form, in the presence of ATP, two types of heterooligomers in solution: an asymmetric GroEL14GroES7 "bullet"-shaped particle and a symmetric GroEL14(GroES7)2 "football"-shaped particle. Under limiting concentrations of ATP or GroES, excess ADP, or in the presence of 5'-adenylyl imidodiphosphate, a correlation is seen between protein folding and the amount of symmetric GroEL14(GroES7)2 particles in a chaperonin solution, as detected by electron microscopy or by chemical crosslinking. Kinetic analysis suggests that protein folding is more efficient when carried out by a chaperonin solution populated with a majority of symmetric GroEL14(GroES7)2 particles than by a majority of asymmetric GroEL14GroES7 particles. The symmetric heterooligomer behaves as a highly efficient intermediate of the chaperonin protein folding cycle in vitro.

Bidirectional motion observed in the compact symmetric object 1946+708.

We present the first direct measurements of bidirectional motions in an extragalactic radio jet. The radio source 1946+708 is a compact symmetric object with striking S-symmetry identified with a galaxy at a redshift of 0.101. From observations 2 years apart we have determined the velocities of four compact components in the jet, the fastest of which has an apparent velocity of 1.09 h-1c. By pairing up the components, assuming they were simultaneously ejected in opposite directions, we derive a 1 lower limit on the Hubble constant, H0 > 42 km.s-1.Mpc-1.