Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Glutamate is required to maintain the steady-state potassium pool in Salmonella typhimurium.

In many bacteria, accumulation of K+ at high external osmolalities is accompanied by accumulation of glutamate. To determine whether there is an obligatory relationship between glutamate and K+ pools, we studied mutant strains of Salmonella typhimurium with defects in glutamate synthesis. Enteric bacteria synthesize glutamate by the combined action of glutamine synthetase and glutamate synthase (GS/GOGAT cycle) or the action of biosynthetic glutamate dehydrogenase (GDH). Activity of the GS/GOGAT cycle is required under nitrogen-limiting conditions and is decreased at high external ammonium/ammonia ((NH4)+) concentrations by lowered synthesis of GS and a decrease in its catalytic activity due to covalent modification (adenylylation by GS adenylyltransferase). By contrast, GDH functions efficiently only at high external (NH4)+ concentrations, because it has a low affinity for (NH4)+. When grown at low concentrations of (NH4)+ (< or = 2 mM), mutant strains of S. typhimurium that lack GOGAT and therefore are dependent on GDH have a low glutamate pool and grow slowly; we now demonstrate that they have a low K+ pool. When subjected to a sudden (NH4)+ upshift, strains lacking GS adenylyltransferase drain their glutamate pool into glutamine and grow very slowly; we now find that they also drain their K+ pool. Restoration of the glutamate pool in these strains at late times after shift was accompanied by restoration of the K+ pool and a normal growth rate. Taken together, the results indicate that glutamate is required to maintain the steady-state K+ pool -- apparently no other anion can substitute as a counter-ion for free K+ -- and that K+ glutamate is required for optimal growth.

Visualization of intermediate and transition-state structures in protein-tyrosine phosphatase catalysis.

Engineering site-specific amino acid substitutions into the protein-tyrosine phosphatase (PTPase) PTP1 and the dual-specific vaccinia H1-related phosphatase (VHR), has kinetically isolated the two chemical steps of the reaction and provided a rare opportunity for examining transition states and directly observing the phosphoenzyme intermediate. Changing serine to alanine in the active-site sequence motif HCXXGXXRS shifted the rate-limiting step from intermediate formation to intermediate hydrolysis. Using phosphorus 31P NMR, the covalent thiol-phosphate intermediate was directly observed during catalytic turnover. The importance of the conserved aspartic acid (D92 in VHR and D181 in PTP1) in both chemical steps was established. Kinetic analysis of D92N and D181N mutants indicated that aspartic acid acts as a general acid by protonating the leaving-group phenolic oxygen. Structure-reactivity experiments with native and aspartate mutant enzymes established that proton transfer is concomitant with P-O cleavage, such that no charge develops on the phenolic oxygen. Steady- and presteady-state kinetics, as well as NMR analysis of the double mutant D92N/S131A (VHR), suggested that the conserved aspartic acid functions as a general base during intermediate hydrolysis. As a general base, aspartate would activate a water molecule to facilitate nucleophilic attack. The amino acids involved in transition-state stabilization for cysteinylphosphate hydrolysis were confirmed by the x-ray structure of the Yersinia PTPase complexed with vanadate, a transition-state mimic that binds covalently to the active-site cysteine. Consistent with the NMR, x-ray, biochemical, and kinetic data, a unifying mechanism for catalysis is proposed.