Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

How a reacting system climbs through a transition state during the course of a reaction has been an intriguing subject for decades. Here we present and quantify a technique to identify and characterize local invariances about the transition state of an N-particle Hamiltonian system, using Lie canonical perturbation theory combined with microcanonical molecular dynamics simulation. We show that at least three distinct energy regimes of dynamical behavior occur in the region of the transition state, distinguished by the extent of their local dynamical invariance and regularity. Isomerization of a six-atom Lennard–Jones cluster illustrates this: up to energies high enough to make the system manifestly chaotic, approximate invariants of motion associated with a reaction coordinate in phase space imply a many-body dividing hypersurface in phase space that is free of recrossings even in a sea of chaos. The method makes it possible to visualize the stable and unstable invariant manifolds leading to and from the transition state, i.e., the reaction path in phase space, and how this regularity turns to chaos with increasing total energy of the system. This, in turn, illuminates a new type of phase space bottleneck in the region of a transition state that emerges as the total energy and mode coupling increase, which keeps a reacting system increasingly trapped in that region.

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.

Phase identity of the maize leaf is determined after leaf initiation

The vegetative development of the maize shoot can be divided into juvenile and adult phases based on the types of leaves produced at different times in shoot development. Models for the regulation of phase change make explicit predictions about when the identity of these types of leaves is determined. To test these models, we examined the timing of leaf type determination in maize. Clones induced in transition leaf primordia demonstrated that the juvenile and adult regions of these leaves do not become clonally distinct until after the primordium is 700 μm in length, implying that these cell fates were undetermined at this stage of leaf development. Adult shoot apices were cultured in vitro to induce rejuvenation. We found that leaf primordia as large as 3 mm in length can be at least partially rejuvenated by this treatment, and the location of rejuvenated tissue is correlated with the maturation pattern of the leaf. The amount and distribution of juvenile tissue in rejuvenated leaves suggests that rejuvenation occurs nearly simultaneously in all leaf primordia. In vitro culture rejuvenated existing leaf primordia and the P0 primordium, but did not change the identity of subsequent primordia or the total number of leaves produced by the shoot. This result suggests that leaf identity can be regulated independently of the identity of the shoot apical meristem, and it implies that vegetative phase change is not initiated by a change in the identity of the shoot apical meristem.