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.

From snapshot to movie: φ analysis of protein folding transition states taken one step further

Kinetic anomalies in protein folding can result from changes of the kinetic ground states (D, I, and N), changes of the protein folding transition state, or both. The 102-residue protein U1A has a symmetrically curved chevron plot which seems to result mainly from changes of the transition state. At low concentrations of denaturant the transition state occurs early in the folding reaction, whereas at high denaturant concentration it moves close to the native structure. In this study we use this movement to follow continuously the formation and growth of U1A's folding nucleus by φ analysis. Although U1A's transition state structure is generally delocalized and displays a typical nucleation–condensation pattern, we can still resolve a sequence of folding events. However, these events are sufficiently coupled to start almost simultaneously throughout the transition state structure.

Chemically distinct transition states govern rapid dissociation of single L-selectin bonds under force

Carbohydrate–protein bonds interrupt the rapid flow of leukocytes in the circulation by initiation of rolling and tethering at vessel walls. The cell surface carbohydrate ligands are glycosylated proteins like the mucin P-selectin glycoprotein ligand-1 (PSGL-1), which bind ubiquitously to the family of E-, P-, and L-selectin proteins in membranes of leukocytes and endothelium. The current view is that carbohydrate–selectin bonds dissociate a few times per second, and the unbinding rate increases weakly with force. However, such studies have provided little insight into how numerous hydrogen bonds, a Ca2+ metal ion bond, and other interactions contribute to the mechanical strength of these attachments. Decorating a force probe with very dilute ligands and controlling touch to achieve rare single-bond events, we have varied the unbinding rates of carbohydrate–selectin bonds by detachment with ramps of force/time from 10 to 100,000 pN/sec. Testing PSGL-1, its outer 19 aa (19FT), and sialyl LewisX (sLeX) against L-selectin in vitro on glass microspheres and in situ on neutrophils, we found that the unbinding rates followed the same dependence on force and increased by nearly 1,000-fold as rupture forces rose from a few to ≈200 pN. Plotted on a logarithmic scale of loading rate, the rupture forces reveal two prominent energy barriers along the unbinding pathway. Strengths above 75 pN arise from rapid detachment (<0.01 sec) impeded by an inner barrier that requires a Ca2+ bond between a single sLeX and the lectin domain. Strengths below 75 pN occur under slow detachment (>0.01 sec) impeded by the outer barrier, which appears to involve an array of weak (putatively hydrogen) bonds.

Income distribution, socioeconomic status, and self rated health in the United States: multilevel analysis

Objective: To determine the effect of inequalities in income within a state on self rated health status while controlling for individual characteristics such as socioeconomic status.

Molecular dynamics of a grid-mounted molecular dipolar rotor in a rotating electric field

Classical molecular dynamics is applied to the rotation of a dipolar molecular rotor mounted on a square grid and driven by rotating electric field E(ν) at T ≃ 150 K. The rotor is a complex of Re with two substituted o-phenanthrolines, one positively and one negatively charged, attached to an axial position of Rh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{4+}}}\end{equation*}\end{document} in a [2]staffanedicarboxylate grid through 2-(3-cyanobicyclo[1.1.1]pent-1-yl)malonic dialdehyde. Four regimes are characterized by a, the average lag per turn: (i) synchronous (a < 1/e) at E(ν) = |E(ν)| > Ec(ν) [Ec(ν) is the critical field strength], (ii) asynchronous (1/e < a < 1) at Ec(ν) > E(ν) > Ebo(ν) > kT/μ, [Ebo(ν) is the break-off field strength], (iii) random driven (a ≃ 1) at Ebo(ν) > E(ν) > kT/μ, and (iv) random thermal (a ≃ 1) at kT/μ > E(ν). A fifth regime, (v) strongly hindered, W > kT, Eμ, (W is the rotational barrier), has not been examined. We find Ebo(ν)/kVcm−1 ≃ (kT/μ)/kVcm−1 + 0.13(ν/GHz)1.9 and Ec(ν)/kVcm−1 ≃ (2.3kT/μ)/kVcm−1 + 0.87(ν/GHz)1.6. For ν > 40 GHz, the rotor behaves as a macroscopic body with a friction constant proportional to frequency, η/eVps ≃ 1.14 ν/THz, and for ν < 20 GHz, it exhibits a uniquely molecular behavior.

Changes in the prevalence of chronic disability in the United States black and nonblack population above age 65 from 1982 to 1999

Survey evidence through the early 1990s generally suggests a reduction in disability in the elderly population of the United States. Because the evidence is not fully consistent, several authors have speculated about whether disability declines will continue. This paper reports results from the 1999 National Long-Term Care Survey on disability trends from 1982 through 1999. It is found that disability continued to decline in the 1994 to 1999 period, and that the decline was greater in the 1990s than in the 1980s. The disability decline from 1982 to 1989 was 0.26% per year, from 1989 to 1994 it was 0.38% per year, and from 1994 to 1999 it was 0.56% per year. In addition, disability declined by a greater percentage for blacks than for nonblacks over the 1989 to 1999 period.

Trends and patterns in research and development expenditures in the United States

This paper is a review of recent trends in United States expenditures on research and development (R&D). Real expenditures by both the government and the private sector increased rapidly between the mid-1970s and the mid-1980s, and have since leveled off. This is true of both overall expenditures and expenditures on basic research, as well as funding of academic research. Preliminary estimates indicate that about $170 billion was spent on R&D in the United States in 1995, with ≈60% of that funding coming from the private sector and about 35% from the federal government. In comparison to other countries, we have historically spent more on R&D relative to our economy than other advanced economies, but this advantage appears to be disappearing. If defense-related R&D is excluded, our expenditures relative to the size of the economy are considerably smaller than those of other similar economies.

Evidence for a circulating islet cell growth factor in insulin-resistant states

Insulin resistance is a feature of many common disorders including obesity and type 2 diabetes mellitus. In these disorders, the β-cells compensate for the insulin resistance for long periods of time with an increase in secretory capacity, an increase in β-cell mass, or both. To determine whether the β-cell response might relate to a circulating growth factor, we have transplanted normal islets under the kidney capsule of normoglycemic insulin-resistant mice with two different models of insulin resistance: lean mice that have a double heterozygous deletion of the insulin receptor and insulin receptor substrate-1 (DH) or the obese, hyperglycemic ob/ob mice. In the grafts transplanted into both hosts, there was a marked increase in β-cell mitotic activity and islet mass that was comparable with that observed in the endogenous pancreas. By contrast, islets of the DH mouse transplanted into normal mice showed reduced mitotic index. These data suggest the insulin resistance is associated with a circulating islet cell growth factor that is independent of glucose and obesity.