The photoisomerization of retinal in bacteriorhodopsin: Experimental evidence for a three-state model

The primary events in the all-trans to 13-cis photoisomerization of retinal in bacteriorhodopsin have been investigated with femtosecond time-resolved absorbance spectroscopy. Spectra measured over a broad range extending from 7000 to 22,400 cm−1 reveal features whose dynamics are inconsistent with a model proposed earlier to account for the highly efficient photoisomerization process. Emerging from this work is a new three-state model. Photoexcitation of retinal with visible light accesses a shallow well on the excited state potential energy surface. This well is bounded by a small barrier, arising from an avoided crossing that separates the Franck–Condon region from the nearby reactive region of the photoisomerization coordinate. At ambient temperatures, the reactive region is accessed with a time constant of ≈500 fs, whereupon the retinal rapidly twists and encounters a second avoided crossing region. The protein mediates the passage into the second avoided crossing region and thereby exerts control over the quantum yield for forming 13-cis retinal. The driving force for photoisomerization resides in the retinal, not in the surrounding protein. This view contrasts with an earlier model where photoexcitation was thought to access directly a reactive region of the excited-state potential and thereby drive the retinal to a twisted conformation within 100–200 fs.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Simple model of protein folding kinetics.

A simple model of the kinetics of protein folding is presented. The reaction coordinate is the "correctness" of a configuration compared with the native state. The model has a gap in the energy spectrum, a large configurational entropy, a free energy barrier between folded and partially folded states, and a good thermodynamic folding transition. Folding kinetics is described by a master equation. The folding time is estimated by means of a local thermodynamic equilibrium assumption and then is calculated both numerically and analytically by solving the master equation. The folding time has a maximum near the folding transition temperature and can have a minimum at a lower temperature.

Population regulation in snowshoe hare and Canadian lynx: Asymmetric food web configurations between hare and lynx

The snowshoe hare and the Canadian lynx in the boreal forests of North America show 9- to 11-year density cycles. These are generally assumed to be linked to each other because lynx are specialist predators on hares. Based on time series data for hare and lynx, we show that the dominant dimensional structure of the hare series appears to be three whereas that of the lynx is two. The three-dimensional structure of the hare time series is hypothesized to be due to a three-trophic level model in which the hare may be seen as simultaneously regulated from below and above. The plant species in the hare diet appear compensatory to one another, and the predator species may, likewise, be seen as an internally compensatory guild. The lynx time series are, in contrast, consistent with a model of donor control in which their populations are regulated from below by prey availability. Thus our analysis suggests that the classic view of a symmetric hare–lynx interaction is too simplistic. Specifically, we argue that the classic food chain structure is inappropriate: the hare is influenced by many predators other than the lynx, and the lynx is primarily influenced by the snowshoe hare.

Folding thermodynamics of a model three-helix-bundle protein

The calculated folding thermodynamics of a simple off-lattice three-helix-bundle protein model under equilibrium conditions shows the experimentally observed protein transitions: a collapse transition, a disordered-to-ordered globule transition, a globule to native-state transition, and the transition from the active native state to a frozen inactive state. The cooperativity and physical origin of the various transitions are explored with a single “optimization” parameter and characterized with the Lindemann criterion for liquid versus solid-state dynamics. Below the folding temperature, the model has a simple free energy surface with a single basin near the native state; the surface is similar to that calculated from a simulation of the same three-helix-bundle protein with an all-atom representation [Boczko, E. M. & Brooks III, C. L. (1995) Science 269, 393–396].

The "allosteric three-site model" of elongation cannot be confirmed in a well-defined ribosome system from Escherichia coli.

For the functional role of the ribosomal tRNA exit (E) site, two different models have been proposed. It has been suggested that transient E-site binding of the tRNA leaving the peptidyl (P) site promotes elongation factor G (EF-G)-dependent translocation by lowering the energetic barrier of tRNA release [Lill, R., Robertson, J. M. & Wintermeyer, W. (1989) EMBO J. 8, 3933-3938]. The alternative "allosteric three-site model" [Nierhaus, K.H. (1990) Biochemistry 29, 4997-5008] features stable, codon-dependent tRNA binding to the E site and postulates a coupling between E and aminoacyl (A) sites that regulates the tRNA binding affinity of the two sites in an anticooperative manner. Extending our testing of the two conflicting models, we have performed translocation experiments with fully active ribosomes programmed with heteropolymeric mRNA. The results confirm that the deacylated tRNA released from the P site is bound to the E site in a kinetically labile fashion, and that the affinity of binding, i.e., the occupancy of the E site, is increased by Mg2+ or polyamines. At conditions of high E-site occupancy in the posttranslocation complex, filling the A site with aminoacyl-tRNA had no influence on the E site, i.e., there was no detectable anticooperative coupling between the two sites, provided that second-round translocation was avoided by removing EF-G. On the basis of these results, which are entirely consistent with our previous results, we consider the allosteric three-site model of elongation untenable. Rather, as proposed earlier, the E site-bound state of the leaving tRNA is a transient intermediate and, as such, is a mechanistic feature of the classic two-state model of the elongating ribosome.