Laser-induced transient grating analysis of dynamics of interaction between sensory rhodopsin II D75N and the HtrII transducer.

The interaction between sensory rhodopsin II (SRII) and its transducer HtrII was studied by the time-resolved laser-induced transient grating method using the D75N mutant of SRII, which exhibits minimal visible light absorption changes during its photocycle, but mediates normal phototaxis responses. Flash-induced transient absorption spectra of transducer-free D75N and D75N joined to 120 amino-acid residues of the N-terminal part of the SRII transducer protein HtrII (DeltaHtrII) showed only one spectrally distinct K-like intermediate in their photocycles, but the transient grating method resolved four intermediates (K(1)-K(4)) distinct in their volumes. D75N bound to HtrII exhibited one additional slower kinetic species, which persists after complete recovery of the initial state as assessed by absorption changes in the UV-visible region. The kinetics indicate a conformationally changed form of the transducer portion (designated Tr*), which persists after the photoreceptor returns to the unphotolyzed state. The largest conformational change in the DeltaHtrII portion was found to cause a DeltaHtrII-dependent increase in volume rising in 8 micros in the K(4) state and a drastic decrease in the diffusion coefficient (D) of K(4) relatively to those of the unphotolyzed state and Tr*. The magnitude of the decrease in D indicates a large structural change, presumably in the solvent-exposed HAMP domain of DeltaHtrII, where rearrangement of interacting molecules in the solvent would substantially change friction between the protein and the solvent.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^