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.

Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Performance evaluation in Bayesian adaptive randomization

Bayesian adaptive randomization (BAR) is an attractive approach to allocate more patients to the putatively superior arm based on the interim data while maintains good statistical properties attributed to randomization. Under this approach, patients are adaptively assigned to a treatment group based on the probability that the treatment is better. The basic randomization scheme can be modified by introducing a tuning parameter, replacing the posterior estimated response probability, setting a boundary to randomization probabilities. Under randomization settings comprised of the above modifications, operating characteristics, including type I error, power, sample size, imbalance of sample size, interim success rate, and overall success rate, were evaluated through simulation. All randomization settings have low and comparable type I errors. Increasing tuning parameter decreases power, but increases imbalance of sample size and interim success rate. Compared with settings using the posterior probability, settings using the estimated response rates have higher power and overall success rate, but less imbalance of sample size and lower interim success rate. Bounded settings have higher power but less imbalance of sample size than unbounded settings. All settings have better performance in the Bayesian design than in the frequentist design. This simulation study provided practical guidance on the choice of how to implement the adaptive design. ^