A comparison of fixed-step-size and Bayesian staircases for sensory threshold estimation

Fixed-step-size (FSS) and Bayesian staircases are widely used methods to estimate sensory thresholds in 2AFC tasks, although a direct comparison of both types of procedure under identical conditions has not previously been reported. A simulation study and an empirical test were conducted to compare the performance of optimized Bayesian staircases with that of four optimized variants of FSS staircase differing as to up-down rule. The ultimate goal was to determine whether FSS or Bayesian staircases are the best choice in experimental psychophysics. The comparison considered the properties of the estimates (i.e. bias and standard errors) in relation to their cost (i.e. the number of trials to completion). The simulation study showed that mean estimates of Bayesian and FSS staircases are dependable when sufficient trials are given and that, in both cases, the standard deviation (SD) of the estimates decreases with number of trials, although the SD of Bayesian estimates is always lower than that of FSS estimates (and thus, Bayesian staircases are more efficient). The empirical test did not support these conclusions, as (1) neither procedure rendered estimates converging on some value, (2) standard deviations did not follow the expected pattern of decrease with number of trials, and (3) both procedures appeared to be equally efficient. Potential factors explaining the discrepancies between simulation and empirical results are commented upon and, all things considered, a sensible recommendation is for psychophysicists to run no fewer than 18 and no more than 30 reversals of an FSS staircase implementing the 1-up/3-down rule.

Kinetic modeling of molecular motors: pause model and parameter determination from single-molecule experiments

Single-molecule manipulation experiments of molecular motors provide essential information about the rate and conformational changes of the steps of the reaction located along the manipulation coordinate. This information is not always sufficient to define a particular kinetic cycle. Recent single-molecule experiments with optical tweezers showed that the DNA unwinding activity of a Phi29 DNA polymerase mutant presents a complex pause behavior, which includes short and long pauses. Here we show that different kinetic models, considering different connections between the active and the pause states, can explain the experimental pause behavior. Both the two independent pause model and the two connected pause model are able to describe the pause behavior of a mutated Phi29 DNA polymerase observed in an optical tweezers single-molecule experiment. For the two independent pause model all parameters are fixed by the observed data, while for the more general two connected pause model there is a range of values of the parameters compatible with the observed data (which can be expressed in terms of two of the rates and their force dependencies). This general model includes models with indirect entry and exit to the long-pause state, and also models with cycling in both directions. Additionally, assuming that detailed balance is verified, which forbids cycling, this reduces the ranges of the values of the parameters (which can then be expressed in terms of one rate and its force dependency). The resulting model interpolates between the independent pause model and the indirect entry and exit to the long-pause state model