Four theorems on the psychometric function

In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by [Formula: see text], where [Formula: see text] is the β of the Weibull function that fits best to the cumulative noise distribution, and [Formula: see text] depends on the transducer. We derive general expressions for [Formula: see text] and [Formula: see text], from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when [Formula: see text], [Formula: see text]. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian

Contrast and Phase Combination in Binocular Vision

BACKGROUND: How the visual system combines information from the two eyes to form a unitary binocular representation of the external world is a fundamental question in vision science that has been the focus of many psychophysical and physiological investigations. Ding & Sperling (2006) measured perceived phase of the cyclopean image, and developed a binocular combination model in which each eye exerts gain control on the other eye's signal and over the other eye's gain control. Critically, the relative phase of the monocular sine-waves plays a central role. METHODOLOGY/PRINCIPAL FINDINGS: We used the Ding-Sperling paradigm but measured both the perceived contrast and phase of cyclopean images in three hundred and eighty combinations of base contrast, interocular contrast ratio, eye origin of the probe, and interocular phase difference. We found that the perceived contrast of the cyclopean image was independent of the relative phase of the two monocular gratings, although the perceived phase depended on the relative phase and contrast ratio of the monocular images. We developed a new multi-pathway contrast-gain control model (MCM) that elaborates the Ding-Sperling binocular combination model in two ways: (1) phase and contrast of the cyclopean images are computed in separate pathways, although with shared cross-eye contrast-gain control; and (2) phase-independent local energy from the two monocular images are used in binocular contrast combination. With three free parameters, the model yielded an excellent account of data from all the experimental conditions. CONCLUSIONS/SIGNIFICANCE: Binocular phase combination depends on the relative phase and contrast ratio of the monocular images but binocular contrast combination is phase-invariant. Our findings suggest the involvement of at least two separate pathways in binocular combination

Structural Basis and Kinetics of Force-Induced Conformational Changes of an αA Domain-Containing Integrin

Integrin α(L)β₂ (lymphocyte function-associated antigen, LFA-1) bears force upon binding to its ligand intercellular adhesion molecule 1 (ICAM-1) when a leukocyte adheres to vascular endothelium or an antigen presenting cell (APC) during immune responses. The ligand binding propensity of LFA-1 is related to its conformations, which can be regulated by force. Three conformations of the LFA-1 αA domain, determined by the position of its α₇-helix, have been suggested to correspond to three different affinity states for ligand binding.The kinetics of the force-driven transitions between these conformations has not been defined and dynamically coupled to the force-dependent dissociation from ligand. Here we show, by steered molecular dynamics (SMD) simulations, that the αA domain was successively transitioned through three distinct conformations upon pulling the C-terminus of its α₇-helix. Based on these sequential transitions, we have constructed a mathematical model to describe the coupling between the αA domain conformational changes of LFA-1 and its dissociation from ICAM-1 under force. Using this model to analyze the published data on the force-induced dissociation of single LFA-1/ICAM-1 bonds, we estimated the force-dependent kinetic rates of interstate transition from the short-lived to intermediate-lived and from intermediate-lived to long-lived states. Interestingly, force increased these transition rates; hence activation of LFA-1 was accelerated by pulling it via an engaged ICAM-1.Our study defines the structural basis for mechanical regulation of the kinetics of LFA-1 αA domain conformational changes and relates these simulation results to experimental data of force-induced dissociation of single LFA-1/ICAM-1 bonds by a new mathematical model, thus provided detailed structural and kinetic characterizations for force-stabilization of LFA-1/ICAM-1 interaction