Finding the common bond: stereoacuity and the other hyperacuities.

Hyperacuity thresholds for disparity, motion displacement and relative width (widths less than 10 min arc) were measured as a function of the separation between test and reference targets for separations ranging from 18-288 min arc. All three thresholds were similar in magnitude, and showed a nearly identical rise with increasing separation. Nevertheless, eccentricity, not separation, is the variable limiting all of these thresholds. This point is underscored by the fact that relative width judgments, made by comparing the narrow widths separating two pairs of lines (test and reference widths), are equally good without the reference pair. The most precise foveal judgments of stereo and motion do require a visible reference target because the observer cannot otherwise distinguish between oculomotor "jitter" and target-driven changes in disparity or motion. At eccentricities greater than 2 deg, stereo and motion thresholds for a single unreferenced line (150 msec duration) were equal to the referenced thresholds, presumably because the oculomotor noise is less than the positional uncertainty associated with these peripheral loci.

The imprecision of stereopsis.

In comparison to lateral judgments of distance, stereoscopic judgments are not precise. Although stereoacuity thresholds for targets presented in the fixation plane can equal the best thresholds for the monocular hyperacuities, i.e. a few sec arc, the increment thresholds for disparity are substantially larger than the increment thresholds for lateral separation (width). We measured the minimum detectable change in the three-dimensional distance separating two features, one presented in the fixation plane, and the other some distance in front of it, i.e. with a significant standing disparity between the two features. For briefly-presented targets (150 msec), the Weber fraction for disparity was 10-20% over the range from 1 to 20 min arc, while the Weber fraction for width was only 2-3% under comparable conditions. The disparity thresholds were substantially improved for a longer duration target (1000 msec), but they were still a factor of two worse than the monocular width thresholds. In a related experiment, the vernier acuity for a standard vernier target was profoundly degraded by pairing the offset upper line presented to one eye with a disparate line in the other eye; the vernier threshold was elevated for disparities ranging from 3 to 30 min arc. This finding shows that the more precise monocular signals are actively suppressed in fused or partially-fused stereoscopic images.

Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination.

Current models of spatial frequency (SF) and orientation discrimination are based on contrast discrimination data. In these "error propagation" models, the precision of all discrimination tasks is limited by "peripheral" noise in contrast-sensitive channels. Therefore, all discrimination thresholds should be proportional to the contrast Weber fraction delta c/c. To test this prediction, increment thresholds were measured for contrast, SF, orientation and temporal frequency (TF) for contrasts ranging from 2 to 50%. All measurements used the same stimuli, procedures and observers. For contrasts of 2% and higher, the contrast discrimination threshold delta c rises with approximately the 0.6 power of contrast, while SF and TF discrimination are independent of contrast. Furthermore, orientation discrimination is nearly independent of contrast at a SF of 4 cpd. No error-propagation model can explain these results. Therefore, SF and TF discrimination, and orientation discrimination at 4 cpd are limited by contrast-independent central noise.

Coherence determines speed discrimination.

The visual system must determine which elements in a scene to regard as parts of a single object and which to regard as different objects. We can create stimuli that are ambiguous, ie consistent with more than one interpretation, and ask in what situations the stimulus elements are interpreted as part of a single object and when they are interpreted as multiple objects. The ambiguous stimuli in this study were moving plaid patterns--the sum of two drifting gratings with different orientations. Observers may see a rigid coherent plaid object moving in one direction, or may see two gratings moving in different directions sliding over one another. When the gratings have similar contrasts they appear to cohere and only the plaid speed is perceptually available; when the gratings have different contrasts they appear to slide and only the speeds of the gratings are perceived. Coherence thus determines what speed information is passed to higher stages of motion processing. A two-stage model of plaid motion perception is presented which agrees with the model proposed by Adelson and Movshon and extends it, detailing the relationship between coherence and speed discrimination.

Motion interference in speed discrimination.

Human speed discrimination can be degraded by additional stimuli in close spatial and temporal proximity to the designated test target. In these experiments, observers judged the relative asynchrony between a pair of briefly flashed dots: speed discrimination for two-dot apparent motion. The addition of two irrelevant (interfering) flashed dots to the stimulus, which produces accelerating apparent motion, impaired speed discrimination. We call this impairment motion interference; adjacent stimuli are not processed independently by the motion system. Motion interference is time selective; interfering dots simultaneous with the target dots do not impair speed discrimination, nor do interfering dots that precede or follow the target by 200 msec or more. Motion interference was observed even when the interfering dots were as far away as 1 deg from the test pair. Similar effects were observed with a smoothly moving test target and with interfering stimuli composed only of high spatial frequencies. A multiple-independent-channel model containing several parallel motion-energy detectors with different receptive-field sizes is considered and rejected. We conclude that speed discrimination depends on a time-selective combination of local motion signals from many detectors. These aggregate detectors combine information from local subunits, degrading information about acceleration.

Recombination of carbon monoxide to ferrous horseradish peroxidase types A and C.

The recombination of carbon monoxide to isoenzymes A2 and C of horseradish peroxidase (HRP) was studied as a function of temperature (2 to 320 K) and pH (5 to 8.3) with flash photolysis and infrared difference absorption. At low temperatures three geminate recombination processes are observed. One of these internal processes, denoted by I*, is exponential in time with a rate coefficient that deviates strongly from an Arrhenius behavior below 100 K, implying phonon-assisted tunneling. The two other processes, denoted by I, are non-exponential in time and related to different carbonyl isomers, as shown by the infrared difference spectra. The existence of three internal processes indicates that HRP differs considerably from myoglobin where only one internal process, I, is seen. Moreover, the internal processes in HRP are faster than process I in myoglobin. At 300 K, only one recombination process from the solvent is observed and it is very slow (lambda s approximately 1 s-1 at 1 atm CO (1 atm = 101,325 Pa)), much slower than the corresponding association process in myoglobin. Since process I is fast, but binding from the solvent is slow, the barrier at the heme cannot be responsible for the small association rate. The infrared absorption difference spectra of the amide I/II bands indicate that photolysis and recombination trigger a two-step structural change. The slow recombination rate at 300 K can thus be explained by the large Gibbs energy of the conformational transition that is necessary to let CO move into the heme pocket. The partition coefficient for the CO in the heme pocket and the solvent is extremely small, while bond formation with the heme iron occurs in less than 100 nanoseconds.

Protein states and proteinquakes.

After photodissociation of carbon monoxide bound to myoglobin, the protein relaxes to the deoxy equilibrium structure in a quake-like motion. Investigation of the proteinquake and of related intramolecular equilibrium motions shows that states and motions have a hierarchical glass-like structure.

Dynamics of dioxygen and carbon monoxide binding to soybean leghemoglobin.

The association of dioxygen and carbon monoxide to soybean leghemoglobin (Lb) has been studied by laser flash photolysis at temperatures from 10 to 320 K and times from 50 ns to 100 s. Infrared spectra of the bound and the photodissociated state were investigated between 10 and 20 K. The general features of the binding process in leghemoglobin are similar to the ones found in myoglobin. Below about 200 K, the photodissociated ligands stay in the heme pocket and rebinding is not exponential in time, implying a distributed enthalpy barrier between pocket and heme. At around 300 K, ligands migrate from the solvent through the protein to the heme pocket, and a steady state is set up between the ligands in the solvent and in the heme pocket. The association rate, lambda on, is mainly controlled by the final binding step at the heme, the bond formation with the heme iron. Differences between Lb and other heme proteins show up in the details of the various steps. The faster association rate in Lb compared to sperm whale myoglobin (Mb) is due to a faster bond formation. The migration from the solvent to the heme pocket is much faster in Lb than in Mb. The low-temperature binding (B----A) and the infrared spectra of CO in the bound state A and the photodissociated state B are essentially solvent-independent in Mb, but depend strongly on solvent in Lb. These features can be correlated with the x-ray structure.

Comparison of the magnetic properties of deoxy- and photodissociated myoglobin.

The magnetic susceptibility of photodissociated carbon monoxy myoglobin has been measured over the temperature range from 1.7 to 25 K at 10 and 50 kG with a superconducting susceptometer. The spin and the crystal field parameters of the iron ion were extracted by a spin Hamiltonian approach. Under equivalent conditions the magnetic susceptibility of deoxy myoglobin was measured. In both experiments the CO-bound protein was used as a diamagnetic reference. Above about 5 K the metastable photolysed state and the equilibrium deoxy form of myoglobin are magnetically indistinguishable and can be fitted with S = 2 and g = 2. The transition from spin 0 to spin 2 and the conformational changes known to accompany the electronic change thus also occur after photolysis at low temperature. At temperatures below 5 K, differences become apparent, indicating a somewhat smaller zero-field splitting in the photoproduct as compared to the ligand-free state at equilibrium. In qualitative agreement with observations made by other techniques, the data imply that even at 1.7 K substantial structural relaxation occurs in the heme region of myoglobin after photodissociation. The results are important for the interpretation of the ligand binding kinetics after flash photolysis at low temperature and contribute to the understanding of the relationship between electronic structure and function in heme proteins.

Control and pH dependence of ligand binding to heme proteins.

The recombination after flash photolysis of dioxygen and carbon monoxide with sperm whale myoglobin (Mb), and separated beta chains of human hemoglobin (beta A) and hemoglobin Zürich (beta ZH), has been studied as a function of pH and temperature from 300 to 60 K. At physiological temperatures, a preequilibrium is established between the ligand molecules in the solvent and in the heme pocket. The ligand in the pocket binds to the heme iron by overcoming a barrier at the heme. The association rate is controlled by this final binding step. The association rate of CO to Mb and beta A is modulated by a single titratable group with a pK at 300 K of 5.7. The binding of CO to beta ZH, in which the distal histidine is replaced by arginine, does not depend on pH. Oxygen recombination is independent of pH in all three proteins. Comparison of the binding of CO at 300 K and at low temperatures shows that pH does not affect the preequilibrium but changes the barrier height at the heme. The pH dependence and the difference between O2 and CO binding can be explained by a charge-dipole interaction between the distal histidine and CO.

Infrared spectroscopy of photodissociated carboxymyoglobin at low temperatures.

We have studied the infrared spectra of the bound and photodissociated states of Mb-12CO and Mb-13CO from 5.2 to 300 K. The absorbance peaks seen between 1800 and 2200 cm-1 correspond to CO stretching vibrations. In the bound state of Mb-12CO, the known lines A0 at 1969, A1 at 1945, and A2 at 1927 cm-1, have center frequencies, widths, and absorbances that are independent of temperature between 5.2 and 160 K. Above 160 K, A2 gradually shifts to 1933 cm-1. The low-temperature photodissociated state (Mb) shows three lines (B0, B1, B2) at 2144, 2131, and 2119 cm-1 for 12CO. The absorbances of the three lines depend on temperature. B0 is tentatively assigned to free CO in the heme pocket and B1 and B2, to CO weakly bound to the heme or heme pocket wall. The data are consistent with a model in which photodissociation of MbCO leads to B1 and B2. B2 decays thermally to B1 above 13 K; rebinding to A occurs from B1. The barriers between B2 and B1 and between B1 and A are described by activation enthalpy spectra. Heme and the central metal atom in state Mb have near-infrared, EPR, and Mössbauer spectra that differ slightly from those of deoxyMb. The observation of essentially free CO in state B implies that the difference between Mb and deoxyMb is not due to an interaction of the flashed-off ligand with the protein but is caused by an incomplete relaxation of the protein structure at low temperatures.