The origin of orientation selectivity in visual cortical responses is a central problem for understanding cerebral cortical circuitry. In cats, many experiments suggest that orientation selectivity arises from the arrangement of lateral geniculate nucleus (LGN) afferents to layer 4 simple cells. However, this explanation is not sufficient to account for the contrast invariance of orientation tuning. To understand contrast invariance, we first characterize the input to cat simple cells generated by the oriented arrangement of LGN afferents. We demonstrate that it has two components: a spatial-phase-specific component (i.e., one that depends on receptive field spatial phase), which is tuned for orientation, and a phase-nonspecific component, which is untuned. Both components grow with contrast. Second, we show that a correlation-based intracortical circuit, in which connectivity between cell pairs is determined by the correlation of their LGN inputs, is sufficient to achieve well tuned, contrast-invariant orientation tuning. This circuit generates both spatially opponent, "antiphase" inhibition ("push-pull"), and spatially matched, "same-phase" excitation. The inhibition, if sufficiently strong, suppresses the untuned input component and sharpens responses to the tuned component at all contrasts. The excitation amplifies tuned responses. This circuit agrees with experimental evidence showing spatial opponency between, and similar orientation tuning of, the excitatory and inhibitory inputs received by a simple cell. Orientation tuning is primarily input driven, accounting for the observed invariance of tuning width after removal of intracortical synaptic input, as well as for the dependence of orientation tuning on stimulus spatial frequency. The model differs from previous push-pull models in requiring dominant rather than balanced inhibition and in predicting that a population of layer 4 inhibitory neurons should respond in a contrast-dependent manner to stimuli of all orientations, although their tuning width may be similar to that of excitatory neurons. The model demonstrates that fundamental response properties of cortical layer 4 can be explained by circuitry expected to develop under correlation-based rules of synaptic plasticity, and shows how such circuitry allows the cortex to distinguish stimulus intensity from stimulus form.

An improved protocol for crystallographic refinement by simulated annealing is presented. It consists of slow cooling starting at high temperatures. Tests of refinements of aspartate aminotransferase and porcin pepsin show that the slow-cooling protocol produces lower R factors and better geometry than other protocols previously published. The influence of the temperature-control method, weighting, cooling rate and duration of the heating stage on the success of the slow-cooling protocol is studied. Analysis of the time course of the potential-energy fluctuations indicates no global changes in the state of order of the system. Fluctuations of the potential energy are interpreted as localized conformational changes during the course of the refinement. AbbreviationsCPU, central processing unit; mAATase, K258A mutant of aspartate aminotransferase; M I R, multiple isomorphous replacement; r.m.s., root-mean-square; SA refinement, crystallographic refinement by simulated annealing with molecular dynamics.

It is well established that perceptual direction discrimination shows an oblique effect; thresholds are higher for motion along diagonal directions than for motion along cardinal directions. Here, we compare simultaneous direction judgments and pursuit responses for the same motion stimuli and find that both pursuit and perceptual thresholds show similar anisotropies. The pursuit oblique effect is robust under a wide range of experimental manipulations, being largely resistant to changes in trajectory (radial versus tangential motion), speed (10 versus 25 deg/s), directional uncertainty (blocked versus randomly interleaved), and cognitive state (tracking alone versus concurrent tracking and perceptual tasks). Our data show that the pursuit oblique effect is caused by an effective expansion of direction space surrounding the cardinal directions and the requisite compression of space for other directions. This expansion suggests that the directions around the cardinal directions are in some way overrepresented in the visual cortical pathways that drive both smooth pursuit and perception.

Cells in cerebral cortex fail to respond to fast-moving stimuli that evoke strong responses in the thalamic nuclei innervating the cortex. The reason for this behavior has remained a mystery. We study an experimentally motivated model of the thalamic input-recipient layer of cat primary visual cortex that accounts for many aspects of cortical orientation tuning. In this circuit, inhibition dominates over excitation, but temporal modulations of excitation and inhibition occur out of phase with one another, allowing excitation to transiently drive cells. We show that this circuit provides a natural explanation of cortical low-pass temporal frequency tuning, provided N-methyl-D-aspartate (NMDA) receptors are present in thalamocortical synapses in proportions measured experimentally. This suggests a new and unanticipated role for NMDA conductances in shaping the temporal response properties of cortical cells, and suggests that common cortical circuit mechanisms underlie both spatial and temporal response tuning.

We develop a new analysis of the lateral geniculate nucleus (LGN) input to a cortical simple cell, demonstrating that this input is the sum of two terms, a linear term and a nonlinear term. In response to a drifting grating, the linear term represents the temporal modulation of input, and the nonlinear term represents the mean input. The nonlinear term, which grows with stimulus contrast, has been neglected in many previous models of simple cell response. We then analyze two scenarios by which contrast-invariance of orientation tuning may arise. In the first scenario, at larger contrasts, the nonlinear part of the LGN input, in combination with strong push-pull inhibition, counteracts the nonlinear effects of cortical spike threshold, giving the result that orientation tuning scales with contrast. In the second scenario, at low contrasts, the nonlinear component of LGN input is negligible, and noise smooths the nonlinearity of spike threshold so that the input-output function approximates a power-law function. These scenarios can be combined to yield contrast-invariant tuning over the full range of stimulus contrast. The model clarifies the contribution of LGN nonlinearities to the orientation tuning of simple cells and demonstrates how these nonlinearities may impact different models of contrast-invariant tuning.

It has long been known that ocular pursuit of a moving target has a major influence on its perceived speed (Aubert, 1886; Fleischl, 1882). However, little is known about the effect of smooth pursuit on the perception of target direction. Here we compare the precision of human visual-direction judgments under two oculomotor conditions (pursuit vs. fixation). We also examine the impact of stimulus duration (200 ms vs. ~800 ms) and absolute direction (cardinal vs. oblique). Our main finding is that direction discrimination thresholds in the fixation and pursuit conditions are indistinguishable. Furthermore, the two oculomotor conditions showed oblique effects of similar magnitudes. These data suggest that the neural direction signals supporting perception are the same with or without pursuit, despite remarkably different retinal stimulation. During fixation, the stimulus information is restricted to large, purely peripheral retinal motion, while during steady-state pursuit, the stimulus information consists of small, unreliable foveal retinal motion and a large efference-copy signal. A parsimonious explanation of our findings is that the signal limiting the precision of direction judgments is a neural estimate of target motion in head-centered (or world-centered) coordinates (i.e., a combined retinal and eye motion signal) as found in the medial superior temporal area (MST), and not simply an estimate of retinal motion as found in the middle temporal area (MT).

For the theoretical modeling of physical transformations such as boiling, freezing, glassification, or mixing, it is necessary to know how the partition function of a system depends on its density. Many current treatments rely either on low density expansions or they apply to very simple and symmetric molecular shapes, like spheres or rods. Here we develop an exact analytical lattice theory of materials and mixtures that applies to arbitrarily complex molecular shapes over the full range of densities from gas to crystal. The approach is to compute partition functions for small numbers of shapes and to explore the dependence on density by varying the volume of the system. Recently a question has been raised about whether entropies of dissolution are better treated using classical solvation theories or Flory–Huggins theory. We explore this for a range of molecular sizes and shapes, from lattice squares and cubes, to rods, polymers, crosses, and other shapes. Beyond low densities, the entropic component of the chemical potential depends on shape due to the different degrees to which molecules ‘‘interfere’’ with each other. We find that neither Flory–Huggins nor classical solvation theories is correct for all shapes. Molecules that are ‘‘articulated’’ are remarkably well treated by Flory–Huggins theory, over all densities, but globular molecules are qualitatively and quantitatively different, and are better treated by the classical chemical potential, consistent with experiments of Shinoda and Hildebrand. These results confirm that the Flory–Huggins theory differs from classical theory not because of molecular size differences per se; it accounts for the coupling between translations and conformational steric interference.

The crystallographic phase problem is indeterminate in the absence of additional chemical information. A successful ab initio approach to the macromolecular phase problem must employ sufficient chemical constraints to limit the solutions to a manageably small number. Here we show that commonly employed chemical constraints - positivity, atomicity and a solvent boundary - leave the phase problem greatly underdetermined for Fourier data sets of moderate (2.5-3.0 A) resolution. Entropy maximization is also beset by multiple false solutions: electron-density maps are readily generated which satisfy the same Fourier amplitude constraints but have higher entropies than the true solution. We conclude that a successful ab initio approach must make use of high-resolution Fourier data and/or stronger chemical constraints. One such constraint is the connectivity of the macromolecule. We describe a rapid algorithm for measuring the connectivity of a map, and show its utility in reducing the multiplicity of solutions to the phase problem.