Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Contributions of parietal cortex to reach planning

Sensory-motor circuits course through the parietal cortex of the human and monkey brain. How parietal cortex manipulates these signals has been an important question in behavioral neuroscience. This thesis presents experiments that explore the contributions of monkey parietal cortex to sensory-motor processing, with an emphasis on the area's contributions to reaching. First, it is shown that parietal cortex is organized into subregions devoted to specific movements. Area LIP encodes plans to make saccadic eye movements. A nearby area, the parietal reach region (PRR), plans reaches. A series of experiments are then described which explore the contributions of PRR to reach planning. Reach plans are represented in an eye-centered reference frame in PRR. This representation is shown to be stable across eye movements. When a sequence of reaches is planned, only the impending movement is represented in PRR, showing that the area is more related to movement planning than to storing the memory of reach targets. PRR resembles area LIP in each of these properties: the two areas may provide a substrate for hand-eye coordination. These findings yield new perspectives on the functions of the parietal cortex and on the organization of sensory-motor processing in primate brains.

Responses to auditory stimuli in macaque lateral intraparietal area

The lateral intraparietal area (LIP) of macaque posterior parietal cortex participates in the sensorimotor transformations underlying visually guided eye movements. Area LIP has long been considered unresponsive to auditory stimulation. However, recent studies have shown that neurons in LIP respond to auditory stimuli during an auditory-saccade task, suggesting possible involvement of this area in auditory-to-oculomotor as well as visual-to-oculomotor processing. This dissertation describes investigations which clarify the role of area LIP in auditory-to-oculomotor processing.

Extracellular recordings were obtained from a total of 332 LIP neurons in two macaque monkeys, while the animals performed fixation and saccade tasks involving auditory and visual stimuli. No auditory activity was observed in area LIP before animals were trained to make saccades to auditory stimuli, but responses to auditory stimuli did emerge after auditory-saccade training. Auditory responses in area LIP after auditory-saccade training were significantly stronger in the context of an auditory-saccade task than in the context of a fixation task. Compared to visual responses, auditory responses were also significantly more predictive of movement-related activity in the saccade task. Moreover, while visual responses often had a fast transient component, responses to auditory stimuli in area LIP tended to be gradual in onset and relatively prolonged in duration.

Overall, the analyses demonstrate that responses to auditory stimuli in area LIP are dependent on auditory-saccade training, modulated by behavioral context, and characterized by slow-onset, sustained response profiles. These findings suggest that responses to auditory stimuli are best interpreted as supramodal (cognitive or motor) responses, rather than as modality-specific sensory responses. Auditory responses in area LIP seem to reflect the significance of auditory stimuli as potential targets for eye movements, and may differ from most visual responses in the extent to which they arc abstracted from the sensory parameters of the stimulus.

Macaque lateral intraparietal area and oculomotor behaviors

Neurons in the primate lateral intraparietal area (area LIP) carry visual, saccade-related and eye position activities. The visual and saccade activities are anchored in a retinotopic framework and the overall response magnitude is modulated by eye position. It was proposed that the modulation by eye position might be the basis of a distributed coding of target locations in a head-centered space. Other recording studies demonstrated that area LIP is involved in oculomotor planning. These results overall suggest that area LIP transforms sensory information for motor functions. In this thesis I further explore the role of area LIP in processing saccadic eye movements by observing the effects of reversible inactivation of this area. Macaque monkeys were trained to do visually guided and memory saccades and a double saccade task to examine the use of eye position signal. Finally, by intermixing visual saccades with trials in which two targets were presented at opposite sides of the fixation point, I examined the behavior of visual extinction.

In chapter 2, I will show that lesion of area LIP results in increased latency of contralesional visual and memory saccades. Contralesional memory saccades are also hypometric and slower in velocity. Moreover, the impairment of memory saccades does not vary with the duration of the delay period. This suggests that the oculomotor deficits observed after inactivation of area LIP is not due to the disruption of spatial memory.

In chapter 3, I will show that lesion of area LIP does not severely affect the processing of spontaneous eye movement. However, the monkeys made fewer contralesional saccades and tended to confine their gaze to the ipsilesional field after inactivation of area LIP. On the other hand, lesion of area LIP results in extinction of the contralesional stimulus. When the initial fixation position was varied so that the retinal and spatial locations of the targets could be dissociated, it was found that the extinction behavior could best be described in a head-centered coordinate.

In chapter 4, I will show that inactivation of area LIP disrupts the use of eye position signal to compute the second movement correctly in the double saccade task. If the first saccade steps into the contralesional field, the error rate and latency of the second saccade are both increased. Furthermore, the direction of the first eye movement largely does not have any effect on the impairment of the second saccade. I will argue that this study provides important evidence that the extraretinal signal used for saccadic localization is eye position rather than a displacement vector.

In chapter 5, I will demonstrate that in parietal monkeys the eye drifts toward the lesion side at the end of the memory saccade in darkness. This result suggests that the eye position activity in the posterior parietal cortex is active in nature and subserves gaze holding.

Overall, these results further support the view that area LIP neurons encode spatial locations in a craniotopic framework and is involved in processing voluntary eye movements.

Direct visualization of the dynamics of membrane-anchor proteins in living cells

Dynamic properties of proteins have crucial roles in understanding protein function and molecular mechanism within cells. In this paper, we combined total internal reflection fluorescence microscopy with oblique illumination fluorescence microscopy to observe directly the movement and localization of membrane-anchored green fluorescence proteins in living cells. Total internal reflect illumination allowed the observation of proteins in the cell membrane of living cells since the penetrate depth could be adjusted to about 80 nm, and oblique illumination allowed the observation of proteins both in the cytoplasm and apical membrane, which made this combination a promising tool to investigate the dynamics of proteins through the whole cell. Not only individual protein molecule tracks have been analyzed quantitatively but also cumulative probability distribution function analysis of ensemble trajectories has been done to reveal the mobility of proteins. Finally, single particle tracking has acted as a compensation for single molecule tracking. All the results exhibited green fluorescence protein dynamics within cytoplasm, on the membrane and from cytoplasm to plasma membrane.

Molecular neurogenetics of eye development in Drosophila

The compound eye of Drosophila melanogaster begins to differentiate during the late third larval instar in the eye-antennal imaginal disc. A wave of morphogenesis crosses the disc from posterior to anterior, leaving behind precisely patterned clusters of photoreceptor cells and accessory cells that will constitute the adult ommatidia of the retina. By the analysis of genetically mosaic eyes, it appears that any cell in the eye disc can adopt the characteristics of any one of the different cell types found in the mature eye, including photoreceptor cells and non-neuronal accessory cells such as cone cells. Therefore, cells within the prospective retinal epithelium assume different fates presumably via information present in the environment. The sevenless^+ (sev^+) gene appears to play a role in the expression of one of the possible fates, since the mutant phenotype is the lack of one of the pattern elements, namely, photoreceptor cell R7. The sev^+ gene product had been shown to be required during development of the eye, and had also been shown in genetic mosaics to be autonomous to presumptive R7. As a means of better understanding the pathway instructing the differentiation R7, the gene and its protein product were characterized.

The sev+ gene was cloned by P-element transposon tagging, and was found to encode an 8.2 kb transcript expressed in developing eye discs and adult heads. By raising monoclonal antibodies (MAbs) against a sev^+- β-galactosidase fusion protein, the expression of the protein in the eye disc was localized by immuno-electronmicroscopy. The protein localizes to the apical cell membranes and microvilli of cells in the eye disc epithelium. It appears during development at a time coincident with the initial formation of clusters, and in all the developing photoreceptors and accessory cone cells at a time prior to the overt differentiation of R7. This result is consistent with the pluripotency of cells in the eye disc. Its localization in the membranes suggests that it may receive information directing the development of R7. Its localization in the apical membranes and microvilli is away from the bulk of the cell contacts, which have been cited as a likely regions for information presentation and processing. Biochemical characterization of the sev^+ protein will be necessary to describe further its role in development.

Other mutations in Drosophila have eye phenotypes. These were analyzed to find which ones affected the initial patterning of cells in the eye disc, in order to identify other genes, like sev, whose gene products may be involved in generating the pattern. The adult eye phenotypes ranged from severe reduction of the eye, to variable numbers of photoreceptor cells per ommatidium, to sub de defects in the organization of the supporting cells. Developing eye discs from the different strains were screened using a panel of MAbs, which highlight various developmental stages. Two identified matrix elements in and anterior to the furrow, while others identified the developing ommatidia themselves, like the anti-sev MAb. Mutation phenotypes were shown to appear at many stages of development. Some mutations seem to affect the precursor cells, others, the setting up of the pattern, and still others, the maintenance of the pattern. Thus, additional genes have now been identified that may function to support the development of a complex pattern.