Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

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.

Analysis of temporal structure in spike trains of visual cortical area MT

The temporal structure of neuronal spike trains in the visual cortex can provide detailed information about the stimulus and about the neuronal implementation of visual processing. Spike trains recorded from the macaque motion area MT in previous studies (Newsome et al., 1989a; Britten et al., 1992; Zohary et al., 1994) are analyzed here in the context of the dynamic random dot stimulus which was used to evoke them. If the stimulus is incoherent, the spike trains can be highly modulated and precisely locked in time to the stimulus. In contrast, the coherent motion stimulus creates little or no temporal modulation and allows us to study patterns in the spike train that may be intrinsic to the cortical circuitry in area MT. Long gaps in the spike train evoked by the preferred direction motion stimulus are found, and they appear to be symmetrical to bursts in the response to the anti-preferred direction of motion. A novel cross-correlation technique is used to establish that the gaps are correlated between pairs of neurons. Temporal modulation is also found in psychophysical experiments using a modified stimulus. A model is made that can account for the temporal modulation in terms of the computational theory of biological image motion processing. A frequency domain analysis of the stimulus reveals that it contains a repeated power spectrum that may account for psychophysical and electrophysiological observations.

Some neurons tend to fire bursts of action potentials while others avoid burst firing. Using numerical and analytical models of spike trains as Poisson processes with the addition of refractory periods and bursting, we are able to account for peaks in the power spectrum near 40 Hz without assuming the existence of an underlying oscillatory signal. A preliminary examination of the local field potential reveals that stimulus-locked oscillation appears briefly at the beginning of the trial.

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.

Experimental and theoretical studies of Notch signaling-mediated spatial pattern

Notch signaling acts in many diverse developmental spatial patterning processes. To better understand why this particular pathway is employed where it is and how downstream feedbacks interact with the signaling system to drive patterning, we have pursued three aims: (i) to quantitatively measure the Notch system's signal input/output (I/O) relationship in cell culture, (ii) to use the quantitative I/O relationship to computationally predict patterning outcomes of downstream feedbacks, and (iii) to reconstitute a Notch-mediated lateral induction feedback (in which Notch signaling upregulates the expression of Delta) in cell culture. The quantitative Notch I/O relationship revealed that in addition to the trans-activation between Notch and Delta on neighboring cells there is also a strong, mutual cis-inactivation between Notch and Delta on the same cell. This feature tends to amplify small differences between cells. Incorporating our improved understanding of the signaling system into simulations of different types of downstream feedbacks and boundary conditions lent us several insights into their function. The Notch system converts a shallow gradient of Delta expression into a sharp band of Notch signaling without any sort of feedback at all, in a system motivated by the Drosophila wing vein. It also improves the robustness of lateral inhibition patterning, where signal downregulates ligand expression, by removing the requirement for explicit cooperativity in the feedback and permitting an exceptionally simple mechanism for the pattern. When coupled to a downstream lateral induction feedback, the Notch system supports the propagation of a signaling front across a tissue to convert a large area from one state to another with only a local source of initial stimulation. It is also capable of converting a slowly-varying gradient in parameters into a sharp delineation between high- and low-ligand populations of cells, a pattern reminiscent of smooth muscle specification around artery walls. Finally, by implementing a version of the lateral induction feedback architecture modified with the addition of an autoregulatory positive feedback loop, we were able to generate cells that produce enough cis ligand when stimulated by trans ligand to themselves transmit signal to neighboring cells, which is the hallmark of lateral induction.

Binding Studies of Neuronal Nicotinic Acetylcholine Receptors Expressing Unnatural Amino Acids

Nicotinic acetylcholine receptors are pentameric ligand-gated ion channels mediating fast synaptic transmission throughout the peripheral and central nervous systems. They have been implicated in various processes related to cognitive functions, learning and memory, arousal, reward, motor control and analgesia. Therefore, these receptors present alluring potential therapeutic targets for the treatment of pain, epilepsy, Alzheimer’s disease, Parkinson’s disease, Tourette’s syndrome, schizophrenia, anxiety, depression and nicotine addiction. The work detailed in this thesis focuses on binding studies of neuronal nicotinic receptors and aims to further our knowledge of subtype specific functional and structural information.

Chapter 1 is an introductory chapter describing the structure and function of nicotinic acetylcholine receptors as well as the methodologies used for the dissertation work described herein. There are several different subtypes of nicotinic acetylcholine receptors known to date and the subtle variations in their structure and function present a challenging area of study. The work presented in this thesis deals specifically with the α4β2 subtype of nicotinic acetylcholine receptor. This subtype assembles into 2 closely related stoichiometries, termed throughout this thesis as A3B2 and A2B3 after their respective subunit composition. Chapter 2 describes binding studies of select nicotinic agonists on A3B2 and A2B3 receptors determined by whole-cell recording. Three key binding interactions, a cation-π and two hydrogen bonds, were probed for four nicotinic agonists, acetylcholine, nicotine, smoking cessation drug varenicline (Chantix®) and the related natural product cytisine.

Results from the binding studies presented in Chapter 2 show that the major difference in binding of these four agonists to A3B2 and A2B3 receptors lies in one of the two hydrogen bond interactions where the agonist acts as the hydrogen bond acceptor and the backbone NH of a conserved leucine residue in the receptor acts as the hydrogen bond donor. Chapter 3 focuses on studying the effect of modulating the hydrogen bond acceptor ability of nicotine and epibatidine on A3B2 receptor function determined by whole-cell recording. Finally, Chapter 4 describes single-channel recording studies of varenicline binding to A2B3 and A3B2 receptors.

Information-theoretic Studies and Capacity Bounds: Group Network Codes and Energy Harvesting Communication Systems

Network information theory and channels with memory are two important but difficult frontiers of information theory. In this two-parted dissertation, we study these two areas, each comprising one part. For the first area we study the so-called entropy vectors via finite group theory, and the network codes constructed from finite groups. In particular, we identify the smallest finite group that violates the Ingleton inequality, an inequality respected by all linear network codes, but not satisfied by all entropy vectors. Based on the analysis of this group we generalize it to several families of Ingleton-violating groups, which may be used to design good network codes. Regarding that aspect, we study the network codes constructed with finite groups, and especially show that linear network codes are embedded in the group network codes constructed with these Ingleton-violating families. Furthermore, such codes are strictly more powerful than linear network codes, as they are able to violate the Ingleton inequality while linear network codes cannot. For the second area, we study the impact of memory to the channel capacity through a novel communication system: the energy harvesting channel. Different from traditional communication systems, the transmitter of an energy harvesting channel is powered by an exogenous energy harvesting device and a finite-sized battery. As a consequence, each time the system can only transmit a symbol whose energy consumption is no more than the energy currently available. This new type of power supply introduces an unprecedented input constraint for the channel, which is random, instantaneous, and has memory. Furthermore, naturally, the energy harvesting process is observed causally at the transmitter, but no such information is provided to the receiver. Both of these features pose great challenges for the analysis of the channel capacity. In this work we use techniques from channels with side information, and finite state channels, to obtain lower and upper bounds of the energy harvesting channel. In particular, we study the stationarity and ergodicity conditions of a surrogate channel to compute and optimize the achievable rates for the original channel. In addition, for practical code design of the system we study the pairwise error probabilities of the input sequences.

I. Electron spin relaxation studies of manganese(II) complexes in acetonitrile. II. Nuclear spin relaxation studies of bromine in tetrabromomanganese(II) in acetonitrile

Magnetic resonance techniques have given us a powerful means for investigating dynamical processes in gases, liquids and solids. Dynamical effects manifest themselves in both resonance line shifts and linewidths, and, accordingly, require detailed analyses to extract desired information. The success of a magnetic resonance experiment depends critically on relaxation mechanisms to maintain thermal equilibrium between spin states. Consequently, there must be an interaction between the excited spin states and their immediate molecular environment which promote changes in spin orientation while excess magnetic energy is coupled into other degrees of freedom by non-radiative processes. This is well known as spin-lattice relaxation. Certain dynamical processes cause fluctuations in the spin state energy levels leading to spin-spin relaxation and, here again, the environment at the molecular level plays a significant role in the magnitude of interaction. Relatively few electron spin relaxation studies of solutions have been conducted and the present work is addressed toward the extension of our knowledge in this area and the retrieval of dynamical information from line shape analyses on a time scale comparable to diffusion controlled phenomena.

Specifically, the electron spin relaxation of three Mn⁺²3d⁵ complexes, Mn(CH₃CN)₆⁺², MnCl₄^-2 in acetonitrile has been studied in considerable detail. The effective spin Hamiltonian constants were carefully evaluated under a wide range of experimental conditions. Resonance widths of these Mn⁺² complexes were studied in the presence of various excess ligand ions and as a function of concentration, viscosity, temperature and frequency (X-band, ~9.5 Ԍ Hz and K-band, ~35 Ԍ Hz).

A number of interesting conclusions were drawn from these studies. For the Et₄NCl-₄^-2 system several relaxation mechanisms leading to resonance broadening were observed. One source appears to arise through spin-orbit interactions caused by modulation of the ligand field resulting from transient distortions of the complex imparted by solvent fluctuations in the immediate surroundings of the paramagnetic ion. An additional spin relaxation was assigned to the formation of ion pairs [Et₄N⁺…MnCl₄^-2] and it was possible to estimate the dissociation constant for this specie in acetonitrile.

The Bu₄NBr-MnBr₄^-2 study was considerably more interesting. As in the former case, solvent fluctuations and ion-pairing of the paramagnetic complex [Bu₄N⁺…MnBr₄^-2] provide significant relaxation for the electronic spin system. Most interesting, without doubt, is the onset of a new relaxation mechanism leading to resonance broadening which is best interpreted as chemical exchange. Thus, assuming that resonance widths were simply governed by electron spin state lifetimes, we were able to extract dynamical information from an interaction in which the initial and final states are the same

MnBr₄^-2 + Br^- = MnBr₄^-2 + Br^-.

The bimolecular rate constants were obtained at six different temperatures and their magnitudes suggested that the exchange is probably diffusion controlled with essentially a zero energy of activation. The most important source of spin relaxation in this system stems directly from dipolar interactions between the manganese 3d⁵ electrons. Moreover, the dipolar broadening is strongly frequency dependent indicating a deviation between the transverse and longitudinal relaxation times. We are led to the conclusion that the 3d⁵ spin states of ion-paired MnBr₄^-2 are significantly correlated so that dynamical processes are also entering the picture. It was possible to estimate the correlation time, ^Td, characterizing this dynamical process.

In Part II we study nuclear magnetic relaxation of bromine ions in the MnBr4-2-Bu4NBr-acetonitrile system. Essentially we monitor the 79Br and 81Br linewidths in response to the [MnBr4-2]/[Br-] ratio with the express purpose of supporting our contention that exchange is occurring between "free" bromine ions in the solvent and bromine in the first coordination sphere of the paramagnetic anion. The complexity of the system elicited a two-part study: (1) the linewidth behavior of Bu4NBr in anhydrous CH3CN in the absence of MnBr4-2 and (2) in the presence of MnBr4-2. It was concluded in study (1) that dynamical association, Bu4NBr k1= Bu4N+ + Br-, was modulating field-gradient interactions at frequencies high enough to provide an estimation of the unimolecular rate constant, k1. A comparison of the two isotopic bromine linewidth-mole fraction results led to the conclusion that quadrupole interactions provided the dominant relaxation mechanism. In study (2) the "residual" bromine linewidths for both 79Br and 81Br are clearly controlled by quadrupole interactions which appear to be modulated by very rapid dynamical processes other than molecular reorientation. We conclude that the "residual" linewidth has its origin in chemical exchange and that bromine nuclei exchange rapidly between a "free" solvated ion and the paramagnetic complex, MnBr4-2.