Biophysical and network mechanisms of high frequency extracellular potentials in the rat hippocampus

A fundamental question in neuroscience is how distributed networks of neurons communicate and coordinate dynamically and specifically. Several models propose that oscillating local networks can transiently couple to each other through phase-locked firing. Coherent local field potentials (LFP) between synaptically connected regions is often presented as evidence for such coupling. The physiological correlates of LFP signals depend on many anatomical and physiological factors, however, and how the underlying neural processes collectively generate features of different spatiotemporal scales is poorly understood. High frequency oscillations in the hippocampus, including gamma rhythms (30-100 Hz) that are organized by the theta oscillations (5-10 Hz) during active exploration and REM sleep, as well as sharp wave-ripples (SWRs, 140-200 Hz) during immobility or slow wave sleep, have each been associated with various aspects of learning and memory. Deciphering their physiology and functional consequences is crucial to understanding the operation of the hippocampal network.

We investigated the origins and coordination of high frequency LFPs in the hippocampo-entorhinal network using both biophysical models and analyses of large-scale recordings in behaving and sleeping rats. We found that the synchronization of pyramidal cell spikes substantially shapes, or even dominates, the electrical signature of SWRs in area CA1 of the hippocampus. The precise mechanisms coordinating this synchrony are still unresolved, but they appear to also affect CA1 activity during theta oscillations. The input to CA1, which often arrives in the form of gamma-frequency waves of activity from area CA3 and layer 3 of entorhinal cortex (EC3), did not strongly influence the timing of CA1 pyramidal cells. Rather, our data are more consistent with local network interactions governing pyramidal cells' spike timing during the integration of their inputs. Furthermore, the relative timing of input from EC3 and CA3 during the theta cycle matched that found in previous work to engage mechanisms for synapse modification and active dendritic processes. Our work demonstrates how local networks interact with upstream inputs to generate a coordinated hippocampal output during behavior and sleep, in the form of theta-gamma coupling and SWRs.

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.

Magnetohydrodynamic turbulence

We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows.

1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves.

2) MHD turbulence is anisotropic with energy cascading more rapidly along k_⊥ than along k_∥, where k_⊥ and k_∥ refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_⊥ such that excited modes are confined inside a cone bounded by k_∥ ∝ k^γ_⊥ where γ less than 1. The opening angle of the cone, θ(k_⊥) ∝ k^-(1-γ)_⊥, defines the scale dependent anisotropy.

3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ² (k_⊥)≪1.

4) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/θ(k_⊥) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations.

6) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k by δ(t) correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance.

7) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up.

8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth by Goldreich and Sridhar (1995, 1997). Results from our simulations are also consistent with the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D power law spectra, E(k_⊥) ∝ k^-∝_⊥, determined from our simulations exhibit ∝ ≈ 3/2, whereas the GS model predicts ∝ = 5/3.

Neural representation of auditory temporal structure

Neurons in the songbird forebrain nucleus HVc are highly sensitive to auditory temporal context and have some of the most complex auditory tuning properties yet discovered. HVc is crucial for learning, perceiving, and producing song, thus it is important to understand the neural circuitry and mechanisms that give rise to these remarkable auditory response properties. This thesis investigates these issues experimentally and computationally.

Extracellular studies reported here compare the auditory context sensitivity of neurons in HV c with neurons in the afferent areas of field L. These demonstrate that there is a substantial increase in the auditory temporal context sensitivity from the areas of field L to HVc. Whole-cell recordings of HVc neurons from acute brain slices are described which show that excitatory synaptic transmission between HVc neurons involve the release of glutamate and the activation of both AMPA/kainate and NMDA-type glutamate receptors. Additionally, widespread inhibitory interactions exist between HVc neurons that are mediated by postsynaptic GABA_A receptors. Intracellular recordings of HVc auditory neurons in vivo provides evidence that HV c neurons encode information about temporal structure using a variety of cellular and synaptic mechanisms including syllable-specific inhibition, excitatory post-synaptic potentials with a range of different time courses, and burst-firing, and song-specific hyperpolarization.

The final part of this thesis presents two computational approaches for representing and learning temporal structure. The first method utilizes comput ational elements that are analogous to temporal combination sensitive neurons in HVc. A network of these elements can learn using local information and lateral inhibition. The second method presents a more general framework which allows a network to discover mixtures of temporal features in a continuous stream of input.

The electric field of a weakly electric fish

Freshwater fish of the genus Apteronotus (family Gymnotidae) generate a weak, high frequency electric field (< 100 mV/cm, 0.5-10 kHz) which permeates their local environment. These nocturnal fish are acutely sensitive to perturbations in their electric field caused by other electric fish, and nearby objects whose impedance is different from the surrounding water. This thesis presents high temporal and spatial resolution maps of the electric potential and field on and near Apteronotus. The fish's electric field is a complicated and highly stable function of space and time. Its characteristics, such as spectral composition, timing, and rate of attenuation, are examined in terms of physical constraints, and their possible functional roles in electroreception.

Temporal jitter of the periodic field is less than 1 µsec. However, electrocyte activity is not globally synchronous along the fish 's electric organ. The propagation of electrocyte activation down the fish's body produces a rotation of the electric field vector in the caudal part of the fish. This may assist the fish in identifying nonsymmetrical objects, and could also confuse electrosensory predators that try to locate Apteronotus by following its fieldlines. The propagation also results in a complex spatiotemporal pattern of the EOD potential near the fish. Visualizing the potential on the same and different fish over timescales of several months suggests that it is stable and could serve as a unique signature for individual fish.

Measurements of the electric field were used to calculate the effects of simple objects on the fish's electric field. The shape of the perturbation or "electric image" on the fish's skin is relatively independent of a simple object's size, conductivity, and rostrocaudal location, and therefore could unambiguously determine object distance. The range of electrolocation may depend on both the size of objects and their rostrocaudal location. Only objects with very large dielectric constants cause appreciable phase shifts, and these are strongly dependent on the water conductivity.

Relativistic mean field theory: methods and applications

We develop a method for performing one-loop calculations in finite systems that is based on using the WKB approximation for the high energy states. This approximation allows us to absorb all the counterterms analytically and thereby avoids the need for extreme numerical precision that was required by previous methods. In addition, the local approximation makes this method well suited for self-consistent calculations. We then discuss the application of relativistic mean field methods to the atomic nucleus. Self-consistent, one loop calculations in the Walecka model are performed and the role of the vacuum in this model is analyzed. This model predicts that vacuum polarization effects are responsible for up to five percent of the local nucleon density. Within this framework the possible role of strangeness degrees of freedom is studied. We find that strangeness polarization can increase the kaon-nucleus scattering cross section by ten percent. By introducing a cutoff into the model, the dependence of the model on short-distance physics, where its validity is doubtful, is calculated. The model is very sensitive to cutoffs around one GeV.

I. Electronic processes in α-sulfur. II. Polaron motion in a D.C. electric field

Part I: The mobilities of photo-generated electrons and holes in orthorhombic sulfur are determined by drift mobility techniques. At room temperature electron mobilities between 0.4 cm²/V-sec and 4.8 cm²/V-sec and hole mobilities of about 5.0 cm²/V-sec are reported. The temperature dependence of the electron mobility is attributed to a level of traps whose effective depth is about 0.12 eV. This value is further supported by both the voltage dependence of the space-charge-limited, D.C. photocurrents and the photocurrent versus photon energy measurements.

As the field is increased from 10 kV/cm to 30 kV/cm a second mechanism for electron transport becomes appreciable and eventually dominates. Evidence that this is due to impurity band conduction at an appreciably lower mobility (4.10^-4 cm²/V-sec) is presented. No low mobility hole current could be detected. When fields exceeding 30 kV/cm for electron transport and 35 kV/cm for hole transport are applied, avalanche phenomena are observed. The results obtained are consistent with recent energy gap studies in sulfur.

The theory of the transport of photo-generated carriers is modified to include the case of appreciable thermos-regeneration from the traps in one transit time.

Part II: An explicit formula for the electric field E necessary to accelerate an electron to a steady-state velocity v in a polarizable crystal at arbitrary temperature is determined via two methods utilizing Feynman Path Integrals. No approximation is made regarding the magnitude of the velocity or the strength of the field. However, the actual electron-lattice Coulombic interaction is approximated by a distribution of harmonic oscillator potentials. One may be able to find the “best possible” distribution of oscillators using a variational principle, but we have not been able to find the expected criterion. However, our result is relatively insensitive to the actual distribution of oscillators used, and our E-v relationship exhibits the physical behavior expected for the polaron. Threshold fields for ejecting the electron for the polaron state are calculated for several substances using numerical results for a simple oscillator distribution.

Structure theorems for noncommutative complete local rings

If R is a ring with identity, let N(R) denote the Jacobson radical of R. R is local if R/N(R) is an artinian simple ring and ∩N(R)ⁱ = 0. It is known that if R is complete in the N(R)-adic topology then R is equal to (B)_n, the full n by n matrix ring over B where E/N(E) is a division ring. The main results of the thesis deal with the structure of such rings B. In fact we have the following.

If B is a complete local algebra over F where B/N(B) is a finite dimensional normal extension of F and N(B) is finitely generated as a left ideal by k elements, then there exist automorphisms g_i,...,g_k of B/N(B) over F such that B is a homomorphic image of B/N[[x₁,…,x_k;g₁,…,g_k]] the power series ring over B/N(B) in noncommuting indeterminates x_i, where x_ib = g_i(b)x_i for all b ϵ B/N.

Another theorem generalizes this result to complete local rings which have suitable commutative subrings. As a corollary of this we have the following. Let B be a complete local ring with B/N(B) a finite field. If N(B) is finitely generated as a left ideal by k elements then there exist automorphisms g₁,…,g_k of a v-ring V such that B is a homomorphic image of V [[x₁,…,x_k;g₁,…,g_k]].

In both these results it is essential to know the structure of N(B) as a two sided module over a suitable subring of B.