Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave

Neural Processing in the Three Layer Turtle Visual Cortex

In this thesis we investigate neural processing in turtle visual cortex. To this end, we characterize the nature of both spontaneous, ongoing neural activity as well as activity evoked by visual stimulation. Data are collected from whole brain eye-attached preparations, recording with extracellular and intracellular electrodes. We investigate the activity of action potentials as well as the slower local field potential activity. To investigate response properties, we explore spatial properties of receptive fields, temporal properties of spontaneous and evoked activity, response adaptation, and correlations between different types of activity as well as between activity recorded in different regions. To study the roles of rhythmic oscillations in the local field potential, we examine temporal and spectral properties of oscillations. We look at the distributions of durations of oscillatory bursts as well as the distributions of the dominant frequencies within those oscillations. We also investigate the variability of these features and produce similar results in a model simulation. Lastly, we investigate criticality and the statistics of neural activity over a range of scales in the turtle visual cortex. We use neuronal avalanches to reveal scale-free cortical dynamics and power-law statistics, which have been hypothesized to optimize information processing

Large-scale Spatiotemporal Spike Patterning Consistent with Wave Propagation in Motor Cortex

Aggregate signals in cortex are known to be spatiotemporally organized as propagating waves across the cortical surface, but it remains unclear whether the same is true for spiking activity in individual neurons. Furthermore, the functional interactions between cortical neurons are well documented but their spatial arrangement on the cortical surface has been largely ignored. Here we use a functional network analysis to demonstrate that a subset of motor cortical neurons in non-human primates spatially coordinate their spiking activity in a manner that closely matches wave propagation measured in the beta oscillatory band of the local field potential. We also demonstrate that sequential spiking of pairs of neuron contains task-relevant information that peaks when the neurons are spatially oriented along the wave axis. We hypothesize that the spatial anisotropy of spike patterning may reflect the underlying organization of motor cortex and may be a general property shared by other cortical areas

Experimental and Computational Studies of Cortical Neural Network Properties Through Signal Processing

Previous studies, both theoretical and experimental, of network level dynamics in the cerebral cortex show evidence for a statistical phenomenon called criticality; a phenomenon originally studied in the context of phase transitions in physical systems and that is associated with favorable information processing in the context of the brain. The focus of this thesis is to expand upon past results with new experimentation and modeling to show a relationship between criticality and the ability to detect and discriminate sensory input. A line of theoretical work predicts maximal sensory discrimination as a functional benefit of criticality, which can then be characterized using mutual information between sensory input, visual stimulus, and neural response,. The primary finding of our experiments in the visual cortex in turtles and neuronal network modeling confirms this theoretical prediction. We show that sensory discrimination is maximized when visual cortex operates near criticality. In addition to presenting this primary finding in detail, this thesis will also address our preliminary results on change-point-detection in experimentally measured cortical dynamics

The Mechanisms and Roles of Neural Feedback Loops for Visual Processing

Feedback pathways are widely present in various sensory systems transmitting time-delayed and partly-processed information from higher to lower visual centers. Although feedback loops are abundant in visual systems, investigations focusing on the mechanisms and roles of feedback in terms of micro-circuitry and system dynamics have been largely ignored. Here, we investigate the cellular, synaptic and circuit level properties of a cholinergic isthmic neuron: Ipc) to understand the role of isthmotectal feedback loop in visual processing of red-ear turtles, Trachemys scripta elegans. Turtle isthmotectal complex contains two distinct nuclei, Ipc and Imc, which interact exclusively with the optic tectum, but are otherwise isolated from other brain areas. The cholinergic Ipc neurons receive topographic glutamatergic inputs from tectal SGP neurons and project back to upper tectal layers in a topographic manner while GABAergic Imc neurons, which also get inputs from the SGP neurons project back non-topographically to both the tectum and Ipc nucleus. We have used an isolated eye-attached whole-brain preparation for our investigations of turtle isthmotectal feedback loop. We have investigated the cellular properties of the Ipc neurons by whole-cell blind-patch recordings and found that all Ipc neurons exhibit tonic firing responses to somatic current injections that are well-modeled by a leaky integrate-and-fire neuron with spike rate adaptation. Further investigations reveal that the optic nerve stimulations generate balanced excitatory and inhibitory synaptic currents in the Ipc neurons. We have also found that synaptic connection between the Imc to Ipc neuron is inhibitory. The visual response properties of the Ipc neurons to a range of computer-generated stimuli are investigated using extracellular recordings. We have found that the Ipc neurons have a localized excitatory receptive field and show stimulus selectivity and stimulus-size tuning. We also investigate lateral interactions in the Ipc neurons in response to multiple stimuli within the visual field. Finally, we quantify the oscillatory bursts observed in Ipc responses under visual stimulations

Distributed Dynamical Computation in Neural Circuits with Propagating Coherent Activity Patterns

Activity in neural circuits is spatiotemporally organized. Its spatial organization consists of multiple, localized coherent patterns, or patchy clusters. These patterns propagate across the circuits over time. This type of collective behavior has ubiquitously been observed, both in spontaneous activity and evoked responses; its function, however, has remained unclear. We construct a spatially extended, spiking neural circuit that generates emergent spatiotemporal activity patterns, thereby capturing some of the complexities of the patterns observed empirically. We elucidate what kind of fundamental function these patterns can serve by showing how they process information. As self-sustained objects, localized coherent patterns can signal information by propagating across the neural circuit. Computational operations occur when these emergent patterns interact, or collide with each other. The ongoing behaviors of these patterns naturally embody both distributed, parallel computation and cascaded logical operations. Such distributed computations enable the system to work in an inherently flexible and efficient way. Our work leads us to propose that propagating coherent activity patterns are the underlying primitives with which neural circuits carry out distributed dynamical computation

A reaction-diffusion model of cholinergic retinal waves

Prior to receiving visual stimuli, spontaneous, correlated activity called retinal waves drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their extended inter-wave intervals and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In contrast with previous, simulation-based models, we are able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how the noise rate and sAHP refractory period contributes to critical wave size variability.Comment: 38 pages, 10 figure

The Dynamic Brain in Action: Cortical Oscillations and Coordination Dynamics

Cortical oscillations are electrical activities with rhythmic and/or repetitive nature generated spontaneously and in response to stimuli. Study of cortical oscillations has become an area of converging interests since the last two decades and has deepened our understanding of its physiological basis across different behavioral states. Experimental and modeling work has taught us that there is a wide diversity of cellular and circuit mechanisms underlying the generation of cortical rhythms. A wildly diverse set of functions has pertained to synchronous oscillations but their significance in cognition should be better appraised in the more general framework of correlation between spike times of neurons. Oscillations are the core mechanism in adjusting neuronal interactions and shaping temporal coordination of neural activity. In the first part of this thesis, we review essential feature of cortical oscillations in membrane potentials and local field potentials recorded from turtle ex vivo preparation. Then we develop a simple computational model that reproduces the observed features. This modeling investigation suggests a plausible underlying mechanism for rhythmogenesis through cellular and circuit properties. The second part of the thesis is about temporal coordination dynamics quantified by signal and noise correlations. Here, again, we present a computational model to show how temporal coordination and synchronous oscillations can be sewn together. More importantly, what biophysical ingrediants are necessary for a network to reproduce the observed coordination dynamics

Fast and robust learning by reinforcement signals: explorations in the insect brain

We propose a model for pattern recognition in the insect brain. Departing from a well-known body of knowledge about the insect brain, we investigate which of the potentially present features may be useful to learn input patterns rapidly and in a stable manner. The plasticity underlying pattern recognition is situated in the insect mushroom bodies and requires an error signal to associate the stimulus with a proper response. As a proof of concept, we used our model insect brain to classify the well-known MNIST database of handwritten digits, a popular benchmark for classifiers. We show that the structural organization of the insect brain appears to be suitable for both fast learning of new stimuli and reasonable performance in stationary conditions. Furthermore, it is extremely robust to damage to the brain structures involved in sensory processing. Finally, we suggest that spatiotemporal dynamics can improve the level of confidence in a classification decision. The proposed approach allows testing the effect of hypothesized mechanisms rather than speculating on their benefit for system performance or confidence in its responses