Optimal Properties of Analog Perceptrons with Excitatory Weights

The cerebellum is a brain structure which has been traditionally devoted to supervised learning. According to this theory, plasticity at the Parallel Fiber (PF) to Purkinje Cell (PC) synapses is guided by the Climbing fibers (CF), which encode an ‘error signal’. Purkinje cells have thus been modeled as perceptrons, learning input/output binary associations. At maximal capacity, a perceptron with excitatory weights expresses a large fraction of zero-weight synapses, in agreement with experimental findings. However, numerous experiments indicate that the firing rate of Purkinje cells varies in an analog, not binary, manner. In this paper, we study the perceptron with analog inputs and outputs. We show that the optimal input has a sparse binary distribution, in good agreement with the burst firing of the Granule cells. In addition, we show that the weight distribution consists of a large fraction of silent synapses, as in previously studied binary perceptron models, and as seen experimentally

The Role of Neuromodulators in Cortical Plasticity. A Computational Perspective

Neuromodulators play a ubiquitous role across the brain in regulating plasticity. With recent advances in experimental techniques, it is possible to study the effects of diverse neuromodulatory states in specific brain regions. Neuromodulators are thought to impact plasticity predominantly through two mechanisms: the gating of plasticity and the upregulation of neuronal activity. However, the consequences of these mechanisms are poorly understood and there is a need for both experimental and theoretical exploration. Here we illustrate how neuromodulatory state affects cortical plasticity through these two mechanisms. First, we explore the ability of neuromodulators to gate plasticity by reshaping the learning window for spike-timing-dependent plasticity. Using a simple computational model, we implement four different learning rules and demonstrate their effects on receptive field plasticity. We then compare the neuromodulatory effects of upregulating learning rate versus the effects of upregulating neuronal activity. We find that these seemingly similar mechanisms do not yield the same outcome: upregulating neuronal activity can lead to either a broadening or a sharpening of receptive field tuning, whereas upregulating learning rate only intensifies the sharpening of receptive field tuning. This simple model demonstrates the need for further exploration of the rich landscape of neuromodulator-mediated plasticity. Future experiments, coupled with biologically detailed computational models, will elucidate the diversity of mechanisms by which neuromodulatory state regulates cortical plasticity

Connectivity reflects coding: A model of voltage-based spike-timing-dependent-plasticity with homeostasis

Electrophysiological connectivity patterns in cortex often show a few strong connections in a sea of weak connections. In some brain areas a large fraction of strong connections are bidirectional, in others they are mainly unidirectional. In order to explain these connectivity patterns, we use a model of Spike-Timing-Dependent Plasticity where synaptic changes depend on presynaptic spike arrival and the postsynaptic membrane potential. The model describes several nonlinear effects in STDP experiments, as well as the voltage dependence of plasticity under voltage clamp and classical paradigms of LTP/LTD induction. We show that in a simulated recurrent network of spiking neurons our plasticity rule leads not only to receptive field development, but also to connectivity patterns that reflect the neural code: for temporal coding paradigms strong connections are predominantly unidirectional, whereas they are bidirectional under rate coding. Thus variable connectivity patterns in the brain could reflect different coding principles across brain areas

Synaptic plasticity across different time scales and its functional implications

Humans and animals learn by modifying the synaptic strength between neurons, a phenomenon known as synaptic plasticity. These changes can be induced by rather short stimuli (lasting, for instance, only a few seconds), yet, in order to be useful for long-term memory, they should remain stable for months or years. Experimentalists study synaptic plasticity by applying a vast variety of protocols. In the present thesis we focus on protocols that fall under two main categories: (i) Those that induce synaptic modifications that last for only a few hours ("early phase" of plasticity) (ii) Those that allow synapses to undergo a sequence of steps that transforms the rapid changes occurring during the "early phase" into a stable memory trace ("late phase" of plasticity). The goal of this thesis is to better understand synaptic plasticity across these different phases, early and late, by creating compact mathematic models to describe the plasticity mechanisms. Our approach allows for a synthetic view of the field as well as the exploration of functional consequences of learning. In this direction, we propose a model for the induction of synaptic plasticity that depends on the presynaptic spike time and nonlinearly on the postsynaptic voltage. The model is able to reproduce a broad range of experimental protocols such as voltage-clamp experiments and spike-timing experiments. Since the voltage is a key element in the model, we describe the neuronal activity by using a compact neuron model that faithfully reproduces the voltage time course of pyramidal neurons. In addition, this model of the induction of synaptic plasticity is combined with a trigger process for protein synthesis, and the final stabilization mechanism in order to describe the "late phase". In this combinatory form, it is able to explain experimental phenomena known as tagging experiments and to make testable predictions. A study of functional consequences of the induction model reveals selectivity in the inputs, independent component analysis computation and a tight relation between connectivity and coding. In parallel a top-down approach finding independent components is used to derive a rate-based learning rule which shows structural correlations with the induction model. This unified model across different time scales allowing the stabilization of synapses is crucial to understand learning and memory processes in animals and humans, and a necessary ingredient for any large-scale model of the brain

Firing patterns in the adaptive exponential integrate-and-fire model

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulation

Firing patterns in the adaptive exponential integrate-and-fire model

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations