Synaptic dynamics contribute to long-term single neuron response fluctuations

Firing rate variability at the single neuron level is characterized by long-memory processes and complex statistics over a wide range of time scales (from milliseconds up to several hours). Here, we focus on the contribution of non-stationary efficacy of the ensemble of synapses-activated in response to a given stimulus-on single neuron response variability. We present and validate a method tailored for controlled and specific long-term activation of a single cortical neuron in vitro via synaptic or antidromic stimulation, enabling a clear separation between two determinants of neuronal response variability: membrane excitability dynamics vs. synaptic dynamics. Applying this method we show that, within the range of physiological activation frequencies, the synaptic ensemble of a given neuron is a key contributor to the neuronal response variability, long-memory processes and complex statistics observed over extended time scales. Synaptic transmission dynamics impact on response variability in stimulation rates that are substantially lower compared to stimulation rates that drive excitability resources to fluctuate. Implications to network embedded neurons are discussed.

Theory of representation learning in cortical neural networks

Carlos Stein Naves de Brito

Our brain continuously self-organizes to construct and maintain an internal representation of the world based on the information arriving through sensory stimuli. Remarkably, cortical areas related to different sensory modalities appear to share the same functional unit, the neuron, and develop through the same learning mechanism, synaptic plasticity. It motivates the conjecture of a unifying theory to explain cortical representational learning across sensory modalities. In this thesis we present theories and computational models of learning and optimization in neural networks, postulating functional properties of synaptic plasticity that support the apparent universal learning capacity of cortical networks. In the past decades, a variety of theories and models have been proposed to describe receptive field formation in sensory areas. They include normative models such as sparse coding, and bottom-up models such as spike-timing dependent plasticity. We bring together candidate explanations by demonstrating that in fact a single principle is sufficient to explain receptive field development. First, we show that many representative models of sensory development are in fact implementing variations of a common principle: nonlinear Hebbian learning. Second, we reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs. A surprising result is that our findings are independent of specific details, and allow for robust predictions of the learned receptive fields. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. The Hebbian learning theory substantiates that synaptic plasticity can be interpreted as an optimization procedure, implementing stochastic gradient descent. In stochastic gradient descent inputs arrive sequentially, as in sensory streams. However, individual data samples have very little information about the correct learning signal, and it becomes a fundamental problem to know how many samples are required for reliable synaptic changes. Through estimation theory, we develop a novel adaptive learning rate model, that adapts the magnitude of synaptic changes based on the statistics of the learning signal, enabling an optimal use of data samples. Our model has a simple implementation and demonstrates improved learning speed, making this a promising candidate for large artificial neural network applications. The model also makes predictions on how cortical plasticity may modulate synaptic plasticity for optimal learning. The optimal sampling size for reliable learning allows us to estimate optimal learning times for a given model. We apply this theory to derive analytical bounds on times for the optimization of synaptic connections. First, we show this optimization problem to have exponentially many saddle-nodes, which lead to small gradients and slow learning. Second, we show that the number of input synapses to a neuron modulates the magnitude of the initial gradient, determining the duration of learning. Our final result reveals that the learning duration increases supra-linearly with the number of synapses, suggesting an effective limit on synaptic connections and receptive field sizes in developing neural networks.

EPFL2016

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

Michele Giugliano, Walter Senn

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

Springer-Verlag2008

Emergent Properties of in silico Synaptic Transmission in a Model of the Rat Neocortical Column

Srikanth Ramaswamy

The cerebral cortex occupies nearly 80% of the entire volume of the mammalian brain and is thought to subserve higher cognitive functions like memory, attention and sensory perception. The neocortex is the newest part in the evolution of the cerebral cortex and is perhaps the most intricate brain region ever studied. The neocortical microcircuit is the smallest Œecosystem‚ of the neocortex that consists of a rich assortment of neurons, which are diverse in both their morphological and electrical properties. In the neocortical microcircuit, neurons are horizontally arranged in 6 distinct sheets called layers. The fundamental operating unit of the neocortical microcircuit is believed to be the Neocortical Column (NCC). Functionally, a single NCC is an arrangement of thousands of neurons in a vertical fashion spanning across all the 6 layers. The structure of the entire neocortex arises from a repeated and stereotypical arrangement of several thousands of such columns, where neurons transmit information to each other through specialized points of information transfer called synapses. The dynamics of synaptic transmission can be as diverse as the neurons defining a connection and are crucial to foster the functional properties of the neocortical microcircuit. The Blue Brain Project (BBP) is the first comprehensive endeavour to build a unifying model of the NCC by systematic data integration and biologically detailed simulations. Through the past 5 years, the BBP has built a facility for a data-constraint driven approach towards modelling and integrating biological information across multiple levels of complexity. Guided by fundamental principles derived from biological experiments, the BBP simulation toolchain has undergone a process of continuous refinement to facilitate the frequent construction of detailed in silico models of the NCC. The focus of this thesis lies in characterizing the functional properties of in silico synaptic transmission by incorporating principles of synaptic communication derived through biological experiments. In order to study in silico synaptic transmission it is crucial to gain an understanding of the key players influencing the manner in which synaptic signals are processed in the neocortical microcircuit - ion channel kinetics and distribution profiles, single neuron models and dynamics of synaptic pathways. First, by means of exhaustive literature survey, I identified ion channel kinetics and their distribution profiles on neocortical neurons to build in silico ion channel models. Thereafter, I developed a prototype framework to analyze the somatic and dendritic features of single neuron models constrained by ion channel kinetics. Finally, within a simulation framework integrating the ion channels, single neuron models and dynamics of synaptic transmission, I replicated in vitro experimental protocols in silico, to characterize the transmission properties of monosynaptic connections. These synaptic connections, arising from the axo-dendritric apposition of neuronal arbours were sampled across many instances of in silico NCC models constructed a priori through the BBP simulation toolchain. In this thesis, I show that when principles of synaptic transmission derived from in vitro experiments are incorporated to model in silico synaptic connections, the resulting anatomy and physiology of synaptic connections modelled from elementary biological rules closely match in vitro data. This thesis work demonstrates that the average synaptic response properties in silico are robust to perturbations in the anatomical and physiological properties of modelled connections in the local neocortical microcircuit. A fundamental discovery through this thesis is an insight into the function of the local neocortical microcircuit by examining the effect of morphological diversity on in silico synaptic transmission. I demonstrate here that intrinsic morphological diversity confers an invariance to the average synaptic response properties in silico in the local neocortical microcircuit, termed "microcircuit level robustness and invariance".

EPFL2011