Detecting and Estimating Signals in Noisy Cable Structures, II: Information Theoretical Analysis

This is the second in a series of articles that seek to recast classical single-neuron biophysics in information-theoretical terms. Classical cable theory focuses on analyzing the voltage or current attenuation of a synaptic signal as it propagates from its dendritic input location to the spike initiation zone. On the other hand, we are interested in analyzing the amount of information lost about the signal in this process due to the presence of various noise sources distributed throughout the neuronal membrane. We use a stochastic version of the linear one-dimensional cable equation to derive closed-form expressions for the second-order moments of the fluctuations of the membrane potential associated with different membrane current noise sources: thermal noise, noise due to the random opening and closing of sodium and potassium channels, and noise due to the presence of “spontaneous” synaptic input. We consider two different scenarios. In the signal estimation paradigm, the time course of the membrane potential at a location on the cable is used to reconstruct the detailed time course of a random, band-limited current injected some distance away. Estimation performance is characterized in terms of the coding fraction and the mutual information. In the signal detection paradigm, the membrane potential is used to determine whether a distant synaptic event occurred within a given observation interval. In the light of our analytical results, we speculate that the length of weakly active apical dendrites might be limited by the information loss due to the accumulated noise between distal synaptic input sites and the soma and that the presence of dendritic nonlinearities probably serves to increase dendritic information transfer

Detecting and Estimating Signals over Noisy and Unreliable Synapses: Information-Theoretic Analysis

The temporal precision with which neurons respond to synaptic inputs has a direct bearing on the nature of the neural code. A characterization of the neuronal noise sources associated with different sub-cellular components (synapse, dendrite, soma, axon, and so on) is needed to understand the relationship between noise and information transfer. Here we study the effect of the unreliable, probabilistic nature of synaptic transmission on information transfer in the absence of interaction among presynaptic inputs. We derive theoretical lower bounds on the capacity of a simple model of a cortical synapse under two different paradigms. In signal estimation, the signal is assumed to be encoded in the mean firing rate of the presynaptic neuron, and the objective is to estimate the continuous input signal from the postsynaptic voltage. In signal detection, the input is binary, and the presence or absence of a presynaptic action potential is to be detected from the postsynaptic voltage. The efficacy of information transfer in synaptic transmission is characterized by deriving optimal strategies under these two paradigms. On the basis of parameter values derived from neocortex, we find that single cortical synapses cannot transmit information reliably, but redundancy obtained using a small number of multiple synapses leads to a significant improvement in the information capacity of synaptic transmission

Neural mechanisms of economic choices in mice

Economic choices entail computing and comparing subjective values. Evidence from primates indicates that this behavior relies on the orbitofrontal cortex. Conversely, previous work in rodents provided conflicting results. Here we present a mouse model of economic choice behavior, and we show that the lateral orbital (LO) area is intimately related to the decision process. In the experiments, mice chose between different juices offered in variable amounts. Choice patterns closely resembled those measured in primates. Optogenetic inactivation of LO dramatically disrupted choices by inducing erratic changes of relative value and by increasing choice variability. Neuronal recordings revealed that different groups of cells encoded the values of individual options, the binary choice outcome and the chosen value. These groups match those previously identified in primates, except that the neuronal representation in mice is spatial (in monkeys it is good-based). Our results lay the foundations for a circuit-level analysis of economic decisions

SIMPEL: Circuit model for photonic spike processing laser neurons

We propose an equivalent circuit model for photonic spike processing laser neurons with an embedded saturable absorber---a simulation model for photonic excitable lasers (SIMPEL). We show that by mapping the laser neuron rate equations into a circuit model, SPICE analysis can be used as an efficient and accurate engine for numerical calculations, capable of generalization to a variety of different laser neuron types found in literature. The development of this model parallels the Hodgkin--Huxley model of neuron biophysics, a circuit framework which brought efficiency, modularity, and generalizability to the study of neural dynamics. We employ the model to study various signal-processing effects such as excitability with excitatory and inhibitory pulses, binary all-or-nothing response, and bistable dynamics.Comment: 16 pages, 7 figure

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area