Optimal decoding and information transmission in Hodgkin-Huxley neurons under metabolic cost constraints

Estimation of firing rate from instantaneous interspike intervals

The rate coding hypothesis is the oldest and still one of the most accepted hypotheses of neural coding. Consequently, many approaches have been devised for the firing rate estimation, ranging from simple binning of the time axis to advanced statistical methods. Nonetheless the concept of firing rate, while informally understood, can be mathematically defined in several distinct ways. These definitions may yield mutually incompatible results unless implemented properly. Recently it has been shown that the notions of the instantaneous and the classical firing rates can be made compatible, at least in terms of their averages, by carefully discerning the time instant at which the neuronal activity is observed. In this paper we revisit the properties of instantaneous interspike intervals in order to derive several novel firing rate estimators, which are free of additional assumptions or parameters and their temporal resolution is 'locally self-adaptive'. The estimators are simple to implement and are numerically efficient even for very large sets of data.

Shared input and recurrency in neural networks for metabolically efficient information transmission

Shared input to a population of neurons induces noise correlations, which can decrease the information carried by a population activity. Inhibitory feedback in recurrent neural networks can reduce the noise correlations and thus increase the information carried by the population activity. However, the activity of inhibitory neurons is costly. This inhibitory feedback decreases the gain of the population. Thus, depolarization of its neurons requires stronger excitatory synaptic input, which is associated with higher ATP consumption. Given that the goal of neural populations is to transmit as much information as possible at minimal metabolic costs, it is unclear whether the increased information transmission reliability provided by inhibitory feedback compensates for the additional costs. We analyze this problem in a network of leaky integrate-and-fire neurons receiving correlated input. By maximizing mutual information with metabolic cost constraints, we show that there is an optimal strength of recurrent connections in the network, which maximizes the value of mutual information-per-cost. For higher values of input correlation, the mutual information-per-cost is higher for recurrent networks with inhibitory feedback compared to feedforward networks without any inhibitory neurons. Our results, therefore, show that the optimal synaptic strength of a recurrent network can be inferred from metabolically efficient coding arguments and that decorrelation of the input by inhibitory feedback compensates for the associated increased metabolic costs.

The computational cost of active information sampling before decision-making under uncertainty

Humans often seek information to minimize the pervasive effect of uncertainty on decisions. Current theories explain how much knowledge people should gather before a decision, based on the cost-benefit structure of the problem at hand. Here, we demonstrate that this framework omits a crucial agent-related factor: the cognitive effort expended while collecting information. Using an active sampling model, we unveil a speed-efficiency trade-off whereby more informative samples take longer to find. Crucially, under sufficient time pressure, humans can break this trade-off, sampling both faster and more efficiently. Computational modelling demonstrates the existence of a cost of cognitive effort which, when incorporated into theoretical models, provides a better account of people's behaviour and also relates to self-reported fatigue accumulated during active sampling. Thus, the way people seek knowledge to guide their decisions is shaped not only by task-related costs and benefits, but also crucially by the quantifiable computational costs incurred.

The effect of inhibition on rate code efficiency indicators

In this paper we investigate the rate coding capabilities of neurons whose input signal are alterations of the base state of balanced inhibitory and excitatory synaptic currents. We consider different regimes of excitation-inhibition relationship and an established conductance-based leaky integrator model with adaptive threshold and parameter sets recreating biologically relevant spiking regimes. We find that given mean post-synaptic firing rate, counter-intuitively, increased ratio of inhibition to excitation generally leads to higher signal to noise ratio (SNR). On the other hand, the inhibitory input significantly reduces the dynamic coding range of the neuron. We quantify the joint effect of SNR and dynamic coding range by computing the metabolic efficiency-the maximal amount of information per one ATP molecule expended (in bits/ATP). Moreover, by calculating the metabolic efficiency we are able to predict the shapes of the post-synaptic firing rate histograms that may be tested on experimental data. Likewise, optimal stimulus input distributions are predicted, however, we show that the optimum can essentially be reached with a broad range of input distributions. Finally, we examine which parameters of the used neuronal model are the most important for the metabolically efficient information transfer.

Energy-information coupling during integrative cognitive processes

The physical conception of energy is a natural and general approach to describe functional interactions in the brain at different levels starting from studies of molecular interactions up to the integrative studies of cognitive neuroimaging. In this article, we describe the representation of the brain as a fluctuating energy field, which adaptively reflects the environment. Within this neuroenergetic conception, we indicate a physically solid approach to the problem of the link between brain function and information processing - transmission and integration of information between neuroglial populations is coupled with the corresponding energy increase used for information encoding. We develop the integrative neuroenergetic model of face recognition, in which the input to the model tries to modify the fluctuations of activity according to the free-energy minimization principle corresponding to metabolic efficiency. Once the spatial path of integration in neural activity is known, the processed information can be decoded by spatial differentiation. Energy-based feedback with activity rescaling does not influence the possibility of decoding the information. The model provides further evidence that the conception of energy facilitates at both the computational and conceptual levels the understanding of brain function and its relation to cognition.

Moth olfactory receptor neurons adjust their encoding efficiency to temporal statistics of pheromone fluctuations

The efficient coding hypothesis predicts that sensory neurons adjust their coding resources to optimally represent the stimulus statistics of their environment. To test this prediction in the moth olfactory system, we have developed a stimulation protocol that mimics the natural temporal structure within a turbulent pheromone plume. We report that responses of antennal olfactory receptor neurons to pheromone encounters follow the temporal fluctuations in such a way that the most frequent stimulus timescales are encoded with maximum accuracy. We also observe that the average coding precision of the neurons adjusted to the stimulus-timescale statistics at a given distance from the pheromone source is higher than if the same encoding model is applied at a shorter, non-matching, distance. Finally, the coding accuracy profile and the stimulus-timescale distribution are related in the manner predicted by the information theory for the many-to-one convergence scenario of the moth peripheral sensory system.

Sum Rate of MISO Neuro-Spike Communication Channel With Constant Spiking Threshold

Communication among neurons, known as neuro-spike communication, is the most promising technique for realization of a bio-inspired nanoscale communication paradigm to achieve biocompatible nanonetworks. In neuro-spike communication, the information, encoded into spike trains, is communicated to various brain regions through neuronal network. An output neuron needs to receive signal from multiple input neurons to generate a spike. Hence, in this paper, we aim to quantify the information transmitted through the multiple-input single-output (MISO) neuro-spike communication channel by considering models for axonal propagation, synaptic transmission, and spike generation. Moreover, the spike generation and propagation in each neuron requires opening and closing of numerous ionic channels on the cell membrane, which consumes considerable amount of ATP molecules called metabolic energy. Thus, we evaluate how applying a constraint on available metabolic energy affects the maximum achievable mutual information of this system. To this aim, we derive a closed form equation for the sum rate of the MISO neuro-spike communication channel and analyze it under the metabolic cost constraints. Finally, we discuss the impacts of changes in number of pre-synaptic neurons on the achievable rate and quantify the tradeoff between maximum achievable sum rate and the consumed metabolic energy.

Coordinate invariance as a fundamental constraint on the form of stimulus-specific information measures

The value of Shannon's mutual information is commonly used to describe the total amount of information that the neural code transfers between the ensemble of stimuli and the ensemble of neural responses. In addition, it is often desirable to know which features of the stimulus or response are most informative. The literature offers several different decompositions of the mutual information into its stimulus or response-specific components, such as the specific surprise or the uncertainty reduction, but the number of mutually distinct measures is in fact infinite. We resolve this ambiguity by requiring the specific information measures to be invariant under invertible coordinate transformations of the stimulus and the response ensembles. We prove that the Kullback-Leibler divergence is then the only suitable measure of the specific information. On a more general level, we discuss the necessity and the fundamental aspects of the coordinate invariance as a selection principle. We believe that our results will encourage further research into invariant statistical methods for the analysis of neural coding.

Efficiency of rate and latency coding with respect to metabolic cost and time

Recent studies on the theoretical performance of latency and rate code in single neurons have revealed that the ultimate accuracy is affected in a nontrivial way by aspects such as the level of spontaneous activity of presynaptic neurons, amount of neuronal noise or the duration of the time window used to determine the firing rate. This study explores how the optimal decoding performance and the corresponding conditions change when the energy expenditure of a neuron in order to spike and maintain the resting membrane potential is accounted for. It is shown that a nonzero amount of spontaneous activity remains essential for both the latency and the rate coding. Moreover, the optimal level of spontaneous activity does not change so much with respect to the intensity of the applied stimulus. Furthermore, the efficiency of the temporal and the rate code converge to an identical finite value if the neuronal activity is observed for an unlimited period of time.

Efficient information transfer by Poisson neurons

Recently, it has been suggested that certain neurons with Poissonian spiking statistics may communicate by discontinuously switching between two levels of firing intensity. Such a situation resembles in many ways the optimal information transmission protocol for the continuous-time Poisson channel known from information theory. In this contribution we employ the classical information-theoretic results to analyze the efficiency of such a transmission from different perspectives, emphasising the neurobiological viewpoint. We address both the ultimate limits, in terms of the information capacity under metabolic cost constraints, and the achievable bounds on performance at rates below capacity with fixed decoding error probability. In doing so we discuss optimal values of experimentally measurable quantities that can be compared with the actual neuronal recordings in a future effort.

Coding accuracy on the psychophysical scale

Sensory neurons are often reported to adjust their coding accuracy to the stimulus statistics. The observed match is not always perfect and the maximal accuracy does not align with the most frequent stimuli. As an alternative to a physiological explanation we show that the match critically depends on the chosen stimulus measurement scale. More generally, we argue that if we measure the stimulus intensity on the scale which is proportional to the perception intensity, an improved adjustment in the coding accuracy is revealed. The unique feature of stimulus units based on the psychophysical scale is that the coding accuracy can be meaningfully compared for different stimuli intensities, unlike in the standard case of a metric scale.