Special issue on quantitative neuron modeling

Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity

The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here, we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal spiking activity. Since analytical expressions of the first passage time density are not available, we propose to approximate the curved boundary by means of a continuous two-piecewise linear threshold. Explicit expressions for the first passage time density towards the new boundary are provided. First, we introduce different approximating linear thresholds. Then, we describe how to choose the optimal one minimizing the distance to the curved boundary, and hence the error in the corresponding passage time density. Theoretical means, variances and coefficients of variation given by our method are compared with empirical quantities from simulated data. Moreover, a further comparison with firing statistics derived under the assumption of a small amplitude of the time-dependent change in the threshold, is also carried out. Finally, maximum likelihood and moment estimators of the parameters of the model are derived and applied on simulated data.

Automatic parameter estimation of multicompartmental neuron models via minimization of trace error with control adjustment

We describe a new technique to fit conductance-based neuron models to intracellular voltage traces from isolated biological neurons. The biological neurons are recorded in current-clamp with pink (1/f) noise injected to perturb the activity of the neuron. The new algorithm finds a set of parameters that allows a multicompartmental model neuron to match the recorded voltage trace. Attempting to match a recorded voltage trace directly has a well-known problem: mismatch in the timing of action potentials between biological and model neuron is inevitable and results in poor phenomenological match between the model and data. Our approach avoids this by applying a weak control adjustment to the model to promote alignment during the fitting procedure. This approach is closely related to the control theoretic concept of a Luenberger observer. We tested this approach on synthetic data and on data recorded from an anterior gastric receptor neuron from the stomatogastric ganglion of the crab Cancer borealis. To test the flexibility of this approach, the synthetic data were constructed with conductance models that were different from the ones used in the fitting model. For both synthetic and biological data, the resultant models had good spike-timing accuracy.

Transmission efficiency in ring, brain inspired neuronal networks. Information and energetic aspects

Organisms often evolve as compromises, and many of these compromises can be expressed in terms of energy efficiency. Thus, many authors analyze energetic costs processes during information transmission in the brain. In this paper we study information transmission rate per energy used in a class of ring, brain inspired neural networks, which we assume to involve components like excitatory and inhibitory neurons or long-range connections. Choosing model of neuron we followed a probabilistic approach proposed by Levy and Baxter (2002), which contains all essential qualitative mechanisms participating in the transmission process and provides results consistent with physiologically observed values. Our research shows that all network components, in broad range of conditions, significantly improve the information-energetic efficiency. It turned out that inhibitory neurons can improve the information-energetic transmission efficiency by 50%, while long-range connections can improve the efficiency even by 70%. We also found that the most effective is the network with the smallest size: we observed that two times increase of the size can cause even three times decrease of the information-energetic efficiency. This article is part of a Special Issue entitled Neural Coding 2012.