Attractor Reliability Reveals Deterministic Structure in Neuronal Spike Trains

• Published in: Neural computation 2002-07, Vol.14 (7), p.1629-1650
• Main Authors: Tiesinga, P. H. E., Fellous, J.-M., Sejnowski, Terrence J.
• Format: Article
• Language: English
• Subjects: Action Potentials - physiology; Algorithms; Animals; Biological and medical sciences; Computer Simulation; Exact sciences and technology; Fundamental and applied biological sciences. Psychology; General aspects; Lattice theory and statistics (ising, potts, etc.); Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Models, Neurological; Neurons - physiology; Physics; Reproducibility of Results; Statistical physics, thermodynamics, and nonlinear dynamical systems
• ISSN: 0899-7667; 1530-888X
• DOI: 10.1162/08997660260028647

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewal-like processes with the same spike-time histogram.