VOLUME 86, NUMBER 16 PHYSICAL REVIEW LETTERS 16 APRIL 2001 Correlation Detection and Resonance in Neural Systems with Distributed Noise Sources Michael Rudolph Department of Physiology, Laval University, Québec G1K 7P4, Canada Alain Destexhe Unité de Neurosciences Intégratives et Computationnelles, CNRS, UPR-2191 Gif-sur-Yvette, France (Received 18 September 2000) We investigated the resonance behavior in model neurons receiving a large number of random synaptic inputs, whose distributed nature permits one to introduce correlations between them and investigate its effect on cellular responsiveness. A change in the strength of this background led to enhanced responsive- ness, consistent with stochastic resonance. Altering the correlation revealed a type of resonance behavior in which the neuron is sensitive to statistical properties rather than the strength of the noise. Remarkably, the neuron could detect weak correlations among the distributed inputs within millisecond time scales. DOI: 10.1103/PhysRevLett.86.3662 PACS numbers: 87.10.+e, 02.50.Fz, 05.40. –a Phenomena such as the amplification of weak signals or the improvement of information transfer capacity in non- linear dynamical systems in the presence of noise, origi- nally proposed as a possible explanation for the periodicity of Earth’s ice ages [1] and now well established under the term stochastic resonance (SR) [2], have been shown to be inherent properties of many physical, chemical, and biological systems (see [3] for a comprehensive review). Especially neural systems, whose excitable dynamical properties, highly nonlinear responses, and noisy envi- ronments provide one of the most natural system that could display SR, are subject to an increasing number of theoretical [4,5] and experimental [6,7] investigations. However, although these studies indicate that stochastic mechanisms could play an essential role in sensory and pe- ripheral nervous systems, due to experimental difficulties, the presence of SR in more central neural systems, such as the cerebral cortex, remains only poorly characterized [8]. Neocortical pyramidal cells are embedded in a very dense network and receive several thousand synaptic in- puts from other neurons [9]. Given that, on average, cor- tical neurons fire tonically at frequencies up to 20 Hz in awake animals [10], these neurons are subject to a tremen- dous synaptic background activity [11,12]. The release characteristics at each synapse (frequency, conductance, random nature) during background activity were estimated from a combination of intracellular recordings with mod- els of reconstructed cortical neurons [13]. These models established that background activity could be reproduced by distributed random inputs, in which all synapses release randomly according to Poisson processes with an average frequency of 1 and 5.5 Hz for excitatory and inhibitory synapses, respectively. Because this background activity is omnipresent in cortical neurons, a natural question to ask is whether this activity could induce effects comparable to SR, and there- fore could play a similar role as the external noise in sensory neural systems. We have investigated this possi- bility by using detailed biophysical models of neocortical neurons with spatially extended dendrites, subject to dis- tributed random inputs. In contrast to previous studies [8], this extended dendritic structure allows one to modulate different aspects of the noise applied to the system. The membrane equation was described by the standard cable equation (e.g., [14]), voltage-dependent currents for gener- ating action potentials were described by Hodgkin-Huxley equations [15], and synaptic currents were described by kinetic equations of transmitter-receptor interactions [16] (see Appendix and [13]). These models successfully reflect experimental measurements obtained in living biological systems and, thus, can be viewed as realistic models of the neuronal biophysics in active states. We first investigated the presence of classical SR [2] in this system. The signal to be detected, a subthreshold pe- riodic stimulation, was added by introducing a supplemen- tary set of excitatory synapses uniformly distributed in the dendrites and firing with a constant period of 100 ms (see details in [17]). To quantify the response to this additional stimulus, we made use of a special coherence measure based upon the statistical properties of spike trains, defined by COS  N ISI N spikes , where N ISI denotes the number of interspike intervals of length equal to the stimulus pe- riod, and N spikes denotes the total number of spikes within a fixed time interval [6]. In contrast to other well-known measures like the signal-to-noise ratio or the synchroniza- tion index [18], this coherence measure reflects in a direct way the threshold nature of the response and, thus, is well suited to capture the response behavior of spiking systems with simple stimulation patterns. To vary the strength of the noise in this distributed sys- tem, the release frequency of excitatory synapses generat- ing the background activity was changed within a range of 50%–200% around the optimal value of 1 Hz established previously [13]. This frequency change directly impacted on the amplitude of the internal membrane voltage fluc- tuations (Fig. 1A). The response coherence showed a resonance peak when depicted as a function of the background strength or the resulting internal noise level 3662 0031-9007 01  86(16)  3662(4)$15.00 © 2001 The American Physical Society