Comparison of local measures of spike time irregularity and relating variability to firing rate in motor cortical neurons Adrián Ponce-Alvarez & Bjørg Elisabeth Kilavik & Alexa Riehle Received: 20 December 2008 / Revised: 13 March 2009 / Accepted: 21 April 2009 / Published online: 16 May 2009 # Springer Science + Business Media, LLC 2009 Abstract Spike time irregularity can be measured by the coefficient of variation. However, it overestimates the irregularity in the case of pronounced firing rate changes. Several alternative measures that are local in time and therefore relatively rate-independent were proposed. Here we compared four such measures: CV 2 , LV, IR and SI. First, we asked which measure is the most efficient for time-resolved analyses of experimental data. Analytical results show that CV 2 has the less variable estimates. Second, we derived useful properties of CV 2 for gamma processes. Third, we applied CV 2 on recordings from the motor cortex of a monkey performing a delayed motor task to characterize the irregularity, that can be modulated or not, and decoupled or not from firing rate. Neurons with a CV 2 -rate decoupling have a rather constant CV 2 and discharge mainly irregularly. Neurons with a CV 2 -rate coupling can modulate their CV 2 and explore a larger range of CV 2 values. Keywords Spike time irregularity . Firing rate . Monkey motor cortex 1 Introduction Cortical neurons exhibit highly irregular inter-spike inter- vals (ISIs) (Softky and Koch 1993). The irregularity of spike timing has recently been the subject of considerable discussion in the literature. Understanding the origins and the functional meanings of spike time irregularity has important implications for elucidating the neural code, in particular it is not clear if it facilitates or rather impairs the flow of information. It was proposed that differences in irregularity could be in part due to differences in single cell intrinsic characteristics (Gutkin and Ermentrout 1998; Christodoulou and Bugmann 2001), input synchrony (Stevens and Zador 1998; Sakai et al. 1999), or differences in the balance of excitatory and inhibitory inputs to the neurons, which determines the statistics of the net input (Nawrot et al. 2008; Salinas and Sejnowski 2000; Amit and Brunel 1997; van Vreeswijk and Sompolinsky 1996; Shadlen and Newsome 1994, 1998). It has recently been shown that a neuron receiving balanced synaptic inputs can keep constant its irregularity and thus the estimation of its instantaneous firing rate is improved (Miura et al. 2007). There is experimental evidence that the intrinsic irregularity of neurons in the awake monkey is constant (Shinomoto et al. 2003). However, changes in irregularity have also been reported (Davies et al. 2006; Compte et al. 2003) in different cortical areas and different behavioral tasks. According to this view, irregularity is thought to indicate the presence of temporal coding (Stevens and Zador 1998; Mainen and Sejnowski 1995). The classical measure of spike time irregularity is the coefficient of variation (CV), which is a global measure defined as the dispersion of the ISIs, i.e. SD(ISI)/mean(ISI). The CV of cortical neurons falls roughly in the range between 0.2 and 1.5 (Softky and Koch 1993). However, the CV largely overestimates the irregularity of firing in the case of pronounced changes in firing rate. This led several researchers to propose alternative measures of irregularity that are local in time and therefore relatively independent of rate changes. However, to our knowledge, these measures J Comput Neurosci (2010) 29:351–365 DOI 10.1007/s10827-009-0158-2 Action Editor: Rob Kass A. Ponce-Alvarez (*) : B. E. Kilavik : A. Riehle Institut de Neurosciences Cognitives de la Méditerranée, CNRS-Université de la Méditerranée, Marseille, France e-mail: adrian.ponce@incm.cnrs-mrs.fr