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Michael Stiber - One of the best experts on this subject based on the ideXlab platform.
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statistics of inverse interspike intervals the Instantaneous Firing Rate revisited
Chaos, 2018Co-Authors: Lubomir Kostal, Petr Lansky, Michael StiberAbstract:The Rate coding hypothesis is the oldest and still one of the most accepted and investigated scenarios in neuronal activity analyses. However, the actual neuronal Firing Rate, while informally understood, can be mathematically defined in several different ways. These definitions yield distinct results; even their average values may differ dramatically for the simplest neuronal models. Such an inconsistency, together with the importance of “Firing Rate,” motivates us to revisit the classical concept of the Instantaneous Firing Rate. We confirm that different notions of Firing Rate can in fact be compatible, at least in terms of their averages, by carefully discerning the time instant at which the neuronal activity is observed. Two general cases are distinguished: either the inspection time is synchronised with a reference time or with the neuronal spiking. The statistical properties of the Instantaneous Firing Rate, including parameter estimation, are analyzed, and compatibility with the intuitively understood concept is demonstRated.The Rate coding hypothesis is the oldest and still one of the most accepted and investigated scenarios in neuronal activity analyses. However, the actual neuronal Firing Rate, while informally understood, can be mathematically defined in several different ways. These definitions yield distinct results; even their average values may differ dramatically for the simplest neuronal models. Such an inconsistency, together with the importance of “Firing Rate,” motivates us to revisit the classical concept of the Instantaneous Firing Rate. We confirm that different notions of Firing Rate can in fact be compatible, at least in terms of their averages, by carefully discerning the time instant at which the neuronal activity is observed. Two general cases are distinguished: either the inspection time is synchronised with a reference time or with the neuronal spiking. The statistical properties of the Instantaneous Firing Rate, including parameter estimation, are analyzed, and compatibility with the intuitively unders...
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periodically modulated inhibition and its postsynaptic consequences ii influence of modulation slope depth range noise and of postsynaptic natural discharges
Neuroscience, 1995Co-Authors: J P Segundo, Michael Stiber, J F Vibert, Sylvain HannetonAbstract:This paper examines the relation, or "synaptic coding", between the discharges of inhibitory fibres whose Instantaneous Firing Rate is modulated periodically and pacemaker postsynaptic neurons using crayfish synapses and point process statistics. Several control parameters were varied individually, and the other maintained constant as far as possible: it extends the preceding publication that described the general features and varied only the modulation frequency [Segundo et al. (1995) Neuroscience 68, 657-692]. Statistics were mainly cycle histograms and Lissajous diagrams (with presynaptic and post-synaptic histograms on the abscissae and ordinate, respectively), complemented occasionally by displays of intervals along time and of interval differences along order ("basic graphs" and "recurrence plots", respectively). The postsynaptic influence of modulated inhibitory discharges is characteristically sensitive to all control parameters examined. (1) The frequency was reported in the companion paper [Segundo et al. (1995) Neuroscience 68, 657-692]. (2) The average slope per half-cycle, controlled via either frequency or depth, acts by way of its magnitude and sign in ways revealed by hysteretic loops. Hysteresis increases and varies as the modulation's steepness increases: it is minor and with a single clockwise loop at small slopes, but major and multi-looped at the larger ones. Slopes, because of their different postsynaptic consequences, were sepaRated into the categories of "steep", "gentle" and "abrupt" if around, respectively, 1.0, 30.0 and 150.0 s-2. The influence of slopes in restricted portions of the cycle depends on their position on the inhibitory Rate scale. (3) The modulation's range acts by way of its depth and of its position on the inhibitory Rate scale. Deeper ranges, when compared with the shallower ones they contain, induce effects similar to those of shallower modulations with their central portion, plus effects peculiar to them at extreme Rates. Changes in range position from the centre to the extremes of the inhibitory Rate scale are influential (e.g., saturations appear). Changes within the centre can be highly influential, particularly when ranges are narrow and close to the postsynaptic natural Rate, and modulation frequencies are low: relations between corresponding Rates can be linear increasing, linear decreasing or piecewise linear. Changes around extreme Rates are negligible, however, and saturations are present. (4) The usual modulations whose individual cycles did not differ from the cycle histogram were compared to others with the same cycle histograms but whose individual cycles had an unpredictable fast variability referred to as "noise".(ABSTRACT TRUNCATED AT 400 WORDS)
Nicolas Brunel - One of the best experts on this subject based on the ideXlab platform.
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from spiking neuron models to linear nonlinear models
PLOS Computational Biology, 2011Co-Authors: Srdjan Ostojic, Nicolas BrunelAbstract:Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent Rate. The mapping from current input to output Firing Rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output Firing Rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integRate-and-fire (LIF), exponential integRate-and-fire (EIF) and conductance-based Wang-Buzsaki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accuRate estimates of the Firing Rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsaki models, we show that the LN cascade can be reduced to a Firing Rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale Rate model in which the timescale of the linear filter depends on the Instantaneous Firing Rate. This model leads to highly accuRate estimates of Instantaneous Firing Rates.
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dynamics of the Instantaneous Firing Rate in response to changes in input statistics
Journal of Computational Neuroscience, 2005Co-Authors: Nicolas Fourcaudtrocme, Nicolas BrunelAbstract:We review and extend recent results on the Instantaneous Firing Rate dynamics of simplified models of spiking neurons in response to noisy current inputs. It has been shown recently that the response of the Instantaneous Firing Rate to small amplitude oscillations in the mean inputs depends in the large frequency limit f on the spike initiation dynamics. A particular simplified model, the exponential integRate-and-fire (EIF) model, has a response that decays as 1/f in the large frequency limit and describes very well the response of conductance-based models with a Hodgkin-Huxley type fast sodium current. Here, we show that the response of the EIF Instantaneous Firing Rate also decays as 1/f in the case of an oscillation in the variance of the inputs for both white and colored noise. We then compute the initial transient response of the Firing Rate of the EIF model to a step change in its mean inputs and/or in the variance of its inputs. We show that in both cases the response speed is proportional to the neuron stationary Firing Rate and inversely proportional to a ‘spike slope factor’ Δ T that controls the sharpness of spike initiation: as 1/Δ T for a step change in mean inputs, and as 1/Δ T 2 for a step change in the variance in the inputs.
Aftab E Patla - One of the best experts on this subject based on the ideXlab platform.
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models of recruitment and Rate coding organization in motor unit pools
Journal of Neurophysiology, 1993Co-Authors: Andrew J Fuglevand, David A Winter, Aftab E PatlaAbstract:1. Isometric muscle force and the surface electromyogram (EMG) were simulated from a model that predicted recruitment and Firing times in a pool of 120 motor units under different levels of excitatory drive. The EMG-force relationships that emerged from simulations using various schedules of recruitment and Rate coding were compared with those observed experimentally to determine which of the modeled schemes were plausible representations of the actual organization in motor-unit pools. 2. The model was comprised of three elements: a motoneuron model, a motor-unit force model, and a model of the surface EMG. Input to the neuron model was an excitatory drive function representing the net synaptic input to motoneurons during voluntary muscle contractions. Recruitment thresholds were assigned such that many motoneurons had low thresholds and relatively few neurons had high thresholds. Motoneuron Firing Rate increased as a linear function of excitatory drive between recruitment threshold and peak Firing Rate levels. The sequence of discharge times for each motoneuron was simulated as a random renewal process. 3. Motor-unit twitch force was estimated as an impulse response of a critically damped, second-order system. Twitch amplitudes were assigned according to rank in the recruitment order, and twitch contraction times were inversely related to twitch amplitude. Nonlinear force-Firing Rate behavior was simulated by varying motor-unit force gain as a function of the Instantaneous Firing Rate and the contraction time of the unit. The total force exerted by the muscle was computed as the sum of the motor-unit forces. 4. Motor-unit action potentials were simulated on the basis of estimates of the number and location of motor-unit muscle fibers and the propagation velocity of the fiber action potentials. The number of fibers innervated by each unit was assumed to be directly proportional to the twitch force. The area of muscle encompassing unit fibers was proportional to the number of fibers innervated, and the location of motor-unit territories were randomly assigned within the muscle cross section. Action-potential propagation velocities were estimated from an inverse function of contraction time. The train of discharge times predicted from the motoneuron model determined the occurrence of each motor-unit action potential. The surface EMG was synthesized as the sum of all motor-unit action-potential trains. 5. Two recruitment conditions were tested: narrow (limit of recruitment 70% maximum excitation).(ABSTRACT TRUNCATED AT 400 WORDS)
R N Lemon - One of the best experts on this subject based on the ideXlab platform.
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synchronization in monkey motor cortex during a precision grip task i task dependent modulation in single unit synchrony
Journal of Neurophysiology, 2001Co-Authors: Stuart N Baker, Rachel L Spinks, Andrew Jackson, R N LemonAbstract:Neural synchronization in the cortex, and its potential role in information coding, has attracted much recent attention. In this study, we have recorded long spike trains (mean, 33,000 spikes) simultaneously from multiple single neurons in the primary motor cortex (M1) of two conscious macaque monkeys performing a precision grip task. The task required the monkey to use its index finger and thumb to move two spring-loaded levers into a target, hold them there for 1 s, and release for a food reward. Synchrony was analyzed using a time-resolved cross-correlation method, normalized using an estimate of the Instantaneous Firing Rate of the cell. This was shown to be more reliable than methods using trial-averaged Firing Rate. A total of 375 neurons was recorded from the M1 hand area; 235 were identified as pyramidal tract neurons. Synchrony was weak [mean k' = 1.05 +/- 0.04 (SD)] but widespread among pairs of M1 neurons (218/1359 pairs with above-chance synchrony), including output neurons. Synchrony usually took the form of a broad central peak [average width, 18.7 +/- 8.7 (SD) ms]. There were marked changes during different phases of the task. As a population, synchrony was greatest during the steady hold period in striking contrast to the averaged cell Firing Rate, which was maximal when the animal was moving the levers into target. However, the modulation of synchrony during task performance showed considerable variation across individual cell pairs. Two types of synchrony were identified: oscillatory (with periodic side lobes in the cross-correlation) and nonoscillatory. Their relative contributions were quantified by filtering the cross-correlations to exclude either frequencies from 18 to 37 Hz or all higher and lower frequencies. At the peak of population synchrony during the hold period, about half (51.7% in one monkey, 56.2% in the other) of the synchronization was within this oscillatory bandwidth. This study provides strong support for assemblies of neurons being synchronized during specific phases of a complex task with potentially important consequences for both information processing within M1 and for the impact of M1 commands on target motoneurons.
Timothy C Cope - One of the best experts on this subject based on the ideXlab platform.
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modulation of motoneuron Firing by recurrent inhibition in the adult rat in vivo
Journal of Neurophysiology, 2014Co-Authors: Ahmed Z. Obeidat, Paul Nardelli, Randall K Powers, Timothy C CopeAbstract:Recent reports show that synaptic inhibition can modulate postsynaptic spike timing without having strong effects on Firing Rate. Thus synaptic inhibition can achieve multiplicity in neural circuit operation through variable modulation of postsynaptic Firing Rate vs. timing. We tested this possibility for recurrent inhibition (RI) of spinal motoneurons. In in vivo electrophysiological studies of adult Wistar rats anesthetized by isoflurane, we examined repetitive Firing of individual lumbosacral motoneurons recorded in current clamp and modulated by synchronous antidromic electrical stimulation of multiple motor axons and their centrally projecting collateral branches. Antidromic stimulation produced recurrent inhibitory postsynaptic potentials (RIPSPs) having properties similar to those detailed in the cat. Although synchronous RI produced marked short-term modulation of motoneuron spike timing and Instantaneous Firing Rate, there was little or no suppression of average Firing Rate. The bias in Firing modulation of timing over average Rate was observed even for high-frequency RI stimulation (100 Hz), perhaps because of the brevity of RIPSPs, which were more than twofold shorter during motoneuron Firing compared with rest. These findings demonstRate that RI in the mammalian spinal cord has the capacity to support and not impede heightened motor pool activity, possibly during rapid, forceful movements.