Quantal Neurotransmitter Secretion Rate Exhibits Fractal Behavior

Abstract

The rate of exocytic events from both neurons and nonneuronal cells exhibits fluctuations consistent with fractal (selfsimilar) behavior in time, as evidenced by a number of statistical measures. We explicitly demonstrate this for neurotransmitter secretion at Xenopus neuromuscular junctions and for rat hippocampal synapses in culture; the exocytosis of exogenously supplied neurotransmitter from cultured Xenopus myocytes and from rat fibroblasts behaves similarly. The magnitude of the fluctuations of the rate of exocytic events about the mean decreases slowly as the rate is computed over longer and longer time periods, the periodogram decreases in power-law manner with frequency, and the Allan factor (relative variance of the number of exocytic events) increases as a power-law function of the counting time. These features are hallmarks of self-similar behavior. Their description requires models that exhibit long-range correlation (memory) in event occurrences. We have developed a physiologically plausible model that accords with all of the statistical measures that we have examined. The appearance of fractal behavior at synapses, as well as in systems comprising collections of synapses, indicates that such behavior is ubiquitous in neural signaling. Key words: quantal secretion; vesicular exocytosis; miniature endplate currents; fractal; long-term correlation; lognormal process; Xenopus neuromuscular junction; myocyte autoreception; fibroblast; hippocampal synapseCommunication in the nervous system is mediated by actionpotential-initiated exocytosis of multiple vesicular packets (quanta) of neurotransmitter (Katz, 1966). Even in the absence of such action potentials, however, many neurons spontaneously release individual packets of neurotransmitter (Fatt and Katz, 1952). A packet may contain from 7000 to 10,000 molecules of acetylcholine (ACh), if we use the neuromuscular junction as an example (Kuffler and Yoshikami, 1975). On arrival at the postsynaptic membrane, the ACh molecules induce elementary endplate currents (EEC s), which take the form of nonstationary two-(or multi-) state on -off sequences (Sakmann, 1992). Current flows when the ACh channel is open (i.e., when its two binding sites are occupied by agonist) and ceases when the channel is closed. A postsynaptic miniature endplate current (M EPC) comprises some 1000 EEC s (Sakmann, 1992). It was shown by Del Castillo and Katz (1954) that superpositions of M EPC -like events comprise the postsynaptic endplate currents elicited by nerve impulses.It generally has been assumed that the sequence of MEPCs forms a memoryless stochastic process (Fatt and Katz, 1952). However, Rotshenker and Rahamimoff (1970) discovered that exocytosis in the frog neuromuscular junction can exhibit correlation (memory) over a period of seconds, provided that extracellular C a 2ϩ levels are elevated above their normal values. Cohen et al. (1974b) subsequently found such correlation (event clustering) even in the absence of elevated Ca 2ϩ levels. In this paper we study the statis...

Nonrenewal spike train statistics: causes and functional consequences on neural coding

“…It has been observed that the Fano factor increases as a power law (i.e. F(T) ∞ T a with "a" being the power law exponent) for large T for a wide variety of spike trains Teich 1992, 1996;Lowen et al 1997;Teich et al 1997;Ratnam and Nelson 2000;Gussin et al 2007). As power law dependencies are self-similar on multiple timescales, this phenomenon has been referred to a fractal firing pattern and has been reviewed extensively.…”

History-Dependent Multiple-Time-Scale Dynamics in a Single-Neuron Model

“…Although this work has focused on models of a single neuron, it is acknowledged that multiple-time-scale dynamics are abundant at other levels of neural systems, for example, in single synapses (Lowen et al, 1997;Drew and Abbott, 2003;Fusi et al, 2005) or in networks of connected neurons. Computational or learning abilities will be significantly affected by the combination of all these levels in a way that is currently not understood.…”

“…Nonexponential adaptation and relaxation have been measured in several systems (Thorson and Biederman-Thorson, 1974;Xu et al, 1996); it has also been reported in the dynamics of synapses (Lowen et al, 1997) as well as in memory functions at the cognitive level (Wixted and Ebbesen, 1991;Anderson, 1995). At the level of the neuron, channel inactivation plays a role in spike frequency adaptation to step stimuli (Fleidervish et al, 1996), and in this context, we would like to understand how the model presented here, which is based on channel inactivation to modulate neural excitability, responds to the classic step stimulus experiment.…”

“…Indirect evidence for history dependent dynamics comes from scale-free fluctuations in the activity of neurons (Teich, 1989), heart cells (Soen and Braun, 2000), and synapses (Lowen et al, 1997). At a still higher level of organization, in vivo measurements on flies have shown that the time scales characteristic of adaptation in a visual interneuron depend on the conditioning stimulus parameters (de Ruyter van Steveninck et al, 1986;Fairhall et al, 2001).…”

The Pervasiveness of 1/f Scaling in Speech Reflects the Metastable Basis of Cognition

“…1/f scaling has also been found in intrinsic fluctuations of neural activity, such as current flow through neuronal ion channels (Banerjee, Verma, Manna, & Ghosh, 2006), rate of neurotransmitter secretion (Lowen, Cash, Poo, & Teich, 1997), interspike intervals between action potentials (Bhattacharya, Edwards, Mamelak, & Schuman, 2005), fluctuations in local field potentials (Leopold, Murayama, & Logothetis, 2003), amplitude levels within EEG and MEG frequency bands (Linkenkaer-Hansen, Nikouline, Palva, & Ilmoniemi, 2001), fluctuations in interchannel EEG synchronization (Gong, Nikolaev, & van Leeuwen, 2003;Stam & de Bruin, 2004), and voxel activations in functional magnetic resonance imaging (fMRI; Thurner, Windischberger, Moser, Walla, & Barth, 2003;Zarahn, Aguirre, & Desposito, 1997). Again, all of these protocols were well-suited for observing intrinsic fluctuations.…”