Abstract
The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential (AP) at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of AP arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic AP, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.
Highlights
The release of vesicles following arrival of a pre-synaptic action potential (AP) at a synapse is inherently probabilistic (Vere-Jones, 1966; Melkonian and Kostopoulos, 1996; Branco and Staras, 2009)
The amount of neurotransmitter released by each AP can vary stochastically over time, in a manner dependent on the timing of previously arriving APs (Dobrunz and Stevens, 1997)
It has been suggested that the short term dynamics such plasticity introduces may play an important role in information processing in the cortex (Abbott and Regehr, 2004; Branco and Staras, 2009)
Summary
The release of vesicles following arrival of a pre-synaptic action potential (AP) at a synapse is inherently probabilistic (Vere-Jones, 1966; Melkonian and Kostopoulos, 1996; Branco and Staras, 2009). It has been suggested that the short term dynamics such plasticity introduces may play an important role in information processing in the cortex (Abbott and Regehr, 2004; Branco and Staras, 2009) This has been demonstrated in studies of the influence of shortterm plasticity on: gain control (Abbott et al, 1997); coding and detection mechanisms (Tsodyks and Markram, 1997; Maass and Zador, 1999); filtering effects (Matveev and Wang, 2000a; Merkel and Lindner, 2010; Rosenbaum et al, 2012); redundancy reduction (Goldman et al, 2002); information transmission (Goldman, 2004); membrane potential estimation (Pfister et al, 2010); attractor networks (Fung et al, 2012); and correlations in neural activity (Rosenbaum et al, 2013). The consequence of this assumption is that simulations of this type of model of short term plasticity provides deterministic outcomes, in the sense that they do not produce varying outcomes if repeated trials with identical initial conditions are simulated
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