Abstract
At many synapses, repeated firing of the pre-synaptic neuron can lead to a transient decrease in the strengths of post-synaptic currents, for instance, because of neurotransmitter depletion [53]. This is called short-term depression. A phenomenological model of short-term depression was proposed by Tsodyks and Markram [165]. We describe it in Section 39.1.
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Notes
- 1.
If you know the definition of the Dirac delta function δ, then you will realize that γ is a smooth approximation of δ. However, I am presenting this derivation without assuming that you know what the delta function is.
- 2.
The function 1 + tanh(v∕10) is a fairly arbitrary choice here; compare exercise 20.1.
Bibliography
G. J. Augustine, How does calcium trigger neurotransmitter release?, Current Opinion in Neurobiology, 11 (2001), pp. 320–326.
D. Fioravante and W. G. Regehr, Short-term forms of presynaptic plasticity, Current Opinion in Neurobiology, 21 (2011), pp. 269–274.
T. Ishikawa, M. Kaneko, H.-S. Shin, and T. Takahashi, Presynaptic N-type and P/Q-type Ca2+ channels mediating synaptic transmission at the calyx of Held of mice, J. Physiol., 568 (2005), pp. 199–209.
B. Katz and R. Miledi, The role of calcium in neuromuscular facilitation, J. Physiol., 195 (1968), pp. 481–492.
M. Tsodyks, K. Pawelzik, and H. Markram, Neural networks with dynamic synapses, Neural Comp., 10 (1998), pp. 821–835.
M. V. Tsodyks and H. Markram, The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability, Proc. Natl. Acad. Sci. USA, 94 (1997), pp. 719–723.
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Börgers, C. (2017). Short-Term Depression and Facilitation. In: An Introduction to Modeling Neuronal Dynamics. Texts in Applied Mathematics, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-319-51171-9_39
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DOI: https://doi.org/10.1007/978-3-319-51171-9_39
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