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Short-term plasticity (STP) ([[#Stevens95|Stevens 95]], [[#Markram96|Markram 96]], [[#Abbott97|Abbott 97]], [[#Zucker02|Zucker 02]], [[#Abbott04|Abbott 04]]), also called dynamical synapses, refers to a phenomenon in which synaptic efficacy changes over time in a way that reflects the history of presynaptic activity. Two types of STP, with opposite effects on synaptic efficacy, have been observed in experiments. They are known as Short-Term Depression (STD) and Short-Term Facilitation (STF). STD is caused by depletion of neurotransmitters consumed during the synaptic signaling process at the axon terminal of a pre-synaptic neuron, whereas STF is caused by influx of calcium into the axon terminal after spike generation, which increases the release probability of neurotransmitters. STP has been found in various cortical regions and exhibits great diversity in properties ([[#Markram98|Markram 98]], [[#Dittman00|Dittman 00]], [[#Wang06|Wang 06]]). Synapses in different cortical areas can have varied forms of plasticity, being either STD-dominated, STF-dominated, or showing a mixture of both forms.

Short-term plasticity (STP) ([[#Stevens95|Stevens 95]], [[#Markram96|Markram 96]], [[#Abbott97|Abbott 97]], [[#Zucker02|Zucker 02]], [[#Abbott04|Abbott 04]]), also called dynamical synapses, refers to a phenomenon in which synaptic efficacy changes over time in a way that reflects the history of presynaptic activity. Two types of STP, with opposite effects on synaptic efficacy, have been observed in experiments. They are known as Short-Term Depression (STD) and Short-Term Facilitation (STF). STD is caused by depletion of neurotransmitters consumed during the synaptic signaling process at the axon terminal of a pre-synaptic neuron, whereas STF is caused by influx of calcium into the axon terminal after spike generation, which increases the release probability of neurotransmitters. STP has been found in various cortical regions and exhibits great diversity in properties ([[#Markram98|Markram 98]], [[#Dittman00|Dittman 00]], [[#Wang06|Wang 06]]). Synapses in different cortical areas can have varied forms of plasticity, being either STD-dominated, STF-dominated, or showing a mixture of both forms.

短期可塑性 (STP) (Stevens 95, Markram 96, Abbott 97, Zucker 02, Abbott 04)，也称为动态突触，是指突触功效随时间以反映突触前活动历史的方式变化的现象 . 在实验中观察到两种对突触功效具有相反影响的 STP。 它们被称为短期抑郁症（STD）和短期促进（STF）。 STD 是由突触前神经元轴突末端的突触信号传导过程中消耗的神经递质消耗引起的，而 STF 是由尖峰产生后钙流入轴突末端引起的，这增加了神经递质的释放概率。 STP 已在不同的皮层区域发现并表现出极大的多样性（Markram 98、Dittman 00、Wang 06）。 不同皮层区域的突触可以具有不同形式的可塑性，要么以 STD 为主，要么以 STF 为主，或显示两种形式的混合。

短期可塑性 (STP) ([[#Stevens95|Stevens 95]], [[#Markram96|Markram 96]], [[#Abbott97|Abbott 97]], [[#Zucker02|Zucker 02]], [[#Abbott04|Abbott 04]])，也称为动态突触，是指突触功效随时间以反映突触前活动历史的方式变化的现象 . 在实验中观察到两种对突触功效具有相反影响的 STP。 它们被称为短期抑郁症（STD）和短期促进（STF）。 STD 是由突触前神经元轴突末端的突触信号传导过程中消耗的神经递质消耗引起的，而 STF 是由尖峰产生后钙流入轴突末端引起的，这增加了神经递质的释放概率。 STP 已在不同的皮层区域发现并表现出极大的多样性（Markram 98、Dittman 00、Wang 06）。 不同皮层区域的突触可以具有不同形式的可塑性，要么以 STD 为主，要么以 STF 为主，或显示两种形式的混合。

Compared with long-term plasticity ([[#Bi01|Bi 01]]), which is hypothesized as the neural substrate for experience-dependent modification of neural circuit, STP has a shorter time scale, typically on the order of hundreds to thousands of milliseconds.  The modification it induces to synaptic efficacy is temporary.  Without continued presynaptic activity, the synaptic efficacy will quickly return to its baseline level.

Compared with long-term plasticity ([[#Bi01|Bi 01]]), which is hypothesized as the neural substrate for experience-dependent modification of neural circuit, STP has a shorter time scale, typically on the order of hundreds to thousands of milliseconds.  The modification it induces to synaptic efficacy is temporary.  Without continued presynaptic activity, the synaptic efficacy will quickly return to its baseline level.

The biophysical processes underlying STP are complex. Studies of the computational roles of STP have relied on the creation of simplified phenomenological models ([[#Abbott97|Abbott 97]],[[#Markram98|Markram 98]],[[#Tsodyks98|Tsodyks 98]]).

The biophysical processes underlying STP are complex. Studies of the computational roles of STP have relied on the creation of simplified phenomenological models ([[#Abbott97|Abbott 97]],[[#Markram98|Markram 98]],[[#Tsodyks98|Tsodyks 98]]).

In the model proposed by Tsodyks and Markram ([[#Tsodyks98|Tsodyks 98]]), the STD effect is modeled by a normalized variable <math>x</math> (<math>0\leq x \leq1</math>), denoting the fraction of resources that remain available after neurotransmitter depletion. The STF effect is modeled by a utilization parameter <math>u</math>, representing the fraction of available resources ready for use (release probability). Following a spike, (i) <math>u</math> increases due to spike-induced calcium influx to the presynaptic terminal, after which (ii) a fraction <math>u</math> of available resources is consumed to produce the post-synaptic current. Between spikes, <math>u</math> decays back to zero with time constant <math>\tau_f</math> and <math>x</math> recovers to 1 with time constant <math>\tau_d </math>. In summary, the dynamics of STP is given by

In the model proposed by Tsodyks and Markram ([[#Tsodyks98|Tsodyks 98]]), the STD effect is modeled by a normalized variable <math>x</math> (<math>0\leq x \leq1</math>), denoting the fraction of resources that remain available after neurotransmitter depletion. The STF effect is modeled by a utilization parameter <math>u</math>, representing the fraction of available resources ready for use (release probability). Following a spike, (i) <math>u</math> increases due to spike-induced calcium influx to the presynaptic terminal, after which (ii) a fraction <math>u</math> of available resources is consumed to produce the post-synaptic current. Between spikes, <math>u</math> decays back to zero with time constant <math>\tau_f</math> and <math>x</math> recovers to 1 with time constant <math>\tau_d </math>. In summary, the dynamics of STP is given by

:<math>\begin{aligned}

:<math>\begin{aligned}

where <math>t_{sp}</math> denotes the spike time and <math>U</math> is the increment of <math>u</math> produced by a spike. We denote as <math>u^-, x^-</math> the corresponding variables just before the arrival of the spike, and <math>u^+</math> refers to the moment just after the spike. From the first equation, <math>u^+ = u^- + U(1-u^-)</math>. The synaptic current generated at the synapse by the spike arriving at <math>t_{sp}</math> is then given by

where <math>t_{sp}</math> denotes the spike time and <math>U</math> is the increment of <math>u</math> produced by a spike. We denote as <math>u^-, x^-</math> the corresponding variables just before the arrival of the spike, and <math>u^+</math> refers to the moment just after the spike. From the first equation, <math>u^+ = u^- + U(1-u^-)</math>. The synaptic current generated at the synapse by the spike arriving at <math>t_{sp}</math> is then given by

:<math>\Delta I(t_{sp}) = Au^+x^-,

:<math>\Delta I(t_{sp}) = Au^+x^-,

where <math>A</math> denotes the response amplitude that would be produced by total release of all the neurotransmitter (<math>u=x=1</math>), called absolute synaptic efficacy of the connections (see Fig. 1A).

where <math>A</math> denotes the response amplitude that would be produced by total release of all the neurotransmitter (<math>u=x=1</math>), called absolute synaptic efficacy of the connections (see Fig. 1A).

The interplay between the dynamics of <math>u</math> and <math>x</math> determines whether the joint effect of <math>ux</math> is dominated by depression or facilitation. In the parameter regime of <math>\tau_d\gg \tau_f</math> and large <math>U</math>, an initial spike incurs a large drop in <math>x</math> that takes a long time to recover; therefore the synapse is STD-dominated (Fig.1B). In the regime of <math>\tau_f \gg \tau_d</math> and small <math>U</math>, the synaptic efficacy is increased gradually by spikes, and consequently the synapse is STF-dominated (Fig.1C). This phenomenological model successfully reproduces the kinetic dynamics of depressed and facilitated synapses observed in many cortical areas.

The interplay between the dynamics of <math>u</math> and <math>x</math> determines whether the joint effect of <math>ux</math> is dominated by depression or facilitation. In the parameter regime of <math>\tau_d\gg \tau_f</math> and large <math>U</math>, an initial spike incurs a large drop in <math>x</math> that takes a long time to recover; therefore the synapse is STD-dominated (Fig.1B). In the regime of <math>\tau_f \gg \tau_d</math> and small <math>U</math>, the synaptic efficacy is increased gradually by spikes, and consequently the synapse is STF-dominated (Fig.1C). This phenomenological model successfully reproduces the kinetic dynamics of depressed and facilitated synapses observed in many cortical areas.

[[Image:Fig1A_short_term_plasticity.png|400px|链接=Special:FilePath/Fig1A_short_term_plasticity.png]]

[[Image:Fig1A_short_term_plasticity.png|400px|链接=Special:FilePath/Fig1A_short_term_plasticity.png]]

Figure 1. (A) The phenomenological model for STP given by Eqs.\ref{model} and \ref{current}. (B) The post-synaptic current generated by an STD-dominated synapse. The neuronal firing rate <math>R=15</math>Hz. The parameters <math>A=1</math>, <math>U=0.45</math>, <math>\tau_s=20</math>ms, <math>\tau_d=750</math>ms, and <math>\tau_f=50</math>ms. (C) The dynamics of a STF-dominating synapse. The parameters <math>U=0.15</math>, <math>\tau_f=750</math>ms, and <math>\tau_d=50</math>ms.

Figure 1. (A) The phenomenological model for STP given by Eqs.\ref{model} and \ref{current}. (B) The post-synaptic current generated by an STD-dominated synapse. The neuronal firing rate <math>R=15</math>Hz. The parameters <math>A=1</math>, <math>U=0.45</math>, <math>\tau_s=20</math>ms, <math>\tau_d=750</math>ms, and <math>\tau_f=50</math>ms. (C) The dynamics of a STF-dominating synapse. The parameters <math>U=0.15</math>, <math>\tau_f=750</math>ms, and <math>\tau_d=50</math>ms.

== Effects on information transmission==

图 1. (A) 由 Eqs.\ref{model} 和 \ref{current} 给出的 STP 现象学模型。 (B) 由 STD 主导的突触产生的突触后电流。 神经元放电率 [math]\displaystyle{ R=15 }[/math]Hz。 参数 [math]\displaystyle{ A=1 }[/math], [math]\displaystyle{ U=0.45 }[/math], [math]\displaystyle{ \tau_s=20 }[/math]ms, [ math]\displaystyle{ \tau_d=750 }[/math]ms 和 [math]\displaystyle{ \tau_f=50 }[/math]ms。 (C) STF 主导突触的动力学。 参数 [math]\displaystyle{ U=0.15 }[/math]、[math]\displaystyle{ \tau_f=750 }[/math]ms 和 [math]\displaystyle{ \tau_d=50 }[/math] 小姐。

 

== 对信息传输的影响Effects on information transmission==

Because STP modifies synaptic efficacy based on the history of presynaptic activity, it can alter neural information transmission ([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]]). In general, an STD-dominated synapse favors information transfer for low firing rates, since high-frequency spikes rapidly deactivate the synapse. An STF-dominated synapse, however, tends to optimize information transfer for high-frequency bursts, which increase the synaptic strength.  

Because STP modifies synaptic efficacy based on the history of presynaptic activity, it can alter neural information transmission ([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]]). In general, an STD-dominated synapse favors information transfer for low firing rates, since high-frequency spikes rapidly deactivate the synapse. An STF-dominated synapse, however, tends to optimize information transfer for high-frequency bursts, which increase the synaptic strength.  

Firing-rate-dependent transmission via dynamic synapses can be analyzed by examining the transmission of uncorrelated Poisson spike trains from a large neuronal population with global firing rate <math>R(t)</math>. The time evolution for the postsynaptic current <math>I(t)</math> can be obtained by averaging Eq. \ref{model} over different realization of Poisson processes corresponding to different spike trains ([[#Tsodyks98|Tsodyks 98]]):

Firing-rate-dependent transmission via dynamic synapses can be analyzed by examining the transmission of uncorrelated Poisson spike trains from a large neuronal population with global firing rate <math>R(t)</math>. The time evolution for the postsynaptic current <math>I(t)</math> can be obtained by averaging Eq. \ref{model} over different realization of Poisson processes corresponding to different spike trains ([[#Tsodyks98|Tsodyks 98]]):

:<math>\begin{aligned}

:<math>\begin{aligned}

where again <math>u^+ = u^- + U(1-u^-)</math> and we neglect time scales on the order of the synaptic time constant. For the stationary rate, <math>R(t) \equiv R_0</math>, we obtain

where again <math>u^+ = u^- + U(1-u^-)</math> and we neglect time scales on the order of the synaptic time constant. For the stationary rate, <math>R(t) \equiv R_0</math>, we obtain

:<math>\begin{aligned}

:<math>\begin{aligned}

which is shown in Fig. 2A,B. In particular, for depression-dominated synapses (<math>u^+ \approx U</math>), the average synaptic efficacy <math>E=Au^+x</math> decays inversely with the rate, and the stationary synaptic current saturates at the limiting frequency <math>\lambda \sim \frac{1}{U\tau_d}</math>, above which dynamic synapses cannot transmit information about the stationary firing rate (Fig. 2A). On the other hand, facilitating synapses can be tuned for a particular presynaptic rate that depends on STP parameters (Fig. 2B).

which is shown in Fig. 2A,B. In particular, for depression-dominated synapses (<math>u^+ \approx U</math>), the average synaptic efficacy <math>E=Au^+x</math> decays inversely with the rate, and the stationary synaptic current saturates at the limiting frequency <math>\lambda \sim \frac{1}{U\tau_d}</math>, above which dynamic synapses cannot transmit information about the stationary firing rate (Fig. 2A). On the other hand, facilitating synapses can be tuned for a particular presynaptic rate that depends on STP parameters (Fig. 2B).

===Temporal filtering===

===Temporal filtering===

The above analysis only describes neural population firing with stationary firing rates. Eq. \ref{poisson} can be used to derive the filtering properties of dynamic synapses when the presynaptic population firing rate changes arbitrarily with time. In [[#Appendix A: Derivation of a temporal filter for short-term depression|Appendix A]] we present the corresponding calculation for depression-dominated synapses (<math>u^+ \approx U</math>). By considering small perturbations $R(t):=R_0 + R_1 \rho (t)$ with $R_1\ll R_0$ around the constant rate $R_0>0 $, the Fourier transform of the synaptic current $I$ is approximated by

The above analysis only describes neural population firing with stationary firing rates. Eq. \ref{poisson} can be used to derive the filtering properties of dynamic synapses when the presynaptic population firing rate changes arbitrarily with time. In [[#Appendix A: Derivation of a temporal filter for short-term depression|Appendix A]] we present the corresponding calculation for depression-dominated synapses (<math>u^+ \approx U</math>). By considering small perturbations $R(t):=R_0 + R_1 \rho (t)$ with $R_1\ll R_0$ around the constant rate $R_0>0 $, the Fourier transform of the synaptic current $I$ is approximated by

<math>

<math>

where we defined the filter

where we defined the filter

<math>

<math>

\begin{eqnarray}

\begin{eqnarray}

\widehat{\chi}(\omega) := 1- \frac{1/x_0 -1}{1/x_0 + j\omega \tau_{d}} = \frac{1+(\tau_{d}\omega)^2x_0+j\omega\tau_{d}(1-x_0)}{1/x_0+(\tau_{d}\omega)^2 x_0}\,,

\widehat{\chi}(\omega) := 1- \frac{1/x_0 -1}{1/x_0 + j\omega \tau_{d}} = \frac{1+(\tau_{d}\omega)^2x_0+j\omega\tau_{d}(1-x_0)}{1/x_0+(\tau_{d}\omega)^2 x_0}\,,