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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) ([[#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 ([[#Markram98|Markram 98]], [[#Dittman00|Dittman 00]], [[#Wang06|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 ([[#Markram98|Markram 98]], [[#Dittman00|Dittman 00]], [[#Wang06|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.

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.

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。

图 1. (A) 由 Eqs.（1） 和 （2） 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>R=15</math>Hz。 参数<math>A=1</math> , <math>U=0.45</math>, <math>\tau_s=20</math>ms,<math>\tau_d=750</math>ms 和 <math>\tau_f=50</math>ms。 (C) STF 主导突触的动力学。 参数 <math>U=0.15</math>、<math>\tau_f=750</math>ms 和 <math>\tau_d=50</math>ms。

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

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

因为 STP 根据突触前活动的历史来修改突触功效，所以它可以改变神经信息传递([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]])。 一般来说，以 STD 为主的突触有利于低发射率的信息传递，因为高频尖峰会迅速使突触失活。 然而，以 STF 为主的突触倾向于优化高频突发的信息传递，从而增加突触强度。  

因为 STP 根据突触前活动的历史来修改突触功效，所以它可以改变神经信息传递([[#Abbott97|Abbott 97]], [[#Tsodyks97|Tsodyks 97]], [[#Fuhrmann02|Fuhrmann 02]], [[#Rotman11|Rotman 11]], [[#Rosenbaum12|Rosenbaum 12]])。 一般来说，以 STD 为主的突触有利于低发射率的信息传递，因为高频尖峰会迅速使突触失活。 然而，以 STF 为主的突触倾向于优化高频突发的信息传递，从而增加突触强度。  

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. （1）over different realization of Poisson processes corresponding to different spike trains ([[#Tsodyks98|Tsodyks 98]]):

可以通过检查来自具有全局放电率 [math]\displaystyle{ R(t) }[/math] 的大型神经元群体的不相关 Poisson 尖峰序列的传输来分析通过动态突触的放电率依赖性传输。 突触后电流 [math]\displaystyle{ I(t) }[/math] 的时间演化可以通过对等式求平均来获得。 \ref{model} 对应于不同尖峰序列的泊松过程的不同实现([[#Tsodyks98|Tsodyks 98]])：

可以通过检查来自具有全局放电率 <math>R(t)</math>的大型神经元群体的不相关 Poisson 尖峰序列的传输来分析通过动态突触的放电率依赖性传输。 突触后电流<math>I(t)</math>的时间演化可以通过对等式求平均来获得。 等式（1）对应于不同尖峰序列的泊松过程的不同实现([[#Tsodyks98|Tsodyks 98]])：

:<math>\begin{aligned}

:<math>\begin{aligned}

如图 2A、B 所示。 特别是，对于抑郁为主的突触 <math>u^+ \approx U</math>，平均突触效能<math>E=Au^+x</math>衰减 与速率成反比，静态突触电流在极限频率<math>\lambda \sim \frac{1}{U\tau_d}</math>处饱和，高于该频率的动态突触不能传输有关 固定发射率（图 2A）。 另一方面，促进突触可以针对取决于 STP 参数的特定突触前速率进行调整（图 2B）。

如图 2A、B 所示。 特别是，对于抑郁为主的突触 <math>u^+ \approx U</math>，平均突触效能<math>E=Au^+x</math>衰减 与速率成反比，静态突触电流在极限频率<math>\lambda \sim \frac{1}{U\tau_d}</math>处饱和，高于该频率的动态突触不能传输有关 固定发射率（图 2A）。 另一方面，促进突触可以针对取决于 STP 参数的特定突触前速率进行调整（图 2B）。

==='''时间过滤'''Temporal filtering===

===时间过滤Temporal filtering===

The above analysis only describes neural population firing with stationary firing rates. Eq. （3）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<math>R(t):=R_0 + R_1 \rho (t)</math>with <math>R_1\ll R_0</math>around the constant rate <math>R_0>0</math>, the Fourier transform of the synaptic current <math>I</math>is approximated by

The above analysis only describes neural population firing with stationary firing rates. Eq. （3）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<math>R(t):=R_0 + R_1 \rho (t)</math>with <math>R_1\ll R_0</math>around the constant rate <math>R_0>0</math>, the Fourier transform of the synaptic current <math>I</math>is approximated by

Since STP modifies synaptic efficacy instantly, it can modulate the network response to sustained external inputs. An example of this is bursty synchronous firing in an STD-dominated network, either spontaneously or in response to external inputs.  The resulting bursts of activity are called population spikes ([[#Loebel02|Loebel 02]]). To understand this effect, consider a network with strong recurrent interactions between neurons. When a sufficiently large group of neurons fire together, e.g. triggered by external stimulus, they can recruit other neurons via an avalanche-like process. However, after a large synchronous burst of activity, the synapses are weakened by STD, reducing the recurrent currents rapidly, and consequently the network activity returns to baseline. The network will not be activated again until the synapses are sufficiently recovered from depression. Therefore, the rate of population spikes is determined by the time constant of STD (Fig.3A,B). STF can also modulate the network response to external inputs, but in a very different manner ([[#Barak07|Barak 07]]). The varied response properties mediated by STP may provide different ways of representing and conveying the stimulus information in a network.

Since STP modifies synaptic efficacy instantly, it can modulate the network response to sustained external inputs. An example of this is bursty synchronous firing in an STD-dominated network, either spontaneously or in response to external inputs.  The resulting bursts of activity are called population spikes ([[#Loebel02|Loebel 02]]). To understand this effect, consider a network with strong recurrent interactions between neurons. When a sufficiently large group of neurons fire together, e.g. triggered by external stimulus, they can recruit other neurons via an avalanche-like process. However, after a large synchronous burst of activity, the synapses are weakened by STD, reducing the recurrent currents rapidly, and consequently the network activity returns to baseline. The network will not be activated again until the synapses are sufficiently recovered from depression. Therefore, the rate of population spikes is determined by the time constant of STD (Fig.3A,B). STF can also modulate the network response to external inputs, but in a very different manner ([[#Barak07|Barak 07]]). The varied response properties mediated by STP may provide different ways of representing and conveying the stimulus information in a network.

由于 STP 会立即修改突触功效，因此它可以调节网络对持续外部输入的响应。这方面的一个例子是 STD 主导网络中的突发同步触发，无论是自发地还是响应外部输入。由此产生的活动爆发称为人口高峰（[[#Loebel02|Loebel 02]]）。要理解这种效应，请考虑一个神经元之间具有强循环交互的网络。当足够大的一组神经元一起发射时，例如由外部刺激触发，它们可以通过类似雪崩的过程招募其他神经元。然而，在大量同步突发活动之后，突触被 STD 削弱，快速减少循环电流，因此网络活动恢复到基线。在突触从抑郁症中充分恢复之前，网络不会再次被激活。因此，人口峰值的速率由 STD 的时间常数决定（图 3A，B）。STF 还可以调制网络对外部输入的响应，但方式非常不同（([[#Barak07|Barak 07]]）。由 STP 介导的不同响应属性可以提供在网络中表示和传达刺激信息的不同方式。

由于 STP 会立即修改突触功效，因此它可以调节网络对持续外部输入的响应。这方面的一个例子是 STD 主导网络中的突发同步触发，无论是自发地还是响应外部输入。由此产生的活动爆发称为人口高峰（[[#Loebel02|Loebel 02]]）。要理解这种效应，请考虑一个神经元之间具有强循环交互的网络。当足够大的一组神经元一起发射时，例如由外部刺激触发，它们可以通过类似雪崩的过程招募其他神经元。然而，在大量同步突发活动之后，突触被 STD 削弱，快速减少循环电流，因此网络活动恢复到基线。在突触从抑郁症中充分恢复之前，网络不会再次被激活。因此，人口峰值的速率由 STD 的时间常数决定（图 3A，B）。STF 还可以调制网络对外部输入的响应，但方式非常不同（([[#Barak07|Barak 07]]）。由 STP 介导的不同响应属性可以提供在网络中表示和传达刺激信息的不同方式。

Persistent firing, referring to situations in which a group of neurons continue firing without external drive, is widely regarded as a neural substrate for information representation ([[#Fuster71|Fuster 71]]). To maintain persistent activity in a network, strong excitatory recurrent interactions between neurons are needed to establish a positive-feedback loop sustaining neuronal responses. Mathematically, persistent activity is often modeled as an active stationary state (attractor) of the network. Since STD weakens synaptic efficacy depending on the level of neuronal activity, it can suppress an attractor state. This property, however, can be used to carry out valuable computations.

Persistent firing, referring to situations in which a group of neurons continue firing without external drive, is widely regarded as a neural substrate for information representation ([[#Fuster71|Fuster 71]]). To maintain persistent activity in a network, strong excitatory recurrent interactions between neurons are needed to establish a positive-feedback loop sustaining neuronal responses. Mathematically, persistent activity is often modeled as an active stationary state (attractor) of the network. Since STD weakens synaptic efficacy depending on the level of neuronal activity, it can suppress an attractor state. This property, however, can be used to carry out valuable computations.

Continuous Attractor Neural Networks (CANNs), also called neural field models or ring models ([[#Amari77|Amari 77]]), have been widely used to describe the encoding of continuous stimuli in the neural system, such as for head-direction, orientation, movement direction, and spatial location of objects. A CANN, due to its translation-invariant recurrent interactions between neurons, holds a continuous family of localized stationary states, called bumps. These stationary states form a subspace on which the network is neutrally stable, enabling the network to track time-varying stimuli smoothly.

Continuous Attractor Neural Networks (CANNs), also called neural field models or ring models ([[#Amari77|Amari 77]]), have been widely used to describe the encoding of continuous stimuli in the neural system, such as for head-direction, orientation, movement direction, and spatial location of objects. A CANN, due to its translation-invariant recurrent interactions between neurons, holds a continuous family of localized stationary states, called bumps. These stationary states form a subspace on which the network is neutrally stable, enabling the network to track time-varying stimuli smoothly.