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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.
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]]).
STP 背后的生物物理过程很复杂。 对 STP 计算作用的研究依赖于创建简化的现象学模型（Abbott 97、Markram 98、Tsodyks 98）。
STP 背后的生物物理过程很复杂。 对 STP 计算作用的研究依赖于创建简化的现象学模型（Abbott 97，Markram 98，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
在 Tsodyks 和 Markram (Tsodyks 98) 提出的模型中，STD 效应由归一化变量 [math]\displaystyle{ x }[/math] ([math]\displaystyle{ 0\leq x \leq1 }[/ 数学]），表示在神经递质耗尽后仍然可用的资源比例。 STF 效应由利用率参数 [math]\displaystyle{ u }[/math] 建模，表示可供使用的可用资源的比例（释放概率）。 在一个尖峰之后，(i) [math]\displaystyle{ u }[/math] 由于尖峰诱导的钙流入突触前末端而增加，之后 (ii) 一小部分 [math]\displaystyle{ u }[/math ] 的可用资源被消耗以产生突触后电流。 在尖峰之间，[math]\displaystyle{ u }[/math] 衰减回零，时间常数为 [math]\displaystyle{ \tau_f }[/math] 和 [math]\displaystyle{ x }[/math] 恢复到 1 具有时间常数 [math]\displaystyle{ \tau_d }[/math]。 总之，STP 的动态由下式给出
在 Tsodyks 和 Markram (Tsodyks 98) 提出的模型中，STD 效应由归一化变量 <math>x</math> (<math>0\leq x \leq1</math>），表示在神经递质耗尽后仍然可用的资源比例。 STF 效应由利用率参数 建模，表示可供使用的可用资源的比例（释放概率）。 在一个尖峰之后，(i)由于尖峰诱导的钙流入突触前末端而增加，之后 (ii) 一小部分<math>u</math> 的可用资源被消耗以产生突触后电流。 在尖峰之间，<math>u</math>衰减回零，时间常数为 <math>\tau_f</math>和 <math>x</math>恢复到 1 具有时间常数 <math>\tau_d </math>。 总之，STP 的动态由下式给出
:<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
其中 [math]\displaystyle{ t_{sp} }[/math] 表示尖峰时间， [math]\displaystyle{ U }[/math] 是 [math]\displaystyle{ u }[/math] 产生的增量 通过一个尖峰。 我们将尖峰到来之前的对应变量表示为 [math]\displaystyle{ u^-, x^- }[/math]，而 [math]\displaystyle{ u^+ }[/math] 指的是 就在秒杀之后的那一刻。 根据第一个方程，[math]\displaystyle{ u^+ = u^- + U(1-u^-) }[/math]。 然后由到达 [math]\displaystyle{ t_{sp} }[/math] 的尖峰在突触处产生的突触电流由下式给出
其中<math>t_{sp}</math>表示尖峰时间， <math>U</math>是<math>u</math> 产生的增量 通过一个尖峰。 我们将尖峰到来之前的对应变量表示为 <math>u^-, x^-</math>，而<math>u^+</math> 指的是 就在秒杀之后的那一刻。 根据第一个方程，<math>u^+ = u^- + U(1-u^-)</math>。 然后由到达 <math>t_{sp}</math>的尖峰在突触处产生的突触电流由下式给出
:<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).
其中 [math]\displaystyle{ A }[/math] 表示所有神经递质 ([math]\displaystyle{ u=x=1 }[/math]) 总释放所产生的反应幅度，称为绝对突触 连接的功效（见图1A）。
其中 <math>A</math>表示所有神经递质<math>u=x=1</math> 总释放所产生的反应幅度，称为绝对突触 连接的功效（见图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.
<math>u</math>和 <math>x</math>的动力学相互作用决定了 <math>ux</math>的联合效应是否为 以抑郁或便利为主。 在<math>\tau_d\gg \tau_f</math> 和大<math>U</math>的参数机制中，初始尖峰会导致<math>x</math>大幅下降，需要很长时间才能恢复； 因此突触以 STD 为主（图 1B）。 在 <math>\tau_f \gg \tau_d</math>和小 <math>U</math>的情况下，突触的功效随着尖峰逐渐增加，因此突触是 STF 为主（图 1C）。 这种现象学模型成功地再现了在许多皮层区域观察到的抑制和促进突触的动力学动力学。
[[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]]
\end{eqnarray}
\end{eqnarray}
</math>
</math>
<nowiki>最后，等式的傅里叶逆变换。 \ref{eq:appA_Ihat_final} 读取 [math]\displaystyle{ \begin{eqnarray} I(t) = I_0 + \frac{I_0 R_1}{R_0} \int {\rm d}\tau \, \chi(\ tau) \rho(t-\tau) \label{eq:appA_I_final} \end{eqnarray} }[/math] with [math]\displaystyle{ \begin{eqnarray} \chi(t)=\delta(t) - \frac{1/x_0-1}{\tau_{d}} \begin{cases} \displaystyle {\exp\left(-\frac{t}{x_0\tau_{d}}\right)} & \ text{for}\quad t\ge0 \\ 0 & \text{for}\quad t\lt 0 \end{cases}\,. \label{eq:appA_chi_final} \end{eqnarray} }[/math]</nowiki>
Therefore the output current $I$ is the sum of the steady-state current $I_0$ and the filtered perturbation $\frac{I_0 R_1}{R_0} \int {\rm d}\tau \, \chi(\tau) \rho(t-\tau)$ where $\chi$ is the filter we are interested in.
Therefore the output current $I$ is the sum of the steady-state current $I_0$ and the filtered perturbation $\frac{I_0 R_1}{R_0} \int {\rm d}\tau \, \chi(\tau) \rho(t-\tau)$ where $\chi$ is the filter we are interested in.
因此输出电流 $I$ 是稳态电流 $I_0$ 和滤波后的扰动 $\frac{I_0 R_1}{R_0} \int {\rm d}\tau \, \chi(\tau) 之和\rho(t-\tau)$ 其中 $\chi$ 是过滤器
<nowiki>我们假设 $R$ 中的这种小扰动会在变量 $x$ 中围绕其稳态值 $x_0>0$ 产生小的扰动： [math]\displaystyle{ x(t) = x_0 + x_1(t)\quad\ text{with}\quad x_0 = \frac{1}{1+UR_0\tau_{d}} \quad\text{and}\quad |x_1(t)| \ll x_0 \, . \label{eq:appA_x01} }[/math]</nowiki>
<nowiki>我们假设 $R$ 中的这种小扰动会在变量 $x$ 中围绕其稳态值 $x_0>0$ 产生小的扰动： [math]\displaystyle{ x(t) = x_0 + x_1(t)\quad\ text{with}\quad x_0 = \frac{1}{1+UR_0\tau_{d}} \quad\text{and}\quad |x_1(t)| \ll x_0 \, . \label{eq:appA_x01} }[/math]</nowiki>
[数学]\displaystyle{ \begin{eqnarray} \widehat{I}(\omega) = I_0 \delta(\omega) + \frac{I_0 R_1}{R_0} \widehat{\chi}(\omega) \widehat {\rho}(\omega)\,. \label{eq:appA_Ihat_final} \end{eqnarray} }[/math]
[数学]\displaystyle{ \begin{eqnarray} \widehat{I}(\omega) = I_0 \delta(\omega) + \frac{I_0 R_1}{R_0} \widehat{\chi}(\omega) \widehat {\rho}(\omega)\,. \label{eq:appA_Ihat_final} \end{eqnarray} }[/math]
==参考文献References==
==参考文献References==
*<span id="ResearchTopic" /> '''Research Topic''': ''Neural Information Processing with Dynamical Synapses''. S. Wu, K. Y. Michael Wong and M. Tsodyks. ''Frontiers in Computational Neuroscience'', 2013 [http://www.frontiersin.org/Computational_Neuroscience/researchtopics/Neural_Information_Processing_/821 link]
*<span id="ResearchTopic" /> '''Research Topic''': ''Neural Information Processing with Dynamical Synapses''. S. Wu, K. Y. Michael Wong and M. Tsodyks. ''Frontiers in Computational Neuroscience'', 2013 [http://www.frontiersin.org/Computational_Neuroscience/researchtopics/Neural_Information_Processing_/821 link]