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短期突触可塑性 (查看源代码)

2022年6月18日 (六) 20:33的版本

添加274字节、 2022年6月18日 (六) 20:33

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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

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:<math>\begin{aligned}

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\frac{du}{dt} & = & -\frac{u}{\tau_f}+U(1-u^-)\delta(t-t_{sp}),\nonumber \\ \frac{dx}{dt} & = & \frac{1-x}{\tau_d}-u^+x^-\delta(t-t_{sp}), \\

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\frac{dI}{dt} & = & -\frac{I}{\tau_s} + Au^+x^-\delta(t-t_{sp}), \nonumber

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\label{model}\end{aligned}</math>

:<math>\begin{aligned}

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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。

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

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==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.

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除了前馈和反馈传输之外，神经回路还会在神经元之间产生循环交互。由于 STP 包含在循环交互中，网络动力学表现出许多新的有趣行为，这些行为不会出现在纯静态突触中。因此，这些新的动态特性可以实现 STP 介导的网络计算。

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===Prolongation of neural responses to transient inputs ===

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===Prolongation of neural responses to transient inputs===

Since STP has a much longer time scale than that of single neuron dynamics (the latter is typically in the time order of <math>10-20</math> milliseconds), a new feature STP can bring to the network dynamics is prolongation of neural responses to a transient input. This stimulus-induced residual activity therefore holds a memory trace of the input, lasting up to several hundred milliseconds in a large-size network, and can serve as a buffer for information processing. For example, it has been shown that STD-mediated residual activity can cause a neural system to discriminate between rhythmic inputs of different periods ([[#Karmorkar07|Karmorkar 07]]). STP also plays an important role in a general computation framework called a reservoir network. In this framework, STP, together with other dynamical elements of a large-size network, effectively map the input features from a low-dimensional space to the high-dimensional state space of the network that includes both active (neural) and hidden (synaptic) components, so that the input information can be more easily read out ([[#Buonomano09|Buonomano 09]]). In a recent development it was proposed that STF-enhanced synapses themselves can hold the memory trace of an input without recruiting persistent firing of neurons, potentially providing the most economical and robust way to implement working memory ([[#Mongillo08|Mongillo 08]]).

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[数学]\displaystyle{ \begin{eqnarray} {\frac<nowiki>{{\rm d} x}{{\rm d}t}} = \frac{1-x}{\tau_{d}}</nowiki> - U R_0 x - U x_0 R + U x_0 R_0\,.\label{eq:appA_xlin} \end{eqnarray} }[/math]

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<nowiki>我们现在对等式两边进行傅里叶变换。 \ref{eq:appA_xlin} [数学]\displaystyle{ \begin{eqnarray} j\omega \tau_{d} \widehat{x} = -\widehat{x} - U R_0 \tau_{d} \widehat{x } - U x_0 \tau_{d}\widehat{R} + (1+ U R_0 \tau_{d} x_0) \delta(\omega) \label{eq:appA_xhat0} \end{eqnarray} }[/math]我们定义了傅里叶变换对 [math]\displaystyle{ \begin{eqnarray} \widehat{x}(\omega) := \int \!{\rm d}{t}\, x(t) \exp( -j\omega t ) \quad; \quad x(t) = \frac{1}{2\pi}\int \!{\rm d}\omega\, \widehat{x}(\omega) \exp(j\omega t) \label{ eq:appA_ft} \end{eqnarray} }[/math] 和 $j=\sqrt{-1}$ 是虚数单位。求解方程。 \ref{eq:appA_xhat0} 对于变量 $\widehat{x}$，我们找到 [math]\displaystyle{ \begin{eqnarray} \widehat{x} = -\frac{U\tau_{d}x_0}{ 1/x_0 + j \omega \tau_{d}} \widehat{R} + x_0 (2-x_0) \delta(\omega) \label{eq:appA_xhat} \end{eqnarray} }[/math] 从哪里方程。 \ref{eq:appA_x01} 我们使用了 $U R_0 \tau_{d}=1/x_0 - 1$。</nowiki>

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<nowiki>我们现在对等式两边进行傅里叶变换。 \ref{eq:appA_xlin} [数学]\displaystyle{ \begin{eqnarray} j\omega \tau_{d} \widehat{x} = -\widehat{x} - U R_0 \tau_{d} \widehat{x } - U x_0 \tau_{d}\widehat{R} + (1+ U R_0 \tau_{d} x_0) \delta(\omega) \label{eq:appA_xhat0} \end{eqnarray} }[/math]我们定义了傅里叶变换对 [math]\displaystyle{ \begin{eqnarray} \widehat{x}(\omega) := \int \!{\rm d}{t}\, x(t) \exp( -j\omega t ) \quad; \quad x(t) = \frac{1}{2\pi}\int \!{\rm d}\omega\, \widehat{x}(\omega) \exp(j\omega t) \label{ eq:appA_ft} \end{eqnarray} }[/math] 和 $j=\sqrt{-1}$ 是虚数单位。求解方程。 \ref{eq:appA_xhat0} 对于变量 $\widehat{x}$，我们找到 [math]\displaystyle{ \begin{eqnarray} \widehat{x} = -\frac{U\tau_{d}x_0}{ 1/x_0 + j \omega \tau_{d}} \widehat{R} + x_0 (2-x_0) \delta(\omega) \label{eq:appA_xhat} \end{eqnarray} }[/math] 从哪里方程。 \ref{eq:appA_x01} 我们使用了 $U R_0 \tau_{d}=1/x_0 - 1$。</nowiki>

接下来，我们插入方程式。 \ref{eq:appA_rx} 转化为等式。 \ref{eq:appA_I} 线性化突触电流的动态

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[数学]\displaystyle{ \begin{eqnarray} I &=& \tau_{s}AU (R_0x+x_0R-x_0R_0)\\ &=& I_0 \left( \frac{x}{x_0}+ \frac{R }{R_0}-1\right) \label{eq:appA_Ilin} \end{eqnarray} }[/math] 围绕稳态值 $I_0 = \tau_{s}AU x_0 R_0$。

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<nowiki>通过对等式两边进行傅里叶变换。 \ref{eq:appA_Ilin}，使用等式。 \ref{eq:appA_xhat}，我们得到 [math]\displaystyle{ \begin{eqnarray} \widehat{I} &=& I_0 \frac{\widehat{x}}{x_0} + I_0 \frac{\widehat{ R}}{R_0} - I_0 \delta(\omega) \\ &=& \frac{I_0}{R_0} \widehat{\chi} \widehat{R} + I_0(1-x_0) \delta(\omega ) \label{eq:appA_Ihat} \end{eqnarray} }[/math] 我们定义了过滤器 [math]\displaystyle{ \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}\,. \label{eq:appA_chihat} \end{eqnarray} }[/math]</nowiki>

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<nowiki>通过对等式两边进行傅里叶变换。 \ref{eq:appA_Ilin}，使用等式。 \ref{eq:appA_xhat}，我们得到 [math]\displaystyle{ \begin{eqnarray} \widehat{I} &=& I_0 \frac{\widehat{x}}{x_0} + I_0 \frac{\widehat{ R}}{R_0} - I_0 \delta(\omega) \\ &=& \frac{I_0}{R_0} \widehat{\chi} \widehat{R} + I_0(1-x_0) \delta(\omega ) \label{eq:appA_Ihat} \end{eqnarray} }[/math] 我们定义了过滤器 [math]\displaystyle{ \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}\,. \label{eq:appA_chihat} \end{eqnarray} }[/math]</nowiki>

为了解释结果，我们插入方程式。 \ref{eq:appA_Ihat} 傅里叶变换 $\widehat{R}=R_0\delta(\omega)+R_1 \widehat{\rho}$，产生

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* J. S. Dittman, A. C. Kreitzer and W. G. Regehr. Interplay between facilitation, depression, and residual calcium at three presynaptic terminals. J. Neurosci. 20: 1374-1385, 2000.

*{{Bibitem article 2|Short-term synaptic plasticity as a temporal filter.|Trends in Neurosciences.|24(7)|2001|381-385|Fortune|Eric S.|Rose|Gary J.|preprint=[http://dx.doi.org/10.1016/S0166-2236(00)01835-X doi:10.1016/S0166-2236(00)01835-X]|label=Fortune01|doi=10.1016/s0166-2236(00)01835-x}}

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* G. Fuhrmann et al. Coding of Temporal Information by Activity-Dependent Synapses. J. Neurophysiol. 87: 140-148, 2002.

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* G. Fuhrmann et al. Coding of Temporal Information by Activity-Dependent Synapses. J. Neurophysiol. 87: 140-148, 2002.

*{{Bibitem article 4|Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy, and Mobility.|Neural Computation.|24(5)|2012|1147-1185|Fung|C. C. Alan|Wong|K. Y. Michael|Wang|He|Wu|Si|preprint=[http://dx.doi.org/10.1162/NECO_a_00269 doi:10.1162/NECO_a_00269]|label=Fung12a|doi=10.1162/neco_a_00269}}

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* C. C. Fung, K. Y. Michael Wong and S. Wu. Delay Compensation with Dynamical Synapses. Advances in Neural Information Processing Systems 16, 2012.

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* C. C. Fung, K. Y. Michael Wong and S. Wu. Delay Compensation with Dynamical Synapses. Advances in Neural Information Processing Systems 16, 2012.

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* C. C. A. Fung, H. Wang, K. Lam, K. Y. M. Wong and S. Wu. Resolution enhancement in neural networks with dynamical synapses. Front. Comput. Neurosci. 7:73. doi: 10.3389/fncom.2013.00073, 2013.

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* C. C. A. Fung, H. Wang, K. Lam, K. Y. M. Wong and S. Wu. Resolution enhancement in neural networks with dynamical synapses. Front. Comput. Neurosci. 7:73. doi: 10.3389/fncom.2013.00073, 2013.

*{{Bibitem article 2|Neuron Activity Related to Short-Term Memory.|Science.|173(3997)|1971|652-654|Fuster|J. M.|Alexander|G. E.|preprint=[http://dx.doi.org/10.1126/science.173.3997.652 doi:10.1126/science.173.3997.652]|label=Fuster71|doi=10.1126/science.173.3997.652}}

*{{Bibitem article 3 |Redundancy Reduction and Sustained Firing with Stochastic Depressing Synapses|The Journal of Neuroscience|22(2)|2002|584-591|Goldman|Mark S.|Maldonado|Pedro|Abbott|L. F.|label=Goldman02}}

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