自適應可激發系統中的預期性動力學

Abstract

很多生物系統具有與週期性刺激同步，並在刺激被忽略時產生預期 性反應的能力。這種預期性的動力學在生物的生存以及資訊傳遞上 扮演了重要的角色。由於類似的預期性反應被發現於不同時間尺度 的生物系統中，理當有一個普適的數學模型來解釋這類的現象。藉 由考慮一個簡單的可激發系統，我們發現引進一個針對可激發性的 適應力可以使系統產生相似於實驗發現的預期性反應，而這樣的適 應力在一個神經網路的平均場近似中，對應到突觸的短期性增強。 在這個平均場模型中，不同連結強度或不同背景雜訊強度的系統皆 可以具有良好的預期性反應。然而，因為背景雜訊或者可能的連結 隨機性的存在，這類的預期性反應勢必具有一定的隨機程度。為了 解這種預期性反應的可信度，我們緊接著模擬一個具有短期突觸可 塑性的隨機神經網路。首先，我們必須先了解隨機網路的自發性反 應的是否可以具有良好的週期性，或稱為同調性。我們發現在一個 中等強度的背景雜訊中，自發性的反應具備最大的同調性，名為同 調性共振。接著，藉由對系統施加週期性的刺激，我們可以發現良 好的預期性反應的確存在與許多不同參數條件中。更重要的是，網 路中的預期性反應可信度可以與同調性共振相互呼應。最後，可激 發性的適應能力引進了一階相變化到系統中，而對於預期性反應而 言，我們發現在接近此一階相變點上的系統具有最大的動態範圍。

Many biological systems have the ability to adaptively synchronize with a periodic stimulus and produce anticipatory responses after the stimulus stopped. This kind of anticipatory dynamics, called omitted stimulus response (OSR), is a crucial computational power for biological systems. Since OSR exists on several different timescales observed in these biological systems, one expects a universal mathematical scheme to describe its mechanism. By considering a simple excitable system, we show that an adaptive dynamic on the excitability can produce well-timed OSR similar to that observed in the experiments. Moreover, the adaptation dynamics can be provided by the short-term synaptic facilitation in a network system from a mean field approximation for a spatially-localized neural networks. The well-timed OSR in this system can even be found at various background noise levels and coupling strengths. However, with the background noise and the possible randomness from the connectivity, the OSR in the network is necessarily stochastic. To understand the reliability of the well-timed OSR, we then study a network of randomly connected, noisy, leaky integrate-and-fire neurons with short-term synaptic plasticity. OSR can be found as predicted in the mean field approximation. And more importantly, there exists an optimal background noise level that leads to a most coherent spontaneous synchronous response in the network, known as coherence resonance. This coherence resonance determines the reliability of the OSR observed in the simulation. Additionally, adaptive dynamics from the short-term synaptic facilitation further leads to a first-order transition with a hysteresis in the coherence of the network. Near this phase transition point, the system possesses a maximum dynamic range for OSR.