為了及時反應，動物一定要透過預測來克服神經處理的延遲。過去的 研究已經證明視網膜的細胞能夠預測預測物體移動。為了去了解這樣的特 性，我們給視網膜看隨機移動的物體，並用多電極去量測。物體移動的軌 跡是由一種隨機過程產生，並且會由低通濾波過濾，而產生不同頻率的軌 跡。我們接著計算神經細胞輸出與軌跡的相互資訊。並且我們發現有兩種 細胞—可預測性與不可預測的細胞。可預測性與軌跡頻率也有關係。最後 我們發展一種模型，這個模型包括前饋與反饋的抑制，並且這個抑制是來 自於水平細胞。這種模型可以解釋為什麼視網膜能預測物體移動。

To produce timely responses, animals must conquer delays from visual pro­ cessing pathway by predicting motion. Previous studies [1] revealed that predic­ tive information of motion is encoded in spiking activities of retinal ganglion cells (RGCs) early in the visual pathway. In order to study the predictive properties of a retina in a more systematic manner, stimuli in the form of a stochastic moving bar are used in experiments with retinas from bull frogs in a multi­electrode sys­ tem. We then investigated the predictive properties of single RGC by calculating the time shifted (δt) mutual information (MI(x,r;δt)) between spiking output (r(t)) from a single RGC and the bar trajectories (x(t)). Two kinds of cells are charac­ terized: predictive RGCs and non­predictive RGCs. In order to further understand the mechanism of prediction, we develop a negative group delay model which is based on Voss＇s [2] paper to generate anticipatory responses. We extend our model to spatial version and use the same stimulation condition as we use in experiments. The model indicates that delayed negative feedback is crucial for producing antic­ ipation dynamics. Besides, we also show feedforward inhibition can also generate similar prediction dynamics. Besides, our feedback and feedforward model can also predict constant velocity moving bar [3]. After adding LPOU noises into con­ stant velocity moving bar, our model even predicts better than Berry gain control model [3] which explains anticipation of constant velocity moving bar. To sum up, our feedback and feedforward model can anticipate both stochastic and constant velocity moving bar with and without noises.

摘要 i
Abstract ii
Acknowledgements
1 Introduction to the retina 5
1.1 Organization of the retina 5
1.1.1 Photoreceptors 5
1.1.2 Horizontal cells 6
1.1.3 Bipolar cells 6
1.1.4 Amacrine cells 7
1.1.5 Ganglion cells 8
1.2 Anticipation in retina 8
1.2.1 Anticipation of a constant velocity moving bar 9
1.2.2 Anticipation of a stochastic moving bar 11
1.2.3 Review of previous works 11
1.3 Organization of the thesis 11
2 Material and Method 13
2.1 MEA recordings in the bull frog retina 13
2.1.1 Tissue Preparation 13
2.1.2 Experimental setup (Fig. 2.2) 14
2.1.3 Recording and spike sorting 15
2.1.4 Calibration of stimulus 16
2.2 Protocols of stimulation 16
2.2.1 On­off test 16
2.2.2 Contrast spike triggered average (cSTA) 17
2.2.3 Random checkerboard 19
2.2.4 Stochastic moving bar 19
2.3 Data analysis 22
2.3.1 Receptive field analysis 22
2.3.2 Mutual information 23
2.3.3 Mutual information between light intensity and firing rate 25
3 Results 27
3.1 Receptive field 27
3.2 Contrast tuning 29
3.2.1 On Off response 29
3.2.2 cSTA 30
3.3 Response of RGCs under stimulation of stochastic moving bar 31
3.3.1 Predictive (P) cell and non­predictive (NP) cell under HMM stimulation 31
3.3.2 Predictive (P) cell under OU stimulation 32
3.3.3 Predictive (P) cell and non­predictive (NP) cell under LPOU stimulation 32
3.3.4 MI between light intensity and firing rate 34
3.4 STA of a HMM bar 34
4 Model 37
4.1 Feedback and Feedforward model (FBFF model) 37
4.1.1 Numerical method 39
4.2 Nonlinearity in FBFF model 39
4.3 MI calculation in FBFF model 39
4.4 Berry Gain control model 41
4.5 Gain control 43
4.5.1 Period doubling 43
4.5.2 Combination of FBFF model and gain control (FBFF gain control model) 44
5 Model Results 47
5.1 Period doubling 47
5.2 Constant velocity moving bar 49
5.2.1 Berry Gain control model 49
5.2.2 Feedback and Feedforward model 51
5.2.3 FBFF gain control model 51
5.3 Constant velocity moving bar with fluctuation 54
5.3.1 Quantification of constant velocity bar with noise 54
5.3.2 Berry Gain control model 55
5.3.3 Feedback and Feedforward model 56
5.3.4 FBFF gain control model 56
5.4 LPOU moving bar 58
5.4.1 Berry Gain control model 58
5.4.2 Feedback and Feedforward model 59
5.4.3 MI between light intensity and firing rate 59
5.5 Effect of bar width 61
5.5.1 Square bar 61
5.5.2 Gaussian bar 63
6 Discussion 65
6.1 Comparison between FBFF model and Berry Gain control model 65
6.1.1 Constant velocity moving bar 65
6.1.2 Constant velocity moving bar with fluctuation 65
6.1.3 LPOU moving bar 66
6.2 Biophysical mechanism 66
6.3 Why Berry gain control model can predict constant velocity moving bar? . . . 68
6.4 Why Gain control doesn’t improve anticipation about LPOU moving bar? . . . 68
6.5 Why FBFF model can predict LPOU moving bar? 69
6.6 Which inhibition does the retina use? 69
6.7 Effect of contrast on prediction 69
7 Conclusion 71
References 73
Appendix 75

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