How the nervous system computes and represents dynamical stimulus are fundamen-tal questions in neuroscience. Benefit from development in neural technologies, it is possible to record activities from neural population in real-time and manipulate spe-cific subsets of cells in the network[82, 17]. However, complex recurrent structures and diverse response types may hinder the understanding towards neural dynamics in the brain[41]. Early sensory systems, on the other hand, provide a relatively simple and accessible platform that enables the study of generic phenomena and biophysical mechanisms across nervous systems. For instance, neural responses in the visual, auditory, olfactory, and somatosensory systems could be recorded under controllable stimuli, allowing us to explore the neural code that represent the corre-sponding input signals[70]. Specifically, the retina has been an ideal model for these studies, since the cell composition and circuits are relatively well-studied[48, 51].
Recording methods for a population of retinal activity and computational descrip-tion of the retinal circuits facilitate our understanding for computadescrip-tion and coding
cells (⇠ 2 types), bipolar cells (⇠ 12 types), amacrine cells (⇠ 30 types), and the ganglion cells (⇠ 20 types)[51]. Note that these five main types are preserved across vertebrates and the number of subtypes in parenthesis is an approximation for mam-malian retina. Light signals are transformed into change in membrane potential, namely phototransduction, starting in the photoreceptor cells through biochemical signal pathways. These signals are sent to horizontal cells and bipolar cells. The horizontal cells forms the inner nuclear layer and provide negative feedback to the surrounding photoreceptors. Bipolar cells transmit signals to the ganglion cells, but can invert the response phase, forming ON and OFF pathways. Bipolar inputs are innervated to the inner plexiform layer, where they connect to the amacrine cells and retinal ganglion cells. Amacrine cells receive signals from multiple parallel units mediated by bipolar cells across the horizontal axis, inhibiting lateral bipolar termi-nals and ganglion cells. In the last stage, retinal ganglion cells integrate inputs from bipolar cells and amacrine cells, then produce action potential that projects to the next stage in the visual system (Fig. 1.1). Note that this is a general description for signal processing in the retina that discards a number of physiological details, such as electrical coupling between cells and long-range modulatory signals[12, 97].
The cell types and connections are critically related to its functional proper-ties. For instance, parallel processes of diverse bipolar cells are sampled by different types of ganglion cells, forming feature selection in different channels[28]. Lateral and feedback inhibition from the amacrince cells regulate ganglion activities in space, developing array structure and direction selectivity[46]. Many studies attempt to describe these circuits with functional units. “Receptive fields ” are defined by the area in space where the neuron receives input from[42]. Classical receptive fields of a retinal ganglion cell forms a “center-surround” structure. Light signals that fall in the center and surround regions may evoke opposite response in the ganglion cell, possibly forming a “Mexican hat” spatial kernel that enhances spatial contrast through lateral inhibition[2]. These operation on spatiotemporal signals could be approximated as a linear filter that weights the stimuli across space-time before
Figure 1.1: Structure of the retina. Five layers of cells are shown in the retinal tissue on the left. Light is projected from the bottom in the physiological condition.
Examples of the evoked activity in membrane potential of different cells are shown on the right. Note that G1 and G2 ganglion cells firing in a different phase due to the inverted signal in their upstream bipolar cells. Also, only amacrine cells and retinal ganglion cells produce action potentials. Figure reprinted from [26].
summation (summing across the dynamics range of multiple bipolar channels). To convert these analog signals to spiking activities generated in the retinal ganglion cells, the linear-nonlinear model adds a nonlinear function or threshold that approxi-mates the effective spiking threshold to the filtered signal[23]. This simplified model can characterize certain retinal activities and parameters could be fitted through experimental data. However, the static parameters and reduced functional units fails to capture a number of retinal function.
A set of generic neural computations has been observed in the retina, includ-ing adaptation, detection, and prediction[36, 44]. These phenomena could not be
cise timing between spikes from ganglion cells are shown to be crucial in encoding spatial patterns[35]. For prediction, it is shown that the retina could anticipate the motion of a moving bar, periodic light flashes, and adjusts its receptive field structure dynamically according to the stimuli in a predictive manner[4, 78, 77, 38].
Furthermore, one of the main goals in computational neuroscience is to eventually understand these neural codes in a population level as well. Pair-wised interactions, synergy and redundancy, thesaurus for population code, thermodynamic signatures, and robust “modes” of population firing patterns have also been discovered in the retina[74, 75, 32, 89, 67].
In this study, we focus on prediction and coding for temporal patterns in the retina. Following up the studies on sophisticate temporal patterns observed in reti-nal activities, we sought to compare these phenomena with an adaptive model, quantify the performance of temporal prediction, and generalize the measurement under more complex temrpoal patterns. Linking to the aforementioned aspiration in neuroscience research, we expect that these observed phenomena and analytic methods could be realized in other nervous systems.