The optimal synapse for sparse, binary signals in the rod pathway

Nonlinearity and noise at the rod-rod bipolar cell synapse

In the retina, rod bipolar (RBP) cells synapse with many rods, and suppression of rod outer segment and synaptic noise is necessary for their detection of rod single-photon responses (SPRs). Depending on the rods' signal-to-noise ratio (SNR), the suppression mechanism will likely eliminate some SPRs as well, resulting in decreased quantum efficiency. We examined this synapse in rabbit, where 100 rods converge onto each RBP. Suction electrode recordings showed that rabbit rod SPRs were difficult to distinguish from noise (independent SNR estimates were 2.3 and 2.8). Nonlinear transmission from rods to RBPs improved response detection (SNR = 8.7), but a large portion of the rod SPRs was discarded. For the dimmest flashes, the loss approached 90%. Despite the high rejection ratio, noise of two distinct types was apparent in the RBP traces: low-amplitude rumblings and discrete events that resembled the SPR. The SPR-like event frequency suggests that they result from thermal isomerizations of rhodopsin, which occurred at the rate 0.033/s/rod. The presence of low-amplitude noise is explained by a sigmoidal input-output relationship at the rod-RBP synapse and the input of noisy rods. The rabbit rod SNR and RBP quantum efficiency are the lowest yet reported, suggesting that the quantum efficiency of the rod-RBP synapse may depend on the SNR in rods. These results point to the possibility that fewer photoisomerizations are discarded for species such as primate, which has a higher rod SNR.

Optimal learning rules for discrete synapses

There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity.

It is believed that the neural basis of learning and memory is change in the strength of synaptic connections between neurons. Much theoretical work on this topic assumes that the strength, or weight, of a synapse may vary continuously and be unbounded. More recent studies have considered synapses that have a limited number of discrete states. In dynamical models of such synapses, old memories are automatically overwritten by new memories, and it has been previously difficult to optimize performance using standard capacity measures, for stronger learning typically implies faster forgetting. Here, we propose an information theoretic measure of storage capacity of such forgetting systems, and use this to optimize the learning rules. We find that for parameters comparable to those found in biology, capacity of discrete synapses is similar to that of unbounded, continuous synapses, provided the number of synapses per neuron is limited. Our findings are relevant for experiments investigating the precise nature of synaptic changes during learning, and also pave a path for further work on building biologically realistic memory models.

Optimization of single-photon response transmission at the rod-to-rod bipolar synapse

Our ability to see in dim light is limited by the statistics of light absorption in rod photoreceptors and the faithful transmission of the light-evoked signals through the retina. This article reviews the physiological mechanisms at the synapse between rods and rod bipolar cells, the first relay in a pathway that mediates vision near absolute threshold.