Calmodulin promotes vesicle replenishment at photoreceptor ribbon synapses, enabling cones to transmit higher-frequency visual information.

Post-synaptic responses are a product of quantal amplitude (Q), size of the releasable vesicle pool (N), and release probability (P). Voltage-dependent changes in presynaptic Ca2+ entry alter post-synaptic responses primarily by changing P but have also been shown to influence N. With simultaneous whole cell recordings from cone photoreceptors and horizontal cells in tiger salamander retinal slices, we measured N and P at cone ribbon synapses by using a train of depolarizing pulses to stimulate release and deplete the pool. We developed an analytical model that calculates the total pool size contributing to release under different stimulus conditions by taking into account the prior history of release and empirically-determined properties of replenishment. The model provided a formula that calculates vesicle pool size from measurements of the initial post-synaptic response and limiting rate of release evoked by a train of pulses, the fraction of release sites available for replenishment, and the time constant for replenishment. Results of the model showed that weak and strong depolarizing stimuli evoked release with differing probabilities but the same size vesicle pool. Enhancing intraterminal Ca2+ spread by lowering Ca2+ buffering or applying BayK8644 did not increase PSCs evoked with strong test steps showing there is a fixed upper limit to pool size. Together, these results suggest that light-evoked changes in cone membrane potential alter synaptic release solely by changing release probability.

At the first synapse in the vertebrate visual pathway, light-evoked changes in photoreceptor membrane potential alter the rate of glutamate release onto second-order retinal neurons. This process depends on the synaptic ribbon, a specialized structure found at various sensory synapses, to provide a supply of primed vesicles for release. Calcium (Ca 2+ ) accelerates the replenishment of vesicles at cone ribbon synapses, but the mechanisms underlying this acceleration and its functional implications for vision are unknown. We studied vesicle replenishment using paired whole-cell recordings of cones and postsynaptic neurons in tiger salamander retinas and found that it involves two kinetic mechanisms, the faster of which was diminished by calmodulin (CaM) inhibitors. We developed an analytical model that can be applied to both conventional and ribbon synapses and showed that vesicle resupply is limited by a simple time constant,  = 1/(Ds), where D is the vesicle diffusion coefficient,  is the vesicle diameter,  is the vesicle density, and s is the probability of vesicle attachment. The combination of electrophysiological measurements, modeling, and total internal reflection fluorescence microscopy of single synaptic vesicles suggested that CaM speeds replenishment by enhancing vesicle attachment to the ribbon. Using electroretinogram and whole-cell recordings of light responses, we found that enhanced replenishment improves the ability of cone synapses to signal darkness after brief flashes of light and enhances the amplitude of responses to higherfrequency stimuli. By accelerating the resupply of vesicles to the ribbon, CaM extends the temporal range of synaptic transmission, allowing cones to transmit higher-frequency visual information to downstream neurons. Thus, the ability of the visual system to encode time-varying stimuli is shaped by the dynamics of vesicle replenishment at photoreceptor synaptic ribbons.

Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety of nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos. In prior work, we have developed a detailed mathematical theory relating stable and unstable fixed points of CTLNs to graph-theoretic properties of the underlying network. Here we find that a special type of fixed points, corresponding to core motifs, are predictive of both static and dynamic attractors. Moreover, the attractors can be found by choosing initial conditions that are small perturbations of these fixed points. This motivates us to hypothesize that dynamic attractors of a network correspond to unstable fixed points supported on core motifs. We tested this hypothesis on a large family of directed graphs of size n = 5, and found remarkable agreement. Furthermore, we discovered that core motifs with similar embeddings give rise to nearly identical attractors. This allowed us to classify attractors based on structurally-defined graph families. Our results suggest that graphical properties of the connectivity can be used to predict a network’s complex repertoire of nonlinear dynamics.

Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. While network architectures supporting sequence generation vary considerably, a common feature is an abundance of inhibition. In this work, we focus on architectures that support sequential activity in recurrently connected networks with inhibitiondominated dynamics. Specifically, we study emergent sequences in a special family of threshold-linear networks, called combinatorial threshold-linear networks (CTLNs), whose connectivity matrices are defined from directed graphs. Such networks naturally give rise to an abundance of sequences whose dynamics are tightly connected to the underlying graph. We find that architectures based on generalizations of cycle graphs produce limit cycle attractors that can be activated to generate transient or persistent (repeating) sequences. Each architecture type gives rise to an infinite family of graphs that can be built from arbitrary component subgraphs. Moreover, we prove a number of graph rules for the corresponding CTLNs in each family. The graph rules allow us to strongly constrain, and in some cases fully determine, the fixed points of the network in terms of the fixed points of the component subnetworks. Finally, we apply these results to identify all graphs up to size n = 5 that are parameter-independent core motifs. Core motifs are special graphs with a single fixed point that are in some sense irreducible, and typically support a single attractor. Additionally, we show how the structure of certain architectures gives insight into the sequential dynamics of the corresponding attractor. Conclusion 49