Victor Matveev

Facilitation through Buffer Saturation: Constraints on Endogenous Buffering Properties

Synaptic facilitation (SF) is a ubiquitous form of short-term plasticity, regulating synaptic dynamics on fast timescales. Although SF is known to depend on the presynaptic accumulation of Ca(2+), its precise mechanism is still under debate. Recently it has been shown that at certain central synapses SF results at least in part from the progressive saturation of an endogenous Ca(2+) buffer (Blatow et al., 2003), as proposed by Klingauf and Neher (1997). Using computer simulations, we study the magnitude of SF that can be achieved by a buffer saturation mechanism (BSM), and explore its dependence on the endogenous buffering properties. We find that a high SF magnitude can be obtained either by a global saturation of a highly mobile buffer in the entire presynaptic terminal, or a local saturation of a completely immobilized buffer. A characteristic feature of BSM in both cases is that SF magnitude depends nonmonotonically on the buffer concentration. In agreement with results of Blatow et al. (2003), we find that SF grows with increasing distance from the Ca(2+) channel cluster, and increases with increasing external Ca(2+), [Ca(2+)](ext), for small levels of [Ca(2+)](ext). We compare our modeling results with the experimental properties of SF at the crayfish neuromuscular junction, and find that the saturation of an endogenous mobile buffer can explain the observed SF magnitude and its supralinear accumulation time course. However, we show that the BSM predicts slowing of the SF decay rate in the presence of exogenous Ca(2+) buffers, contrary to experimental observations at the crayfish neuromuscular junction. Further modeling and data are required to resolve this aspect of the BSM.

N-type Ca2+ channels carry the largest current: implications for nanodomains and transmitter release.

Presynaptic terminals favor intermediate-conductance CaV2.2 (N type) over high-conductance CaV1 (L type) channels for single-channel, Ca2+ nanodomain–triggered synaptic vesicle fusion. However, the standard CaV1>CaV2>CaV3 conductance hierarchy is based on recordings using nonphysiological divalent ion concentrations. We found that, with physiological Ca2+ gradients, the hierarchy was CaV2.2>CaV1>CaV3. Mathematical modeling predicts that the CaV2.2 Ca2+ nanodomain, which is ∼25% more extensive than that generated by CaV1, can activate a calcium-fusion sensor located on the proximal face of the synaptic vesicle.

New and Corrected Simulations of Synaptic Facilitation

Tang et al. (2000) demonstrated that, at the crayfish neuromuscular junction, both the accumulation and the decay properties of short-term synaptic facilitation (STF) are strongly affected by the addition of a fast high-affinity Ca2+ buffer, suggesting a role of residual free Ca2+ in the induction of STF. The authors proposed that the experimental results can be explained by a secretion model with two Ca2+ binding sites, a secretory site mediating exocytosis and located close to the Ca2+ channel (∼10–20 nm), and a high-affinity facilitation site located further away (∼80–100 nm) from the channel.

Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons

Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems. While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks, it is known that strong coupling can destabilize phase-locked firing. Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of type-I Morris–Lecar model oscillators, which is characterized by a period-doubling cascade and leads to mode-locked states with alternation in the firing order of the two cells, as reported recently by Maran and Canavier (J Comput Nerosci, 2008) for a network of Wang-Buzsáki model neurons. Although alternating-order firing has been previously reported as a near-synchronous state, we show that the stable phase difference between the spikes of the two Morris–Lecar cells can constitute as much as 70% of the unperturbed oscillation period. Further, we examine the generality of this phenomenon for a class of type-I oscillators that are close to their excitation thresholds, and provide an intuitive geometric description of such “leap-frog” dynamics. In the Morris–Lecar model network, the alternation in the firing order arises under the condition of fast closing of K +  channels at hyperpolarized potentials, which leads to slow dynamics of membrane potential upon synaptic inhibition, allowing the presynaptic cell to advance past the postsynaptic cell in each cycle of the oscillation. Further, we show that non-zero synaptic decay time is crucial for the existence of leap-frog firing in networks of phase oscillators. However, we demonstrate that leap-frog spiking can also be obtained in pulse-coupled inhibitory networks of one-dimensional oscillators with a multi-branched phase domain, for instance in a network of quadratic integrate-and-fire model cells. Finally, for the case of a homogeneous network, we establish quantitative conditions on the phase resetting properties of each cell necessary for stable alternating-order spiking, complementing the analysis of Goel and Ermentrout (Physica D 163:191–216, 2002) of the order-preserving phase transition map.

Reduced endogenous Ca2+ buffering speeds active zone Ca2+ signaling

Significance Calcium influx during action potentials triggers neurotransmitter release at presynaptic active zones. Calcium buffers limit the spread of calcium and restrict neurotransmitter release to the vicinity of calcium channels. To sustain synchronous release during repetitive activity, rapid removal of calcium from the active zone is essential, but the underlying mechanisms are unclear. Therefore, we focused on cerebellar mossy fiber synapses, which are among the fastest synapses in the mammalian brain and found very weak presynaptic calcium buffering. One might assume that strong calcium buffering has the potential to efficiently remove calcium from active zones. In contrast, our results show that weak calcium buffering speeds active zone calcium clearance. Thus, the strength of presynaptic buffering limits the rate of synaptic transmission. Fast synchronous neurotransmitter release at the presynaptic active zone is triggered by local Ca2+ signals, which are confined in their spatiotemporal extent by endogenous Ca2+ buffers. However, it remains elusive how rapid and reliable Ca2+ signaling can be sustained during repetitive release. Here, we established quantitative two-photon Ca2+ imaging in cerebellar mossy fiber boutons, which fire at exceptionally high rates. We show that endogenous fixed buffers have a surprisingly low Ca2+-binding ratio (∼15) and low affinity, whereas mobile buffers have high affinity. Experimentally constrained modeling revealed that the low endogenous buffering promotes fast clearance of Ca2+ from the active zone during repetitive firing. Measuring Ca2+ signals at different distances from active zones with ultra-high-resolution confirmed our model predictions. Our results lead to the concept that reduced Ca2+ buffering enables fast active zone Ca2+ signaling, suggesting that the strength of endogenous Ca2+ buffering limits the rate of synchronous synaptic transmission.

Ca2+ Current versus Ca2+ Channel Cooperativity of Exocytosis

Recently there has been significant interest and progress in the study of spatiotemporal dynamics of Ca2+ that triggers exocytosis at a fast chemical synapse, which requires understanding the contribution of individual calcium channels to the release of a single vesicle. Experimental protocols provide insight into this question by probing the sensitivity of exocytosis to Ca2+ influx. While varying extracellular or intracellular Ca2+ concentration assesses the intrinsic biochemical Ca2+ cooperativity of neurotransmitter release, varying the number of open Ca2+ channels using pharmacological channel block or the tail current titration probes the cooperativity between individual Ca2+ channels in triggering exocytosis. Despite the wide use of these Ca2+ sensitivity measurements, their interpretation often relies on heuristic arguments. Here we provide a detailed analysis of the Ca2+ sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the Ca2+ current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal Ca2+ current magnitude, and the underlying Ca2+ channel cooperativity, defined as the average number of channels involved in the release of a single vesicle. We find simple algebraic expressions that show that the two are different but linearly related. Further, we use three-dimensional computational modeling of buffered Ca2+ diffusion to analyze these distinct Ca2+ cooperativity measures, and demonstrate the role of endogenous Ca2+ buffers on such measures. We show that buffers can either increase or decrease the Ca2+ current cooperativity of exocytosis, depending on their concentration and the single-channel Ca2+ current.

COMPLEX-TEMPERATURE SINGULARITIES IN POTTS MODELS ON THE SQUARE LATTICE

We report some new results on the complex-temperature (CT) singularities of

Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices

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Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map

-state Potts models on the square lattice. We concentrate on the problematic region

A connection between complex-temperature properties of the 1D and 2D spin s Ising model☆

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