Data Driven Models of Short-Term Synaptic Plasticity.

Simple models of short term synaptic plasticity that incorporate facilitation and/or depression have been created in abundance for different synapse types and circumstances. The analysis of these models has included computing mutual information between a stochastic input spike train and some sort of representation of the postsynaptic response. While this approach has proven useful in many contexts, for the purpose of determining the type of process underlying a stochastic output train, it ignores the ordering of the responses, leaving an important characterizing feature on the table. In this paper we use a broader class of information measures on output only, and specifically construct hidden Markov models (HMMs) (known as epsilon machines or causal state models) to differentiate between synapse type, and classify the complexity of the process. We find that the machines allow us to differentiate between processes in a way not possible by considering distributions alone. We are also able to understand these differences in terms of the dynamics of the model used to create the output response, bringing the analysis full circle. Hence this technique provides a complimentary description of the synaptic filtering process, and potentially expands the interpretation of future experimental results.

Effect of Neuromodulation of Short-term Plasticity on Information Processing in Hippocampal Interneuron Synapses.

Neurons in a micro-circuit connected by chemical synapses can have their connectivity affected by the prior activity of the cells. The number of synapses available for releasing neurotransmitter can be decreased by repetitive activation through depletion of readily releasable neurotransmitter (NT), or increased through facilitation, where the probability of release of NT is increased by prior activation. These competing effects can create a complicated and subtle range of time-dependent connectivity. Here we investigate the probabilistic properties of facilitation and depression (FD) for a presynaptic neuron that is receiving a Poisson spike train of input. We use a model of FD that is parameterized with experimental data from a hippocampal basket cell and pyramidal cell connection, for fixed frequency input spikes at frequencies in the range of theta (3-8 Hz) and gamma (20-100 Hz) oscillations. Hence our results will apply to micro-circuits in the hippocampus that are responsible for the interaction of theta and gamma rhythms associated with learning and memory. A control situation is compared with one in which a pharmaceutical neuromodulator (muscarine) is employed. We apply standard information-theoretic measures such as entropy and mutual information, and find a closed form approximate expression for the probability distribution of release probability. We also use techniques that measure the dependence of the response on the exact history of stimulation the synapse has received, which uncovers some unexpected differences between control and muscarine-added cases.

Modeling Relapsing Disease Dynamics in a Host-Vector Community.

Vector-borne diseases represent a threat to human and wildlife populations and mathematical models provide a means to understand and control epidemics involved in complex host-vector systems. The disease model studied here is a host-vector system with a relapsing class of host individuals, used to investigate tick-borne relapsing fever (TBRF). Equilibrium analysis is performed for models with increasing numbers of relapses and multiple hosts and the disease reproduction number, R0, is generalized to establish relationships with parameters that would result in the elimination of the disease. We show that host relapses in a single competent host-vector system is needed to maintain an endemic state. We show that the addition of an incompetent second host with no relapses increases the number of relapses needed for maintaining the pathogen in the first competent host system. Further, coupling of the system with hosts of differing competencies will always reduce R0, making it more difficult for the system to reach an endemic state.

Presynaptic cholinergic neuromodulation alters the temporal dynamics of short-term depression at parvalbumin-positive basket cell synapses from juvenile CA1 mouse hippocampus.

Parvalbumin-positive basket cells (PV BCs) of the CA1 hippocampus are active participants in theta (5-12 Hz) and gamma (20-80 Hz) oscillations in vivo. When PV BCs are driven at these frequencies in vitro, inhibitory postsynaptic currents (IPSCs) in synaptically connected CA1 pyramidal cells exhibit paired-pulse depression (PPD) and multiple-pulse depression (MPD). Moreover, PV BCs express presynaptic muscarinic acetylcholine receptors (mAChRs) that may be activated by synaptically released acetylcholine during learning behaviors in vivo. Using acute hippocampal slices from the CA1 hippocampus of juvenile PV-GFP mice, we performed whole cell recordings from synaptically connected PV BC-CA1 pyramidal cell pairs to investigate how bath application of 10 µM muscarine impacts PPD and MPD at CA1 PV BC-pyramidal cell synapses. In accordance with previous studies, PPD and MPD magnitude increased with stimulation frequency. mAChR activation reduced IPSC amplitude and transiently reduced PPD, but MPD was largely maintained. Consistent with a reduction in release probability (pr), MPD and mAChR activation increased both the coefficient of variation of IPSC amplitudes and the fraction of failures. Using variance-mean analysis, we converted MPD trains to pr functions and developed a kinetic model that optimally fit six distinct pr conditions. The model revealed that vesicular depletion caused MPD and that recovery from depression was dependent on calcium. mAChR activation reduced the presynaptic calcium transient fourfold and initial pr twofold, thereby reducing PPD. However, mAChR activation slowed calcium-dependent recovery from depression during sustained repetitive activity, thereby preserving MPD. Thus the activation of presynaptic mAChRs optimally protects PV BCs from vesicular depletion during short bursts of high-frequency activity.

The central cavity in trimeric glutamate transporters restricts ligand diffusion.

A prominent aqueous cavity is formed by the junction of three identical subunits in the excitatory amino acid transporter (EAAT) family. To investigate the effect of this structure on the interaction of ligands with the transporter, we recorded currents in voltage-clamped Xenopus oocytes expressing EAATs and used concentration jumps to measure binding and unbinding rates of a high-affinity aspartate analog that competitively blocks transport (ß-2-fluorenyl-aspartylamide; 2-FAA). The binding rates of the blocker were approximately one order of magnitude slower than l-Glu and were not significantly different for EAAT1, EAAT2, or EAAT3, but 2-FAA exhibited higher affinity for the neuronal transporter EAAT3 as a result of a slower dissociation rate. Unexpectedly, the rate of recovery from block was increased by l-Glu in a saturable and concentration-dependent manner, ruling out a first-order mechanism and suggesting that following unbinding, there is a significant probability of ligand rebinding to the same or neighboring subunits within a trimer. Consistent with such a mechanism, coexpression of wild-type subunits with mutant (R447C) subunits that do not bind glutamate or 2-FAA also increased the unblocking rate. The data suggest that electrostatic and steric factors result in an effective dissociation rate that is approximately sevenfold slower than the microscopic subunit unbinding rate. The quaternary structure, which has been conserved through evolution, is expected to increase the transporters' capture efficiency by increasing the probability that following unbinding, a ligand will rebind as opposed to being lost to diffusion.

The glutamate and chloride permeation pathways are colocalized in individual neuronal glutamate transporter subunits.

Glutamate transporters have a homotrimeric subunit structure with a large central water-filled cavity that extends partially into the plane of the lipid bilayer (Yernool et al., 2004). In addition to uptake of glutamate, the transporters also mediate a chloride conductance that is increased in the presence of substrate. Whether the chloride channel is located in the central pore of the trimer or within the individual subunits has been controversial. We find that coexpression of wild-type neuronal glutamate transporter EAAT3 subunits with subunits mutated at R447, a residue governing substrate selectivity (Bendahan et al., 2000), results in transport activity consistent with two distinct noninteracting populations of transporters, in agreement with previous work suggesting that each subunit operates independently to transport substrate (Awes et al., 2004; Grewer et al., 2005; Koch and Larsson, 2005). In wild-type homotrimeric transporters, the glutamate concentration dependence of the anion conductance and the kinetics of glutamate flux were isolated and measured, and the anion channel activation was fitted to analytical expressions corresponding to (1) a central pore gated by binding to one or more subunits and (2) a channel pore in each subunit. The data indicate that glutamate-binding sites, transport pathways, and chloride channels reside in individual subunits in a trimer and function independently.