Models of Short-Term Synaptic Plasticity.

We focus on dynamical descriptions of short-term synaptic plasticity. Instead of focusing on the molecular machinery that has been reviewed recently by several authors, we concentrate on the dynamics and functional significance of synaptic plasticity, and review some mathematical models that reproduce different properties of the dynamics of short term synaptic plasticity that have been observed experimentally. The complexity and shortcomings of these models point to the need of simple, yet physiologically meaningful models. We propose a simplified model to be tested in synapses displaying different types of short-term plasticity.

Diverse Short-Term Dynamics of Inhibitory Synapses Converging on Striatal Projection Neurons: Differential Changes in a Rodent Model of Parkinson's Disease.

Most neurons in the striatum are projection neurons (SPNs) which make synapses with each other within distances of approximately 100 µm. About 5% of striatal neurons are GABAergic interneurons whose axons expand hundreds of microns. Short-term synaptic plasticity (STSP) between fast-spiking (FS) interneurons and SPNs and between SPNs has been described with electrophysiological and optogenetic techniques. It is difficult to obtain pair recordings from some classes of interneurons and due to limitations of actual techniques, no other types of STSP have been described on SPNs. Diverse STSPs may reflect differences in presynaptic release machineries. Therefore, we focused the present work on answering two questions: Are there different identifiable classes of STSP between GABAergic synapses on SPNs? And, if so, are synapses exhibiting different classes of STSP differentially affected by dopamine depletion? Whole-cell voltage-clamp recordings on SPNs revealed three classes of STSPs: depressing, facilitating, and biphasic (facilitating-depressing), in response to stimulation trains at 20 Hz, in a constant ionic environment. We then used the 6-hydroxydopamine (6-OHDA) rodent model of Parkinson's disease to show that synapses with different STSPs are differentially affected by dopamine depletion. We propose a general model of STSP that fits all the dynamics found in our recordings.

Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron.

Neurons show diverse firing patterns. Even neurons belonging to a single chemical or morphological class, or the same identified neuron, can display different types of electrical activity. For example, motor neuron MN5, which innervates a flight muscle of adult Drosophila, can show distinct firing patterns under the same recording conditions. We developed a two-dimensional biophysical model and show that a core complement of just two voltage-gated channels is sufficient to generate firing pattern diversity. We propose Shab and DmNa v to be two candidate genes that could encode these core currents, and find that changes in Shab channel expression in the model can reproduce activity resembling the main firing patterns observed in MN5 recordings. We use bifurcation analysis to describe the different transitions between rest and spiking states that result from variations in Shab channel expression, exposing a connection between ion channel expression, bifurcation structure, and firing patterns in models of membrane potential dynamics.

Ensemble response in mushroom body output neurons of the honey bee outpaces spatiotemporal odor processing two synapses earlier in the antennal lobe.

Neural representations of odors are subject to computations that involve sequentially convergent and divergent anatomical connections across different areas of the brains in both mammals and insects. Furthermore, in both mammals and insects higher order brain areas are connected via feedback connections. In order to understand the transformations and interactions that this connectivity make possible, an ideal experiment would compare neural responses across different, sequential processing levels. Here we present results of recordings from a first order olfactory neuropile - the antennal lobe (AL) - and a higher order multimodal integration and learning center - the mushroom body (MB) - in the honey bee brain. We recorded projection neurons (PN) of the AL and extrinsic neurons (EN) of the MB, which provide the outputs from the two neuropils. Recordings at each level were made in different animals in some experiments and simultaneously in the same animal in others. We presented two odors and their mixture to compare odor response dynamics as well as classification speed and accuracy at each neural processing level. Surprisingly, the EN ensemble significantly starts separating odor stimuli rapidly and before the PN ensemble has reached significant separation. Furthermore the EN ensemble at the MB output reaches a maximum separation of odors between 84-120 ms after odor onset, which is 26 to 133 ms faster than the maximum separation at the AL output ensemble two synapses earlier in processing. It is likely that a subset of very fast PNs, which respond before the ENs, may initiate the rapid EN ensemble response. We suggest therefore that the timing of the EN ensemble activity would allow retroactive integration of its signal into the ongoing computation of the AL via centrifugal feedback.

Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administration capacity.

BACKGROUND: Influenza viruses are a major cause of morbidity and mortality worldwide. Vaccination remains a powerful tool for preventing or mitigating influenza outbreaks. Yet, vaccine supplies and daily administration capacities are limited, even in developed countries. Understanding how such constraints can alter the mitigating effects of vaccination is a crucial part of influenza preparedness plans. Mathematical models provide tools for government and medical officials to assess the impact of different vaccination strategies and plan accordingly. However, many existing models of vaccination employ several questionable assumptions, including a rate of vaccination proportional to the population at each point in time. METHODS: We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters. We refer to this as the non-proportional model of vaccination and compare it to the proportional scheme typically found in the literature. RESULTS: The proportional and non-proportional models behave similarly for a few different vaccination scenarios. However, there are parameter regimes involving the vaccination campaign duration and daily supply limit for which the non-proportional model predicts smaller epidemics that peak later, but may last longer, than those of the proportional model. We also use the non-proportional model to predict the mitigating effects of variably timed vaccination campaigns for different levels of vaccination coverage, using specific constraints on daily administration capacity. CONCLUSIONS: The non-proportional model of vaccination is a theoretical improvement that provides more accurate predictions of the mitigating effects of vaccination on influenza outbreaks than the proportional model. In addition, parameters such as vaccine supply and daily administration limit can be easily adjusted to simulate conditions in developed and developing nations with a wide variety of financial and medical resources. Finally, the model can be used by government and medical officials to create customized pandemic preparedness plans based on the supply and administration constraints of specific communities.