Statistical analysis of synaptic transmission: model discrimination and confidence limits.

Procedures for discriminating between competing statistical models of synaptic transmission, and for providing confidence limits on the parameters of these models, have been developed. These procedures were tested against simulated data and were used to analyze the fluctuations in synaptic currents evoked in hippocampal neurones. All models were fitted to data using the Expectation-Maximization algorithm and a maximum likelihood criterion. Competing models were evaluated using the log-likelihood ratio (Wilks statistic). When the competing models were not nested, Monte Carlo sampling of the model used as the null hypothesis (H0) provided density functions against which H0 and the alternate model (H1) were tested. The statistic for the log-likelihood ratio was determined from the fit of H0 and H1 to these probability densities. This statistic was used to determine the significance level at which H0 could be rejected for the original data. When the competing models were nested, log-likelihood ratios and the chi 2 statistic were used to determine the confidence level for rejection. Once the model that provided the best statistical fit to the data was identified, many estimates for the model parameters were calculated by resampling the original data. Bootstrap techniques were then used to obtain the confidence limits of these parameters.     

An expectation-maximization algorithm for the analysis of allelic expression imbalance

A significant proportion of the variation between individuals in gene expression levels is genetic, and it is likely that these differences correlate with phenotypic differences or with risk of disease. Cis-acting polymorphisms are important in determining interindividual differences in gene expression that lead to allelic expression imbalance, which is the unequal expression of homologous alleles in individuals heterozygous for such a polymorphism. This expression imbalance can be detected using a transcribed polymorphism, and, once it is established, the next step is to identify the polymorphisms that are responsible for or predictive of allelic expression levels. We present an expectation-maximization algorithm for such analyses, providing a formal statistical framework to test whether a candidate polymorphism is associated with allelic expression differences.     

Analysis of synaptic transmission in the neuromuscular junction using a continuum finite element model.

There is a steadily growing body of experimental data describing the diffusion of acetylcholine in the neuromuscular junction and the subsequent miniature endplate currents produced at the postsynaptic membrane. To gain further insights into the structural features governing synaptic transmission, we have performed calculations using a simplified finite element model of the neuromuscular junction. The diffusing acetylcholine molecules are modeled as a continuum, whose spatial and temporal distribution is governed by the force-free diffusion equation. The finite element method was adopted because of its flexibility in modeling irregular geometries and complex boundary conditions. The resulting simulations are shown to be in accord with experiment and other simulations.     

Analysis of synaptic transmission in Caenorhabditis elegans using an aldicarb-sensitivity assay

Caenorhabditis elegans has emerged as a powerful model system for studying the biology of the synapse. Here we describe a widely used assay for synaptic transmission at the C. elegans neuromuscular junction. This protocol monitors the sensitivity of C. elegans to the paralyzing affects of an acetylcholinesterase inhibitor, aldicarb. Briefly, adult worms are incubated in the presence of aldicarb and scored for the time-course of aldicarb-induced paralysis. Animals harboring mutations in genes that affect synaptic transmission generally exhibit a change in their sensitivity to aldicarb (either increased sensitivity for enhancements in synaptic transmission or decreased sensitivity for blockage in synaptic transmission). This technique provides a simple assay for the accurate comparative analysis of synaptic transmission in multiple C. elegans strains. The protocol described can be performed relatively quickly and is a practical alternative to other techniques used to study synaptic transmission. This protocol can also be modified to follow the paralytic effects with other pharmacological reagents. The assay can be performed in about 3-6 hours depending on the severity of synaptic transmission defects.     

Role of the synaptic microenvironment in functional modification of synaptic transmission

Experiments on hippocampal slices showed that perfusion with a dextran solution more effectively facilitates AMPA-mediated transmission in structurally complex synapses of mossy fibers of Shaffer collaterals. Estimates for changes in the extracellular Ca²⁺ concentration in the close vicinity of a reconstructed synapse during the action potential development are obtained. The results together with data about the rather small (0.5 μm) characteristics distance between neighboring synapses showed that the probability of mutual intersynaptic influence via the microenvironment is high. A probable functional role of such influences is discussed.     

Calcium channels and synaptic transmission in familial hemiplegic migraine type 1 animal models

One of the outstanding developments in clinical neurology has been the identification of ion channel mutations as the origin of a wide variety of inherited disorders like migraine, epilepsy, and ataxia. The study of several channelopathies has provided crucial insights into the molecular mechanisms, pathogenesis, and therapeutic approaches to complex neurological diseases. This review addresses the mutations underlying familial hemiplegic migraine (FHM) with particular interest in Cav2.1 (i.e., P/Q-type) voltage-activated Ca²⁺ channel FHM type-1 mutations (FHM1). Transgenic mice harboring the human pathogenic FHM1 mutation R192Q or S218L (KI) have been used as models to study neurotransmission at several central and peripheral synapses. FHM1 KI mice are a powerful tool to explore presynaptic regulation associated with expression of Cav2.1 channels. FHM1 Cav2.1 channels activate at more hyperpolarizing potentials and show an increased open probability. These biophysical alterations may lead to a gain-of-function on synaptic transmission depending upon factors such as action potential waveform and/or Cav2.1 splice variants and auxiliary subunits. Analysis of FHM knock-in mouse models has demonstrated a deficient regulation of the cortical excitation/inhibition (E/I) balance. The resulting excessive increases in cortical excitation may be the mechanisms that underlie abnormal sensory processing together with an increase in the susceptibility to cortical spreading depression (CSD). Increasing evidence from FHM KI animal studies support the idea that CSD, the underlying mechanism of aura, can activate trigeminal nociception, and thus trigger the headache mechanisms.     

Calcium-induced modulation of synaptic transmission

Calcium (Ca²⁺) is a second messenger regulating a wide variety of intracellular processes. Using GABA-and glycinergic synapses as examples, this review analyzes two functions of this unique ion: postsynaptic Ca²⁺-dependent modulation of receptor-operated channels and Ca²⁺-induced retrograde regulation of neurotransmitter release from the presynaptic terminals. Phosphorylation, rapid Ca²⁺-induced modulation via intermediate Ca²⁺-binding proteins, and changes in the number of functional receptors represent the main pathways of short-and long-term plasticity of postsynaptic receptor-operated channel machinery. Retrograde signaling is an example of synaptic modulation triggered by stimulation of postsynaptic cells and mediated via regulation of presynaptic neurotransmitter release. This mechanism provides postsynaptic neurons with efficient tools to control the presynaptic afferents in an activity-dependent mode. Elevation of intracellular Ca²⁺ in a postsynaptic neuron triggers the synthesis of endocannabinoids (derivatives of arachidonic acid). Their retrograde diffusion through the synaptic cleft and consequent activation of presynaptic G-protein coupled to CB1 receptors inhibits the release of neurotransmitter. These mechanisms of double modulation, which include control over the function of postsynaptic ion channels and retrograde suppression of the release machinery, play an important role in Ca²⁺-dependent control of the main excitatory and inhibitory synaptic pathways in the mammalian nervous system.     

Astrocyte-induced modulation of synaptic transmission

The idea that astrocytes simply provide structural and trophic support to neurons has been challenged by recent evidence demonstrating that astrocytes exhibit a form of excitability and communication based on intracellular Ca2+ variations and intercellular Ca2+ waves, which can be initiated by neuronal activity. These astrocyte Ca2+ variations have now been shown to induce glutamate-dependent Ca2+ elevations and slow inward currents in neurons. More recently, it has been demonstrated that synaptic transmission between cultured hippocampal neurons can be directly modulated by astrocytes. We have reported that astrocyte stimulation can increase the frequency of miniature synaptic currents. Furthermore, we also have demonstrated that an elevation in the intracellular Ca2+ in astrocytes induces a reduction in both excitatory and inhibitory evoked synaptic transmission through the activation of selective presynaptic metabotropic glutamate receptors.     

Neurotrophin regulation of synaptic transmission

Examples of signaling molecules that are devoted to neuronal development at the exclusion of other functions are scarce. It may then come as no surprise to learn that a family of molecules that promote neuronal survival, differentiation and outgrowth also regulate synaptic transmission at both developing and mature synapses. Indeed, many studies over the past five years have shown that neurotrophins, including nerve growth factor (NGF), neurotrophin-3 (NT-3), NT-4/5 and brain-derived neurotrophic factor (BDNF), have both rapid and long-latency influences on synaptic strength. New research has highlighted the enormous range of neurotrophin actions at both developing and mature synapses, demonstrating that transmission can be enhanced or reduced at excitatory and inhibitory synapses by either pre- or postsynaptic mechanisms.     

Modeling synaptic transmission of the tripartite synapse

The tripartite synapse denotes the junction of a pre- and postsynaptic neuron modulated by a synaptic astrocyte. Enhanced transmission probability and frequency of the postsynaptic current-events are among the significant effects of the astrocyte on the synapse as experimentally characterized by several groups. In this paper we provide a mathematical framework for the relevant synaptic interactions between neurons and astrocytes that can account quantitatively for both the astrocytic effects on the synaptic transmission and the spontaneous postsynaptic events. Inferred from experiments, the model assumes that glutamate released by the astrocytes in response to synaptic activity regulates store-operated calcium in the presynaptic terminal. This source of calcium is distinct from voltage-gated calcium influx and accounts for the long timescale of facilitation at the synapse seen in correlation with calcium activity in the astrocytes. Our model predicts the inter-event interval distribution of spontaneous current activity mediated by a synaptic astrocyte and provides an additional insight into a novel mechanism for plasticity in which a low fidelity synapse gets transformed into a high fidelity synapse via astrocytic coupling.     

Astrocytes optimize the synaptic transmission of information

Chemical synapses transmit information via the release of neurotransmitter-filled vesicles from the presynaptic terminal. Using computational modeling, we predict that the limited availability of neurotransmitter resources in combination with the spontaneous release of vesicles limits the maximum degree of enhancement of synaptic transmission. This gives rise to an optimal tuning that depends on the number of active zones. There is strong experimental evidence that astrocytes that enwrap synapses can modulate the probabilities of vesicle release through bidirectional signaling and hence regulate synaptic transmission. For low-fidelity hippocampal synapses, which typically have only one or two active zones, the predicted optimal values lie close to those determined by experimentally measured astrocytic feedback, suggesting that astrocytes optimize synaptic transmission of information.     

Statistical models for trisomic phenotypes.

Certain genetic disorders are rare in the general population but more common in individuals with specific trisomies, which suggests that the genes involved in the etiology of these disorders may be located on the trisomic chromosome. As with all aneuploid syndromes, however, a considerable degree of variation exists within each phenotype so that any given trait is present only among a subset of the trisomic population. We have previously presented a simple gene-dosage model to explain this phenotypic variation and developed a strategy to map genes for such traits. The mapping strategy does not depend on the simple model but works in theory under any model that predicts that affected individuals have an increased likelihood of disomic homozygosity at the trait locus. This paper explores the robustness of our mapping method by investigating what kinds of models give an expected increase in disomic homozygosity. We describe a number of basic statistical models for trisomic phenotypes. Some of these are logical extensions of standard models for disomic phenotypes, and some are more specific to trisomy. Where possible, we discuss genetic mechanisms applicable to each model. We investigate which models and which parameter values give an expected increase in disomic homozygosity in individuals with the trait. Finally, we determine the sample sizes required to identify the increased disomic homozygosity under each model. Most of the models we explore yield detectable increases in disomic homozygosity for some reasonable range of parameter values, usually corresponding to smaller trait frequencies. It therefore appears that our mapping method should be effective for a wide variety of moderately infrequent traits, even though the exact mode of inheritance is unlikely to be known.