Summation of Spatiotemporal Input Patterns in Leaky Integrate-and-Fire Neurons: Application to Neurons in the Cochlear Nucleus Receiving Converging Auditory Nerve Fiber Input

The response of leaky integrate-and-fire neurons is analyzed for periodic inputs whose phases vary with their spatial location. The model gives the relationship between the spatial summation distance and the degree of phase locking of the output spikes (i.e., locking to the periodic stochastic inputs, measured by the synchronization index). The synaptic inputs are modeled as an inhomogeneous Poisson process, and the analysis is carried out in the Gaussian approximation. The model has been applied to globular bushy cells of the cochlear nucleus, which receive converging inputs from auditory nerve fibers that originate at neighboring sites in the cochlea. The model elucidates the roles played by spatial summation and coincidence detection, showing how synchronization decreases with an increase in both frequency and spatial spread of inputs. It also shows under what conditions an enhancement of synchronization of the output relative to the input takes place.     

Analytical and Simulation Results for Stochastic Fitzhugh-Nagumo Neurons and Neural Networks

An analytical approach is presented for determining the response of a neuron or of the activity in a network of connected neurons, represented by systems of nonlinear ordinary stochastic differential equations—the Fitzhugh-Nagumo system with Gaussian white noise current. For a single neuron, five equations hold for the first- and second-order central moments of the voltage and recovery variables. From this system we obtain, under certain assumptions, five differential equations for the means, variances, and covariance of the two components. One may use these quantities to estimate the probability that a neuron is emitting an action potential at any given time. The differential equations are solved by numerical methods. We also perform simulations on the stochastic Fitzugh-Nagumo system and compare the results with those obtained from the differential equations for both sustained and intermittent deterministic current inputs withsuperimposed noise. For intermittent currents, which mimic synaptic input, the agreement between the analytical and simulation results for the moments is excellent. For sustained input, the analytical approximations perform well for small noise as there is excellent agreement for the moments. In addition, the probability that a neuron is spiking as obtained from the empirical distribution of the potential in the simulations gives a result almost identical to that obtained using the analytical approach. However, when there is sustained large-amplitude noise, the analytical method is only accurate for short time intervals. Using the simulation method, we study the distribution of the interspike interval directly from simulated sample paths. We confirm that noise extends the range of input currents over which (nonperiodic) spike trains may exist and investigate the dependence of such firing on the magnitude of the mean input current and the noise amplitude. For networks we find the differential equations for the means, variances, and covariances of the voltage and recovery variables and show how solving them leads to an expression for the probability that a given neuron, or given set of neurons, is firing at time t. Using such expressions one may implement dynamical rules for changing synaptic strengths directly without sampling. The present analytical method applies equally well to temporally nonhomogeneous input currents and is expected to be useful for computational studies of information processing in various nervous system centers.     

Nonlinear Relationships in the Patterns of Neuronal Spiking in Cortical Neurons

The pattern of neuronal spiking of cortical neurons was investigated in an awake nonimmobilized rabbit. Thecharacteristics of the interspike intervals (total numberof intervals, mean interval, mean-square deviation) and of the burst (group) activity (burst number, mean spikefrequency in a burst, mean spike number for a burst, meanburst duration) were considered. Nonlinear relationshipbetween the values of mean interspike intervals and thenumber of spike bursts was found. A number of functionswere applied to describe the observed phenomena. On thebasis of regression analysis two populations of corticalneurons with distinct neuronal spiking patterns wereidentified. Bursts occur at a higher rate in one populationthan the other, although both populations exhibit burstsand are otherwise indistinguishable.     

The Use of a Symbol Processing Computer Language in Point Estimation of Parameters and in Construction of Confidence Intervals

This paper presents a method to generate automatically computer programs which are necessary for parameter estimation, hypothesis tests and construction of confidence intervals by the maximum likelihood method. The spectral or density function of the random variable is arbitrary, but must be known and given in closed form. The programming language used is the symbol processing language LIBAFORM, whose statements are interpreted by a package of LISP-routines. The application of the method is illustrated by the analysis of a linear model whose residuals follow a logarithmic F-distribution, and the analysis of a dose-response curve.     

Comparison of Coding Capabilities of Type I and Type II Neurons

We consider the dependence of information transfer by neurons on the Type I vs. Type II classification of their dynamics. Our computational study is based on Type I and II implementations of the Morris-Lecar model. It mainly concerns neurons, such as those in the auditory or electrosensory system, which encode band-limited amplitude modulations of a periodic carrier signal, and which fire at random cycles yet preferred phases of this carrier. We first show that the Morris-Lecar model with additive broadband noise ("synaptic noise") can exhibit such firing patterns with either Type I or II dynamics, with or without amplitude modulations of the carrier. We then compare the encoding of band-limited random amplitude modulations for both dynamical types. The comparison relies on a parameter calibration that closely matches firing rates for both models across a range of parameters. In the absence of synaptic noise, Type I performs slightly better than Type II, and its performance is optimal for perithreshold signals. However, Type II performs well over a slightly larger range of inputs, and this range lies mostly in the subthreshold region. Further, Type II performs marginally better than Type I when synaptic noise, which yields more realistic baseline firing patterns, is present in both models. These results are discussed in terms of the tuning and phase locking properties of the models with deterministic and stochastic inputs.     

The selective control of glycolysis,gluconeogenesis and glycogenesis by temporal insulin patterns

Insulin governs systemic glucose metabolism, including glycolysis, gluconeogenesis and glycogenesis, through temporal change and absolute concentration. However, how insulin‐signalling pathway selectively regulates glycolysis, gluconeogenesis and glycogenesis remains to be elucidated. To address this issue, we experimentally measured metabolites in glucose metabolism in response to insulin. Step stimulation of insulin induced transient response of glycolysis and glycogenesis, and sustained response of gluconeogenesis and extracellular glucose concentration (GLC _ex ). Based on the experimental results, we constructed a simple computational model that characterises response of insulin‐signalling‐dependent glucose metabolism. The model revealed that the network motifs of glycolysis and glycogenesis pathways constitute a feedforward (FF) with substrate depletion and incoherent feedforward loop (iFFL), respectively, enabling glycolysis and glycogenesis responsive to temporal changes of insulin rather than its absolute concentration. In contrast, the network motifs of gluconeogenesis pathway constituted a FF inhibition, enabling gluconeogenesis responsive to absolute concentration of insulin regardless of its temporal patterns. GLC _ex was regulated by gluconeogenesis and glycolysis. These results demonstrate the selective control mechanism of glucose metabolism by temporal patterns of insulin.     

A Connectionist Model of Left-Right Sound Discrimination by the Mauthner System

Artificial neural networks were used to explore the auditory function of the Mauthner system, the brainstem circuit in teleost fishes that initiates fast-start escape responses. The artificial neural networks were trained with backpropagation to assign connectivity and receptive fields in an architecture consistent with the known anatomy of the Mauthner system. Our first goal was to develop neurally specific hypotheses for how the Mauthner system discriminates right from left in the onset of a sound. Our model was consistent with the phase model for directional hearing underwater, the prevalent theory for sound source localization by fishes. Our second goal was to demonstrate how the neural mechanisms that permit sound localization according to the phase model can coexist with the mechanisms that permit the Mauthner system to discriminate between stimuli based on amplitude. Our results indicate possible computational roles for elements of the Mauthner system, which has provided us a theoretical context within which to consider past and future experiments on the cellular physiology. Thus, these findings demonstrate the potential significance of this approach in generating experimentally testable hypotheses for small systems of identified cells.     

Input–output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data

The ErbB signaling pathways, which regulate diverse physiological responses such as cell survival, proliferation and motility, have been subjected to extensive molecular analysis. Nonetheless, it remains poorly understood how different ligands induce different responses and how this is affected by oncogenic mutations. To quantify signal flow through ErbB‐activated pathways we have constructed, trained and analyzed a mass action model of immediate‐early signaling involving ErbB1–4 receptors (EGFR, HER2/Neu2, ErbB3 and ErbB4), and the MAPK and PI3K/Akt cascades. We find that parameter sensitivity is strongly dependent on the feature (e.g. ERK or Akt activation) or condition (e.g. EGF or heregulin stimulation) under examination and that this context dependence is informative with respect to mechanisms of signal propagation. Modeling predicts log‐linear amplification so that significant ERK and Akt activation is observed at ligand concentrations far below the K_d for receptor binding. However, MAPK and Akt modules isolated from the ErbB model continue to exhibit switch‐like responses. Thus, key system‐wide features of ErbB signaling arise from nonlinear interaction among signaling elements, the properties of which appear quite different in context and in isolation.     

Detection of Protein Palmitoylation in Cultured Hippocampal Neurons by Immunoprecipitation and Acyl-Biotin Exchange (ABE)

Palmitoylation is a post-translational lipid modification involving the attachment of a 16-carbon saturated fatty acid, palmitate, to cysteine residues of substrate proteins through a labile thioester bond [reviewed in¹]. Palmitoylation of a substrate protein increases its hydrophobicity, and typically facilitates its trafficking toward cellular membranes. Recent studies have shown palmitoylation to be one of the most common lipid modifications in neurons^{1, 2}, suggesting that palmitate turnover is an important mechanism by which these cells regulate the targeting and trafficking of proteins. The identification and detection of palmitoylated substrates can therefore better our understanding of protein trafficking in neurons.Detection of protein palmitoylation in the past has been technically hindered due to the lack of a consensus sequence among substrate proteins, and the reliance on metabolic labeling of palmitoyl-proteins with ³H-palmitate, a time-consuming biochemical assay with low sensitivity. Development of the Acyl-Biotin Exchange (ABE) assay enables more rapid and high sensitivity detection of palmitoylated proteins^2-4, and is optimal for measuring the dynamic turnover of palmitate on neuronal proteins. The ABE assay is comprised of three biochemical steps (Figure 1): 1) irreversible blockade of unmodified cysteine thiol groups using N-ethylmaliemide (NEM), 2) specific cleavage and unmasking of the palmitoylated cysteine''s thiol group by hydroxylamine (HAM), and 3) selective labeling of the palmitoylated cysteine using a thiol-reactive biotinylation reagent, biotin-BMCC. Purification of the thiol-biotinylated proteins following the ABE steps has differed, depending on the overall goal of the experiment.Here, we describe a method to purify a palmitoylated protein of interest in primary hippocampal neurons by an initial immunoprecipitation (IP) step using an antibody directed against the protein, followed by the ABE assay and western blotting to directly measure palmitoylation levels of that protein, which is termed the IP-ABE assay. Low-density cultures of embryonic rat hippocampal neurons have been widely used to study the localization, function, and trafficking of neuronal proteins, making them ideally suited for studying neuronal protein palmitoylation using the IP-ABE assay. The IP-ABE assay mainly requires standard IP and western blotting reagents, and is only limited by the availability of antibodies against the target substrate. This assay can easily be adapted for the purification and detection of transfected palmitoylated proteins in heterologous cell cultures, primary neuronal cultures derived from various brain tissues of both mouse and rat, and even primary brain tissue itself.