Unitary Inputs Research Articles

Spontaneous Activity of the Local GABAergic Synaptic Network Causes Irregular Neuronal Firing in the External Globus Pallidus.

Autonomously firing GABAergic neurons in the external globus pallidus (GPe) form a local synaptic network. In slices, most GPe neurons receive a continuous inhibitory synaptic barrage from 1 or 2 presynaptic GPe neurons. We measured the barrage's effect on the firing rate and regularity of GPe neurons in male and female mice using perforated patch recordings. Silencing the firing of parvalbumin-positive (PV+) GPe neurons by activating genetically expressed Archaerhodopsin current increased the firing rate and regularity of PV- neurons. In contrast, silencing Npas1+ GPe neurons with Archaerhodopsin had insignificant effects on Npas1- neuron firing. Blocking spontaneous GABAergic synaptic input with gabazine reproduced the effects of silencing PV+ neuron firing on the firing rate and regularity of Npas1+ neurons and had similar effects on PV+ neuron firing. To simulate the barrage, we constructed conductance waveforms for dynamic clamp based on experimentally measured inhibitory postsynaptic conductance trains from 1 or 2 unitary local connections. The resulting inhibition replicated the effect on firing seen in the intact active network in the slice. We then increased the number of unitary inputs to match estimates of local network connectivity in vivo As few as 5 unitary inputs produced large increases in firing irregularity. The firing rate was also reduced initially, but PV+ neurons exhibited a slow spike-frequency adaptation that partially restored the rate despite sustained inhibition. We conclude that the irregular firing pattern of GPe neurons in vivo is largely due to the ongoing local inhibitory synaptic barrage produced by the spontaneous firing of other GPe neurons.SIGNIFICANCE STATEMENT Functional roles of local axon collaterals in the external globus pallidus (GPe) have remained elusive because of difficulty in isolating local inhibition from other GABAergic inputs in vivo, and in preserving the autonomous firing of GPe neurons and detecting their spontaneous local inputs in slices. We used perforated patch recordings to detect spontaneous local inputs during rhythmic firing. We found that the autonomous firing of single presynaptic GPe neurons produces inhibitory synaptic barrages that significantly alter the firing regularity of other GPe neurons. Our findings suggest that, although GPe neurons receive input from only a few other GPe neurons, each local connection has a large impact on their firing.

Unitary synaptic connections among substantia nigra pars reticulata neurons

Neurons in substantia nigra pars reticulata (SNr) are synaptically coupled by local axon collaterals, providing a potential mechanism for local signal processing. Because SNr neurons fire spontaneously, these synapses are constantly active. To investigate their properties, we recorded spontaneous inhibitory postsynaptic currents (sIPSCs) from SNr neurons in brain slices, in which afferents from upstream nuclei are severed, and the cells fire rhythmically. The sIPSC trains contained a mixture of periodic and aperiodic events. Autocorrelation analysis of sIPSC trains showed that a majority of cells had one to four active unitary inputs. The properties of the unitary IPSCs (uIPSCs) were analyzed for cells with one unitary input, using a model of periodic presynaptic firing and stochastic synaptic transmission. The inferred presynaptic firing rates and coefficient of variation of interspike intervals (ISIs) corresponded well with direct measurements of spiking in SNr neurons. Methods were developed to estimate the success probability, amplitude distributions, and kinetics of the uIPSCs, while removing the contribution from aperiodic sIPSCs. The sIPSC amplitudes were not increased upon release from halorhodopsin silencing, suggesting that most synapses were not depressed at the spontaneous firing rate. Gramicidin perforated-patch recordings indicated that the average reversal potential of spontaneous inhibitory postsynaptic potentials was -64 mV. Because of the change in driving force across the ISI, the unitary inputs are predicted to have a larger postsynaptic impact when they arrive late in the ISI. Simulations of network activity suggest that this very sparse inhibitory coupling may act to desynchronize the activity of SNr neurons while having only a small effect on firing rate.

Random multipliers numerically stabilize Gaussian and block Gaussian elimination: Proofs and an extension to low-rank approximation

We study two applications of standard Gaussian random multipliers. At first we prove that with a probability close to 1 such a multiplier is expected to numerically stabilize Gaussian elimination with no pivoting as well as block Gaussian elimination. Then, by extending our analysis, we prove that such a multiplier is also expected to support low-rank approximation of a matrix without customary oversampling. Our test results are in good accordance with this formal study. The results remain similar when we replace Gaussian multipliers with random circulant or Toeplitz multipliers, which involve fewer random parameters and enable faster multiplication. We formally support the observed efficiency of random structured multipliers applied to approximation, but we still continue our research in the case of elimination. We specify a narrow class of unitary inputs for which Gaussian elimination with no pivoting is numerically unstable and then prove that, with a probability close to 1, a Gaussian random circulant multiplier does not fix numerical stability problems for such inputs. We also prove that the power of the random circulant preprocessing increases if we also include random permutations.

Modeling the LFP footprint of unitary thalamic inputs to sensory cortex

The depth-resolved synaptic local-field potential (LFP) footprint in sensory cortex following firing in individual thalamic projection neurons can be accurately measured by averaging cortical multielectrode (ME) LFP signals over thousands of spontaneous thalamic firing events [1,2]. This spike-triggered LFP method offers a unique window into the thalamocortical connection. However, the interpretation of the detailed spatiotemporal profile of this LFP footprint is not trivial as the LFP signal reflects a weighted sum over contributions from all dendritic transmembrane currents located in the vicinity of the recording electrode [3]. We here present results from a biophysically detailed computational study of this LFP footprint, focusing on the thalamocortical LFP response in layer 4 of rodent barrel cortex [1]. As illustrated in Fig. ​Fig.1,1, the model considers large populations of synaptically activated RS (regular spiking cells) and/or FS (fast-spiking cells) (Fig. 1AB). The computational model, implemented in Python with NEURON, is constrained to predict plausible intracellular EPSCs [4] (Fig. ​(Fig.1C)1C) and EPSPs (Fig. ​(Fig.1D).1D). The model not only predicts the LFP (Fig. ​(Fig.1E),1E), but also the ground-truth CSD (current source-density) (Fig. ​(Fig.1F)1F) that can be used to test CSD estimation methods [5]. Candidate models mimicking experimental findings [1,2] will be presented. Figure 1 Model overview. A. Schematic of recording of unitary thalamic projection pattern to layer 4 with thalamic single-unit electrode (el.e), cortical clamp electrodes (el.i) and cortical multielectrode (ME) [1,2,4]. B. Example model population of reconstructed ...

Phase response analysis during in vivo-like high conductance states; dendritic SK determines the mean and variance of responses to dendritic excitation

A neuron’s phase response curve (PRC) describes how synaptic inputs at different times during the spike cycle affect the timing of subsequent spikes, and PRC analysis is a powerful technique for predicting and interpreting the emergence of synchronous modes in synaptically coupled networks and neuronal populations receiving common input. However, neuronal PRCs are typically measured during intrinsic pacemaking which may not reflect neuronal excitability and dynamics during high conductance states generated by complex network activity in vivo. Using a full morphological model of a globus pallidus (GP) neuron we have recently demonstrated that during intrinsic pacemaking, somatic PRCs for GP neurons are type I, i.e. excitatory inputs at all phases of the spike cycle advance the spontaneous spiking rhythm1. We also demonstrated that synaptic excitation of the distal dendrite can paradoxically delay subsequent spiking when delivered at some phases of the spike cycle (yielding a type II PRC) as a consequence of dendritic activation of the small conductance calcium-activated potassium current, SK1. Since during high conductance states spike timing is determined by a balance between intrinsic mechanisms and synaptic input fluctuations, in this study we investigated how somatic and dendritic phase response properties of the GP model are affected by ongoing stochastic synaptic background activity. We generated high conductance states in the model by applying synaptic backgrounds composed of randomly-timed excitatory and inhibitory synaptic inputs at 1022 GABA synapses and 100 AMPA synapses distributed throughout the dendrite. By varying the synaptic gain and input frequency parameters across the physiological range for inputs to GP, we achieved a diverse set of high conductance states characterized by sub-threshold voltage fluctuations, irregular spiking, and elevated membrane conductance (Figure ​(Figure1A1A &1B) and spanning the range of spike frequencies observed in vivo (15-45 Hz). For each synaptic background parameter set, we generated 100 single-trial PRCs by delivering a single 2.5 nS AMPA-synaptic input to either the soma or distal dendrite at each of 72 time-points (in separate simulations) within the first spike cycle of each of 100 control spike trains (Figure ​(Figure1C1C &1D). We then averaged the single-trial PRCs for each synaptic background to evaluate the dependence of PRC shape on stimulus location, spike frequency, and dendritic SK conductance, in addition to the gain and input frequencies of synaptic backgrounds. Next, we analyzed on a trial-by-trial basis the interactions of PRC stimuli with transient fluctuations in the synaptic background leading to added or skipped spikes. We determined that dendritic SK underlies both the incidence of skipped spikes and the dependence of skipped spike events on stimulus phase. Interestingly, the input-phase dependence of skipped spike events mirrored the phase-dependent variance in the PRC itself (which we plotted as phase response-variance curves, PRVCs). This indicates that dendritic SK determines not only the mean response, but also the variance of responses, to excitatory dendritic inputs. Average somatic and dendritic PRCs were type I and type II, respectively, and are likely to represent the average behavior of populations of GP neurons in response to shared excitation. Furthermore, in-as-much as the GP model and simulated synaptic backgrounds are physiologically realistic, the variance in the model’s responses across trials directly reflects a major source of spike time variance across populations of GP neurons in vivo. Figure 1 A&B. Total synaptic conductance (top) and current (bottom) for synaptic backgrounds composed of 1 nS (A) or 2 nS (B) unitary inputs. C&D. Perturbations of control spike trains (black) by somatic (C) or dendritic (D2D)(D) stimuli. (Trace ...

Sparse but Selective and Potent Synaptic Transmission From the Globus Pallidus to the Subthalamic Nucleus

The reciprocally connected GABAergic globus pallidus (GP)-glutamatergic subthalamic nucleus (STN) network is critical for voluntary movement and an important site of dysfunction in movement disorders such as Parkinson's disease. Although the GP is a key determinant of STN activity, correlated GP-STN activity is rare under normal conditions. Here we define fundamental features of the GP-STN connection that contribute to poorly correlated GP-STN activity. Juxtacellular labeling of single GP neurons in vivo and stereological estimation of the total number of GABAergic GP-STN synapses suggest that the GP-STN connection is surprisingly sparse: single GP neurons maximally contact only 2% of STN neurons and single STN neurons maximally receive input from 2% of GP neurons. However, GP-STN connectivity may be considerably more selective than even these estimates imply. Light and electron microscopic analyses revealed that single GP axons give rise to sparsely distributed terminal clusters, many of which correspond to multiple synapses with individual STN neurons. Application of the minimal stimulation technique in brain slices confirmed that STN neurons receive multisynaptic unitary inputs and that these inputs largely arise from different sets of GABAergic axons. Finally, the dynamic-clamp technique was applied to quantify the impact of GP-STN inputs on STN activity. Small fractions of GP-STN input were sufficiently powerful to inhibit and synchronize the autonomous activity of STN neurons. Together these data are consistent with the conclusion that the rarity of correlated GP-STN activity in vivo is due to the sparsity and selectivity, rather than the potency, of GP-STN synaptic connections.

Constellation Design for the Noncoherent MIMO Rayleigh-Fading Channel at General SNR

Constellation design for the noncoherent multiple-input-multiple-output (MIMO) block Rayleigh-fading channel is considered. For general signal-to-noise ratios (SNRs), starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, input probabilities and per-antenna amplitudes for the constellation points are obtained via a difference of convex programming formulation. Using the mutual information as a performance metric, it is shown that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low-medium SNR regime, and indeed they also similarly outperform the mutual information achieved by isotropically distributed unitary inputs for the continuous input channel [i.e., the so-called unitary space-time capacity (USTC)]. At sufficiently high SNRs, the resulting mutual information coincides with that of the base unitary designs. Thus the optimum constellation design technique works over the entire range of SNRs. The bit energy/spectral efficiency tradeoff of the optimized constellations are also obtained, and these provide valuable insights on modulation and coding, which are especially useful for wideband channels where the SNR per degree of freedom is low

Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form

An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix-having orthonormal columns, and a probability density that is invariant to premultiplication by an independent unitary matrix-plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. We take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for M=min(N, T/2) transmit antennas, where N is the number of receive antennas and T is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna.