Ramana Dodla

Subthreshold outward currents enhance temporal integration in auditory neurons

Abstract.Many auditory neurons possess low-threshold potassium currents (IKLT) that enhance their responsiveness to rapid and coincident inputs. We present recordings from gerbil medial superior olivary (MSO) neurons in vitro and modeling results that illustrate how IKLT improves the detection of brief signals, of weak signals in noise, and of the coincidence of signals (as needed for sound localization). We quantify the enhancing effect of IKLT on temporal processing with several measures: signal-to-noise ratio (SNR), reverse correlation or spike-triggered averaging of input currents, and interaural time difference (ITD) tuning curves. To characterize how IKLT, which activates below spike threshold, influences a neuron’s voltage rise toward threshold, i.e., how it filters the inputs, we focus first on the response to weak and noisy signals. Cells and models were stimulated with a computer-generated steady barrage of random inputs, mimicking weak synaptic conductance transients (the “noise”), together with a larger but still subthreshold postsynaptic conductance, EPSG (the “signal”). Reduction of IKLT decreased the SNR, mainly due to an increase in spontaneous firing (more “false positive”). The spike-triggered reverse correlation indicated that IKLT shortened the integration time for spike generation. IKLT also heightened the model’s timing selectivity for coincidence detection of simulated binaural inputs. Further, ITD tuning is shifted in favor of a slope code rather than a place code by precise and rapid inhibition onto MSO cells (Brand et al. 2002). In several ways, low-threshold outward currents are seen to shape integration of weak and strong signals in auditory neurons.

Firing rate and pattern heterogeneity in the globus pallidus arise from a single neuronal population

Intrinsic heterogeneity in networks of interconnected cells has profound effects on synchrony and spike-time reliability of network responses. Projection neurons of the globus pallidus (GPe) are interconnected by GABAergic inhibitory synapses and in vivo fire continuously but display significant rate and firing pattern heterogeneity. Despite being deprived of most of their synaptic inputs, GPe neurons in slices also fire continuously and vary greatly in their firing rate (1-70 spikes/s) and in regularity of their firing. We asked if this rate and pattern heterogeneity arises from separate cell types differing in rate, local synaptic interconnections, or variability of intrinsic properties. We recorded the resting discharge of GPe neurons using extracellular methods both in vivo and in vitro. Spike-to-spike variability (jitter) was measured as the standard deviation of interspike intervals. Firing rate and jitter covaried continuously, with slow firing being associated with higher variability than faster firing, as would be expected from heterogeneity arising from a single physiologically distinct cell type. The relationship between rate and jitter was unaffected by blockade of GABA and glutamate receptors. When the firing rate of individual neurons was altered with constant current, jitter changed to maintain the rate-jitter relationship seen across neurons. Long duration (30-60 min) recordings showed slow and spontaneous bidirectional drift in rate similar to the across-cell heterogeneity. Paired recordings in vivo and in vitro showed that individual cells wandered in rate independently of each other. Input conductance and rate wandered together, in a manner suggestive that both were due to fluctuations of an inward current.

Amplitude Death, Synchrony, and Chimera States in Delay Coupled Limit Cycle Oscillators

In this chapter we will discuss the effects of time delay on the collective states of a model mathematical system composed of a collection of coupled limit cycle oscillators. Such an assembly of coupled nonlinear oscillators serves as a useful paradigm for the study of collective phenomena in many physical, chemical, and biological systems and has therefore led to a great deal of theoretical and experimental work in the past [1–6]. Examples of practical applications of such models include simulating the interactions of arrays of Josephson junctions [7, 8], semiconductor lasers [9, 10], charge density waves [11], phase-locking of relativistic magnetrons [12], Belousov–Zhabotinskii reactions in coupled Brusselator models [2, 13–15], and neural oscillator networks for circadian pacemakers [16].

Asynchronous response of coupled pacemaker neurons

We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase lock spike to spike for strong mutual coupling. But the shared input can desynchronize the locked spike pairs by selectively eliminating the lagging spike or modulating its timing with respect to the leading spike depending on their separation time window. Such loss of synchrony is also found in a large network of sparsely coupled heterogeneous spiking neurons receiving shared input.

Synchrony-asynchrony transitions in neuronal networks

Irregular spike timing over long durations or relative asynchronous spiking between cells is a ubiquitous phenomenon observed in many brain nuclei both in vivo and in vitro. Subthalamic neurons (STN) and globus pallidus (GP) neurons of the basal ganglia are good examples of such neuronal irregularity. They fire asynchronously normally, but become synchronous in Parkinson’s disease [1,2]. These cells have been shown to be autonomous, i.e., their oscillations are sustained in the absence of synaptic transmission. The prevalence of irregularity in such oscillatory neurons, and their tendency to become synchronous under disease conditions poses several challenges. They necessitate a detailed study of the interaction of oscillatory mechanisms that may contribute to synchronization between neurons with the sparsity of their interactions, the size of the network, and the external synaptic input. We study synchrony-asynchrony transitions in a model network of synaptically coupled STN or GP neurons with varying degrees of network size (N) and connectivity (number of presynaptic neurons per postsynaptic neuron, M <=N). We find the critical size (Ncrit) and critical number of connections (Mcrit for given N) needed in order to achieve global synchrony, as well as explore the nature and size of local cluster sates in the asynchronous state. The STN and GP neurons are modeled using Hodgkin-Huxley type of equations that incorporate sodium, potassium, calcium, a low-threshold calcium (T), and an afterhyperpolarization (AHP) activated potassium current [3]. In a network of two or more mutually excitatory neurons, for example, spike-to-spike synchrony can be achieved by increasing the coupling conductance beyond a critical level. In the unsynchronized regime, a phase drift between spike times of the neurons as well as multiple-frequency locked states can result. The level of mutual coupling required for synchrony in an all-to-all coupled network is found to increase as square root of N. In a sparsely connected network local cluster states emerge for weaker coupling, but spike-to-spike synchrony is also achieved for stronger coupling. Synchrony breaks down if the number of presynaptic neurons is fewer than a critical number. An external common synaptic inhibitory input given at Poisson intervals with a fixed arrival rate can cause asynchrony as well as enhance the frequency of the network at all network sizes.

Effect of Sharp Jumps at the Edges of Phase Response Curves on Synchronization of Electrically Coupled Neuronal Oscillators

We study synchronization phenomenon of coupled neuronal oscillators using the theory of weakly coupled oscillators. The role of sudden jumps in the phase response curve profiles found in some experimental recordings and models on the ability of coupled neurons to exhibit synchronous and antisynchronous behavior is investigated, when the coupling between the neurons is electrical. The level of jumps in the phase response curve at either end, spike width and frequency of voltage time course of the coupled neurons are parameterized using piecewise linear functional forms, and the conditions for stable synchrony and stable antisynchrony in terms of those parameters are computed analytically. The role of the peak position of the phase response curve on phase-locking is also investigated.

Effect of phase response curve skewness on synchronization of electrically coupled neuronal oscillators

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

Spike width and frequency alter stability of phase-locking in electrically coupled neurons

The stability of phase-locked states of electrically coupled type-1 phase response curve neurons is studied using piecewise linear formulations for their voltage profile and phase response curves. We find that at low frequency and/or small spike width, synchrony is stable, and antisynchrony unstable. At high frequency and/or large spike width, these phase-locked states switch their stability. Increasing the ratio of spike width to spike height causes the antisynchronous state to transition into a stable synchronous state. We compute the interaction function and the boundaries of stability of both these phase-locked states, and present analytical expressions for them. We also study the effect of phase response curve skewness on the boundaries of synchrony and antisynchrony.

Quantification of Clustering in Joint Interspike Interval Scattergrams of Spike Trains

Joint interval scattergrams are usually employed in determining serial correlations between events of spike trains. However, any inherent structures in such scattergrams that are often seen in experimental records are not quantifiable by serial correlation coefficients. Here, we develop a method to quantify clustered structures in any two-dimensional scattergram of pairs of interspike intervals. The method gives a cluster coefficient as well as clustering density function that could be used to quantify clustering in scattergrams obtained from first- or higher-order interval return maps of single spike trains, or interspike interval pairs drawn from simultaneously recorded spike trains. The method is illustrated using numerical spike trains as well as in vitro pairwise recordings of rat striatal tonically active neurons.

Effect of Phase Response Curve Shape and Synaptic Driving Force on Synchronization of Coupled Neuronal Oscillators

The role of the phase response curve (PRC) shape on the synchrony of synaptically coupled oscillating neurons is examined. If the PRC is independent of the phase, because of the synaptic form of the coupling, synchrony is found to be stable for both excitatory and inhibitory coupling at all rates, whereas the antisynchrony becomes stable at low rates. A faster synaptic rise helps extend the stability of antisynchrony to higher rates. If the PRC is not constant but has a profile like that of a leaky integrate-and-fire model, then, in contrast to the earlier reports that did not include the voltage effects, mutual excitation could lead to stable synchrony provided the synaptic reversal potential is below the voltage level the neuron would have reached in the absence of the interaction and threshold reset. This level is controlled by the applied current and the leakage parameters. Such synchrony is contingent on significant phase response (that would result, for example, by a sharp PRC jump) occurring during the synaptic rising phase. The rising phase, however, does not contribute significantly if it occurs before the voltage spike reaches its peak. Then a stable near-synchronous state can still exist between type 1 PRC neurons if the PRC shows a left skewness in its shape. These results are examined comprehensively using perfect integrate-and-fire, leaky integrate-and-fire, and skewed PRC shapes under the assumption of the weakly coupled oscillator theory applied to synaptically coupled neuron models.