Sungho Hong

Impact of Neuronal Properties on Network Coding: Roles of Spike Initiation Dynamics and Robust Synchrony Transfer

Neural networks are more than the sum of their parts, but the properties of those parts are nonetheless important. For instance, neuronal properties affect the degree to which neurons receiving common input will spike synchronously, and whether that synchrony will propagate through the network. Stimulus-evoked synchrony can help or hinder network coding depending on the type of code. In this Perspective, we describe how spike initiation dynamics influence neuronal input-output properties, how those properties affect synchronization, and how synchronization affects network coding. We propose that synchronous and asynchronous spiking can be used to multiplex temporal (synchrony) and rate coding and discuss how pyramidal neurons would be well suited for that task.

GABA-mediated repulsive coupling between circadian clock neurons in the SCN encodes seasonal time

Significance How animals track the seasons has long been a mystery. We found a mechanism that explains how day length is encoded within the neuronal network of suprachiasmatic nucleus (SCN). Using an integrated approach combining experiments and modeling, we find evidence for changes in the coupling in the SCN that divides the clock oscillations into two clusters as a function of day length. We show that asymmetric distribution of intracellular chloride across the SCN causes this coupling change. Blocking GABA or chloride import erases the oscillator organization formed by day-length entrainment. These demonstrate that coupling through GABA is a key ingredient of day-length encoding in the SCN. The mammalian suprachiasmatic nucleus (SCN) forms not only the master circadian clock but also a seasonal clock. This neural network of ∼10,000 circadian oscillators encodes season-dependent day-length changes through a largely unknown mechanism. We show that region-intrinsic changes in the SCN fine-tune the degree of network synchrony and reorganize the phase relationship among circadian oscillators to represent day length. We measure oscillations of the clock gene Bmal1, at single-cell and regional levels in cultured SCN explanted from animals raised under short or long days. Coupling estimation using the Kuramoto framework reveals that the network has couplings that can be both phase-attractive (synchronizing) and -repulsive (desynchronizing). The phase gap between the dorsal and ventral regions increases and the overall period of the SCN shortens with longer day length. We find that one of the underlying physiological mechanisms is the modulation of the intracellular chloride concentration, which can adjust the strength and polarity of the ionotropic GABAA-mediated synaptic input. We show that increasing day-length changes the pattern of chloride transporter expression, yielding more excitatory GABA synaptic input, and that blocking GABAA signaling or the chloride transporter disrupts the unique phase and period organization induced by the day length. We test the consequences of this tunable GABA coupling in the context of excitation–inhibition balance through detailed realistic modeling. These results indicate that the network encoding of seasonal time is controlled by modulation of intracellular chloride, which determines the phase relationship among and period difference between the dorsal and ventral SCN.

Single Neuron Firing Properties Impact Correlation-Based Population Coding

Correlated spiking has been widely observed, but its impact on neural coding remains controversial. Correlation arising from comodulation of rates across neurons has been shown to vary with the firing rates of individual neurons. This translates into rate and correlation being equivalently tuned to the stimulus; under those conditions, correlated spiking does not provide information beyond that already available from individual neuron firing rates. Such correlations are irrelevant and can reduce coding efficiency by introducing redundancy. Using simulations and experiments in rat hippocampal neurons, we show here that pairs of neurons receiving correlated input also exhibit correlations arising from precise spike-time synchronization. Contrary to rate comodulation, spike-time synchronization is unaffected by firing rate, thus enabling synchrony- and rate-based coding to operate independently. The type of output correlation depends on whether intrinsic neuron properties promote integration or coincidence detection: “ideal” integrators (with spike generation sensitive to stimulus mean) exhibit rate comodulation, whereas ideal coincidence detectors (with spike generation sensitive to stimulus variance) exhibit precise spike-time synchronization. Pyramidal neurons are sensitive to both stimulus mean and variance, and thus exhibit both types of output correlation proportioned according to which operating mode is dominant. Our results explain how different types of correlations arise based on how individual neurons generate spikes, and why spike-time synchronization and rate comodulation can encode different stimulus properties. Our results also highlight the importance of neuronal properties for population-level coding insofar as neural networks can employ different coding schemes depending on the dominant operating mode of their constituent neurons.

Period Coding of Bmal1 Oscillators in the Suprachiasmatic Nucleus

Circadian oscillators in the suprachiasmatic nucleus (SCN) collectively orchestrate 24 h rhythms in the body while also coding for seasonal rhythms. Although synchronization is required among SCN oscillators to provide robustness for regular timekeeping (Herzog et al., 2004), heterogeneity of period and phase distributions is needed to accommodate seasonal variations in light duration (Pittendrigh and Daan, 1976b). In the mouse SCN, the heterogeneous phase distribution has been recently found in the cycling of clock genes Period 1 and Period 2 (Per1, Per2) and has been shown to reorganize by relative day lengths (Inagaki et al., 2007). However, it is not yet clearly understood what underlies the spatial patterning of Per1 and Per2 expression (Yamaguchi et al., 2003; Foley et al., 2011) and its plasticity. We found that the period of the oscillation in Bmal1 expression, a positive-feedback component of the circadian clock, preserves the behavioral circadian period under culture and drives clustered oscillations in the mouse SCN. Pharmacological and physical isolations of SCN subregions indicate that the period of Bmal1 oscillation is subregion specific and is preserved during culture. Together with computer simulations, we show that either the intercellular coupling does not strongly influence the Bmal1 oscillation or the nature of the coupling is more complex than previously assumed. Furthermore, we have found that the region-specific periods are modulated by the light conditions that an animal is exposed to. Based on these, we suggest that the period forms the basis of seasonal coding in the SCN.

Controlling Ca2+-Activated K+ Channels with Models of Ca2+ Buffering in Purkinje Cells

Intracellular Ca2+ concentrations play a crucial role in the physiological interaction between Ca2+ channels and Ca2+-activated K+ channels. The commonly used model, a Ca2+ pool with a short relaxation time, fails to simulate interactions occurring at multiple time scales. On the other hand, detailed computational models including various Ca2+ buffers and pumps can result in large computational cost due to radial diffusion in large compartments, which may be undesirable when simulating morphologically detailed Purkinje cell models. We present a method using a compensating mechanism to replace radial diffusion and compared the dynamics of different Ca2+ buffering models during generation of a dendritic Ca2+ spike in a single compartment model of a PC dendritic segment with Ca2+ channels of P- and T-type and Ca2+-activated K+ channels of BK- and SK-type. The Ca2+ dynamics models used are (1) a single Ca2+ pool; (2) two Ca2+ pools, respectively, for the fast and slow transients; (3) detailed Ca2+ dynamics with buffers, pump, and diffusion; and (4) detailed Ca2+ dynamics with buffers, pump, and diffusion compensation. Our results show that detailed Ca2+ dynamics models have significantly better control over Ca2+-activated K+ channels and lead to physiologically more realistic simulations of Ca2+ spikes and bursting. Furthermore, the compensating mechanism largely eliminates the effect of removing diffusion from the model on Ca2+ dynamics over multiple time scales.

Intrinsic Gain Modulation and Adaptive Neural Coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.

Multiplexed coding by cerebellar Purkinje neurons.

Purkinje cells (PC), the sole output neurons of the cerebellar cortex, encode sensorimotor information, but how they do it remains a matter of debate. Here we show that PCs use a multiplexed spike code. Synchrony/spike time and firing rate encode different information in behaving monkeys during saccadic eye motion tasks. Using the local field potential (LFP) as a probe of local network activity, we found that infrequent pause spikes, which initiated or terminated intermittent pauses in simple spike trains, provide a temporally reliable signal for eye motion onset, with strong phase-coupling to the β/γ band LFP. Concurrently, regularly firing, non-pause spikes were weakly correlated with the LFP, but were crucial to linear encoding of eye movement kinematics by firing rate. Therefore, PC spike trains can simultaneously convey information necessary to achieve precision in both timing and continuous control of motion. DOI: http://dx.doi.org/10.7554/eLife.13810.001

Purkinje Neurons: What Is the Signal for Complex Spikes?

Cerebellar Purkinje neurons generate characteristic complex spikes; but are these bursts of activity generated by somatic or dendritic excitability? A recent study may have settled this debate by giving the soma the dominant role, but it does not fully resolve the question of what information is transmitted downstream of the Purkinje cells.

The choroid plexus is an important circadian clock component

Mammalian circadian clocks have a hierarchical organization, governed by the suprachiasmatic nucleus (SCN) in the hypothalamus. The brain itself contains multiple loci that maintain autonomous circadian rhythmicity, but the contribution of the non-SCN clocks to this hierarchy remains unclear. We examine circadian oscillations of clock gene expression in various brain loci and discovered that in mouse, robust, higher amplitude, relatively faster oscillations occur in the choroid plexus (CP) compared to the SCN. Our computational analysis and modeling show that the CP achieves these properties by synchronization of “twist” circadian oscillators via gap-junctional connections. Using an in vitro tissue coculture model and in vivo targeted deletion of the Bmal1 gene to silence the CP circadian clock, we demonstrate that the CP clock adjusts the SCN clock likely via circulation of cerebrospinal fluid, thus finely tuning behavioral circadian rhythms.The suprachiasmatic nucleus (SCN) has been thought of as the master circadian clock, but peripheral circadian clocks do exist. Here, the authors show that the choroid plexus displays oscillations more robust than the SCN and that can be described as a Poincaré oscillator with negative twist.

Non-linear leak currents affect mammalian neuron physiology

In their seminal works on squid giant axons, Hodgkin, and Huxley approximated the membrane leak current as Ohmic, i.e., linear, since in their preparation, sub-threshold current rectification due to the influence of ionic concentration is negligible. Most studies on mammalian neurons have made the same, largely untested, assumption. Here we show that the membrane time constant and input resistance of mammalian neurons (when other major voltage-sensitive and ligand-gated ionic currents are discounted) varies non-linearly with membrane voltage, following the prediction of a Goldman-Hodgkin-Katz-based passive membrane model. The model predicts that under such conditions, the time constant/input resistance-voltage relationship will linearize if the concentration differences across the cell membrane are reduced. These properties were observed in patch-clamp recordings of cerebellar Purkinje neurons (in the presence of pharmacological blockers of other background ionic currents) and were more prominent in the sub-threshold region of the membrane potential. Model simulations showed that the non-linear leak affects voltage-clamp recordings and reduces temporal summation of excitatory synaptic input. Together, our results demonstrate the importance of trans-membrane ionic concentration in defining the functional properties of the passive membrane in mammalian neurons as well as other excitable cells.