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1.  Diversity of sympathetic vasoconstrictor pathways and their plasticity after spinal cord injury 
Clinical Autonomic Research  2007;17(1):6-12.
Sympathetic vasoconstrictor pathways pass through paravertebral ganglia carrying ongoing and reflex activity arising within the central nervous system to their vascular targets. The pattern of reflex activity is selective for particular vascular beds and appropriate for the physiological outcome (vasoconstriction or vasodilation). The preganglionic signals are distributed to most postganglionic neurones in ganglia via synapses that are always suprathreshold for action potential initiation (like skeletal neuromuscular junctions).
Most postganglionic neurones receive only one of these “strong” inputs, other preganglionic connections being ineffective. Pre- and postganglionic neurones discharge normally at frequencies of 0.5–1 Hz and maximally in short bursts at <10 Hz. Animal experiments have revealed unexpected changes in these pathways following spinal cord injury. (1) After destruction of preganglionic neurones or axons, surviving terminals in ganglia sprout and rapidly re-establish strong connections, probably even to inappropriate postganglionic neurones. This could explain aberrant reflexes after spinal cord injury. (2) Cutaneous (tail) and splanchnic (mesenteric) arteries taken from below a spinal transection show dramatically enhanced responses in vitro to norepinephrine released from perivascular nerves. However the mechanisms that are modified differ between the two vessels, being mostly postjunctional in the tail artery and mostly prejunctional in the mesenteric artery. The changes are mimicked when postganglionic neurones are silenced by removal of their preganglionic input. Whether or not other arteries are also hyperresponsive to reflex activation, these observations suggest that the greatest contribution to raised peripheral resistance in autonomic dysreflexia follows the modifications of neurovascular transmission.
doi:10.1007/s10286-006-0394-8
PMCID: PMC1797061  PMID: 17264977
sympathetic nervous system; sympathetic ganglia; autonomic dysreflexia; vasoconstriction; norepineph- rine; autonomic nervous system
2.  Chemical Coding for Cardiovascular Sympathetic Preganglionic Neurons in Rats 
Cocaine and amphetamine-regulated transcript peptide (CART) is present in a subset of sympathetic preganglionic neurons in the rat. We examined the distribution of CART-immunoreactive terminals in rat stellate and superior cervical ganglia and adrenal gland and found that they surround neuropeptide Y-immunoreactive postganglionic neurons and noradrenergic chromaffin cells. The targets of CART-immunoreactive preganglionic neurons in the stellate and superior cervical ganglia were shown to be vasoconstrictor neurons supplying muscle and skin and cardiac-projecting postganglionic neurons: they did not target non-vasoconstrictor neurons innervating salivary glands, piloerector muscle, brown fat or adrenergic chromaffin cells. Transneuronal tracing using pseudorabies virus demonstrated that many, but not all, preganglionic neurons in the vasoconstrictor pathway to forelimb skeletal muscle were CART-immunoreactive. Similarly, analysis with the confocal microscope confirmed that 70% of boutons in contact with vasoconstrictor ganglion cells contained CART, while 30% did not. Finally, we show that CART-immunoreactive cells represented 69% of the preganglionic neuron population expressing c-fos after systemic hypoxia. We conclude that CART is present in most, although not all, cardiovascular preganglionic neurons, but not thoracic preganglionic neurons with non-cardiovascular targets. We suggest that CART-immunoreactivity may identify the postulated “accessory” preganglionic neurons, whose actions may amplify vasomotor ganglionic transmission.
doi:10.1523/JNEUROSCI.0796-10.2010
PMCID: PMC2947491  PMID: 20810898
Chemical coding; postganglionic neuron; vasoconstrictor; accessory pathway; c-fos; hypoxia; viral tracing
3.  Weak and Straddling Secondary Nicotinic Synapses Can Drive Firing in Rat Sympathetic Neurons and Thereby Contribute to Ganglionic Amplification 
Interactions between nicotinic excitatory postsynaptic potentials (EPSPs) critically determine whether paravertebral sympathetic ganglia behave as simple synaptic relays or as integrative centers that amplify preganglionic activity. Synaptic connectivity in this system is characterized by an n + 1 pattern of convergence, where each ganglion cell receives one very strong primary input and a variable number (n) of weak secondary inputs that are subthreshold in strength. To test whether pairs of secondary nicotinic EPSPs can summate to fire action potentials (APs) and thus mediate ganglionic gain in the rat superior cervical ganglion, we recorded intracellularly at 34°C and used graded presynaptic stimulation to isolate individual secondary synapses. Weak EPSPs in 40 of 53 neurons had amplitudes of 0.5–7 mV (mean 3.5 ± 0.3 mV). EPSPs evoked by paired pulse stimulation were either depressing (n = 10), facilitating (n = 9), or borderline (n = 10). In 15 of 29 cells, pairs of weak secondary EPSPs initiated spikes when elicited within a temporal window <20 ms, irrespective of EPSP amplitude or paired pulse response type. In six other neurons, we observed novel secondary EPSPs that were strong enough to straddle spike threshold without summation. At stimulus rates <1 Hz straddling EPSPs appeared suprathreshold in strength. However, their limited ability to drive firing could be blocked by the afterhyperpolarization following an AP. When viewed in a computational context, these findings support the concept that weak and straddling secondary nicotinic synapses enable mammalian sympathetic ganglia to behave as use-dependent amplifiers of preganglionic activity.
doi:10.3389/fneur.2010.00130
PMCID: PMC2995956  PMID: 21173895
superior cervical ganglion; synaptic gain; summation; facilitation; depression
4.  Predicting the Responses of Repetitively Firing Neurons to Current Noise 
PLoS Computational Biology  2014;10(5):e1003612.
We used phase resetting methods to predict firing patterns of rat subthalamic nucleus (STN) neurons when their rhythmic firing was densely perturbed by noise. We applied sequences of contiguous brief (0.5–2 ms) current pulses with amplitudes drawn from a Gaussian distribution (10–100 pA standard deviation) to autonomously firing STN neurons in slices. Current noise sequences increased the variability of spike times with little or no effect on the average firing rate. We measured the infinitesimal phase resetting curve (PRC) for each neuron using a noise-based method. A phase model consisting of only a firing rate and PRC was very accurate at predicting spike timing, accounting for more than 80% of spike time variance and reliably reproducing the spike-to-spike pattern of irregular firing. An approximation for the evolution of phase was used to predict the effect of firing rate and noise parameters on spike timing variability. It quantitatively predicted changes in variability of interspike intervals with variation in noise amplitude, pulse duration and firing rate over the normal range of STN spontaneous rates. When constant current was used to drive the cells to higher rates, the PRC was altered in size and shape and accurate predictions of the effects of noise relied on incorporating these changes into the prediction. Application of rate-neutral changes in conductance showed that changes in PRC shape arise from conductance changes known to accompany rate increases in STN neurons, rather than the rate increases themselves. Our results show that firing patterns of densely perturbed oscillators cannot readily be distinguished from those of neurons randomly excited to fire from the rest state. The spike timing of repetitively firing neurons may be quantitatively predicted from the input and their PRCs, even when they are so densely perturbed that they no longer fire rhythmically.
Author Summary
Most neurons receive thousands of synaptic inputs per second. Each of these may be individually weak but collectively they shape the temporal pattern of firing by the postsynaptic neuron. If the postsynaptic neuron fires repetitively, its synaptic inputs need not directly trigger action potentials, but may instead control the timing of action potentials that would occur anyway. The phase resetting curve encapsulates the influence of an input on the timing of the next action potential, depending on its time of arrival. We measured the phase resetting curves of neurons in the subthalamic nucleus and used them to accurately predict the timing of action potentials in a phase model subjected to complex input patterns. A simple approximation to the phase model accurately predicted the changes in firing pattern evoked by dense patterns of noise pulses varying in amplitude and pulse duration, and by changes in firing rate. We also showed that the phase resetting curve changes systematically with changes in total neuron conductance, and doing so predicts corresponding changes in firing pattern. Our results indicate that the phase model may accurately represent the temporal integration of complex patterns of input to repetitively firing neurons.
doi:10.1371/journal.pcbi.1003612
PMCID: PMC4014400  PMID: 24809636
5.  Effects of preganglionic denervation and postganglionic axotomy on acetylcholine receptors in the chick ciliary ganglion 
The Journal of Cell Biology  1987;105(4):1847-1854.
The regulation of nicotinic acetylcholine receptors (AChRs) in chick ciliary ganglia was examined by using a radiolabeled anti-AChR mAb to quantitate the amount of receptor in ganglion detergent extracts after preganglionic denervation or postganglionic axotomy. Surgical transection of the preganglionic input to the ciliary ganglion in newly hatched chicks caused a threefold reduction in the total number of AChRs within 10 d compared with that present in unoperated contralateral control ganglia. Surgical transection of both the choroid and ciliary nerves emerging from the ciliary ganglion in newly hatched chicks to establish postganglionic axotomy led to a nearly 10-fold reduction in AChRs within 5 d compared with unoperated contralateral ganglia. The declines were specific since they could not be accounted for by changes in ganglionic protein or by decreases in neuronal survival or size. Light microscopy revealed no gross morphological differences between neurons in operated and control ganglia. A second membrane component of cholinergic relevance on chick ciliary ganglion neurons is the alpha-bungarotoxin (alpha-Bgt)-binding component. The alpha-Bgt-binding component also declined in number after either postganglionic axotomy or preganglionic denervation, but appeared to do so with a more rapid time course than did ganglionic AChRs. The results imply that cell-cell interactions in vivo specifically regulate both the number of AChRs and the number of alpha-Bgt-binding components in the ganglion. Regulation of these neuronal cholinergic membrane components clearly differs from that previously described for muscle AChRs.
PMCID: PMC2114658  PMID: 3667699
6.  Cellularly-Driven Differences in Network Synchronization Propensity Are Differentially Modulated by Firing Frequency 
PLoS Computational Biology  2011;7(5):e1002062.
Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.
Author Summary
Synchronization of the firing of neurons in the brain is related to many cognitive functions, such as recognizing faces, discriminating odors, and coordinating movement. It is therefore important to understand what properties of neuronal networks promote synchrony of neural firing. One measure that is often used to determine the contribution of individual neurons to network synchrony is called the phase response curve (PRC). PRCs describe how the timing of neuronal firing changes depending on when input, such as a synaptic signal, is received by the neuron. A characteristic of PRCs that has previously not been well understood is that they change dramatically as the neuron's firing frequency is modulated. This effect carries potential significance, since cognitive functions are often associated with specific frequencies of network activity in the brain. We showed computationally that the frequency dependence of PRCs can be explained by the relative timing of ionic membrane currents with respect to the time between spike firings. Our simulations also showed that the frequency dependence of neuronal PRCs leads to frequency-dependent changes in network synchronization that can be different for different neuron types. These results further our understanding of how synchronization is generated in the brain to support various cognitive functions.
doi:10.1371/journal.pcbi.1002062
PMCID: PMC3098201  PMID: 21625571
7.  Inhibitory synchrony as a mechanism for attentional gain modulation☆ 
Journal of physiology, Paris  2005;98(4-6):296-314.
Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30–50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron’s firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f–I) curves. For a large number of inhibitory inputs (~50), the f–I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity—the model neuron responded to weaker inputs I. For a small number (~10), the f–I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response—the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.
doi:10.1016/j.jphysparis.2005.09.002
PMCID: PMC2872773  PMID: 16274973
Selective attention; Synchrony; Noise; Gamma oscillation; Gain modulation; Computer model
8.  Impact of Dendritic Size and Dendritic Topology on Burst Firing in Pyramidal Cells 
PLoS Computational Biology  2010;6(5):e1000781.
Neurons display a wide range of intrinsic firing patterns. A particularly relevant pattern for neuronal signaling and synaptic plasticity is burst firing, the generation of clusters of action potentials with short interspike intervals. Besides ion-channel composition, dendritic morphology appears to be an important factor modulating firing pattern. However, the underlying mechanisms are poorly understood, and the impact of morphology on burst firing remains insufficiently known. Dendritic morphology is not fixed but can undergo significant changes in many pathological conditions. Using computational models of neocortical pyramidal cells, we here show that not only the total length of the apical dendrite but also the topological structure of its branching pattern markedly influences inter- and intraburst spike intervals and even determines whether or not a cell exhibits burst firing. We found that there is only a range of dendritic sizes that supports burst firing, and that this range is modulated by dendritic topology. Either reducing or enlarging the dendritic tree, or merely modifying its topological structure without changing total dendritic length, can transform a cell's firing pattern from bursting to tonic firing. Interestingly, the results are largely independent of whether the cells are stimulated by current injection at the soma or by synapses distributed over the dendritic tree. By means of a novel measure called mean electrotonic path length, we show that the influence of dendritic morphology on burst firing is attributable to the effect both dendritic size and dendritic topology have, not on somatic input conductance, but on the average spatial extent of the dendritic tree and the spatiotemporal dynamics of the dendritic membrane potential. Our results suggest that alterations in size or topology of pyramidal cell morphology, such as observed in Alzheimer's disease, mental retardation, epilepsy, and chronic stress, could change neuronal burst firing and thus ultimately affect information processing and cognition.
Author Summary
Neurons possess highly branched extensions, called dendrites, which form characteristic tree-like structures. The morphology of these dendritic arborizations can undergo significant changes in many pathological conditions. It is still poorly known, however, how alterations in dendritic morphology affect neuronal activity. Using computational models of pyramidal cells, we study the influence of dendritic tree size and branching structure on burst firing. Burst firing is the generation of two or more action potentials in close succession, a form of neuronal activity that is critically involved in neuronal signaling and synaptic plasticity. We found that there is only a range of dendritic tree sizes that supports burst firing, and that this range is modulated by the branching structure of the tree. We show that shortening as well as lengthening the dendritic tree, or even just modifying the pattern in which the branches in the tree are connected, can shift the cell's firing pattern from bursting to tonic firing, as a consequence of changes in the spatiotemporal dynamics of the dendritic membrane potential. Our results suggest that alterations in pyramidal cell morphology could, via their effect on burst firing, ultimately affect cognition.
doi:10.1371/journal.pcbi.1000781
PMCID: PMC2869305  PMID: 20485556
9.  Characteristic Effects of Stochastic Oscillatory Forcing on Neural Firing: Analytical Theory and Comparison to Paddlefish Electroreceptor Data 
PLoS Computational Biology  2013;9(8):e1003170.
Stochastic signals with pronounced oscillatory components are frequently encountered in neural systems. Input currents to a neuron in the form of stochastic oscillations could be of exogenous origin, e.g. sensory input or synaptic input from a network rhythm. They shape spike firing statistics in a characteristic way, which we explore theoretically in this report. We consider a perfect integrate-and-fire neuron that is stimulated by a constant base current (to drive regular spontaneous firing), along with Gaussian narrow-band noise (a simple example of stochastic oscillations), and a broadband noise. We derive expressions for the nth-order interval distribution, its variance, and the serial correlation coefficients of the interspike intervals (ISIs) and confirm these analytical results by computer simulations. The theory is then applied to experimental data from electroreceptors of paddlefish, which have two distinct types of internal noisy oscillators, one forcing the other. The theory provides an analytical description of their afferent spiking statistics during spontaneous firing, and replicates a pronounced dependence of ISI serial correlation coefficients on the relative frequency of the driving oscillations, and furthermore allows extraction of certain parameters of the intrinsic oscillators embedded in these electroreceptors.
Author Summary
We explore how a neuron responds to a special type of input signal which is oscillatory but noisy (narrow-band noise). These fluctuations could be due to sensory input, due to oscillatory activity of a surrounding network, or due to a natural stimulus. We study theoretically the effects of noisy oscillations on an idealized model neuron, which would otherwise produce as output a series of action potentials at regular intervals. Because our model is comparably simple, we can describe the effects on ISI statistics analytically with formulas that we test against computer simulations of the model. Moreover, we can compare our theoretical predictions to experimental data from electroreceptors of paddlefish - a biological example for spiking neurons that are naturally stimulated by stochastic oscillatory input. In particular, our theory provides a simple explanation of the seemingly complicated patterns of correlations between interspike intervals, that are observed for the electro-afferents in paddlefish; the theory shows also good agreement with respect to other independent spike train statistics. Our findings further the understanding of how nervous activity is shaped by oscillatory noisy signals, which can emerge in the neural networks of the brain, in the sensory periphery, and in the environment.
doi:10.1371/journal.pcbi.1003170
PMCID: PMC3744407  PMID: 23966844
10.  Excitatory Muscarinic Modulation Strengthens Virtual Nicotinic Synapses on Sympathetic Neurons and Thereby Enhances Synaptic Gain 
Journal of neurophysiology  2006;96(6):3104-3113.
Acetylcholine excites many neuronal types by binding to postsynaptic m1-muscarinic receptors that signal to ion channels through the Gq/11 protein. To investigate the functional significance of this metabotropic pathway in sympathetic ganglia, we studied how muscarinic excitation modulated the integration of virtual nicotinic excitatory postsynaptic potentials (EPSPs) created in dissociated bullfrog B-type sympathetic neurons with the dynamic-clamp technique. Muscarine (1 μM) strengthened the impact of virtual synapses by reducing the artificial nicotinic conductance required to reach the postsynaptic firing threshold from 20.9 ± 5.4 to 13.1 ± 3.1 nS. Consequently, postganglionic action potential output increased by 4–215% when driven by different patterns of virtual presynaptic activity that were chosen to reflect the range of physiological firing rates and convergence levels seen in amphibian and mammalian sympathetic ganglia. In addition to inhibiting the M-type K+ conductance, muscarine activated a leak conductance in three of 37 cells. When this leak conductance was reproduced with the dynamic clamp, it also acted to strengthen virtual nicotinic synapses and enhance postganglionic spike output. Combining pharmacological M-conductance suppression with virtual leak activation, at resting potentials between −50 and −55 mV, produced synergistic strengthening of nicotinic synapses and an increase in the integrated postganglionic spike output. Together, these results reveal how muscarinic activation of a branched metabotropic pathway can enhance integration of fast EPSPs by modulating their effective strength. The results also support the hypothesis that muscarinic synapses permit faster and more accurate feedback control of autonomic behaviors by generating gain through synaptic amplification in sympathetic ganglia.
doi:10.1152/jn.00589.2006
PMCID: PMC1839880  PMID: 17005615
11.  Characterization of the Vagal Motor Neurons Projecting to the Guinea Pig Airways and Esophagus 
Distinct parasympathetic postganglionic neurons mediate contractions and relaxations of the guinea pig airways. We set out to characterize the vagal inputs that regulate contractile and relaxant airway parasympathetic postganglionic neurons. Single and dual retrograde neuronal tracing from the airways and esophagus revealed that distinct, but intermingled, subsets of neurons in the compact formation of the nucleus ambiguus (nAmb) innervate these two tissues. Tracheal and esophageal neurons identified in the nAmb were cholinergic. Esophageal projecting neurons also preferentially (greater than 70%) expressed the neuropeptide CGRP, but could not otherwise be distinguished immunohistochemically from tracheal projecting preganglionic neurons. Few tracheal or esophageal neurons were located in the dorsal motor nucleus of the vagus. Electrical stimulation of the vagi in vitro elicited stimulus dependent tracheal and esophageal contractions and tracheal relaxations. The voltage required to evoke tracheal smooth muscle relaxation was significantly higher than that required for evoking either tracheal contractions or esophageal longitudinal striated muscle contractions. Together our data support the hypothesis that distinct vagal preganglionic pathways regulate airway contractile and relaxant postganglionic neurons. The relaxant preganglionic neurons can also be differentiated from the vagal motor neurons that innervate the esophageal striated muscle.
doi:10.3389/fneur.2010.00153
PMCID: PMC3007679  PMID: 21188271
airway innervation; parasympathetic nervous system; non-adrenergic non-cholinergic; esophageal motor neurons; nucleus ambiguus
12.  Stimulus Discrimination in Cerebellar Purkinje Neurons 
PLoS ONE  2014;9(2):e87828.
Cerebellar Purkinje neurons fire spontaneously in the absence of synaptic input. Overlaid on this intrinsic activity, excitatory input from parallel fibres can add simple spikes to the output train, whereas inhibitory input from interneurons can introduce pauses. These and other influences lead to an irregular spike train output in Purkinje neurons in vitro and in vivo, supplying a variable inhibitory drive to deep cerebellar nuclear neurons. From a computational perspective, this variability raises some questions, as individual spikes induced by excitatory inputs are indistinguishable from intrinsic firing activity. Although bursts of high-frequency excitatory input could be discriminated unambiguously from background activity, granule neurons are known to fire in vivo over a wide range of frequencies. This would mean that much of the sensory information relayed through the cerebellar cortex would be lost within the random variation in background activity. We speculated that alternative mechanisms for signal discrimination may exist, and sought to identify characteristic motifs within the sequence of spikes that followed stimulation events. We found that under certain conditions, parallel fibre stimulation could reliably add a “couplet” of spikes with an unusually short interspike interval to the output train. Therefore, despite representing a small fraction of the total number of spikes, these signals can be reliably discriminated from background firing on a moment-to-moment basis, and could result in a differential downstream response.
doi:10.1371/journal.pone.0087828
PMCID: PMC3914862  PMID: 24505320
13.  Analysis and Modeling of Ensemble Recordings from Respiratory Pre-Motor Neurons Indicate Changes in Functional Network Architecture after Acute Hypoxia 
We have combined neurophysiologic recording, statistical analysis, and computational modeling to investigate the dynamics of the respiratory network in the brainstem. Using a multielectrode array, we recorded ensembles of respiratory neurons in perfused in situ rat preparations that produce spontaneous breathing patterns, focusing on inspiratory pre-motor neurons. We compared firing rates and neuronal synchronization among these neurons before and after a brief hypoxic stimulus. We observed a significant decrease in the number of spikes after stimulation, in part due to a transient slowing of the respiratory pattern. However, the median interspike interval did not change, suggesting that the firing threshold of the neurons was not affected but rather the synaptic input was. A bootstrap analysis of synchrony between spike trains revealed that both before and after brief hypoxia, up to 45% (but typically less than 5%) of coincident spikes across neuronal pairs was not explained by chance. Most likely, this synchrony resulted from common synaptic input to the pre-motor population, an example of stochastic synchronization. After brief hypoxia most pairs were less synchronized, although some were more, suggesting that the respiratory network was transiently “rewired” after the stimulus. To investigate this hypothesis, we created a simple computational model with feed-forward divergent connections along the inspiratory pathway. Assuming that (1) the number of divergent projections was not the same for all presynaptic cells, but rather spanned a wide range and (2) that the stimulus increased inhibition at the top of the network; this model reproduced the reduction in firing rate and bootstrap-corrected synchrony subsequent to hypoxic stimulation observed in our experimental data.
doi:10.3389/fncom.2010.00131
PMCID: PMC2947924  PMID: 20890445
neural control of respiration; working heart brainstem preparation; hypoxia; spike synchronization; bootstrap analysis; neural network simulation
14.  Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability 
PLoS Computational Biology  2009;5(2):e1000290.
The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.
Author Summary
Neurons use electrical impulses called action potentials to transmit signals from their cell body to their axon terminals, where the impulses trigger release of neurotransmitter. Initiation of an action potential is determined by the balance of currents through ion channels in a neuron's membrane. Although it is well established that membrane ion channels randomly fluctuate between open and closed states, most models of action potentials account for the average current through these channels but not for the current fluctuations caused by this stochastic opening and closing. Here, we examine the consequences of stochastic ion channel gating for stellate neurons found in the entorhinal cortex. The intrinsic properties of these neurons cause characteristic clustered patterns of spiking. We find that in a model of a single stellate neuron that is constrained by previous experimental data clustered action potential patterns are produced only when the model accounts for the random opening and closing of individual ion channels. This stochastic model provides an example of a general mechanism for patterning of neuronal activity and may help to explain the patterns of spikes fired by entorhinal neurons that encode spatial location in behaving animals.
doi:10.1371/journal.pcbi.1000290
PMCID: PMC2631146  PMID: 19214199
15.  Increased intrinsic excitability of muscle vasoconstrictor preganglionic neurons may contribute to the elevated sympathetic activity in hypertensive rats 
Journal of Neurophysiology  2014;112(11):2756-2778.
Hypertension is associated with pathologically increased sympathetic drive to the vasculature. This has been attributed to increased excitatory drive to sympathetic preganglionic neurons (SPN) from brainstem cardiovascular control centers. However, there is also evidence supporting increased intrinsic excitability of SPN. To test this hypothesis, we made whole cell recordings of muscle vasoconstrictor-like (MVClike) SPN in the working-heart brainstem preparation of spontaneously hypertensive (SH) and normotensive Wistar-Kyoto (WKY) rats. The MVClike SPN have a higher spontaneous firing frequency in the SH rat (3.85 ± 0.4 vs. 2.44 ± 0.4 Hz in WKY; P = 0.011) with greater respiratory modulation of their activity. The action potentials of SH SPN had smaller, shorter afterhyperpolarizations (AHPs) and showed diminished transient rectification indicating suppression of an A-type potassium conductance (IA). We developed mathematical models of the SPN to establish if changes in their intrinsic properties in SH rats could account for their altered firing. Reduction of the maximal conductance density of IA by 15–30% changed the excitability and output of the model from the WKY to a SH profile, with increased firing frequency, amplified respiratory modulation, and smaller AHPs. This change in output is predominantly a consequence of altered synaptic integration. Consistent with these in silico predictions, we found that intrathecal 4-aminopyridine (4-AP) increased sympathetic nerve activity, elevated perfusion pressure, and augmented Traube-Hering waves. Our findings indicate that IA acts as a powerful filter on incoming synaptic drive to SPN and that its diminution in the SH rat is potentially sufficient to account for the increased sympathetic output underlying hypertension.
doi:10.1152/jn.00350.2014
PMCID: PMC4254885  PMID: 25122704
sympathetic preganglionic; vasomotor tone; hypertension; transient rectification
16.  Mapping the cellular electrophysiology of rat sympathetic preganglionic neurones to their roles in cardiorespiratory reflex integration: a whole cell recording study in situ 
The Journal of physiology  2014;592(0 10):2215-2236.
Sympathetic preganglionic neurones (SPNs) convey sympathetic activity flowing from the CNS to the periphery to reach the target organs. Although previous in vivo and in vitro cell recording studies have explored their electrophysiological characteristics, it has not been possible to relate these characteristics to their roles in cardiorespiratory reflex integration. We used the working heart–brainstem preparation to make whole cell patch clamp recordings from T3–4 SPNs (n = 98). These SPNs were classified by their distinct responses to activation of the peripheral chemoreflex, diving response and arterial baroreflex, allowing the discrimination of muscle vasoconstrictor-like (MVClike, 39%) from cutaneous vasoconstrictor-like (CVClike, 28%) SPNs. The MVClike SPNs have higher baseline firing frequencies (2.52 ± 0.33 Hz vs. CVClike 1.34 ± 0.17 Hz, P = 0.007). The CVClike have longer after-hyperpolarisations (314 ± 36 ms vs. MVClike 191 ± 13 ms, P < 0.001) and lower input resistance (346 ± 49 MΩ vs. MVClike 496 ± 41 MΩ, P < 0.05). MVClike firing was respiratory-modulated with peak discharge in the late inspiratory/early expiratory phase and this activity was generated by both a tonic and respiratory-modulated barrage of synaptic events that were blocked by intrathecal kynurenate. In contrast, the activity of CVClike SPNs was underpinned by rhythmical membrane potential oscillations suggestive of gap junctional coupling. Thus, we have related the intrinsic electrophysiological properties of two classes of SPNs in situ to their roles in cardiorespiratory reflex integration and have shown that they deploy different cellular mechanisms that are likely to influence how they integrate and shape the distinctive sympathetic outputs.
doi:10.1113/jphysiol.2014.270769
PMCID: PMC4227904  PMID: 24665100
17.  Spike generation estimated from stationary spike trains in a variety of neurons in vivo 
To any model of brain function, the variability of neuronal spike firing is a problem that needs to be taken into account. Whereas the synaptic integration can be described in terms of the original Hodgkin-Huxley (H-H) formulations of conductance-based electrical signaling, the transformation of the resulting membrane potential into patterns of spike output is subjected to stochasticity that may not be captured with standard single neuron H-H models. The dynamics of the spike output is dependent on the normal background synaptic noise present in vivo, but the neuronal spike firing variability in vivo is not well studied. In the present study, we made long-term whole cell patch clamp recordings of stationary spike firing states across a range of membrane potentials from a variety of subcortical neurons in the non-anesthetized, decerebrated state in vivo. Based on the data, we formulated a simple, phenomenological model of the properties of the spike generation in each neuron that accurately captured the stationary spike firing statistics across all membrane potentials. The model consists of a parametric relationship between the mean and standard deviation of the inter-spike intervals, where the parameter is linearly related to the injected current over the membrane. This enabled it to generate accurate approximations of spike firing also under inhomogeneous conditions with input that varies over time. The parameters describing the spike firing statistics for different neuron types overlapped extensively, suggesting that the spike generation had similar properties across neurons.
doi:10.3389/fncel.2014.00199
PMCID: PMC4111083  PMID: 25120429
spike firing statistics; stochasticity; spinal interneurons; purkinje cells; golgi cells; molecular layer interneurons; synaptic integration; whole cell recordings in vivo
18.  Dynamic Gain Changes During Attentional Modulation 
Neural computation  2006;18(8):1847-1867.
Attention causes a multiplicative effect on firing rates of cortical neurons without affecting their selectivity (Motter, 1993; McAdams & Maunsell, 1999a) or the relationship between the spike count mean and variance (McAdams & Maunsell, 1999b). We analyzed attentional modulation of the firing rates of 144 neurons in the secondary somatosensory cortex (SII) of two monkeys trained to switch their attention between a tactile pattern recognition task and a visual task. We found that neurons in SII cortex also undergo a predominantly multiplicative modulation in firing rates without affecting the ratio of variance to mean firing rate (i.e., the Fano factor). Furthermore, both additive and multiplicative components of attentional modulation varied dynamically during the stimulus presentation.
We then used a standard conductance-based integrate-and-fire model neuron to ascertain which mechanisms might account for a multiplicative increase in firing rate without affecting the Fano factor. Six mechanisms were identified as biophysically plausible ways that attention could modify the firing rate: spike threshold, firing rate adaptation, excitatory input synchrony, synchrony between all inputs, membrane leak resistance, and reset potential. Of these, only a change in spike threshold or in firing rate adaptation affected model firing rates in a manner compatible with the observed neural data. The results indicate that only a limited number of biophysical mechanisms can account for observed attentional modulation.
doi:10.1162/neco.2006.18.8.1847
PMCID: PMC1839043  PMID: 16771655
19.  Decorrelation of Neural-Network Activity by Inhibitory Feedback 
PLoS Computational Biology  2012;8(8):e1002596.
Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. Here, we explain this observation by means of a linear network model and simulations of networks of leaky integrate-and-fire neurons. We show that inhibitory feedback efficiently suppresses pairwise correlations and, hence, population-rate fluctuations, thereby assigning inhibitory neurons the new role of active decorrelation. We quantify this decorrelation by comparing the responses of the intact recurrent network (feedback system) and systems where the statistics of the feedback channel is perturbed (feedforward system). Manipulations of the feedback statistics can lead to a significant increase in the power and coherence of the population response. In particular, neglecting correlations within the ensemble of feedback channels or between the external stimulus and the feedback amplifies population-rate fluctuations by orders of magnitude. The fluctuation suppression in homogeneous inhibitory networks is explained by a negative feedback loop in the one-dimensional dynamics of the compound activity. Similarly, a change of coordinates exposes an effective negative feedback loop in the compound dynamics of stable excitatory-inhibitory networks. The suppression of input correlations in finite networks is explained by the population averaged correlations in the linear network model: In purely inhibitory networks, shared-input correlations are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II).
Author Summary
The spatio-temporal activity pattern generated by a recurrent neuronal network can provide a rich dynamical basis which allows readout neurons to generate a variety of responses by tuning the synaptic weights of their inputs. The repertoire of possible responses and the response reliability become maximal if the spike trains of individual neurons are uncorrelated. Spike-train correlations in cortical networks can indeed be very small, even for neighboring neurons. This seems to be at odds with the finding that neighboring neurons receive a considerable fraction of inputs from identical presynaptic sources constituting an inevitable source of correlation. In this article, we show that inhibitory feedback, abundant in biological neuronal networks, actively suppresses correlations. The mechanism is generic: It does not depend on the details of the network nodes and decorrelates networks composed of excitatory and inhibitory neurons as well as purely inhibitory networks. For the case of the leaky integrate-and-fire model, we derive the correlation structure analytically. The new toolbox of formal linearization and a basis transformation exposing the feedback component is applicable to a range of biological systems. We confirm our analytical results by direct simulations.
doi:10.1371/journal.pcbi.1002596
PMCID: PMC3487539  PMID: 23133368
20.  Constraints on the Source of Short-Term Motion Adaptation in Macaque Area MT. I. The Role of Input and Intrinsic Mechanisms 
Journal of neurophysiology  2002;88(1):354-369.
Neurons in area MT, a motion-sensitive area of extrastriate cortex, respond to a step of target velocity with a transient-sustained firing pattern. The transition from a high initial firing rate to a lower sustained rate occurs over a time course of 20–80 ms and is considered a form of short-term adaptation. The present paper asks whether adaptation is due to input-specific mechanisms such as short-term synaptic depression or if it results from intrinsic cellular mechanisms such as spike-rate adaptation. We assessed the contribution of input-specific mechanisms by using a condition/test paradigm to measure the spatial scale of adaptation. Conditioning and test stimuli were placed within MT receptive fields but were spatially segregated so that the two stimuli would activate different populations of inputs from the primary visual cortex (V1). Conditioning motion at one visual location caused a reduction of the transient firing to subsequent test motion at a second location. The adaptation field, estimated as the region of visual space where conditioning motion caused adaptation, was always larger than the MT receptive field. Use of the same stimulus configuration while recording from direction-selective neurons in V1 failed to demonstrate either adaptation or the transient-sustained response pattern that is the signature of short-term adaptation in MT. We conclude that the shift from transient to sustained firing in MT cells does not result from an input-specific mechanism applied to inputs from V1 because it operates over a wider range of the visual field than is covered by receptive fields of V1 neurons. We used a direct analysis of MT neuron spike trains for many repetitions of the same motion stimulus to assess the contribution to adaptation of intrinsic cellular mechanisms related to spiking. On a trial-by-trial basis, there was no correlation between number of spikes in the transient interval and the interval immediately after the transient period. This is opposite the prediction that there should be a correlation if spikes cause adaptation directly. Further, the transient was suppressed or extinguished, not delayed, in trials in which the neuron emitted zero spikes during the interval that showed a transient in average firing rate. We conclude that the transition from transient to sustained firing in neurons in area MT is caused by mechanisms that are neither input-specific nor controlled by the spiking of the adapting neuron. We propose that the short-term adaptation observed in area MT emerges from the intracortical circuit within MT.
doi:10.1152/.00852.2002
PMCID: PMC2581621  PMID: 12091560
21.  Regular Patterns in Cerebellar Purkinje Cell Simple Spike Trains 
PLoS ONE  2007;2(5):e485.
Background
Cerebellar Purkinje cells (PC) in vivo are commonly reported to generate irregular spike trains, documented by high coefficients of variation of interspike-intervals (ISI). In strong contrast, they fire very regularly in the in vitro slice preparation. We studied the nature of this difference in firing properties by focusing on short-term variability and its dependence on behavioral state.
Methodology/Principal Findings
Using an analysis based on CV2 values, we could isolate precise regular spiking patterns, lasting up to hundreds of milliseconds, in PC simple spike trains recorded in both anesthetized and awake rodents. Regular spike patterns, defined by low variability of successive ISIs, comprised over half of the spikes, showed a wide range of mean ISIs, and were affected by behavioral state and tactile stimulation. Interestingly, regular patterns often coincided in nearby Purkinje cells without precise synchronization of individual spikes. Regular patterns exclusively appeared during the up state of the PC membrane potential, while single ISIs occurred both during up and down states. Possible functional consequences of regular spike patterns were investigated by modeling the synaptic conductance in neurons of the deep cerebellar nuclei (DCN). Simulations showed that these regular patterns caused epochs of relatively constant synaptic conductance in DCN neurons.
Conclusions/Significance
Our findings indicate that the apparent irregularity in cerebellar PC simple spike trains in vivo is most likely caused by mixing of different regular spike patterns, separated by single long intervals, over time. We propose that PCs may signal information, at least in part, in regular spike patterns to downstream DCN neurons.
doi:10.1371/journal.pone.0000485
PMCID: PMC1868782  PMID: 17534435
22.  MODIFICATION BY TEMPERATURE OF CONDUCTION AND GANGLIONIC TRANSMISSION IN THE GASTROPOD NERVOUS SYSTEM 
The Journal of General Physiology  1953;36(4):463-471.
The pedal ganglia of the terrestrial gastropod Ariolimax contain junctions between nerve fibers which are shown to be preferential points of fatigue and which exhibit facilitation (summation) of preganglionic impulses to produce a postganglionic spike. These characteristics in conjunction with others previously reported (reversible susceptibility to nicotine, convergence of preganglionic impulses, and inhibition of transmission through setting up a refractory state in the postganglionic fiber) are considered sufficient to indicate synaptic transmission in the pedal ganglia. The mean conduction velocity of the fastest fibers in the pedal nerves is 0.52 meter per second for preganglionic and 0.50 meter per second for postganglionic fibers at 7.56°C. The conduction rates at 21.76°C. are respectively 0.80 meter per second and 0.83 meter per second. The mean ganglionic delay is 0.033 second at 7.56°C. and 0.019 second at 21.76°C. The mean Q10's for conduction velocity are thus 1.37 for preganglionic and 1.42 for postganglionic fibers. The mean Q10 for ganglionic delay is 1.49. If the assumption is made that the Q10 for ganglionic delay is that of a limiting reaction, this figure then represents a value below which the Q10 for synaptic delay is statistically improbable.
PMCID: PMC2147377  PMID: 13035063
23.  Weak Noise in Neurons May Powerfully Inhibit the Generation of Repetitive Spiking but Not Its Propagation 
PLoS Computational Biology  2010;6(5):e1000794.
Many neurons have epochs in which they fire action potentials in an approximately periodic fashion. To see what effects noise of relatively small amplitude has on such repetitive activity we recently examined the response of the Hodgkin-Huxley (HH) space-clamped system to such noise as the mean and variance of the applied current vary, near the bifurcation to periodic firing. This article is concerned with a more realistic neuron model which includes spatial extent. Employing the Hodgkin-Huxley partial differential equation system, the deterministic component of the input current is restricted to a small segment whereas the stochastic component extends over a region which may or may not overlap the deterministic component. For mean values below, near and above the critical values for repetitive spiking, the effects of weak noise of increasing strength is ascertained by simulation. As in the point model, small amplitude noise near the critical value dampens the spiking activity and leads to a minimum as noise level increases. This was the case for both additive noise and conductance-based noise. Uniform noise along the whole neuron is only marginally more effective in silencing the cell than noise which occurs near the region of excitation. In fact it is found that if signal and noise overlap in spatial extent, then weak noise may inhibit spiking. If, however, signal and noise are applied on disjoint intervals, then the noise has no effect on the spiking activity, no matter how large its region of application, though the trajectories are naturally altered slightly by noise. Such effects could not be discerned in a point model and are important for real neuron behavior. Interference with the spike train does nevertheless occur when the noise amplitude is larger, even when noise and signal do not overlap, being due to the instigation of secondary noise-induced wave phenomena rather than switching the system from one attractor (firing regularly) to another (a stable point).
Author Summary
Many neurons, especially those found in subcortical nuclei, often exhibit repetitive approximately periodic firing of action potentials. We have previously demonstrated how weak noise may inhibit repetitive activity in the Hodgkin-Huxley point model and in pairs of coupled type 1 model neurons. Here we investigated the effects of weak noise in the full Hodgkin-Huxley model which includes a spatial dimension. Our first simulations with noise throughout the whole length of the neuron revealed inhibition of repetitive activity with a minimum as the noise level increased, as in the point model. However, when we reduced the region of application of noise, very surprising results were obtained. Noise right alongside the region of excitation had no effect on the spiking activity. The amount of overlap in space of signal and noise was found to be the key variable in determining whether weak noise would inhibit the firing. If the signal and noise were on disjoint intervals, there was no diminution of activity, no matter how large the spatial extent of the noise. Thus, weak noise that occurred within the signal region could powerfully inhibit spike generation, but such noise immediately outside that region had little effect on the propagation of spikes.
doi:10.1371/journal.pcbi.1000794
PMCID: PMC2877724  PMID: 20523741
24.  Auditory nerve inputs to cochlear nucleus neurons studied with cross-correlation 
Neuroscience  2008;154(1):127-138.
The strength of synapses between auditory nerve (AN) fibers and ventral cochlear nucleus (VCN) neurons is an important factor in determining the nature of neural integration in VCN neurons of different response types. Synaptic strength was analyzed using cross-correlation of spike trains recorded simultaneously from an AN fiber and a VCN neuron in anesthetized cats. VCN neurons were classified as chopper, primarylike, and onset using previously defined criteria, although onset neurons usually were not analyzed because of their low discharge rates. The correlograms showed an excitatory peak (EP), consistent with monosynaptic excitation, in AN-VCN pairs with similar best frequencies (49% 24/49 of pairs with best frequencies within ±5%). Chopper and primarylike neurons showed similar EPs, except that the primarylike neurons had shorter latencies and shorter-duration EPs. Large EPs consistent with endbulb terminals on spherical bushy cells were not observed, probably because of the low probability of recording from one. The small EPs observed in primarylike neurons, presumably spherical bushy cells, could be derived from small terminals that accompany endbulbs on these cells. EPs on chopper or primarylike-with-notch neurons were consistent with the smaller synaptic terminals on multipolar and globular bushy cells. Unexpectedly, EPs were observed only at sound levels within about 20 dB of threshold, showing that VCN responses to steady tones shift from a 1:1 relationship between AN and VCN spikes at low sound levels to a more autonomous mode of firing at high levels. In the high level mode, the pattern of output spikes seems to be determined by the properties of the postsynaptic spike generator rather than the input spike patterns. The EP amplitudes did not change significantly when the presynaptic spike was preceded by either a short or long interspike interval, suggesting that synaptic depression and facilitation have little effect under the conditions studied here.
doi:10.1016/j.neuroscience.2008.01.036
PMCID: PMC2478560  PMID: 18343587
cross-correlation; ventral cochlear nucleus; synaptic strength
25.  Intrinsic Gain Modulation and Adaptive Neural Coding 
PLoS Computational Biology  2008;4(7):e1000119.
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.
Author Summary
Many neurons are known to achieve a wide dynamic range by adaptively changing their computational input/output function according to the input statistics. These adaptive changes can be very rapid, and it has been suggested that a component of this adaptation could be purely input-driven: even a fixed neural system can show apparent adaptive behavior since inputs with different statistics interact with the nonlinearity of the system in different ways. In this paper, we show how a single neuron's intrinsic computational function can dictate such input-driven changes in its response to varying input statistics, which begets a relationship between two different characterizations of neural function—in terms of mean firing rate and in terms of generating precise spike timing. We then apply our results to two biophysically defined model neurons, which have significantly different response patterns to inputs with various statistics. Our model of intrinsic adaptation explains their behaviors well. Contrary to the picture that neurons carry out a stereotyped computation on their inputs, our results show that even in the simplest cases they have simple yet effective mechanisms by which they can adapt to their input. Adaptation to stimulus statistics, therefore, is built into the most basic single neuron computations.
doi:10.1371/journal.pcbi.1000119
PMCID: PMC2440820  PMID: 18636100

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