The mechanism of after-bursts in cerebral cortex

Wilson-Cowan Equations for Neocortical Dynamics

In 1972-1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers of activated and quiescent excitatory and inhibitory neurons, and said nothing about fluctuations and correlations of such activity. However, in 1997 Ohira and Cowan, and then in 2007-2009 Buice and Cowan introduced Markov models of such activity that included fluctuation and correlation effects. Here we show how both models can be used to provide a quantitative account of the population dynamics of neocortical activity.We first describe how the Markov models account for many recent measurements of the resting or spontaneous activity of the neocortex. In particular we show that the power spectrum of large-scale neocortical activity has a Brownian motion baseline, and that the statistical structure of the random bursts of spiking activity found near the resting state indicates that such a state can be represented as a percolation process on a random graph, called directed percolation.Other data indicate that resting cortex exhibits pair correlations between neighboring populations of cells, the amplitudes of which decay slowly with distance, whereas stimulated cortex exhibits pair correlations which decay rapidly with distance. Here we show how the Markov model can account for the behavior of the pair correlations.Finally we show how the 1972-1973 Wilson-Cowan equations can account for recent data which indicates that there are at least two distinct modes of cortical responses to stimuli. In mode 1 a low intensity stimulus triggers a wave that propagates at a velocity of about 0.3 m/s, with an amplitude that decays exponentially. In mode 2 a high intensity stimulus triggers a larger response that remains local and does not propagate to neighboring regions.

Rebuilding a realistic corticostriatal "social network" from dissociated cells

Many of the methods available for the study of cortical influences on striatal neurons have serious problems. In vivo the connectivity is so complex that the study of input from an individual cortical neuron to a single striatal cell is nearly impossible. Mixed corticostriatal cultures develop many connections from striatal cells to cortical cells, in striking contrast to the fact that only connections from cortical cells to striatal cells are present in vivo. Furthermore, interneuron populations are over-represented in organotypic cultures. For these reasons, we have developed a method for growing cortical and striatal neurons in separated compartments that allows cortical neurons to innervate striatal cells in culture. The method works equally well for acutely dissociated or cryopreserved neurons and allows a number of manipulations that are not otherwise possible. Either cortical or striatal compartments can be transfected with channel rhodopsins. The activity of both areas can be recorded in multielectrode arrays or individual patch recordings from pairs of cells. Finally, corticostriatal connections can be severed acutely. This procedure enables determination of the importance of corticostriatal interaction in the resting pattern of activity. These cultures also facilitate development of sensitive analytical network methods to track connectivity.

Internodal mechanism of pathological afterdischarges in myelinated axons

INTRODUCTION

Recent optical recordings of transmembrane potentials in the axons of pyramidal neurons have shown that the internodal action potentials (APs) predicted in our previous studies do exist. These novel processes are not well understood. In this study we aim to clarify electrical phenomena in peripheral myelinated axons (MAs).

METHODS

We used a multi-cable Hodgkin-Huxley-type model to simulate MAs with potassium channels that were either normal or inhibited along a short region of the internodal membrane. A brief stimulus was applied to the first node.

RESULTS

We demonstrated peculiarities in the internodal APs induced by a saltatory AP: They existed across internodal membranes, were detectable in periaxonal space but not in intracellular space, propagated continuously, collided near the mid-internodes, and produced internodal sources of afterdischarges.

CONCLUSIONS

These results highlight the importance of the MA internodal regions as new therapeutic targets for avoiding afterdischarges provoked by reduced axonal fast potassium channel expression.

Avalanches in a stochastic model of spiking neurons

Neuronal avalanches are a form of spontaneous activity widely observed in cortical slices and other types of nervous tissue, both in vivo and in vitro. They are characterized by irregular, isolated population bursts when many neurons fire together, where the number of spikes per burst obeys a power law distribution. We simulate, using the Gillespie algorithm, a model of neuronal avalanches based on stochastic single neurons. The network consists of excitatory and inhibitory neurons, first with all-to-all connectivity and later with random sparse connectivity. Analyzing our model using the system size expansion, we show that the model obeys the standard Wilson-Cowan equations for large network sizes ( neurons). When excitation and inhibition are closely balanced, networks of thousands of neurons exhibit irregular synchronous activity, including the characteristic power law distribution of avalanche size. We show that these avalanches are due to the balanced network having weakly stable functionally feedforward dynamics, which amplifies some small fluctuations into the large population bursts. Balanced networks are thought to underlie a variety of observed network behaviours and have useful computational properties, such as responding quickly to changes in input. Thus, the appearance of avalanches in such functionally feedforward networks indicates that avalanches may be a simple consequence of a widely present network structure, when neuron dynamics are noisy. An important implication is that a network need not be “critical” for the production of avalanches, so experimentally observed power laws in burst size may be a signature of noisy functionally feedforward structure rather than of, for example, self-organized criticality.

Networks of neurons display a broad variety of behavior that nonetheless can often be described in very simple statistical terms. Here we explain the basis of one particularly striking statistical rule: that in many systems, the likelihood that groups of neurons burst, or fire together, is linked to the number of neurons involved, or size of the burst, by a power law. The wide-spread presence of these so-called avalanches has been taken to mean that neuronal networks in general operate near criticality, the boundary between two different global behaviors. We model these neuronal avalanches within the context of a network of noisy excitatory and inhibitory neurons interconnected by several different connection rules. We find that neuronal avalanches arise in our model only when excitatory and inhibitory connections are balanced in such a way that small fluctuations in the difference of population activities feed forward into large fluctuations in the sum of activities, creating avalanches. In contrast with the notion that the ubiquity of neuronal avalanches implies that neuronal networks operate near criticality, our work shows that avalanches are ubiquitous because they arise naturally from a network structure, the noisy balanced network, which underlies a wide variety of models.

Intrinsic cellular currents and the temporal precision of EPSP-action potential coupling in CA1 pyramidal cells

We examined relations between cellular currents activated near firing threshold and the initiation of action potentials by excitatory postsynaptic potentials (EPSPs) in CA1 pyramidal cells in vitro. Small voltage steps elicited sequences of inward-outward currents at hyperpolarized potentials, but evoked largely inward currents at near threshold potentials. Similarly small EPSP-like waveforms initiated largely inward currents while larger stimuli evoked sequences of inward followed by outward currents. Shorter rise times of EPSP-like waveforms accentuated a transient component of inward currents. Voltage clamp data were consistent with the voltage dependence of current clamp responses to injection of EPSP shaped waveforms. Small events were prolonged at subthreshold potentials and could elicit action potentials at long latencies while responses to larger EPSP waveforms showed less voltage dependence and tended to induce spikes at shorter, less variable latencies. The precision of action potentials initiated by white noise depended also on stimulus amplitude. High variance stimuli induced firing with high precision, while the timing of spikes induced by lower variance signals was more variable between trials. In voltage clamp records, high variance noise commands induced sequences of inward followed by outward currents, while lower variance versions of the same commands elicited purely inward currents. These data suggest that larger synaptic stimuli recruit outward as well as inward currents. The resulting inward-outward current sequences enhance the temporal precision of EPSP-spike coupling. Thus, CA1 pyramidal cells initiate action potentials with different temporal precision, depending on stimulus properties.

A stochastic model for neuronal bursting

A new stochastic model for bursting of neuronal firing is proposed. It is based on stochastic diffusion and related to the first passage time problem. However, the model is not of renewal type. Its form and parameters are physiologically interpretable. Parametric and non-parametric inferential issues are discussed.

Epileptiform activity in chronically isolated cerebral cortex in humans

The ability of neuronally isolated human cerebral cortex to sustain epileptiform rhythms over long time intervals is unknown. We report here two patients after functional hemispherectomy for infantile hemiplegia and infantile meningoencephalitis. Both patients had intractable seizures. EEG performed early and up to 3 years after surgery showed persistent epileptiform activity in the isolated frontal cortex in both cases. This indicates that human isolated cortex retains its epileptogenic potential for years, independently of subcortical influences. Previous related animal and human studies are briefly reviewed.

A pharmacological study of the effect of carbamazepine on neuromuscular transmission in the rat diaphragm

The effects of carbamazepine (0.042-0.42 mM) on neuromuscular transmission were studied on the isolated rat phrenic nerve diaphragm preparation using standard pharmacological and electrophysiological methods. Carbamazepine decreased (1) the antidromic activity of the phrenic nerve, (2) the amplitude of the endplate potential (EPP) and miniature endplate potential (MEPP), (3) the quantal content of the endplate potential, (4) the indirectly-elicited twitch tension, (5) the muscle contracture in chronically denervated muscle induced by acetylcholine (ACh) and (6) the amplitude of the compound phrenic nerve action potential, in a concentration-dependent manner. The antidromic activity of the phrenic nerve was the most affected, while the phrenic nerve compound action potential was least affected. However, the IC50 for carbamazepine (the concentration of carbamazepine that inhibited 50% of the response) was in the same order of concentration, i.e. 0.11-0.3 mM. Compared with the effect of carbamazepine on the indirectly-elicited twitch tension with its actions described above, it is concluded that carbamazepine interfered with the neuromuscular activity by inhibiting pre- and postsynaptic process and conduction in the phrenic nerve.

Synchronized afterdischarges in the hippocampus: contribution of local synaptic interactions

In the presence of picrotoxin, spontaneous synchronized bursts followed by afterdischarges were recorded from all pyramidal cell regions of the guinea pig hippocampal slice. Excitatory synaptic potentials, which reversed at approx -5 mV, were found to be associated with both the initial burst and each afterdischarge. Afterdischarges were reversibly blocked, leaving the initial synchronized burst intact, by the application of several excitatory amino acid antagonists or by increasing Mg2+ so that the efficacy of synaptic transmission was reduced. All synchronized activity was suppressed by applying an increased concentration of antagonist or by raising Mg2+ and lowering Ca2+ so that synaptic transmission was completely blocked. This synchronized neuronal activity occurred spontaneously in the CA2-3 region when isolated from the CA1 pyramidal cell area and the dentate gyrus. When CA2 was separated from CA3 a synchronized rhythm of single bursts was observed in CA2, while a different, slower, synchronized population discharge consisting of initial bursts followed by afterdischarges occurred in CA3. The smallest completely isolated segments of the CA3 field which spontaneously generated synchronized afterdischarges, comparable to those observed in the intact slice, measured 500-700 microns along the stratum pyramidable. It is concluded that these afterdischarges depend on local neuronal interactions mediated by chemical synaptic mechanisms which may occur within a single population of as few as 1000 CA3 pyramidal cells. The results are consistent with a repeated activation of the same group of synapses, which may release an excitatory amino acid neurotransmitter, being responsible for the initiation of each afterdischarge.

Neuroexcitatory and depressant effects of penicillin at the cat soleus neuromuscular junction

Penicillin administered intraarterially in a dose of 200 units per kg produced high frequency (ca 300 Hz) repetitive discharges originating in motor nerve endings in response to single stimuli applies to the cat soleus nerve. The high frequency repetitive discharges were antidromically conducted and recorded on ventral root filaments. Simultaneously each repetitive burst was transmitted to the muscle, producing an increase in contractile strength by converting a twitch into a brief tetanic contraction. Posttetanic potentiation in this system, which is mediated by repetitive discharges originating in nerve terminals after high frequency stimulation, is augmented by penicillin; larger doses depressed posttetanic potentiation, and still larger doses produced varying degrees of neuromuscular block. Events similar to those observed after intraarterial injections were recorded when penicillin was administered intravenously in larger doses. These data suggest that in the presence of penicillin the motor nerve terminals remain depolarized for a prolonged period after excitation by the stimulus, thus providing a current sink for the parent axon. Under the influence of this constant cathodal focus the axon fires repetitively at the high frequency.

Reliability of computation in the cerebellum

The mossy fiber-granule cell-parallel fiber-Purkinje cell system of the cerebellar cortex is investigated from the viewpoint of reliability of computation. It is shown that the effects of variability in the inputs to a Purkinje cell can be reduced by having a large number of parallel fibers whose activities are statistically independent. The mossy fiber-granule cell relay is shown to be capable of performing the required function of transforming the activity in a small number of mossy fibers into activity in a much larger number of parallel fibers, while ensuring that there is little correlation between the activities of individual parallel fibers. The effects of variability in the outputs of Purkinje cells may be reduced by redundancy and convergence schemes, as evidenced by the geometrical pattern of parallel fibers and Purkinje cells and the convergence of these cells onto their target neurons.

Further study of soma, dendrite, and axon excitation in single neurons

The present investigation continues a previous study in which the soma-dendrite system of sensory neurons was excited by stretch deformation of the peripheral dendrite portions. Recording was done with intracellular leads which were inserted into the cell soma while the neuron was activated orthodromically or antidromically. The analysis was also extended to axon conduction. Crayfish, Procambarus alleni (Faxon) and Orconectes virilis (Hagen), were used. 1. The size and time course of action potentials recorded from the soma-dendrite complex vary greatly with the level of the cell's membrane potential. The latter can be changed over a wide range by stretch deformation which sets up a "generator potential" in the distal portions of the dendrites. If a cell is at its resting unstretched equilibrium potential, antidromic stimulation through the axon causes an impulse which normally overshoots the resting potential and decays into an afternegativity of 15 to 20 msec. duration. The postspike negativity is not followed by an appreciable hyperpolarization (positive) phase. If the membrane potential is reduced to a new steady level a postspike positivity appears and increases linearly over a depolarization range of 12 to 20 mv. in various cells. At those levels the firing threshold of the cell for orthodromic discharges is generally reached. 2. The safety factor for conduction between axon and cell soma is reduced under three unrelated conditions, (a) During the recovery period (2 to 3 msec.) immediately following an impulse which has conducted fully over the cell soma, a second impulse may be delayed, may invade the soma partially, or may be blocked completely. (b) If progressive depolarization is produced by stretch, it leads to a reduction of impulse height and eventually to complete block of antidromic soma invasion, resembling cathodal block, (c) In some cells, when the normal membrane potential is within several millivolts of the relaxed resting state, an antidromic impulse may be blocked and may set up within the soma a local potential only. The local potential can sum with a second one or it may sum with potential changes set up in the dendrites, leading to complete invasion of the soma. Such antidromic invasion block can always be relieved by appropriate stretch which shifts the membrane potential out of the "blocking range" nearer to the soma firing level. During the afterpositivity of an impulse in a stretched cell the membrane potential may fall below or near the blocking range. During that period another impulse may be delayed or blocked. 3. Information regarding activity and conduction in dendrites has been obtained indirectly, mainly by analyzing the generator action under various conditions of stretch. The following conclusions have been reached: The large dendrite branches have similar properties to the cell body from which they arise and carry the same kind of impulses. In the finer distal filaments of even lightly depolarized dendrites, however, no axon type all-or-none conduction occurs since the generator potential persists to a varying degree during antidromic invasion of the cell. With the membrane potential at its resting level the dendrite terminals contribute to the prolonged impulse afternegativity of the soma. 4. Action potentials in impaled axons and in cell bodies have been compared. It is thought that normally the over-all duration of axon impulses is shorter. Local activity during reduction of the safety margin for conduction was studied. 5. An analysis was made of high frequency grouped discharges which occasionally arise in cells. They differ in many essential aspects from the regular discharges set up by the generator action. It is proposed that grouped discharges occur only when invasion of dendrites is not synchronous, due to a delay in excitation spread between soma and dendrites. Each impulse in a group is assumed to be caused by an impulse in at least one of the large dendrite branches. Depolarization of dendrites abolishes the grouped activity by facilitating invasion of the large dendrite branches.