Fluctuation analysis of nonideal shot noise. Application to the neuromuscular junction

Procedures are described for analyzing shot noise and determining the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of the shots under a variety of nonideal conditions that include: (a) slow, spurious changes in the mean, (b) nonstationary shot rates, (c) nonuniform distribution of shot amplitudes, and (d) nonlinear summation of the shots. The procedures are based upon Rice's (1944. Bell Telephone System Journal. 23: 282-332) extension of Campbell's theorem to the second (variance), lambda 2, third (skew), lambda 3, and fourth, lambda 4, semi-invariants (cumulants) of the noise. It is shown that the spectra of lambda 2 and lambda 3 of nonstationary shot noise contain a set of components that are proportional to (r) and arise from w(t), and a set of components that are independent of (r) and arise from the temporal variations in r(t). Since the latter components are additive and are limited by the bandwidth of r(t), they can be removed by appropriate filters; then (r) and (h) can be determined from the lambda 2 and lambda 3 of the filtered noise. We also show that a factor related to the ratio (lambda 3)2/(lambda 2)(lambda 4) monitors the spread in the distribution of shot amplitudes and can be used to correct the estimates of (r) and (h) for the effects of that spread, if the shape of the distribution is known and if r(t) is stationary. The accuracy of the measurements of lambda 4 is assessed and corrections for the effects of nonlinear summation of lambda 2, lambda 3, and lambda 4 are derived. The procedures give valid results when they are used to analyze shot noise produced by the (linear) summation of simulated miniature endplate potentials, which are generated either at nonstationary rates or with a distribution of amplitudes.     

Correlation of receptive field position of mechanosensory neurons and the strength of their connections to AP neurons in the CNS of the leech (Whitmania pigra)

An identified neuron of unknown function in the CNS of the leech, the anterior pagoda (AP) cell, receives multiple synaptic inputs from mechanosensory neurons that innervate the skin. Impulses in touch (T), pressure (P) and nociceptive (N) sensory cells on both sides of the ganglion produced electrical coupling potentials on both AP cells. Sensory cells with receptive fields contralateral to the cell body of the AP neuron always gave rise to larger synaptic potentials. In addition sensory cells supplying dorsal skin gave rise to larger synaptic potentials than those with lateral or ventral fields. It is suggested that integration by the AP cell can provide information about the position of mechanical stimuli impinging on the body wall of the animal.     

Exclusive-OR function of single arborized neuron

We designed four arborized neurons which are able to evaluate the exclusive-or (XOR) function from two inputs. The input neurons form exclusively excitatory synapses on a dendritic tree which is a patchwork of passive (ohmic) and active cable segments. The active segments are described by the Hodgkin-Huxley model. The dynamics of the neurons and their output are obtained by numerical integration of the cable equation. In neurons 1 and 2 the XOR function is based on the annihilation of colliding action potentials. In neuron No. 3 the design takes advantage of the refractory period of action potentials. In neuron No. 4 voltage inversion is used as it occurs for inactivated sodium conductance in the Hodgkin-Huxley model. In all cases the XOR function depends critically on an appropriate timing of the input signals and on delays of the voltage transients in different branches of the dendrite.     

Computer simulation of introductory neurophysiology

A computer-assisted learning (CAL) package, NeuroLab, developed for use by first-year university students undertaking professional programs in the health area, is described and evaluated. NeuroLab is a simulation of a laboratory, in which students are able to impale neurons to measure resting membrane potentials and subsequently undertake experiments including measuring resting membrane potentials, determining threshold potentials, measuring refractory periods, and examining effects on membrane potential through altering the membrane permeability to sodium and potassium ions. Students find the package to be a worthwhile learning experience, with 81 +/- 2.2% reporting the package increased their understanding of neuron function, and 78 +/- 2.5% expressing a desire for more CAL packages. Exposure to the package resulted in significantly higher mean scores in a multiple-choice question test on measuring neuron membrane potentials compared with those who were not exposed (mean scores out of 4 of 2.42 and 2.02, respectively, P < 0.001).     

Clinical neurophysiology in ALS

Amyotrophic lateral sclerosis (ALS) belongs to a group of disorders known as motor neuron diseases. Despite being one of the most devastating diseases known, there is little evidence for diagnosing and managing patients with ALS. Clinical neurophysiologic tests are essential, when no biological marker exists to aid early diagnosis, not only in relation to diagnosis, but also in the development of disease progression, and perhaps, in the future, in measuring patients' response to therapy. The electrophysiological features used in the diagnosis of ALS are based on Awaji-shima consensus recommendations for the application of electrophysiological tests, as applied to the revised El Escorial Criteria. Measurements of axonal excitability through nerve conduction study (ENG) is useful to evaluate axonal degeneration. Electromyography (EMG) recordings with needle examination are essential for confirming lower motor neuron involvement in the initial diagnosis of ALS. EMG abnormalities are frequent and these include fibrillation potentials or positive sharp wave potentials, or both, with fasciculation potentials in resting muscle, and an incomplete interference pattern, with abnormal motor unit potentials. Collateral or terminal nerve sprouting is common in ALS and is frequent large macro-motor unit potentials (MUPs). Motor unit number estimation (MUNE) may be useful in measuring loss of functioning motor units and is an attractive endpoint measure in clinical drug trials in ALS because it directly assesses loss of lower motor neurons and is sensitive to disease progression. Transcortical magnetic stimulation protocols, and cortical excitability may be useful to assess the involvement of upper motor neuron system. In this chapter the advantages, limitations and promise of these various methods are discussed, in order to indicate the direction for further neurophysiological studies in this disorder.     

Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model

After the report of Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350], leaky integrate-and-fire models have been investigated to explain high coefficient of variation (CV) of interspike intervals (ISIs) at high firing rates observed in the cortex. The purpose of this paper is to study the effect of the position of a lower boundary of membrane potential on the possible value of CV of ISIs based on the diffusional leaky integrate-and-fire models with and without reversal potentials. Our result shows that the irregularity of ISIs for the diffusional leaky integrate-and-fire neuron significantly changes by imposing a lower boundary of membrane potential, which suggests the importance of the position of the lower boundary as well as that of the firing threshold when we study the statistical properties of leaky integrate-and-fire neuron models. It is worth pointing out that the mean-CV plot of ISIs for the diffusional leaky integrate-and-fire neuron with reversal potentials shows a close similarity to the experimental result obtained in Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350].     

Pre & postsynaptic tuning of action potential timing by spontaneous GABAergic activity

Frequency and timing of action potential discharge are key elements for coding and transfer of information between neurons. The nature and location of the synaptic contacts, the biophysical parameters of the receptor-operated channels and their kinetics of activation are major determinants of the firing behaviour of each individual neuron. Ultimately the intrinsic excitability of each neuron determines the input-output function. Here we evaluate the influence of spontaneous GABAergic synaptic activity on the timing of action potentials in Layer 2/3 pyramidal neurones in acute brain slices from the somatosensory cortex of young rats. Somatic dynamic current injection to mimic synaptic input events was employed, together with a simple computational model that reproduce subthreshold membrane properties. Besides the well-documented control of neuronal excitability, spontaneous background GABAergic activity has a major detrimental effect on spike timing. In fact, GABA(A) receptors tune the relationship between the excitability and fidelity of pyramidal neurons via a postsynaptic (the reversal potential for GABA(A) activity) and a presynaptic (the frequency of spontaneous activity) mechanism. GABAergic activity can decrease or increase the excitability of pyramidal neurones, depending on the difference between the reversal potential for GABA(A) receptors and the threshold for action potential. In contrast, spike time jitter can only be increased proportionally to the difference between these two membrane potentials. Changes in excitability by background GABAergic activity can therefore only be associated with deterioration of the reliability of spike timing.     

Neural mechanism generating firing patterns in jaw motoneurons during the food-induced response in Aplysia kurodai

1. In each right and left buccal ganglia of Aplysia kurodai, we identified 4 premotor neurons impinging on the ipsilateral jaw-closing and -opening motoneurons. Three of them (MA1 neurons) had features of multifunctional neurons. Current-induced spikes in the MA1 neurons produced excitatory junction potentials (EJPs) in the buccal muscle fibers. In addition, tactile stimulation of the buccal muscle surface produced a train of spikes in the MA1 neurons without synaptic input. The other neuron (MA2) had only a premotor function. 2. The MA1 and MA2 neurons had similar synaptic effects on the jaw-closing and -opening motoneurons. Current-induced spikes in the premotor neurons gave rise to monosynaptic inhibitory postsynaptic potentials (IPSPs) in the ipsilateral jaw-closing motoneurons. Simultaneously, spikes in one of the MA1 neurons and the MA2 also gave rise to monosynaptic excitatory postsynaptic potentials (EPSPs) in the ipsilateral jaw-opening motoneuron. 3. The IPSPs and the EPSPs induced by spikes in the premotor neurons were reversibly blocked by d-tubocurarine and hexamethonium, respectively, suggesting that the MA1 and MA2 neurons are cholinergic. 4. When depolarizing and hyperpolarizing current pulses were passed into one premotor neuron, attenuated but similar potential changes were produced in another randomly selected premotor neuron in the same ganglion, suggesting that they are electronically coupled.     

Amphetamine elicited potential changes in vertebrate and invertebrate central neurons

The effects of amphetamine on potential changes in both vertebrate and invertebrate central neurons and factors affecting the potential changes were tested. The animals studied included mice, newborn rat and African snail. Seizure was elicited after lethal doses of d-amphetamine (75 mg/kg, i.p.) administration in mice. Repetitive firing of the action potentials were elicited after d-amphetamine (1-30 microM) administration in thin thalamic brain slices of newborn rat. Bursting firing of action potentials in the giant African central RP4 neuron were also elicited after d-amphetamine or l-amphetamine (0.27 mM) administration. The amphetamine elicited bursting firing of action potentials was not blocked even after high concentrations of d-tubocurarine, atropine, haloperidol, hexamethonium administration. Therefore, the amphetamine elicited potential changes may not be directly related to the activation of the receptors of the neuron. The bursting firing of action potentials elicited by amphetamine occurred 20-30 min after amphetamine administration extracellularly, even after high concentrations of d-amphetamine administration (0.27, 1 mM). However, the bursting firing of potentials occurred immediately if amphetamine was administrated intracellularly at lower concentration. Extracellular application of ruthenium red, the calcium antagonist, abolished the amphetamine elicited bursting firing of action potentials. If intracellular injection of EGTA, a calcium ion chelator, or injection with high concentrations of magnesium, the bursting firing of potentials were immediately abolished. These results suggested that the active site of amphetamine may be inside of the neuron and the calcium ion in the neuron played an important role on the bursting of potentials. In two-electrode voltage clamped RP4 neuron, amphetamine, at 0.27 mM, decreased the total inward and steady outward currents of the RP4 neuron. d-Amphetamine also decreased the calcium, Ia and the steady-state outward currents of the RP4 neuron. Besides, amphetamine elicited a negative slope resistance (NSR) if membrane potential was in the range of -50 to -10 mV. The NSR was decreased in cobalt substituted calcium free and sodium free solution. The effects of secondary messengers on the amphetamine elicited potential changes were tested. The bursting firing of action potentials elicited by amphetamine in central snail neurons decreased following extracellular application of H8 (N-(2-methyl-amino) ethyl-3-isoquinoline sulphonamide dihydrochloride), a specific protein kinase A inhibitor and anisomycin, a protein synthesis inhibitor. However, the bursting firing of action potentials were not affected after extracellular application of H7 (1,(5-isoquinolinesulphonyl)-2-methylpiperasine dihydrochloride), a specific protein kinase C (PKC) inhibitor, or intracellular application of GDPbetaS, a G protein inhibitor. The oscillation of membrane potential of the bursting activity was blocked after intracellular injection of 3'-deoxyadenosine, an adenylyl-cyclase inhibitor. These results suggested that the bursting firing of action potentials elicited by d-amphetamine in snail neuron may be associated with the cyclic AMP second messenger system; on the other hand, it may not be associated with the G protein and protein kinase C activity. It is concluded that amphetamine elicited potential changes in both vertebrate and invertebrate central neurons. The changes are closely related to the ionic currents and second messengers of the neurons.     

用脑干电位的互相关函数客观估计听力阈值

将脑干诱发电位记录分为大小相等的两个子集均,求其互相关函数。互相关函数在原点附近的平均幅度作为估计听力阈值的参数,并通过实验得出表达该参数与阈上刺激强度关系的直线回归方程,从而求出听力阈值的估计公式。把三种阈上刺激强度下的参数值分别代入估计公式,平均结果作为听力阈值的估计。对8个有不同听力损失的病耳进行了估计,其结果与主观阈值平均相差4.6dB。     

A general pre-steady-state solution to complex kinetic mechanisms

We have developed a general method for solving transient kinetic equations using Laplace transforms. Laplace transforms can be used to transform systems of differential equations that describe pre-steady-state kinetics to systems of linear algebraic equations. The general form of the pre-steady-state solution is (formula; see text) where I(t) is the time dependence of the physically observed property of the system, n is the number of intermediates, lambda i are the observed rate constants (reciprocals of the relaxation times), t is time, and Ii are the amplitude coefficients associated with each observed rate constant. We have written a program in compiled BASIC to run on a personal computer to evaluate Ii and lambda i. The program will evaluate the rate constants and coefficients of a mechanism with eight intermediates and seven relaxation times in 4 s on an 8-MHz PC-XT equipped with a math coprocessor. The most complex mechanism that we have solved, a mechanism containing 20 intermediates and 19 relaxation times, required approximately 5 min. We believe that this method will be useful to evaluate the differences in transient properties of complex biochemical mechanisms.     

Electrical Properties of Hypothalamic Neuroendocrine Cells

Goldfish hypothalamic neuroendocrine cells have been investigated with intracellular recordings. The cells showed resting potentials of 50 mv and action potentials up to 117 mv followed by a long lasting and prominent diphasic hyperpolarizing afterpotential. The action potential occurred in two steps indicating sequential invasion. "Total" neuron (input) resistance was measured to be 3.3 x 10⁷ Ω and total neuron time constant was 42 msec. Orthodromic volleys, produced by olfactory tract stimulation, generated graded excitatory postsynaptic potentials. These neuroendocrine cells seem, therefore, to have electrical membrane properties that are similar to those of other central neurons. Antidromic volleys (pituitary stimulation) produced inhibitory post-synaptic potentials whose latency was only slightly longer than that of the antidromic spike indicating the presence of recurrent collaterals. This finding suggests that the concept of the neuroendocrine cell as a neuron whose axon forms contacts only on blood vessels and not on other neurons or effector cells is too restrictive. Perfusion of the gills with dilute (0.3 per cent) sea water produced an inhibition of spontaneous activity. This inhibition is discussed in relation to recent work which demonstrates that goldfish hypothalamic hormones facilitate Na⁺ influx across the gill membrane.     

Burst firing of action potentials in central snail neurons elicited by d-amphetamine: effect of anticonvulsants

The effect of anticonvulsants on the burst firing of action potentials in snail central neuron elicited by d-amphetamine was studied in the identified RP4 neuron of the African snail, Achatina fulica Ferussac. Oscillation of membrane potential and burst firing of action potentials were elicited by d-amphetamine in a concentration-dependent manner. Voltage clamped studies revealed that d-amphetamine elicited a negative slope resistance (NSR) in steady-state I-V curve between - 40 and - 10 mV. The burst firing of action potentials was alleviated following extracellular application of phenytoin, but was not affected after ethosuximide, carbamazepine, and valproic acid. The NSR elicited by d-amphetamine was blocked by phenytoin. However, the NSR was not altered if carbamazepine was added. These results suggest that of the four anticonvulsants tested, only phenytoin could alleviate the burst firing of action potentials elicited by d-amphetamine in snail neuron.     

Functional organization and structure of the serotonergic neuronal network of terrestrial snail

The extension of knowledge how the brain works requires permanent improvement of methods of recording of neuronal activity and increase in the number of neurons recorded simultaneously to better understand the collective work of neuronal networks and assemblies. Conventional methods allow simultaneous intracellular recording up to 2-5 neurons and their membrane potentials, currents or monosynaptic connections or observation of spiking of neuronal groups with subsequent discrimination of individual spikes with loss of details of the dynamics of membrane potential. We recorded activity of a compact group of serotonergic neurons (up to 56 simultaneously) in the ganglion of a terrestrial mollusk using the method of optical recording of membrane potential that allowed to record individual action potentials in details with action potential parameters and to reveal morphology of the neurons rcorded. We demonstrated clear clustering in the group in relation with the dynamics of action potentials and phasic or tonic components in the neuronal responses to external electrophysiological and tactile stimuli. Also, we showed that identified neuron Pd2 could induce activation of a significant number of neurons in the group whereas neuron Pd4 did not induce any activation. However, its activation is delayed with regard to activation of the reacting group of neurons. Our data strongly support the concept of possible delegation of the integrative function by the network to a single neuron.     

Voltage-dependent actions of endogenous and exogenous serotonin on identified neurones

1. Impulse activity in an identified serotonin-containing neuron (GSN) produces a slow excitatory synaptic response in another identified neuron, the A neuron. An axon process can be traced close to the follower neuron perikaryon after Lucifer Yellow injection of the GSN perikaryon. 2. The synaptic response is markedly voltage-sensitive being increased at depolarized potentials and almost abolished and not inverted at potentials in excess of about -55mV. 3. Serotonin locally applied produces a similar response. 4. The response to serotonin does not involve a change in conductance to either sodium or chloride ions, but calcium ions do appear to be important either because of their influence on potassium ion permeability or in a direct transfer of charge across the membrane. 5. Another follower neuron exhibits a complex GSN-induced synaptic response comprising a slow potential similar to that seen in the A neuron and also a fast, probably sodium dependent, potential. 6. In addition to producing a weak direct excitation of the A neuron, GSN-activation can also partly reverse accommodation and also prolong the duration of the impulse in the A neuron. 7. Exogenously applied serotonin produces a similar voltage-dependent inward current response in the GSN as seen in the A neuron. It is suggested that the receptors mediating the response on the GSNs may normally be involved in feedback regulation. 8. Cyproheptadine (reversibly), methergoline, mianserin and propranolol (all irreversibly) antagonised the response in the GSN. These agents probably all have action on the ionic mechanism underlying the serotonin response.     

Osmometric analysis of quasi-indefinite mixed associations of the first kind

Mixed associations of the type A + B----AB, A + AB----A2B, ..., A + Ai-1 B----AiB, ... are readily analyzed by osmometric methods. The equilibrium molar concentration of A, mA, is obtained very simply from mA = meq-m0B; here meq = c/Meqn is the equilibrium molar concentration of all associating species and m0B denotes the stoichiometric or original molar concentration of B. The quantity mB can then be obtained from methods developed by Steiner. The value of the binding polynomial lambda is given by lambda = m0B/mB; lambda is a function of mA only. In principle, one can evaluate the equilibrium constants (kA,B,etc.) by fitting lambda to the appropriate polynomial in mA of degree n (n = 2, 3, ...). The binding polynomial lambda is analogous to polynomials encountered in the analysis of self-associations. By making some simple assumptions one can develop four analogs of two sequential, equal equilibrium constant (SEK) or two attenuated equilibrium constant (AK) models. With the aid of r (the number average degree of binding), g (the osmotic coefficient), lambda, as well as mA and mB, one can evaluate the equilibrium constant or constants. The methods developed here can be extended to the nonideal case.     

A study of the connection between the interneuron initiating pacemaker activity in a bursting neuron and the bursting neuron of the snailHelix pomatia

The connection between an interneuron initiating pacemaker activity in the bursting RPa1 neuron and the bursting neuron itself (Pin and Gola, 1983) has been analyzed in the snail Helix pomatia. Prolonged depolarization of the interneuronal membrane produced in it a series of action potentials as well as a parallel initiation or enhancement of bursting activity in the RPa1 neuron. If the discharge in the interneuron was evoked by short current pulses of threshold amplitude, no bursting activity was seen in the RPa1 neuron. However, short stimuli delivered on the background of subthreshold depolarization of the interneuronal membrane produced bursting activity in the RPa1 neuron. Under voltage-clamp conditions a slow inward current could be recorded in the RPa1 neuronal membrane after stimulation of the interneuron with a latency of about 2 sec. Short shifts of the holding potential in the hyperpolarizing direction at the maximum of this current produced a transient outward current. Replacement of extracellular Ca2+ by Mg2+ ions, as well as addition of 1 mM CdCl2 to the external solution, prevented the response to the interneuronal stimulation in the RPa1 neuron. Electron microscopic investigation of the interneuron has shown the abundance of Golgi complexes in its cytoplasm with electron-dense granules in their vicinity. It is concluded that the connection between the interneuron and the bursting neuron is of chemical origin, based on secretion by the former of some substances which activate at least two types of ionic channels in the membrane of the RPa1 neuron.