Failure of Averaging in the Construction of a Conductance-Based Neuron Model

2002 ◽  
Vol 87 (2) ◽  
pp. 1129-1131 ◽  
Author(s):  
Jorge Golowasch ◽  
Mark S. Goldman ◽  
L. F. Abbott ◽  
Eve Marder
Keyword(s):  
Membrane Potential ◽  
Action Potential ◽  
Action Potentials ◽  
Neuron Model ◽  
Model Neuron ◽  
Maximal Conductance ◽  
Single Action ◽  
Bursting Neurons ◽  
Voltage Dependent ◽  
Multiple Samples

Parameters for models of biological systems are often obtained by averaging over experimental results from a number of different preparations. To explore the validity of this procedure, we studied the behavior of a conductance-based model neuron with five voltage-dependent conductances. We randomly varied the maximal conductance of each of the active currents in the model and identified sets of maximal conductances that generate bursting neurons that fire a single action potential at the peak of a slow membrane potential depolarization. A model constructed using the means of the maximal conductances of this population is not itself a one-spike burster, but rather fires three action potentials per burst. Averaging fails because the maximal conductances of the population of one-spike bursters lie in a highly concave region of parameter space that does not contain its mean. This demonstrates that averages over multiple samples can fail to characterize a system whose behavior depends on interactions involving a number of highly variable components.

Properties of a tonically active, sodium-permeable current in mouse urinary bladder smooth muscle

2004 ◽  
Vol 286 (6) ◽  
pp. C1246-C1257 ◽  
Author(s):  
Kevin S. Thorneloe ◽  
Mark T. Nelson
Keyword(s):  
Membrane Potential ◽  
Urinary Bladder ◽  
Action Potential ◽  
Action Potentials ◽  
Resting Membrane Potential ◽  
Action Potential Generation ◽  
Potential Generation ◽  
Bladder Smooth Muscle ◽  
Voltage Dependent ◽  
Urinary Bladder Smooth Muscle

Urinary bladder smooth muscle (UBSM) elicits depolarizing action potentials, which underlie contractile events of the urinary bladder. The resting membrane potential of UBSM is approximately −40 mV and is critical for action potential generation, with hyperpolarization reducing action potential frequency. We hypothesized that a tonic, depolarizing conductance was present in UBSM, functioning to maintain the membrane potential significantly positive to the equilibrium potential for K+ ( EK; −85 mV) and thereby facilitate action potentials. Under conditions eliminating the contribution of K+ and voltage-dependent Ca2+ channels, and with a clear separation of cation- and Cl−-selective conductances, we identified a novel background conductance ( Icat) in mouse UBSM cells. Icat was mediated predominantly by the influx of Na+, although a small inward Ca2+ current was detectable with Ca2+ as the sole cation in the bathing solution. Extracellular Ca2+, Mg2+, and Gd3+ blocked Icat in a voltage-dependent manner, with Ki values at −40 mV of 115, 133, and 1.3 μM, respectively. Although UBSM Icat is extensively blocked by physiological extracellular Ca2+ and Mg2+, a tonic, depolarizing Icat was detected at −40 mV. In addition, inhibition of Icat demonstrated a hyperpolarization of the UBSM membrane potential and decreased the amplitude of phasic contractions of isolated UBSM strips. We suggest that Icat contributes tonically to the depolarization of the UBSM resting membrane potential, facilitating action potential generation and thereby a maintenance of urinary bladder tone.

scholarly journals Distinctive Neurophysiological Properties of Embryonic Trigeminal and Geniculate Neurons in Culture

2002 ◽  
Vol 88 (4) ◽  
pp. 2058-2074 ◽  
Author(s):  
Arturas Grigaliunas ◽  
Robert M. Bradley ◽  
Donald K. MacCallum ◽  
Charlotte M. Mistretta
Keyword(s):  
Membrane Potential ◽  
Action Potential ◽  
Action Potentials ◽  
Resting Membrane Potential ◽  
Target Tissue ◽  
Extrinsic Factors ◽  
Single Action ◽  
Trigeminal Neurons ◽  
Ganglion Neurons ◽  
Passive Membrane

Neurons in trigeminal and geniculate ganglia extend neurites that share contiguous target tissue fields in the fungiform papillae and taste buds of the mammalian tongue and thereby have principal roles in lingual somatosensation and gustation. Although functional differentiation of these neurons is central to formation of lingual sensory circuits, there is little known about electrophysiological properties of developing trigeminal and geniculate ganglia or the extrinsic factors that might regulate neural development. We used whole cell recordings from embryonic day 16 rat ganglia, maintained in culture as explants for 3–10 days with neurotrophin support to characterize basic properties of trigeminal and geniculate neurons over time in vitro and in comparison to each other. Each ganglion was cultured with the neurotrophin that supports maximal neuron survival and that would be encountered by growing neurites at highest concentration in target fields. Resting membrane potential and time constant did not alter over days in culture, whereas membrane resistance decreased and capacitance increased in association with small increases in trigeminal and geniculate soma size. Small gradual differences in action potential properties were observed for both ganglion types, including an increase in threshold current to elicit an action potential and a decrease in duration and increase in rise and fall slopes so that action potentials became shorter and sharper with time in culture. Using a period of 5–8 days in culture when neural properties are generally stable, we compared trigeminal and geniculate ganglia and revealed major differences between these embryonic ganglia in passive membrane and action potential characteristics. Geniculate neurons had lower resting membrane potential and higher input resistance and smaller, shorter, and sharper action potentials with lower thresholds than trigeminal neurons. Whereas all trigeminal neurons produced a single action potential at threshold depolarization, 35% of geniculate neurons fired repetitively. Furthermore, all trigeminal neurons produced TTX-resistant action potentials, but geniculate action potentials were abolished in the presence of low concentrations of TTX. Both trigeminal and geniculate neurons had inflections on the falling phase of the action potential that were reduced in the presence of various pharmacological blockers of calcium channel activation. Use of nifedipine, ω-conotoxin-MVIIA and GVIA, and ω-agatoxin-TK indicated that currents through L-, N-, and P/Q- type calcium channels participate in the action potential inflection in embryonic trigeminal and geniculate neurons. The data on passive membrane, action potential, and ion channel characteristics demonstrate clear differences between trigeminal and geniculate ganglion neurons at an embryonic stage when target tissues are innervated but receptor organs have not developed or are still immature. Therefore these electrophysiological distinctions between embryonic ganglia are present before neural activity from differentiated receptive fields can influence functional phenotype.

Limbic Gamma Rhythms. II. Synaptic and Intrinsic Mechanisms Underlying Spike Doublets in Oscillating Subicular Neurons

1998 ◽  
Vol 80 (1) ◽  
pp. 162-171 ◽  
Author(s):  
Ian M. Stanford ◽  
Roger D. Traub ◽  
John G. R. Jefferys
Keyword(s):  
Membrane Potential ◽  
Action Potential ◽  
Action Potentials ◽  
Gamma Oscillations ◽  
Gamma Oscillation ◽  
Population Spike ◽  
Tetanic Stimulation ◽  
Single Action ◽  
Gamma Rhythms ◽  
Afferent Volleys

Stanford, Ian M., Roger D. Traub, and John G. R. Jefferys. Limbic gamma rhythms. II. Synaptic and intrinsic mechanisms underlying spike doublets in oscillating subicular neurons. J. Neurophysiol. 80: 162–171, 1998. Gamma oscillations were evoked in the subiculum in rat transverse hippocampal slices by tetanic stimulation (200 ms/100 Hz) of either CA1 or subiculum. Gamma oscillations in the subiculum differed from those in CA1 in containing population spike doublets as well as singlets. The present study addresses the origin of this more complex form of gamma oscillation in the subiculum. Intracellular recordings from subicular neurons revealed that 63% of them fired double action potentials on cycles of the gamma oscillation that generated population spike doublets after tetanic stimulation of either CA1 or subiculum. The remaining cells produced excitatory postsynaptic potentials (EPSPs), and occasional single spikes, on each cycle. Neurons that fired occasional single action potentials during gamma rhythms were “regular spiking” cells. They did not produce burst discharges during depolarizing steps, had minimal membrane potential sags on hyperpolarizing steps, and responded to single afferent volleys with a single action potential on an EPSP followed by a large inhibitory postsynaptic potential complex. Fast spiking cells were observed too infrequently to be studied in detail. Neurons that fired doublets during gamma rhythms were “intrinsic burst” (IB) cells. They generated bursts of action potentials on step membrane depolarizations, had significant membrane potential sags on step hyperpolarizations with an anodal break potential on return to rest, and fired multiple action potentials in response to high-intensity single afferent volleys. IB neurons did not fire action potential doublets during 1-s membrane depolarizations. Double action potentials, however, were evoked in these cells by depolarizing pulses at 40 Hz from hyperpolarized membrane potentials (−100 mV). Computer simulations suggest that the hyperpolarization between the depolarizations was essential for action potential doublets. The results in this and the previous paper suggest the following: either CA1 or subiculum alone can generate gamma oscillations gated by local networks of interneurons, oscillations in CA1 project through pyramidal cell axons to subiculum with a time lag expected from axon conduction delays, and oscillating sequences of EPSPs and intrinsic and/or synaptic hyperpolarizing potentials in IB subicular neurons generate gamma frequency spike doublets, which depend on both the intrinsic properties of these neurons and their temporally patterned synaptic input. This phenomenon could amplify gamma output from CA1 and modify its coupling to gamma oscillations in the wider limbic system.

Calcium Dynamics and Compartmentalization in Leech Neurons

2005 ◽  
Vol 94 (6) ◽  
pp. 4430-4440 ◽  
Author(s):  
Sofija Andjelic ◽  
Vincent Torre
Keyword(s):  
Information Processing ◽  
Action Potential ◽  
Action Potentials ◽  
Time Course ◽  
Ccd Camera ◽  
Calcium Dynamics ◽  
Single Action ◽  
Single Action Potential ◽  
Calcium Indicator ◽  
Mechanosensory Neurons

Calcium dynamics in leech neurons were studied using a fast CCD camera. Fluorescence changes (Δ F/ F) of the membrane impermeable calcium indicator Oregon Green were measured. The dye was pressure injected into the soma of neurons under investigation. Δ F/ F caused by a single action potential (AP) in mechanosensory neurons had approximately the same amplitude and time course in the soma and in distal processes. By contrast, in other neurons such as the Anterior Pagoda neuron, the Annulus Erector motoneuron, the L motoneuron, and other motoneurons, APs evoked by passing depolarizing current in the soma produced much larger fluorescence changes in distal processes than in the soma. When APs were evoked by stimulating one distal axon through the root, Δ F/ F was large in all distal processes but very small in the soma. Our results show a clear compartmentalization of calcium dynamics in most leech neurons in which the soma does not give propagating action potentials. In such cells, the soma, while not excitable, can affect information processing by modulating the sites of origin and conduction of AP propagation in distal excitable processes.

Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. I. Bursting Pacemaker Neurons

1999 ◽  
Vol 82 (1) ◽  
pp. 382-397 ◽  
Author(s):  
Robert J. Butera ◽  
John Rinzel ◽  
Jeffrey C. Smith
Keyword(s):  
Membrane Potential ◽  
Respiratory Rhythm ◽  
Rhythm Generation ◽  
Minimal Models ◽  
Dynamic Features ◽  
Bursting Neurons ◽  
Wide Range ◽  
Bötzinger Complex ◽  
Voltage Dependent ◽  
Respiratory Rhythm Generation

A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Bötzinger complex (pre-BötC) in mammals. Two minimal models of these neurons are proposed. In model 1, bursting arises via fast activation and slow inactivation of a persistent Na+ current I NaP-h. In model 2, bursting arises via a fast-activating persistent Na+ current INaP and slow activation of a K+ current IKS. In both models, action potentials are generated via fast Na+ and K+currents. The two models have few differences in parameters to facilitate a rigorous comparison of the two different burst-generating mechanisms. Both models are consistent with many of the dynamic features of electrophysiological recordings from pre-BötC oscillatory bursting neurons in vitro, including voltage-dependent activity modes (silence, bursting, and beating), a voltage-dependent burst frequency that can vary from 0.05 to >1 Hz, and a decaying spike frequency during bursting. These results are robust and persist across a wide range of parameter values for both models. However, the dynamics of model 1 are more consistent with experimental data in that the burst duration decreases as the baseline membrane potential is depolarized and the model has a relatively flat membrane potential trajectory during the interburst interval. We propose several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.

Electrophysiological properties of neurons within the nucleus ambiguus of adult guinea pigs

1991 ◽  
Vol 66 (3) ◽  
pp. 744-761 ◽  
Author(s):  
S. M. Johnson ◽  
P. A. Getting
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Outward Current ◽  
Nucleus Ambiguus ◽  
Transient Outward Current ◽  
Maximum Magnitude ◽  
Action Potential Firing ◽  
Onset Of Action ◽  
Electrophysiological Properties ◽  
Single Action

1. The purpose of this study was to determine the electrophysiological properties of neurons within the region of the nucleus ambiguus (NA), an area that contains the ventral respiratory group. By the use of an in vitro brain stem slice preparation, intracellular recordings from neurons in this region (to be referred to as NA neurons, n = 235) revealed the following properties: postinhibitory rebound (PIR), delayed excitation (DE), adaptation, and posttetanic hyperpolarization (PTH). NA neurons were separated into three groups on the basis of their expression of PIR and DE: PIR cells (58%), DE cells (31%), and Non cells (10%). Non cells expressed neither PIR nor DE and no cells expressed both PIR and DE. 2. PIR was a transient depolarization that produced a single action potential or a burst of action potentials when the cell was released from hyperpolarization. In the presence of tetrodotoxin (TTX), the maximum magnitude of PIR was 7-12 mV. Under voltage-clamp conditions, hyperpolarizing voltage steps elicited a small inward current during the hyperpolarization and a small inward tail current on release from hyperpolarization. These currents, which mediate PIR, were most likely due to Q-current because they were blocked with extracellular cesium and were insensitive to barium. 3. DE was a delay in the onset of action potential firing when cells were hyperpolarized before application of depolarizing current. When cells were hyperpolarized to -90 mV for greater than or equal to 300 ms, maximum delays ranged from 150 to 450 ms. The transient outward current underlying DE was presumed to be A-current because of the current's activation and inactivation characteristics and its elimination by 4-aminopyridine (4-AP). 4. Adaptation was examined by applying depolarizing current for 2.0 s and measuring the frequency of evoked action potentials. Although there was a large degree of variability in the degree of adaptation, PIR cells tended to express less adaptation than DE and Non cells. Nearly three-fourths of all NA neurons adapted rapidly (i.e., 50% adaptation in less than 200 ms), but PIR cells tended to adapt faster than DE and Non cells. PTH after a train of action potentials was relatively rare and occurred more often in DE cells (43%) and Non cells (33%) than in PIR cells (13%). PTH had a magnitude of up to 18 mV and time constants that reflected the presence of one (1.7 +/- 1.4 s, mean +/- SD) or two components (0.28 +/- 0.13 and 4.1 +/- 2.2 s).(ABSTRACT TRUNCATED AT 400 WORDS)

Input Resistance, Time Constants, and Spike Initiation

1998 ◽  
Author(s):  
Christof Koch
Keyword(s):  
Membrane Potential ◽  
Time Constant ◽  
Action Potentials ◽  
Input Resistance ◽  
Current Injection ◽  
Membrane Conductances ◽  
Voltage Dependent ◽  
Dc Component ◽  
Definition Of ◽  
A Current

This chapter represents somewhat of a tephnical interlude. Having introduced the reader to both simplified and more complex compartmental single neuron models, we need to revisit terrain with which we are already somewhat familiar. In the following pages we reevaluate two important concepts we defined in the first few chapters: the somatic input resistance and the neuronal time constant. For passive systems, both are simple enough variables: Rin is the change in somatic membrane potential in response to a small sustained current injection divided by the amplitude of the current injection, while τm is the slowest time constant associated with the exponential charging or discharging of the neuronal membrane in response to a current pulse or step. However, because neurons express nonstationary and nonlinear membrane conductances, the measurement and interpretation of these two variables in active structures is not as straightforward as before. Having obtained a more sophisticated understanding of these issues, we will turn toward the question of the existence of a current, voltage, or charge threshold at which a biophysical faithful model of a cell triggers action potentials. We conclude with recent work that suggests how concepts from the subthreshold domain, like the input resistance or the average membrane potential, could be extended to the case in which the cell is discharging a stream of action potentials. This chapter is mainly for the cognoscendi or for those of us that need to make sense of experimental data by comparing therp to theoretical models that usually fail to reflect reality adequately. In Sec. 3.4, we defined Kii (f) for passive cable structures as the voltage change at location i in response to a sinusoidal current injection of frequency f at the same location. Its dc component is also referred to as input resistance or Rin. Three difficulties render this definition of input resistance problematic in real cells: (1) most membranes, in particular at the soma, show voltage-dependent nonlinearities, (2) the associated ionic membrane conductances are time dependent and (3) instrumental aspects, such as the effect of the impedance of the recording electrode on Rin, add uncertainty to the measuring process.

Excitable Membrane Properties of Neurons

2020 ◽  
Author(s):  
Leonard K. Kaczmarek
Keyword(s):  
Action Potential ◽  
Action Potentials ◽  
Cell Biology ◽  
Neuronal Firing ◽  
Membrane Properties ◽  
Potassium Ions ◽  
Single Action ◽  
Sodium Calcium ◽  
Different Types ◽  
Order Of Magnitude

The intrinsic electrical properties of neurons are extremely varied. For example, the width of action potentials in different neurons varies by more than an order of magnitude. In response to prolonged stimulation, some neurons generate repeated action potential hundreds of times a second, while others fire only a single action potential or adapt very rapidly. These differences result from the expression of different types of ion channels in the plasma membrane. The dominant channels that shape neuronal firing patterns are those that are selective for sodium, calcium, and potassium ions. This chapter provides a brief overview of the biophysical properties of each of these classes of channel, their role in shaping the electrical personality of a neuron, and how interactions of these channels with cytoplasmic factors shape the overall cell biology of a neuron.

Effects of ischemic conditions and reperfusion on depolarization-induced automaticity

1988 ◽  
Vol 255 (5) ◽  
pp. H992-H999 ◽  
Author(s):  
R. Mohabir ◽  
G. R. Ferrier
Keyword(s):  
Membrane Potential ◽  
Action Potential ◽  
Action Potentials ◽  
Cycle Length ◽  
Slow Inward Current ◽  
Potential Range ◽  
Ischemia And Reperfusion ◽  
Slow Response ◽  
Inward Current ◽  
High Membrane Potential

The inducibility of slow-response automaticity was assessed during ischemic conditions and reperfusion by application of extracellular current. Isolated canine Purkinje fibers were depolarized to membrane potentials less than -65 mV to elicit depolarization-induced automaticity (DIA). Ischemic conditions increased the cycle length of DIA and, in some tissues, prevented sustained DIA or completely abolished DIA. The magnitude of depolarization required to elicit DIA also increased. Inhibition of DIA occurred at a time when action potential plateaus were abbreviated. The effect of reperfusion on DIA was biphasic. Initial reappearance of DIA was followed by inhibition and reduction of the membrane potential range over which DIA could be elicited. Plateaus of action potentials initiated at high membrane potential were abbreviated at this time. DIA returned again as reperfusion effects dissipated. Phasic changes in the inducibility of DIA may represent changes in availability of the slow inward current and may regulate the timing and types of arrhythmic activity occurring with ischemia and reperfusion.

scholarly journals The Effect of Aconitine on the Giant Axon of the Squid

1964 ◽  
Vol 47 (4) ◽  
pp. 719-733 ◽  
Author(s):  
W. H. Herzog ◽  
R. M. Feibel ◽  
S. H. Bryant
Keyword(s):  
Membrane Potential ◽  
Action Potential ◽  
Action Potentials ◽  
Giant Axon ◽  
Membrane Resistance ◽  
Repetitive Stimulation ◽  
Resting Membrane Potential ◽  
Sustained Activity ◽  
Frequency Of Stimulation ◽  
Sodium And Potassium

In the giant axon of Loligo pealii, "aconitine potent" Merck added to the bath (10-7 to 1.25 x 10-6 gm/ml) (a) had no effect on resting membrane potential, membrane resistance and rectification, membrane response to subthreshold currents, critical depolarization, or action potential, but (b) on repetitive stimulation produced oscillations of membrane potential after the spike, depolarization, and decrease of membrane resistance. The effect sums with successive action potentials; it increases with concentration of aconitine, time of exposure, and frequency of stimulation. When the oscillations are large enough and the membrane potential is 51.6 ± SD 1.5 mv a burst of self-sustained activity begins; it usually lasts 20 to 70 sec. and at its end the membrane potential is 41.5 ± SD 1.9 mv. Repolarization occurs with a time constant of 2.5 to 11.1 min. Substitution of choline for external sodium after a burst hyperpolarizes the membrane to -70 mv, and return to normal external sodium depolarizes again beyond the resting membrane potential. The effect of aconitine on the membrane is attributed to an increase of sodium and potassium or chloride conductances following the action potential.

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