PubMed Health⌕ Search

Biomedical subjects

C C Canavier

Publications and source records attributed to C C Canavier.

15 recordsLinked to original sources

An increase in AMPA and a decrease in SK conductance increase burst firing by different mechanisms in a model of a dopamine neuron in vivo.

A stylized, symmetric, compartmental model of a dopamine neuron in vivo shows how rate and pattern can be modulated either concurrently or differentially. If two or more parameters in the model are varied concurrently, the baseline firing rate and the extent of bursting become de-correlated, which provides an explanation for the lack of a tight correlation in vivo and is consistent with some independence of the mechanisms that generate baseline firing rates versus bursts. We hypothesize that most bursts are triggered by a barrage of synaptic input and that particularly meaningful stimuli recruit larger numbers of synapses in a more synchronous way. An example of concurrent modulation is that increasing the short-lived AMPA current evokes additional spikes without regard to pattern, producing comparable increases in spike frequency and fraction fired in bursts. On the other hand, blocking the SK current evokes additional bursts by allowing a depolarization that previously produced only a single spike to elicit two or more and elongates existing bursts by the same principle, resulting in a greater effect on pattern than rate. A probabilistic algorithm for the random insertion of spikes into the firing pattern produces a good approximation to the pattern changes induced by increasing the AMPA conductance, but not by blocking the SK current, consistent with a differential modulation in the latter case. Furthermore, blocking SK produced a longer burst with a greater intra-burst frequency in response to a simulated meaningful input, suggesting that reduction of this current may augment reward-related responses.

Algorithms↗

Scaling of prediction error does not confirm chaotic dynamics underlying irregular firing using interspike intervals from midbrain dopamine neurons.

Dopamine neurons in the substantia nigra pars compacta often fire in an irregular, single spike mode in vivo, and a similar firing pattern can be observed in vitro when small conductance calcium-activated potassium channel blockers are applied to the bath. It is not clear whether the irregular firing is due to stochastic processes or nonlinear deterministic processes. A previous study [Neuroscience 104 (2001) 829] used nonlinear forecasting methods applied to a continuous function derived from the interspike interval (ISI) data from irregularly firing dopamine neurons to show that the predictability scaled exponentially with forecast horizon and was consistent with nonlinear deterministic chaos. However, we show here that the observed exponential scaling is also consistent with a stochastic process, because it did not differ significantly from that of shuffled surrogate data. On the other hand, nonlinear forecasting directly from the ISI data using the package TISEAN provided some evidence for nonlinear deterministic structure in four of five records obtained in vitro and in two of nine records obtained in vivo. Although we cannot rule out a role for nonlinear chaotic dynamics in structuring the firing pattern, we suggest an alternate hypothesis that includes a mechanism by which the firing pattern can become more variable in the presence of a constant level of background noise.

Algorithms↗

Phase resetting and phase locking in hybrid circuits of one model and one biological neuron.

To determine why elements of central pattern generators phase lock in a particular pattern under some conditions but not others, we tested a theoretical pattern prediction method. The method is based on the tabulated open loop pulsatile interactions of bursting neurons on a cycle-by-cycle basis and was tested in closed loop hybrid circuits composed of one bursting biological neuron and one bursting model neuron coupled using the dynamic clamp. A total of 164 hybrid networks were formed by varying the synaptic conductances. The prediction of 1:1 phase locking agreed qualitatively with the experimental observations, except in three hybrid circuits in which 1:1 locking was predicted but not observed. Correct predictions sometimes required consideration of the second order phase resetting, which measures the change in the timing of the second burst after the perturbation. The method was robust to offsets between the initiation of bursting in the presynaptic neuron and the activation of the synaptic coupling with the postsynaptic neuron. The quantitative accuracy of the predictions fell within the variability (10%) in the experimentally observed intrinsic period and phase resetting curve (PRC), despite changes in the burst duration of the neurons between open and closed loop conditions.

Action Potentials↗

Dynamics from a time series: can we extract the phase resetting curve from a time series?

Recordings of the membrane potential from a bursting neuron were used to reconstruct the phase curve for that neuron for a limited set of perturbations. These perturbations were inhibitory synaptic conductance pulses able to shift the membrane potential below the most hyperpolarized level attained in the free running mode. The extraction of the phase resetting curve from such a one-dimensional time series requires reconstruction of the periodic activity in the form of a limit cycle attractor. Resetting was found to have two components. In the first component, if the pulse was applied during a burst, the burst was truncated, and the time until the next burst was shortened in a manner predicted by movement normal to the limit cycle. By movement normal to the limit cycle, we mean a switch between two well-defined solution branches of a relaxation-like oscillator in a hysteretic manner enabled by the existence of a singular dominant slow process (variable). In the second component, the onset of the burst was delayed until the end of the hyperpolarizing pulse. Thus, for the pulse amplitudes we studied, resetting was independent of amplitude but increased linearly with pulse duration. The predicted and the experimental phase resetting curves for a pyloric dilator neuron show satisfactory agreement. The method was applied to only one pulse per cycle, but our results suggest it could easily be generalized to accommodate multiple inputs.

Action Potentials↗

Apamin-induced irregular firing in vitro and irregular single-spike firing observed in vivo in dopamine neurons is chaotic.

Dopamine neurons of the substantia nigra often fire action potentials irregularly in vivo, but in vitro fire in a regular, pacemaker-like firing pattern. Bath application of apamin, a blocker of calcium-activated potassium channels, can shift a dopamine neuron from pacemaker-like to irregular firing. To determine whether the irregular firing was caused by intrinsic cellular mechanisms rather than random synaptic input or some other form of noise, spike density functions of interspike interval records were analyzed using non-linear forecasting methods to quantify any non-linear (non-periodic) structure. Intrinsic cellular mechanisms are capable of producing chaotic firing, which is deterministic, non-linear, and loses predictability exponentially with increasing forecast time.To determine whether forecasting spike density functions could reliably measure predictability, forecasting was first applied to spike density functions produced by computer simulations of pacemaker-like, chaotic, and random firing, as well as pacemaker-like and chaotic firing that were randomly synaptically driven. Exponential loss of predictability was successfully detected in both chaotic and randomly driven chaotic firing. Predictability scaled faster than exponentially for random spiking, and linearly (slower than exponentially) for randomly driven pacemaker firing. The method was then applied to experimental records of apamin-induced irregular firing of rat dopaminergic neurons of the substantia nigra in vitro and in vivo. Exponential loss of predictability was detected in both cases, consistent with chaotic firing. Experimental records of pacemaker-like firing in vitro showed linear scaling, consistent with a randomly driven pacemaker. Several schemes for neural encoding of synaptic inputs have been suggested, such as rate codes or temporal codes. However, our results suggest that under some conditions, the irregular firing of dopamine neurons does not reflect the random temporal dynamics of its inputs, but rather the intrinsic, deterministic dynamics of dopamine cells themselves, under the tonic neuromodulatory influence of apamin in vitro and possibly that of an unidentified endogenous modulatory substance in vivo.

Action Potentials↗

Sodium dynamics underlying burst firing and putative mechanisms for the regulation of the firing pattern in midbrain dopamine neurons: a computational approach.

A physiologically based multicompartmental computational model of a midbrain dopamine (DA) neuron, calibrated using data from the literature, was developed and used to test the hypothesis that sodium dynamics drive the generation of a slow oscillation postulated to underlie NMDA-evoked bursting activity in a slice preparation. The full compartmental model was reduced to three compartments and ultimately to two variables, while retaining the biophysical interpretation of all parameters. A phase-plane analysis then suggested two mechanisms for the regulation of the firing pattern: (1) bursting activity is favored by manipulations that enhance the region of negative slope in the whole-cell IV curve and inhibited by those manipulations, such as increasing linear currents, that tend to dampen this region and (2) assuming a region of negative slope is present in the IV curve, the bias of the system can be altered, either enabling or disabling bursting. The model provides a coherent framework for interpreting the effects of glutamate, aspartate, NMDA, and GABA agonists and antagonists under current-clamp conditions, as well as the effects of NMDA and barium under voltage-clamp conditions.

Calibration↗

Calcium dynamics underlying pacemaker-like and burst firing oscillations in midbrain dopaminergic neurons: a computational study.

A mathematical model of midbrain dopamine neurons has been developed to understand the mechanisms underlying two types of calcium-dependent firing patterns that these cells exhibit in vitro. The first is the regular, pacemaker-like firing exhibited in a slice preparation, and the second is a burst firing pattern sometimes exhibited in the presence of apamin. Because both types of oscillations are blocked by nifedipine, we have focused on the slow calcium dynamics underlying these firing modes. The underlying oscillations in membrane potential are best observed when action potentials are blocked by the application of TTX. This converts the regular single-spike firing mode to a slow oscillatory potential (SOP) and apamin-induced bursting to a slow square-wave oscillation. We hypothesize that the SOP results from the interplay between the L-type calcium current (I(Ca,L)) and the apamin-sensitive calcium-activated potassium current (I(K,Ca,SK)). We further hypothesize that the square-wave oscillation results from the alternating voltage activation and calcium inactivation of I(Ca,L). Our model consists of two components: a Hodgkin-Huxley-type membrane model and a fluid compartment model. A material balance on Ca(2+) is provided in the cytosolic fluid compartment, whereas calcium concentration is considered constant in the extracellular compartment. Model parameters were determined using both voltage-clamp and calcium-imaging data from the literature. In addition to modeling the SOP and square-wave oscillations in dopaminergic neurons, the model provides reasonable mimicry of the experimentally observed response of SOPs to TEA application and elongation of the plateau duration of the square-wave oscillations in response to calcium chelation.

Animals↗

Computational model of the serotonergic modulation of sensory neurons in Aplysia.

Serotonergic modulation of the sensory neurons that mediate the gill- and tail-withdrawal reflexes of Aplysia is a useful model system for studies of neuronal plasticity that contributes to learning and memory. The effects of serotonin (5-HT) are mediated, in part, via two protein kinases (protein kinase A, PKA, and protein kinase C, PKC), which in turn, modulate at least four membrane currents, including a S ("serotonin-sensitive") K(+) current (I(K, S)), a steeply voltage-dependent K(+) current (I(K-V)), a slow component of the Ca(2+)-activated K(+) current (I(K,Ca-S)), and a L-type Ca(2+) current (I(Ca-L)). The present study investigated how the modulation of these currents altered the spike duration and excitability of sensory neurons and examined the relative contributions of PKA- and PKC-mediated effects to the actions of 5-HT. A Hodgkin-Huxley type model was developed that described the ionic conductances in the somata of sensory neurons. The descriptions of these currents and their modulation were based largely on voltage-clamp data from sensory neurons. Simulations were preformed with the program SNNAP (Simulator for Neural Networks and Action Potentials). The model was sufficient to replicate empirical data that describes the membrane currents, action potential waveform and excitability as well as their modulation by application of 5-HT, increased levels of adenosine cyclic monophosphate or application of active phorbol esters. In the model, modulation of I(K-V) by PKC played a dominate role in 5-HT-induced spike broadening, whereas the concurrent modulation of I(K,S) and I(K,Ca-S) by PKA primarily accounted for 5-HT-induced increases in excitability. Finally, simulations indicated that a PKC-induced increase in excitability resulted from decreases of I(K,S) and I(K,Ca-S), which was likely the indirect result of cross-talk between the PKC and PKA systems. The results provide several predictions that warrant additional experimental investigation and illustrate the importance of considering indirect as well as direct effects of modulatory agents on the modulation of membrane currents.

Action Potentials↗

Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation.

In order to assess the relative contributions to pattern-generation of the intrinsic properties of individual neurons and of their connectivity, we examined a ring circuit composed of four complex physiologically based oscillators. This circuit produced patterns that correspond to several quadrupedal gaits, including the walk, the bound, and the gallop. An analysis using the phase response curve (PRC) of an uncoupled oscillator accurately predicted all modes exhibited by this circuit and their phasic relationships--with the caveat that in certain parameter ranges, bistability in the individual oscillators added nongait patterns that were not amenable to PRC analysis, but further enriched the pattern-generating repertoire of the circuit. The key insights in the PRC analysis were that in a gait pattern, since all oscillators are entrained at the same frequency, the phase advance or delay caused by the action of each oscillator on its postsynaptic oscillator must be the same, and the sum of the normalized phase differences around the ring must equal to an integer. As suggested by several previous studies, our analysis showed that the capacity to exhibit a large number of patterns is inherent in the ring circuit configuration. In addition, our analysis revealed that the shape of the PRC for the individual oscillators determines which of the theoretically possible modes can be generated using these oscillators as circuit elements. PRCs that have a complex shape enable a circuit to produce a wider variety of patterns, and since complex neurons tend to have complex PRCs, enriching the repertoire of patterns exhibited by a circuit may be the function of some intrinsic neuronal complexity. Our analysis showed that gait transitions, or more generally, pattern transitions, in a ring circuit do not require rewiring the circuit or any changes in the strength of the connections. Instead, transitions can be achieved by using a control parameter, such as stimulus intensity, to sculpt the PRC so that it has the appropriate shape for the desired pattern(s). A transition can then be achieved simply by changing the value of the control parameter so that the first pattern either ceases to exist or loses stability, while a second pattern either comes into existence or gains stability. Our analysis illustrates the predictive value of PRCs in circuit analysis and can be extended to provide a design method for pattern-generating circuits.

Animals↗

Analysis of the effects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems.

In a computational model of the bursting neuron R15, we have implemented proposed mechanisms for the modulation of two ionic currents (IR and ISI) that play key roles in regulating its spontaneous electrical activity. The model was sufficient to simulate a wide range of endogenous activity in the presence of various concentrations of serotonin (5-HT) or dopamine (DA). The model was also sufficient to simulate the responses of the neuron to extrinsic current pulses and the ways in which those responses were altered by 5-HT or DA. The results suggest that the actions of modulatory agents and second messengers on this neuron, and presumably other neurons, cannot be understood on the basis of their direct effects alone. It is also necessary to take into account the indirect effects of these agents on other unmodulated ion channels. These indirect effects occur through the dynamic interactions of voltage-dependent and calcium-dependent processes.

Animals↗

Afferent synaptic drive of rat medial nucleus tractus solitarius neurons: dynamic simulation of graded vesicular mobilization, release, and non-NMDA receptor kinetics.

1. We have developed a comprehensive mathematical model of an afferent synaptic connection to the soma of a medial nucleus tractus solitarius (mNTS) neuron. Model development is based on numerical fits to quantitative data recorded in our laboratory. This work is part of a continuing collaborative effort aimed at identifying and characterizing the mechanisms responsible for the non-linear integrative properties of this first synapse in the baroreceptor reflex. 2. The complete model consists of three major parts: 1) a Hodgkin-Huxley (HH)-type membrane model of the prejunctional sensory terminal bouton; 2) a multistage model describing vesicular storage, adenosine 3',5'-cyclic monophosphate (cAMP)- and Ca(2+)-dependent mobilization, release and recycling; and 3) a HH-type membrane model of the postjunctional mNTS cell that includes descriptions for a desensitizing non-N-methyl-D-aspartate (NMDA) ionic current that is responsible for the fast excitatory postsynaptic potentials (EPSPs) observed in mNTS cells. The membrane models for both the terminal bouton and the mNTS neuron are coupled to separate lumped fluid compartment models describing intracellular Ca2+ ion concentration dynamics. 3. Our modeling strategy is twofold. The first is to validate model performance by reproducing a wide variety of experimental data both from our laboratory and from the literature. The second is to explore the functional aspects of the model in order to gain a greater appreciation for the balance between presynaptic mechanisms (e.g., terminal membrane properties and vesicular dynamics) and postsynaptic mechanisms (e.g., non-NMDA receptor kinetics and neuronal dynamics) that underlie the afferent synaptic drive of mNTS neurons. 4. The model accurately reproduces EPSP dynamics recorded with the use of a wide range of stimulus protocols. The model can also mirror the unique pattern of graded frequency- and use-dependent reduction in peak EPSP magnitude observed experimentally through 60 s of constant, suprathreshold synaptic activation. We demonstrate how vesicular mobilization, recycling, and receptor kinetics can function synergistically in establishing synaptic transfer. Furthermore, we show that by allowing the aggregate rate of vesicle mobilization to respond in a use-dependent manner, it is possible to compensate for the attenuating affects of desensitization at elevated rates of stimulation. 5. Our simulations indicate that the low-frequency characteristics of this synapse are dominated by vesicular dynamics, whereas the high-frequency properties arise from a combination of Ca(2+)-dependent vesicular mobilization and the kinetics of the non-NMDA receptor. Desensitization can influence the peak magnitude and decay time of the EPSP, thereby affecting synaptic throughput. However, we demonstrate that, as the time course of neurotransmitter in the synaptic cleft decreases, the influence of desensitization should be somewhat diminished. As a result, the effective bandwidth of the synapse increases and becomes limited by the gating characteristics of the non-NMDA channel. 6. The model also includes a neuromodulatory aspect in that the frequency response of the synapse can be modulated by an adenylate cyclase-mediated regulatory mechanism. Although our simulations indicate the behavior of a limited number of possible neuromodulatory agents, the results demonstrate the pivotal role such agents could play in modifying synaptic transfer characteristics presynaptically. 7. Both continuous and burst-mode tract stimulation evoke patterns of action potentials in spontaneously active mNTS neurons that are mimicked very well by our model. Our simulations demonstrate that, as the rate of stimulation increases beyond approximately 20-30 Hz, the inherent low-pass frequency-response characteristics of the synapse limit the overall dynamic range of the mNTS neuron, causing the postsynaptic cell to "entrain" at frequencies within its normal operating range.

Afferent Pathways↗

Multiple modes of activity in a model neuron suggest a novel mechanism for the effects of neuromodulators.

1. Previous examination of the phase space of a mathematical model of a bursting molluscan neuron has demonstrated the existence of multiple stable oscillatory modes. The present study examined the extent to which multistability could be regulated by known modulatory agents, the consequences of that regulation on the response of the neuron to synaptic inputs, the effects of noise, and the potential of multistability to enrich the repertoire of neuromodulatory effects. 2. Coexisting stable attractors may appear when a change is made in a voltage-dependent conductance in a manner that simulates the application of a neuromodulator. A small transient perturbation can shift the model neuron between stable modes, greatly amplifying the original perturbation. Thus the model becomes more sensitive to conventional synaptic inputs. These mode shifts are robust in the presence of low-amplitude synaptic noise. 3. In response to random high-amplitude synaptic noise, a model neuron rendered multistable by a simulated application of a neuromodulator produces apparently random activity, whereas in response to the same synaptic noise, a monostable model neuron produces barely perturbed regular activity. Thus an increase in the number of attractors enhances sensitivity to both conventional synaptic inputs and noise. Conversely, a decrease is associated with a reduction in sensitivity. 4. The response of a neuron to a subsequent transient perturbation in the level of neuromodulator depends on the steady-state level of the neuromodulator. For example, if the steady-state level is associated with a multistable neuron, a mode shift produced by such a transient change in the level of neuromodulator (manifested in our model as a conductance change) can persist after the conductance is returned gradually to its original value. Thus multistable dynamic activity permits the effects of a neuromodulator to persist when the neuromodulator is no longer present. 5. The mechanism of mode shifting between coexisting stable oscillatory modes introduces a number of novel possibilities with potentially profound implications for information processing and storage in a single neuron.

Animals↗

Nonlinear dynamics in a model neuron provide a novel mechanism for transient synaptic inputs to produce long-term alterations of postsynaptic activity.

1. A mathematical model of a bursting molluscan neuron has been found to possess multiple modes of electrical activity, such as periodic beating (tonic firing), periodic bursting (bursts of action potentials separated by quiescent periods), and potentially chaotic bursting, all at a single set of parameters. The multiple modes correspond to multiple stable attractors, whose existence is an emergent property of the nonlinear dynamics of the system. 2. Transient synaptic inputs can switch the activity of the neuron between different modes. These mode transitions, which do not require any changes in the biochemical or biophysical parameters of the neuron, provide an enduring response to a transient input, as well as a mechanism for phasic sensitivity (i.e., temporal specificity). 3. These results provide new insights into the role of nonlinear dynamics in information processing and storage at the level of the single neuron.

Animals↗

Simulation of the bursting activity of neuron R15 in Aplysia: role of ionic currents, calcium balance, and modulatory transmitters.

1. An equivalent circuit model of the R15 bursting neuron in Aplysia has been combined with a fluid compartment model, resulting in a model that incorporates descriptions of most of the membrane ion channels that are known to exist in the somata of R15, as well as providing a Ca2+ balance on the cell. 2. A voltage-activated, calcium-inactivated Ca2+ current (denoted the slow inward current ISI) was sufficient to produce bursting activity without invoking any other calcium-dependent currents (such as a nonspecific cation current, INS, or a calcium-activated K+ current, IK,Ca). Furthermore, many characteristics of a typical R15 burst could be simulated, such as a parabolic variation in interspike interval, the depolarizing afterpotential (DAP), and the progressive decrease in the undershoots of spikes during a burst. 3. The dynamic activity of R15 was analyzed by separately characterizing two different temporal domains; the fast dynamics associated with action potentials and the slow dynamics associated with low-amplitude oscillations lasting tens of seconds ("slow waves"). The slow dynamics were isolated by setting the Na+ conductance (gNa) to zero and then studied by the use of a system of equations reduced to two variables: intracellular concentration of Ca2+ and membrane potential. The fixed point of the system was located at the intersection of the nullclines for these two variables. A stability analysis of the fixed point was then used to determine whether a given set of parameters would produce slow-wave activity. 4. If the reduced model predicted slow-wave oscillations for a given set of parameters with gNa set to zero, then bursting activity was observed for the same set of parameters in the full model with gNa reset to its control value. However, for certain sets of parameters with gNa at its usual value, the full model exhibited bursting activity because of a slow oscillation produced by the activation of INS by action potentials. This oscillation resulted from an interaction between the fast and slow dynamics that the reduced model alone could not predict and was not observed when gNa was subsequently set to zero. If gNS was also set to zero, this discrepancy disappeared.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

Routes to chaos in a model of a bursting neuron.

Chaotic regimens have been observed experimentally in neurons as well as in deterministic neuronal models. The R15 bursting cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. Previously, the model of Plant and Kim has been shown to exhibit both bursting and beating modes of electrical activity. In this report, we demonstrate (a) that a chaotic regime exists between the bursting and beating modes of the model, and (b) that the model approaches chaos from both modes by a period doubling cascade. The bifurcation parameter employed is the external stimulus current. In addition to the period doubling observed in the model-generated trajectories, a period three "window" was observed, power spectra that demonstrate the approaches to chaos were generated, and the Lyaponov exponents and the fractal dimension of the chaotic attractors were calculated. Chaotic regimes have been observed in several similar models, which suggests that they are a general characteristic of cells that exhibit both bursting and beating modes.

Animals↗