Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons

Activity of neurons in the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem drives the inspiratory phase of the respiratory rhythm. Experimental results have suggested that multiple bursting mechanisms based on a calcium-activated nonspecific cationic (CAN) current, a persistent sodium (NaP) current, and calcium dynamics may be incorporated within the pre-BötC. Previous modeling works have incorporated representations of some or all of these mechanisms. In this study, we consider a single-compartment model of a pre-BötC inspiratory neuron that encompasses particular aspects of all of these features. We present a novel mathematical analysis of the interaction of the corresponding rhythmic mechanisms arising in the model, including square-wave bursting and autonomous calcium oscillations, which requires treatment of a system of differential equations incorporating three slow variables.     

Dual oscillator model of the respiratory neuronal network generating quantal slowing of respiratory rhythm

We developed a dual oscillator model to facilitate the understanding of dynamic interactions between the parafacial respiratory group (pFRG) and the preBötzinger complex (preBötC) neurons in the respiratory rhythm generation. Both neuronal groups were modeled as groups of 81 interconnected pacemaker neurons; the bursting cell model described by Butera and others [model 1 in Butera et al. (J Neurophysiol 81:382–397, 1999a)] were used to model the pacemaker neurons. We assumed (1) both pFRG and preBötC networks are rhythm generators, (2) preBötC receives excitatory inputs from pFRG, and pFRG receives inhibitory inputs from preBötC, and (3) persistent Na⁺ current conductance and synaptic current conductances are randomly distributed within each population. Our model could reproduce 1:1 coupling of bursting rhythms between pFRG and preBötC with the characteristic biphasic firing pattern of pFRG neurons, i.e., firings during pre-inspiratory and post-inspiratory phases. Compatible with experimental results, the model predicted the changes in firing pattern of pFRG neurons from biphasic expiratory to monophasic inspiratory, synchronous with preBötC neurons. Quantal slowing, a phenomena of prolonged respiratory period that jumps non-deterministically to integer multiples of the control period, was observed when the excitability of preBötC network decreased while strengths of synaptic connections between the two groups remained unchanged, suggesting that, in contrast to the earlier suggestions (Mellen et al., Neuron 37:821–826, 2003; Wittmeier et al., Proc Natl Acad Sci USA 105(46):18000–18005, 2008), quantal slowing could occur without suppressed or stochastic excitatory synaptic transmission. With a reduced excitability of preBötC network, the breakdown of synchronous bursting of preBötC neurons was predicted by simulation. We suggest that quantal slowing could result from a breakdown of synchronized bursting within the preBötC.     

Multiple timescale mixed bursting dynamics in a respiratory neuron model

Experimental results in rodent medullary slices containing the pre-Bötzinger complex (pre-BötC) have identified multiple bursting mechanisms based on persistent sodium current (I _NaP) and intracellular Ca²⁺. The classic two-timescale approach to the analysis of pre-BötC bursting treats the inactivation of I _NaP, the calcium concentration, as well as the Ca²⁺-dependent inactivation of IP ₃ as slow variables and considers other evolving quantities as fast variables. Based on its time course, however, it appears that a novel mixed bursting (MB) solution, observed both in recordings and in model pre-BötC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BötC inspiratory neuron that can exhibit both I _NaP and Ca²⁺ oscillations and has the ability to produce MB solutions. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to better understand the mechanisms underlying the MB solution pattern. Rather surprisingly, we discover that a third timescale is not actually required to generate mixed bursting solutions. Through our analysis of timescales, we also elucidate how the pre-BötC neuron model can be tuned to improve the robustness of the MB solution.     

The role of spiking and bursting pacemakers in the neuronal control of breathing

Breathing is controlled by a distributed network involving areas in the neocortex, cerebellum, pons, medulla, spinal cord, and various other subcortical regions. However, only one area seems to be essential and sufficient for generating the respiratory rhythm: the preBötzinger complex (preBötC). Lesioning this area abolishes breathing and following isolation in a brain slice the preBötC continues to generate different forms of respiratory activities. The use of slice preparations led to a thorough understanding of the cellular mechanisms that underlie the generation of inspiratory activity within this network. Two types of inward currents, the persistent sodium current (I_NaP) and the calcium-activated non-specific cation current (I_CAN), play important roles in respiratory rhythm generation. These currents give rise to autonomous pacemaker activity within respiratory neurons, leading to the generation of intrinsic spiking and bursting activity. These membrane properties amplify as well as activate synaptic mechanisms that are critical for the initiation and maintenance of inspiratory activity. In this review, we describe the dynamic interplay between synaptic and intrinsic membrane properties in the generation of the respiratory rhythm and we relate these mechanisms to rhythm generating networks involved in other behaviors.     

Modeling the effects of extracellular potassium on bursting properties in pre-Bötzinger complex neurons

There are many types of neurons that intrinsically generate rhythmic bursting activity, even when isolated, and these neurons underlie several specific motor behaviors. Rhythmic neurons that drive the inspiratory phase of respiration are located in the medullary pre-Bötzinger Complex (pre-BötC). However, it is not known if their rhythmic bursting is the result of intrinsic mechanisms or synaptic interactions. In many cases, for bursting to occur, the excitability of these neurons needs to be elevated. This excitation is provided in vitro (e.g. in slices), by increasing extracellular potassium concentration (K _out ) well beyond physiologic levels. Elevated K _out shifts the reversal potentials for all potassium currents including the potassium component of leakage to higher values. However, how an increase in K _out , and the resultant changes in potassium currents, induce bursting activity, have yet to be established. Moreover, it is not known if the endogenous bursting induced in vitro is representative of neural behavior in vivo. Our modeling study examines the interplay between K _out , excitability, and selected currents, as they relate to endogenous rhythmic bursting. Starting with a Hodgkin-Huxley formalization of a pre-BötC neuron, a potassium ion component was incorporated into the leakage current, and model behaviors were investigated at varying concentrations of K _out . Our simulations show that endogenous bursting activity, evoked in vitro by elevation of K _out , is the result of a specific relationship between the leakage and voltage-dependent, delayed rectifier potassium currents, which may not be observed at physiological levels of extracellular potassium.     

Developmental nicotine exposure enhances inhibitory synaptic transmission in motor neurons and interneurons critical for normal breathing

Nicotine exposure in utero negatively affects neuronal growth, differentiation, and synaptogenesis. We used rhythmic brainstems slices and immunohistochemistry to determine how developmental nicotine exposure (DNE) alters inhibitory neurotransmission in two regions essential to normal breathing, the hypoglossal motor nucleus (XIIn), and preBötzinger complex (preBötC). We microinjected glycine or muscimol (GABA_A agonist) into the XIIn or preBötC of rhythmic brainstem slices from neonatal rats while recording from XII nerve roots to obtain XII motoneuron population activity. Injection of glycine or muscimol into the XIIn reduced XII nerve burst amplitude, while injection into the preBötC altered nerve burst frequency. These responses were exaggerated in preparations from DNE animals. Quantitative immunohistochemistry revealed a significantly higher GABA_A receptor density on XII motoneurons from DNE pups. There were no differences in GABA_A receptor density in the preBötC, and there were no differences in glycine receptor expression in either region. Nicotine, in the absence of other chemicals in tobacco smoke, alters normal development of brainstem circuits that are critical for normal breathing. © 2015 Wiley Periodicals, Inc. Develop Neurobiol 76: 337–354, 2016     

Multiple modes of a conditional neural oscillator

We present a model for a conditional bursting neuron consisting of five conductances: Hodgkin-Huxley type time- and voltage-dependent Na⁺ and K⁺ conductances, a calcium activated voltage-dependent K⁺ conductance, a calcium-inhibited time- and voltage-dependent Ca⁺⁺ conductance, and a leakage Cl(_– conductance. With an initial set of parameters (versionS), the model shows a hyperpolarized steady-state membrane potential at which the neuron is silent. Increasingg _Na and decreasingg _Cl, whereg _i , is the maximal conductance for speciesi, produces bursts of action potentials (BursterN). Alternatively, an increase ing _Ca produces a different bursting state (BursterC). The two bursting states differ in the periods and amplitudes of their bursting pacemaker potentials. They show different steady-stateI–V curves under simulated voltage-clamp conditions; in simulations that mimic a steady-stateI–V curve taken under experimental conditions only BursterN shows a negative slope resistance region. ModelC continues to burst in the presence of TTX, while bursting in ModelN is suppressed in TTX. Hybrid models show a smooth transition between the two states.     

First return maps for the dynamics of synaptically coupled conditional bursters

The pre-Bötzinger complex (preBötc) in the mammalian brainstem has an important role in generating respiratory rhythms. An influential differential equation model for the activity of individual neurons in the preBötc yields transitions from quiescence to bursting to tonic spiking as a parameter is varied. Further, past work has established that bursting dynamics can arise from a pair of tonic model cells coupled with synaptic excitation. In this paper, we analytically derive one- and two-dimensional maps from the differential equations for a self-coupled neuron and a two-neuron network, respectively. Using a combination of analysis and simulations of these maps, we explore the possible forms of dynamics that the model networks can produce as well as which transitions between dynamic regimes are mathematically possible.     

Convergent neuromodulation onto a network neuron can have divergent effects at the network level

Different neuromodulators often target the same ion channel. When such modulators act on different neuron types, this convergent action can enable a rhythmic network to produce distinct outputs. Less clear are the functional consequences when two neuromodulators influence the same ion channel in the same neuron. We examine the consequences of this seeming redundancy using a mathematical model of the crab gastric mill (chewing) network. This network is activated in vitro by the projection neuron MCN1, which elicits a half-center bursting oscillation between the reciprocally-inhibitory neurons LG and Int1. We focus on two neuropeptides which modulate this network, including a MCN1 neurotransmitter and the hormone crustacean cardioactive peptide (CCAP). Both activate the same voltage-gated current (I _MI ) in the LG neuron. However, I _MI-MCN1 , resulting from MCN1 released neuropeptide, has phasic dynamics in its maximal conductance due to LG presynaptic inhibition of MCN1, while I _MI-CCAP retains the same maximal conductance in both phases of the gastric mill rhythm. Separation of time scales allows us to produce a 2D model from which phase plane analysis shows that, as in the biological system, I _MI-MCN1 and I _MI-CCAP primarily influence the durations of opposing phases of this rhythm. Furthermore, I _MI-MCN1 influences the rhythmic output in a manner similar to the Int1-to-LG synapse, whereas I _MI-CCAP has an influence similar to the LG-to-Int1 synapse. These results show that distinct neuromodulators which target the same voltage-gated ion channel in the same network neuron can nevertheless produce distinct effects at the network level, providing divergent neuromodulator actions on network activity.     

Computational study on neuronal activities arising in the pre-Bötzinger complex

Experimental investigations have shown that the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem generates the inspiratory phase of respiratory rhythm. Based on a single-compartment model of a pre-BötC inspiratory neuron, we, in this paper, use semi-analytical, numerical as well as fast-slow dynamical methods to investigate the effects of sodium conductance (\(g_{\text{Na}}\)) and potassium conductance (\(g_{{\text{K}}}\)) on the firing activities of pre-BötC and try to reveal the dynamical mechanisms behind them. We show how \(g_{{\text{Na}}}\) and \(g_{\text{K}}\) affect the bifurcations of the fast-subsystem and how the the firing patterns of pre-BötC transit according to the bifurcations.     

Evolution of protein transport to the chloroplast envelope membranes

Comparing with other angiosperms, most members within the family Orchidaceae have lower photosynthetic capacities. However, the underlying mechanisms remain unclear. Cypripedium and Paphiopedilum are closely related phylogenetically in Orchidaceae, but their photosynthetic performances are different. We explored the roles of internal anatomy and diffusional conductance in determining photosynthesis in three Cypripedium and three Paphiopedilum species, and quantitatively analyzed their diffusional and biochemical limitations to photosynthesis. Paphiopedilum species showed lower light-saturated photosynthetic rate (A _N), stomatal conductance (g _s), and mesophyll conductance (g _m) than Cypripedium species. A _N was positively correlated with g _s and g _m. And yet, in both species A _N was more strongly limited by g _m than by biochemical factors or g _s. The greater g _s of Cypripedium was mainly affected by larger stomatal apparatus area and smaller pore depth, while the less g _m of Paphiopedilum was determined by the reduced surface area of mesophyll cells and chloroplasts exposed to intercellular airspace per unit of leaf area, and much thicker cell wall thickness. These results suggest that leaf anatomical structure is the key factor affecting g _m, which is largely responsible for the difference in photosynthetic capacity between those two genera. Our findings provide new insight into the photosynthetic physiology and functional diversification of orchids.     

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca²⁺ current I _s, and the Ca²⁺ -activated K⁺ current I _KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.     

Mechanisms of membrane potential oscillation in bursting neurons on the snail,Helix pomatia

• 1.1. The mechanism of generation of membrane potential (MP) oscillations was studied in identified bursting neurons from the snail Helix pomatia.
• 2.2. Long-lasting stimulation of an identified peptidergic interneuron produced a persistent bursting activity in a non-active burster.
• 3.3. External application of calcium channel blockers (1 mM Cd²⁺ or 5 mM La²⁺) resulted in a transient increase in the slow-wave amplitude and subsequent prevention of pacemaker activity generation in bursting neurons. Application of these blockers together with endogenous neuropeptide initiating bursting activity generation, increased MP wave amplitude without prevention of bursting activity generation.
• 4.4. Replacement of all NaCl in normal Ringer's solution with isoosmotic CaCl₂, glucose or Tris-HCl produced a reversible block of bursting activity generation. Stationary current-voltage relation (CVR) of bursting neuron membrane has a region of negative resistance (NRR) and does not intersect the potential axis in threshold region for action potential (AP) generation in normal Ringer's solution. In Na-free solution stationary CVR is linear and intersects the potential axis near — 52 mV.
• 5.5. Novel potential- and time-dependent outward (E_rev = − 58 mV) current, I_B, activated by hyperpolarization was found in the bursting neuron membrane. Having achieved a maximal value, this current decayed with a time constant of about 1 sec. Hyperpolarization inactivated maximal conductance, g_B, responsible for I_B, and depolarization abolished inactivation of g_B.
• 6.6. Short-lasting (0.01 sec) hyperpolarization of the bursting neuron membrane by inward current pulse induced the development of prolonged hyperpolarization wave lasting up to 10 sec.
• 7.7. These results suggest that: (a) persistent bursting activity of RPal neuron in the snail Helix pomatia is not endogenous but is due to a constant activation of peptidergic synaptic inputs of these neurons; (b) Ca²⁺ ions do not play a pivotal role in the ionic mechanism of MP oscillations but play a determining role in the process of secretion of a peptide initiating bursting activity by the interneuron presynaptic terminal; (c) depolarizing phase of the MP wave is due to specific properties of stationary CVR and hyperpolarization phase is due to regenerative properties of hyperpolarization-activated outward current I_B. The minimal mathematical version of MP oscillations based on the experimental data is presented.

     

<Emphasis Type="BoldItalic">In vivo</Emphasis> conditions influence the coding of stimulus features by bursts of action potentials

The functional role of burst firing (i.e. the firing of packets of action potentials followed by quiescence) in sensory processing is still under debate. Should bursts be considered as unitary events that signal the presence of a particular feature in the sensory environment or is information about stimulus attributes contained within their temporal structure? We compared the coding of stimulus attributes by bursts in vivo and in vitro of electrosensory pyramidal neurons in weakly electric fish by computing correlations between burst and stimulus attributes. Our results show that, while these correlations were strong in magnitude and significant in vitro, they were actually much weaker in magnitude if at all significant in vivo. We used a mathematical model of pyramidal neuron activity in vivo and showed that such a model could reproduce the correlations seen in vitro, thereby suggesting that differences in burst coding were not due to differences in bursting seen in vivo and in vitro. We next tested whether variability in the baseline (i.e. without stimulation) activity of ELL pyramidal neurons could account for these differences. To do so, we injected noise into our model whose intensity was calibrated to mimic baseline activity variability as quantified by the coefficient of variation. We found that this noise caused significant decreases in the magnitude of correlations between burst and stimulus attributes and could account for differences between in vitro and in vivo conditions. We then tested this prediction experimentally by directly injecting noise in vitro through the recording electrode. Our results show that this caused a lowering in magnitude of the correlations between burst and stimulus attributes in vitro and gave rise to values that were quantitatively similar to those seen under in vivo conditions. While it is expected that noise in the form of baseline activity variability will lower correlations between burst and stimulus attributes, our results show that such variability can account for differences seen in vivo. Thus, the high variability seen under in vivo conditions has profound consequences on the coding of information by bursts in ELL pyramidal neurons. In particular, our results support the viewpoint that bursts serve as a detector of particular stimulus features but do not carry detailed information about such features in their structure.     

Simulation of bursting activity in theHelix RPa1 neuron: Role of calcium ions

A model of bursting activity in the RPal neuron of the snailHelix pomatia has been developed. In this model, calcium conductances do not play a key role in generation of slow oscillations of membrane potential (MP). The possibility of simulating the maintenance of bursting in the presence of cadmium ions is shown. Inclusion in the model of the calcium-inactivated calcium conductance makes it possible to reproduce both adaptation of the neuron to constant polarizing current, which modifies bursting, and the development of slow inward current when MP is clamped at different phases at the slow wave. In our simulations, the characteristic properties of bursts (such as an increase in the frequency of action potentials and a decrease in spike undershoot at the beginning of a burst) are due to the cumulative inactivation of potassium current. The advantages of the presented mathematical model of bursting compared with other models are discussed.Neirofiziologiya/Neurophysiology, Vol. 26, No. 5, pp. 373–381, September–October, 1994.     

Mesophyll conductance to CO<Subscript>2</Subscript> in leaves of Siebold’s beech (<Emphasis Type="Italic">Fagus crenata</Emphasis>) seedlings under elevated ozone

Ozone is an air pollutant that negatively affects photosynthesis in woody plants. Previous studies suggested that ozone-induced reduction in photosynthetic rates is mainly attributable to a decrease of maximum carboxylation rate (V_cmax) and/or maximum electron transport rate (J_max) estimated from response of net photosynthetic rate (A) to intercellular CO₂ concentration (C_i) (A/C_i curve) assuming that mesophyll conductance for CO₂ diffusion (g_m) is infinite. Although it is known that C_i-based V_cmax and J_max are potentially influenced by g_m, its contribution to ozone responses in C_i-based V_cmax and J_max is still unclear. In the present study, therefore, we analysed photosynthetic processes including g_m in leaves of Siebold’s beech (Fagus crenata) seedlings grown under three levels of ozone (charcoal-filtered air or ozone at 1.0- or 1.5-times ambient concentration) for two growing seasons in 2016–2017. Leaf gas exchange and chlorophyll fluorescence were simultaneously measured in July and September of the second growing season. We determined the A, stomatal conductance to water vapor and g_m, and analysed A/C_i curve and A/C_c curve (C_c: chloroplast CO₂ concentration). We also determined the Rubisco and chlorophyll contents in leaves. In September, ozone significantly decreased C_i-based V_cmax. At the same time, ozone decreased g_m, whereas there was no significant effect of ozone on C_c-based V_cmax or the contents of Rubisco and chlorophyll in leaves. These results suggest that ozone-induced reduction in C_i-based V_cmax is a result of the decrease in g_m rather than in carboxylation capacity. The decrease in g_m by elevated ozone was offset by an increase in C_i, and C_c did not differ depending on ozone treatment. Since C_c-based V_cmax was also similar, A was not changed by elevated ozone. We conclude that g_m is an important factor for reduction in C_i-based V_cmax of Siebold’s beech under elevated ozone.     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Stomatal conductance in mature deciduous forest trees exposed to elevated CO<Subscript>2</Subscript>

Stomatal conductance (g _s) of mature trees exposed to elevated CO₂ concentrations was examined in a diverse deciduous forest stand in NW Switzerland. Measurements of g _s were carried out on upper canopy foliage before noon, over four growing seasons, including an exceptionally dry summer (2003). Across all species reductions in stomatal conductance were smaller than 25% most likely around 10%, with much variation among species and trees. Given the large heterogeneity in light conditions within a tree crown, this signal was not statistically significant, but the responses within species were surprisingly consistent throughout the study period. Except during a severe drought, stomatal conductance was always lower in trees of Carpinus betulus exposed to elevated CO₂ compared to Carpinus trees in ambient air, but the difference was only statistically significant on 2 out of 15 days. In contrast, stomatal responses in Fagus sylvatica and Quercus petraea varied around zero with no consistent trend in relation to CO₂ treatment. During the 2003 drought in the third treatment year, the CO₂ effect became reversed in Carpinus, resulting in higher g _s in trees exposed to elevated CO₂ compared to control trees, most likely due to better water supply because of the previous soil water savings. This was supported by less negative predawn leaf water potential in CO₂ enriched Carpinus trees, indicating an improved water status. These findings illustrate (1) smaller than expected CO₂-effects on stomata of mature deciduous forest trees, and (2) the possibility of soil moisture feedback on canopy water relations under elevated CO₂.     

Two types of independent bursting mechanisms in inspiratory neurons: an integrative model

The network of coupled neurons in the pre-Bötzinger complex (pBC) of the medulla generates a bursting rhythm, which underlies the inspiratory phase of respiration. In some of these neurons, bursting persists even when synaptic coupling in the network is blocked and respiratory rhythmic discharge stops. Bursting in inspiratory neurons has been extensively studied, and two classes of bursting neurons have been identified, with bursting mechanism depends on either persistent sodium current or changes in intracellular Ca²⁺, respectively. Motivated by experimental evidence from these intrinsically bursting neurons, we present a two-compartment mathematical model of an isolated pBC neuron with two independent bursting mechanisms. Bursting in the somatic compartment is modeled via inactivation of a persistent sodium current, whereas bursting in the dendritic compartment relies on Ca²⁺ oscillations, which are determined by the neuromodulatory tone. The model explains a number of conflicting experimental results and is able to generate a robust bursting rhythm, over a large range of parameters, with a frequency adjusted by neuromodulators.     

Identifying Crucial Parameter Correlations Maintaining Bursting Activity

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, _Leak; a persistent K current, _K2; and of a persistent Na+ current, _P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of _Leak, _K2, and _P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.