Rhythmic Bursting in the Pre-Bötzinger Complex

Mechanisms and Models

Ilya A. Rybak*,1; Yaroslav I. Molkov*,†; Patrick E. Jasinski*; Natalia A. Shevtsova*; Jeffrey C. Smith‡    * Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, PA, USA
† Department of Mathematical Sciences, Indiana University–Purdue University, Indianapolis, IN, USA
‡ Cellular and Systems Neurobiology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD, USA
1 Corresponding author: Tel.: + 1-215-9918596; Fax: + 1-215-8439082 rybak@drexel.edu

Abstract

The pre-Bötzinger complex (pre-BötC), a neural structure involved in respiratory rhythm generation, can generate rhythmic bursting activity in vitro that persists after blockade of synaptic inhibition. Experimental studies have identified two mechanisms potentially involved in this activity: one based on the persistent sodium current (INaP) and the other involving calcium (ICa) and/or calcium-activated nonspecific cation (ICAN) currents. In this modeling study, we investigated bursting generated in single neurons and excitatory neural populations with randomly distributed conductances of INaP and ICa. We analyzed the possible roles of these currents, the Na+/K+ pump, synaptic mechanisms, and network interactions in rhythmic bursting generated under different conditions. We show that a population of synaptically coupled excitatory neurons with randomly distributed INaP- and/or ICAN-mediated burst generating mechanisms can operate in different oscillatory regimes with bursting dependent on either current or independent of both. The existence of multiple oscillatory regimes and their state dependence may explain rhythmic activities observed in the pre-BötC under different conditions.

Keywords

neural oscillations

respiration

persistent sodium current

calcium-activated nonspecific cation current

sodium–potassium pump

1 Introduction

The pre-Bötzinger complex (pre-BötC), a medullary neural structure critically involved in respiratory rhythm generation in mammals, can in vitro generate synchronized neural oscillations that persist after pharmacological blockade of synaptic inhibition (Ramirez et al., 1996; Rekling and Feldman, 1998; Smith et al., 1991). Despite many years of intensive investigations, the neural mechanisms underlying these oscillations remain largely unknown.

Butera et al. (1999a,b) suggested that population bursting observed in the pre-BötC in vitro arises from the persistent (slowly inactivating) sodium current (INaP) in pre-BötC neurons and the excitatory synaptic interactions between these neurons. The presence of INaP in pre-BötC was confirmed (Del Negro et al., 2002a; Koizumi and Smith, 2008; Rybak et al., 2003a), and the pre-BötC rhythmic activity in medullary slices in vitro from neonatal rats could be abolished by the INaP blocker riluzole (Koizumi and Smith, 2008; Rybak et al., 2003b).

Alternatively, Thoby-Brisson and Ramirez (2001), using medullary slices from P6–P13 mice containing the pre-BötC, found two distinct types of intrinsically bursting cells whose bursting was, respectively, sensitive and insensitive to the calcium current blocker Cd2 +. Later, Peña et al. (2004) found that the Cd2 +-sensitive bursters were riluzole insensitive, whereas most of the Cd2 +-insensitive ones were riluzole sensitive. Furthermore, rhythmic activity in the Cd2 +-sensitive bursters could be blocked by flufenamic acid (FFA), a pharmacological blocker of the calcium-activated nonspecific cation current (ICAN) (Del Negro et al., 2005), suggesting that both ICa and ICAN are involved in bursting generated in the pre-BötC. Further studies of the possible role of ICAN and the metabotropic mechanisms involved in its activation (Beltran-Parrazal et al., 2012; Ben-Mabrouk et al., 2012; Krey et al., 2010; Pace and Del Negro, 2008; Pace et al., 2007; Rubin et al., 2009) produced inconsistent results. As a result, the involvement and specific roles of these and other possible sodium and calcium mechanisms in the bursting activity observed in the pre-BötC remain unresolved and require further investigation.

In this modeling study, we consider the intrinsic Na+- and Ca2 +-dependent bursting generated in single cells and heterogeneous populations of synaptically coupled excitatory neurons with conductances of INaP and ICa randomly distributed across neurons in the populations. We study the possible roles of synaptic interactions, ionotropic and metabotropic synaptic mechanisms, intracellular Ca2 + release, and the Na+/K+ pump in the cellular and network rhythmic bursting. We show that heterogeneous populations of excitatory neurons can generate rhythmic bursting dependent on INaP and/or ICAN, or independent of both, and that the involvement of each mechanism may depend on the neuronal excitation, strength of synaptic interactions, and expression of particular ionic channels. We suggest that the rhythmic bursting activity discovered in the pre-BötC in vitro is state dependent, and hence, depending on the state, the pre-BötC can operate in multiple oscillatory regimes involving different INaP- and/or ICAN-dependent mechanisms. We also support the previous suggestion that the electrogenic Na+/K+ pump can play an important role in the generation of this rhythmic bursting by performing the burst termination function in multiple regimes of oscillations. The results of this theoretical modeling study provide important insights into various rhythmic activities observed in the pre-BötC and possibly other brainstem and spinal cord circuits.

2 Methods

In this study, we used the computational models of single neurons and neuron populations with excitatory synaptic interactions developed and fully described by Jasinski et al. (2013). Specifically, the models of single neurons were developed in the Hodgkin–Huxley style. Formal descriptions of ionic channel kinetics and other cellular biophysical mechanisms in these models were derived from our previous models (Rybak et al., 2003a,b, 2007; Smith et al., 2007) and other recent models (Rubin et al., 2009; Toporikova and Butera, 2011).

The simulated populations contained N = 50 neurons with all-to-all fast glutamatergic-like excitatory synaptic interconnections. The heterogeneity of neurons within the population was provided by the uniformly distributed maximal conductances of leakage, persistent sodium, and calcium channels. The weights of synaptic interactions were also distributed (using a normal distribution).

The initial conditions for membrane potentials, intracellular calcium and sodium concentrations, and channel gating variables were chosen using a uniform distribution within the physiologically realistic ranges of values for each variable, and a settling period of 10–20 s was allowed in each simulation to make sure that the results are independent of initial conditions. Most simulations were repeated 10–20 times and demonstrated qualitatively similar behavior for all values of distributed parameters and initial conditions.

The full mathematical descriptions used the model and all simulation details can be found in our previous paper (Jasinski et al., 2013). All simulations were performed using custom written C++ software for a Linux-based operating system that ran locally on a 6-core workstation in the laboratory or remotely on the high-performance parallel cluster Biowulf at the National Institutes of Health, Bethesda, MD (http://biowulf.nih.gov).

3 Results

3.1 The Intrinsic Na+ and Ca2 +-Dependent Mechanisms for Single-Neuron Bursting

3.1.1 Bursting Mechanisms Involving Persistent (Slowly Inactivating) Sodium Current (INaP)

The presence of persistent (i.e., noninactivating) sodium current is not sufficient for a neuron to generate intrinsic bursting, there should be an additional burst-terminating mechanism. In the classical model of an INaP-dependent bursting neuron proposed by Butera et al. (1999a, Model 1), burst termination was based on the slow inactivation of the persistent sodium channels themselves. The other proposed burst-terminating mechanisms were based on the slowly activating, voltage-dependent (e.g., Butera et al., 1999a, Model 2) or calcium-dependent (e.g., El Manira et al., 1994; Ryczko et al., 2010) potassium currents. In our previous (Jasinski et al., 2013) and present studies, we have suggested and investigated the possible involvement of a mechanism based on the activity-dependent accumulation of sodium ions within the cell ([Na+]in), and subsequent...