Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations Jonathan E. Rubina,1, John A. Hayesb,c,1, Jeffrey L. Mendenhallb, and Christopher A. Del Negrob,2 aDepartment of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, PA 15260; bDepartment of Applied Science, 318 McGlothlin-Street Hall, The College of William and Mary, Williamsburg, VA 23187-8795; and cDepartment of Biology, Integrated Science Center 1, The College of William and Mary, Williamsburg, VA 23187-8795 Edited by Nancy J. Kopell, Boston University, Boston, MA, and approved December 24, 2008 (received for review September 6, 2008) Central pattern generators (CPGs) produce neural-motor rhythms that AMPA receptors that, together, increase intracellular Ca2ϩ (11). 2ϩ often depend on specialized cellular or synaptic properties such as ICAN is normally latent, but this synaptically triggered Ca flux pacemaker neurons or alternating phases of synaptic inhibition. evokes ICAN, which underlies the burst phase of network activity Motivated by experimental evidence suggesting that activity in the (12, 13). ICAN may be well suited to play a central role in a group mammalian respiratory CPG, the preBo¨tzinger complex, does not pacemaker because it contributes to plateau depolarizations in require either of these components, we present and analyze a diverse contexts such as spinal locomotor networks (14), autonomic mathematical model demonstrating an unconventional mechanism motor systems (15), subthalamic neurons (16), and the entorhinal of rhythm generation in which glutamatergic synapses and the cortex (17), among others. short-term depression of excitatory transmission play key rhythmo- Our model shows how recurrent excitation and ICAN generate a -genic roles. Recurrent synaptic excitation triggers postsynaptic Ca2؉ burst and, further, predicts that ICAN hastens burst termination by activated nonspecific cation current (ICAN) to initiate a network-wide causing voltage-dependent spike inactivation. The attenuation of burst. Robust depolarization due to I also causes voltage-depen- CAN spikes diminishes recurrent excitation, yielding a form of synaptic dent spike inactivation, which diminishes recurrent excitation and depression that deactivates I . This deactivation in turn allows thus attenuates postsynaptic Ca2؉ accumulation. Consequently, ac- CAN tivity-dependent outward currents—produced by Na/K ATPase activity-dependent outward currents to interrupt spiking and es- pumps or other ionic mechanisms—can terminate the burst and cause tablish a quiescent phase. The eventual resumption of spontaneous a transient quiescent state in the network. The recovery of sporadic spiking restarts recurrent positive feedback and initiates a new spiking activity rekindles excitatory interactions and initiates a new cycle, leading to systematic burst oscillations of the network. cycle. Because synaptic inputs gate postsynaptic burst-generating With synaptic signals gating burst-generating ion channels in conductances, this rhythm-generating mechanism represents a new postsynaptic neurons, the group pacemaker model provides a new paradigm that can be dubbed a ‘group pacemaker’ in which the basic paradigm for CPG activity in which the rhythmogenic unit is the rhythmogenic unit encompasses a fully interdependent ensemble of ensemble of coupled synaptic and intrinsic membrane properties. synaptic and intrinsic components. This conceptual framework should Physiological studies of respiratory rhythmogenesis guided the be considered as an alternative to traditional models when analyzing model formulation, yet it incorporates general elements that are CPGs for which mechanistic details have not yet been elucidated. found across a variety of brain areas. CPGs are ubiquitous through- out the animal kingdom and the rhythmogenic mechanisms are breathing ͉ burst mechanism ͉ central pattern generator often incompletely understood. Given its relevance to the preBo¨tC and the tendency for successful mechanisms to be harnessed across entral pattern generator networks produce neural rhythms that brain regions and among diverse species, the group pacemaker NEUROSCIENCE Cdrive motor behaviors (1, 2). Many CPGs function in reduced model presents a viable alternative to bursting-pacemaker neurons, preparations in vitro, which facilitates studies at the cellular and reciprocal inhibition, or conventional network oscillations as the synaptic levels. Building blocks such as bursting-pacemaker neurons basis for network-level rhythmogenesis. and reciprocal synaptic inhibition often form the core of the rhythmogenic mechanism (3). However, the CPG for inspiratory Results breathing movements in mammals, the preBo¨tzinger Complex Model neurons with Hodgkin-Huxley-style spike-generating and (preBo¨tC) (4, 5), exhibits rhythmicity after removal of synaptic leak currents, and ICAN, were mutually coupled via ionotropic inhibition (6, 7) and after blockade of bursting-pacemaker activity AMPA receptors and group I mGluRs, which elevated intracellular 2ϩ in individual neurons (8, 9). Ca to activate ICAN (Fig. S1). We set intrinsic properties such that, A group pacemaker has been proposed as the building block of in the absence of coupling, one neuron (N2) was quiescent and the an alternative paradigm for respiratory rhythmogenesis (10). The other (N1) spiked tonically (Fig. 1A). Nevertheless, both neurons group pacemaker concept refers to a network that employs recur- rent synaptic excitation to boost and spread activity like a conven- tional network oscillator (3), yet generates bursting oscillations in Author contributions: J.E.R., J.A.H., and C.A.D.N. designed research; J.E.R., J.A.H., and which cells show a plateau depolarization—or drive potential— C.A.D.N. performed research; J.A.H. and J.L.M. contributed new reagents/analytic tools; during the active phase, as typically associated with intrinsic pace- J.E.R., J.A.H., and C.A.D.N. analyzed data; and J.E.R., J.A.H., and C.A.D.N. wrote the paper. maker properties. Until recently, the group pacemaker model has The authors declare no conflict of interest. remained purely heuristic and hypothetical, without an explicit This article is a PNAS Direct Submission. mathematical instantiation or mechanistic connection to experi- Freely available online through the PNAS open access option. mental findings. 1J.E.R. and J.A.H. contributed equally to this work. We tested the viability of an experimentally motivated group 2To whom correspondence should be addressed. E-mail: [email protected]. 2ϩ pacemaker model, where neurons express a Ca -activated non- This article contains supporting information online at www.pnas.org/cgi/content/full/ specific monovalent cation current (ICAN) with its activation linked 0808776106/DCSupplemental. to group I metabotropic glutamate receptors (mGluRs) and © 2009 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0808776106 PNAS ͉ February 24, 2009 ͉ vol. 106 ͉ no. 8 ͉ 2939–2944 Downloaded by guest on September 25, 2021 Ca2ϩ stopped accumulating. Extrusion and sequestration then A B * 2ϩ 20 mV dominated the Ca dynamics and Ca1 and Ca2 declined, deacti- vating ICAN. After this decline and associated relief of depolariza- V 1 1 µM tion block, the cells resumed tonic spiking, which quickly ramped up Ca1 in frequency through reciprocal synaptic excitation, such that the 0.05 s2 cycle repeated with no significant pauses between bursts (Fig. 1B). 2ϩ * 100 ms We analyzed how Ca and synaptic dynamics govern bursting behavior in the model by computing a bifurcation diagram for a single cell that was tonically active in isolation but, when self- V 2 coupled, displayed burst-like oscillations (Fig. 1C) that resemble the Ca2 2-cell case (Fig. 1B). We determined the voltage and synaptic ϩ s1 dynamics for fixed Ca2 within a range of physiological values, because the rate of change of Ca2ϩ is small compared with voltage C and s. The resulting diagram shows that for each sufficiently low 2ϩ 20 mV level of Ca , the stable feature is a periodic orbit, corresponding to large-amplitude spiking. As Ca2ϩ increases to a critical value 2ϩ 50 ms (Ca )AH, a supercritical Andronov-Hopf (AH) bifurcation occurs, beyond which the only stable state corresponds to depolarization 6 block (Fig. 1D). D E AH Fig. 1D superimposes the voltage and Ca2ϩ components of the 20 solution trajectory onto the bifurcation diagram. Because the 4 ) periodic orbit amplitudes remain relatively constant (red) until very -2 close to the AH bifurcation, spike attenuation does not begin until (10 ϩ ϩ s 2 2 null 2 Ca reaches (Ca )AH (red-blue). Spike amplitudes do not de- V(mV) Ca 2ϩ 2ϩ crease rapidly when Ca exceeds (Ca )AH (blue-green) because -60 0 the depolarization block steady state is weakly attracting, i.e., linearization about this stable state yields eigenvalues with negative 00.51.01.5 0 0.5 1.0 1.5 real parts of small magnitude. 2+ 2+ Ca (µM) Ca (µM) The curve in state space at which the rate of change of Ca2ϩ switches signs is called the Ca2ϩ nullcline and is naturally visualized Fig. 1. Group pacemaker models. (A and B) Uncoupled (A) and coupled (B) 2ϩ 2ϩ model neurons, showing voltage (V), Ca2ϩ, and synaptic dynamics (s). Neuron in the s-Ca phase plane because Ca changes are synaptically 2ϩ 2ϩ 1(N1, top) is initially tonic (A) and Neuron 2 (N2, bottom) is initially quiescent driven (11). During spiking, s and Ca increase (Fig. 1E, red). Ca 2ϩ (A), before coupling (B). (C) Self-coupled single neuron with dynamics that eventually exceeds (Ca )AH, and spikes diminish (blue). Voltage ϩ resemble the 2-neuron case. Color coding applies to phase-plane analyses in is not visible in the s-Ca2 plane, but because Fig. 1 D and E share D and E. (D) V-Ca2ϩ bifurcation diagram (black) with solution trajectory. Solid the same Ca2ϩ axis, the voltage in Fig. 1E can be deduced from Fig. (dashed) black curves denote stable (unstable) structures, which are either 1D based on whether Ca2ϩ is increasing or decreasing along the nodes or the maximal and minimal voltages along families of periodic orbits. bifurcation diagram.