Mechanism, dynamics, and biological existence of multistability in a large class of bursting neurons

📝 Abstract

Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynamical systems, is inherently suited to support multistability. We derive the bifurcation structure and parametric trends leading to multistability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to nonsynaptic mechanisms.

💡 Analysis

Multistability, the coexistence of multiple attractors in a dynamical system, is explored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynamical systems, is inherently suited to support multistability. We derive the bifurcation structure and parametric trends leading to multistability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to nonsynaptic mechanisms.

📄 Content

arXiv:0810.1544v3 [q-bio.NC] 28 Jun 2010 Multistable Bursting Mechanism, Dynamics, and Biological Existence of Multistability in a Large Class of Bursting Neurons Jonathan P Newman1, a) and Robert J Butera1, b) Wallace H. Coulter Dept. of Biomedical Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332-0535, USA (Dated: 18 November 2018) Multistability, the coexistence of multiple attractors in a dynamical system, is ex- plored in bursting nerve cells. A modeling study is performed to show that a large class of bursting systems, as defined by a shared topology when represented as dynam- ical systems, are inherently suited to support multistablity. We derive the bifurcation structure and parametric trends leading to mulitstability in these systems. Evidence for the existence of multirhythmic behavior in neurons of the aquatic mollusc Aplysia Californica that is consistent with our proposed mechanism is presented. Although these experimental results are preliminary, they indicate that single neurons may be capable of dynamically storing information for longer time scales than typically attributed to non-synaptic mechanisms. PACS numbers: 87.17.Aa, 87.85.dm Keywords: bursting, neuron, multistability, short-term memory, one-dimensional maps, invertebrate neuroscience a)Electronic mail: jnewman6@gatech.edu; http://www.prism.gatech.edu/ ˜jnewman6 b)Electronic mail: rbutera@gatech.edu; also atSchool of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332-0250, USA 1 Multistable Bursting Neurons that support bursting dynamics are a common feature of neural sys- tems. Due to their prevalence, great effort has been devoted to understand- ing the mechanisms underlying bursting and information processing capabilities that bursting dynamics afford. In this paper, we provide a link between neu- ronal bursting and information storage. Namely, we show that the mechanism implicit to bursting in certain neurons may allow near instantaneous modifi- cations of activity state that lasts indefinitely following sensory perturbation. Thus the intrinsic, extra-synaptic state of these neurons can serve as a memory of a sensory event. I. INTRODUCTION Bursting is a dynamic state characterized by alternating periods of fast oscillatory behav- ior and quasi-steady-state activity. Nerve cells commonly exhibit autonomous or induced bursting by firing discrete groups of action potentials in time. Autonomously bursting neu- rons are found in a variety of neural systems, from the mammalian cortex1 and brainstem2–4 to identified invertebrate neurons5,6. Multirhythmicity in a dynamical system is a specific type of multistability which describes the coexistence of two or more oscillatory attractors under a fixed parameter set. Multirhyth- micity has been shown to occur in vertebrate motor neurons7, invertebrate interneurons8, and in small networks of coupled invertebrate neurons9. Additionally, multirhythmicity has been demonstrated in models of intracellular calcium oscillations10 and coupled genetic oscillators11. Multistable systems can act as switches in response to an external input. The feasi- bility of multistability as an information storage and processing mechanism in neural sys- tems has been widely discussed in terms of neural recurrent loops and delayed feedback mechanisms12–14. Theoretical studies have shown multirhythmic bursting behavior in a number of single neuron models15,16 as well as in a model two-cell inhibitory (half-center oscillator) network17. In biological neurons, it is possible these dynamics are employed as a short-term memory. In this report provide a general explanation for the existence of multi- rhythmic bursting in previous studies15,16,18 and the characteristics of a bursting neuron that 2 Multistable Bursting allow multirhythmic dynamics. Additionally, we provide experimental evidence suggesting the existence of this behavior in several identified bursting neurons of the aquatic mullusc Aplysia Californica. II. A SIMPLE PARABOLIC BURSTING MODEL Dynamical bursting systems are a subset of the singularly perturbed (SP) class of differ- ential equations, ˙x = f(x, y), (1) ˙y = ǫg(x, y), x ∈Rm, y ∈Rn, (2) where 0 ≤ǫ is a small parameter. Using singular perturbation methods19,20, the dynamics of bursting models can be explored by decomposing the full system into fast and slow- subsystems: Eq. 1 and Eq. 2, respectively. The slow-subsystem can act independently21, be affected synaptically17, or interact locally with the spiking fast-subsystem5,15–17 to produce alternating periods of spiking and silence in time. To examine the dynamical mechanism implicit to a bursting behavior, y is treated as a bifurcation parameter of the fast-subsystem. This is formally correct when ǫ = 0 and Eq. 2 degenerates into an algebraic equation, but the assumption is reasonable when there is large time separation between fast and slow dynamics. Using this technique, all autonomously bursting

This content is AI-processed based on ArXiv data.