Deterministic chaos in mathematical model of pacemaker activity in bursting neurons of snail, Helix pomatia. 1996

A O Komendantov, and N I Kononenko
Department of Mathematical and Technical Methods Application in Biology and Medicine, V. M. Glushkov Institute of Cybernetics, Kiev, Ukraine.

Chaotic regimes in a mathematical model of pacemaker activity in the bursting neurons of a snail Helix pomatia, have been investigated. The model includes a slow-wave generating mechanism, a spike-generating mechanism, an inward Ca current, intracellular Ca ions, [Ca2+]in, their fast buffering and uptake by intracellular Ca stores, and a [Ca2+]in-inhibited Ca current. Chemosensitive voltage-activated conductance, gB*, responsible for termination of the spike burst, and chemosensitive sodium conductance, gNa*, responsible for the depolarization phase of the slow-wave, were used as control parameters. These conductances in intact snail bursting neuron are regulated by neuropeptides. Time courses of the membrane potential and [Ca2+]in were employed to analyse different regimes in the model. Histograms of interspike intervals, autocorrelograms, spectral characteristics, one-dimensional return maps, phase plane trajectories, positive Lyapunov exponent and especially cascades of period-doubling bifurcations demonstrate that approaches to chaos were generated. The bifurcation diagram as a function of gB* and the ([Ca2+]in-V) phase diagram of initial conditions reveal fractal features. It has been observed that a short-lasting depolarizing current of elevation of [Ca2+]in may evoke transformation of chaotic activity into a regular bursting one. These kinds of transitions do not require any changes in the parameters of the model. The results demonstrate that chaotic regimes of neuronal activity modulated by neuropeptides may play a relevant role in information processing and storage at the level of a single neuron.

UI MeSH Term Description Entries
D008564 Membrane Potentials The voltage differences across a membrane. For cellular membranes they are computed by subtracting the voltage measured outside the membrane from the voltage measured inside the membrane. They result from differences of inside versus outside concentration of potassium, sodium, chloride, and other ions across cells' or ORGANELLES membranes. For excitable cells, the resting membrane potentials range between -30 and -100 millivolts. Physical, chemical, or electrical stimuli can make a membrane potential more negative (hyperpolarization), or less negative (depolarization). Resting Potentials,Transmembrane Potentials,Delta Psi,Resting Membrane Potential,Transmembrane Electrical Potential Difference,Transmembrane Potential Difference,Difference, Transmembrane Potential,Differences, Transmembrane Potential,Membrane Potential,Membrane Potential, Resting,Membrane Potentials, Resting,Potential Difference, Transmembrane,Potential Differences, Transmembrane,Potential, Membrane,Potential, Resting,Potential, Transmembrane,Potentials, Membrane,Potentials, Resting,Potentials, Transmembrane,Resting Membrane Potentials,Resting Potential,Transmembrane Potential,Transmembrane Potential Differences
D008959 Models, Neurological Theoretical representations that simulate the behavior or activity of the neurological system, processes or phenomena; includes the use of mathematical equations, computers, and other electronic equipment. Neurologic Models,Model, Neurological,Neurologic Model,Neurological Model,Neurological Models,Model, Neurologic,Models, Neurologic
D009431 Neural Conduction The propagation of the NERVE IMPULSE along the nerve away from the site of an excitation stimulus. Nerve Conduction,Conduction, Nerve,Conduction, Neural,Conductions, Nerve,Conductions, Neural,Nerve Conductions,Neural Conductions
D009474 Neurons The basic cellular units of nervous tissue. Each neuron consists of a body, an axon, and dendrites. Their purpose is to receive, conduct, and transmit impulses in the NERVOUS SYSTEM. Nerve Cells,Cell, Nerve,Cells, Nerve,Nerve Cell,Neuron
D009479 Neuropeptides Peptides released by NEURONS as intercellular messengers. Many neuropeptides are also hormones released by non-neuronal cells. Neuropeptide
D002118 Calcium A basic element found in nearly all tissues. It is a member of the alkaline earth family of metals with the atomic symbol Ca, atomic number 20, and atomic weight 40. Calcium is the most abundant mineral in the body and combines with phosphorus to form calcium phosphate in the bones and teeth. It is essential for the normal functioning of nerves and muscles and plays a role in blood coagulation (as factor IV) and in many enzymatic processes. Coagulation Factor IV,Factor IV,Blood Coagulation Factor IV,Calcium-40,Calcium 40,Factor IV, Coagulation
D006372 Helix, Snails A genus of chiefly Eurasian and African land snails including the principal edible snails as well as several pests of cultivated plants. Helix (Snails),Snails Helix
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D017711 Nonlinear Dynamics The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos. Chaos Theory,Models, Nonlinear,Non-linear Dynamics,Non-linear Models,Chaos Theories,Dynamics, Non-linear,Dynamics, Nonlinear,Model, Non-linear,Model, Nonlinear,Models, Non-linear,Non linear Dynamics,Non linear Models,Non-linear Dynamic,Non-linear Model,Nonlinear Dynamic,Nonlinear Model,Nonlinear Models,Theories, Chaos,Theory, Chaos

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