Stochastic sensitivity analysis of the noise-induced excitability in a model of a hair bundle

How noise can generate calcium spike-type oscillations in deterministic equilibrium modes

Stochastic excitability of spiking oscillatory regimes in the calcium kinetics is studied on the basis of the Li-Rinzel conceptual model. The probabilistic mechanisms of the noise-induced generation of large-amplitude oscillations in parametric zones, where the original deterministic model has only stable equilibria, are investigated numerically and analytically. A parametric statistical description of interspike intervals is curried out and the phenomenon of coherence resonance is discussed. For the analytical study of the stochastic excitement, the confidence domain method using a stochastic sensitivity technique is applied. In this analysis, a key role of mutual arrangement of the confidence ellipses and separatrices detaching the sub- and supercritical regions is demonstrated. It is shown that in the Li-Rinzel model such separatrices are the stable manifolds of the saddle equilibria and the transient semiattractors.

Stochastic sensitivity technique in a persistence analysis of randomly forced population systems with multiple trophic levels

Motivated by important ecological applications we study how noise can reduce a number of trophic levels in hierarchically related multidimensional population systems. A nonlinear model with three trophic levels under the influence of external stochastic forcing is considered as a basic conceptual example. We analyze a probabilistic mechanism of noise-induced extinction of separate populations in this "prey-predator-top predator" system. We propose a new general mathematical approach for the estimation of the proximity of equilibrium regimes of this stochastic model to hazardous borders where abrupt changes in dynamics of ecological systems can occur. Our method is based on the stochastic sensitivity function technique and visualization method of confidence domains. Constructive abilities of this mathematical approach are demonstrated in the analysis of different scenaria of noise-induced reducing of the number of trophic levels.

Effect of bidirectional mechanoelectrical coupling on spontaneous oscillations and sensitivity in a model of hair cells

Sensory hair cells of amphibians exhibit spontaneous activity in their hair bundles and membrane potentials, reflecting two distinct active amplification mechanisms employed in these peripheral mechanosensors. We use a two-compartment model of the bullfrog's saccular hair cell to study how the interaction between its mechanical and electrical compartments affects the emergence of distinct dynamical regimes, and the role of this interaction in shaping the response of the hair cell to weak mechanical stimuli. The model employs a Hodgkin-Huxley-type system for the basolateral electrical compartment and a nonlinear hair bundle oscillator for the mechanical compartment, which are coupled bidirectionally. In the model, forward coupling is provided by the mechanoelectrical transduction current, flowing from the hair bundle to the cell soma. Backward coupling is due to reverse electromechanical transduction, whereby variations of the membrane potential affect adaptation processes in the hair bundle. We isolate oscillation regions in the parameter space of the model and show that bidirectional coupling affects significantly the dynamics of the cell. In particular, self-sustained oscillations of the hair bundles and membrane potential can result from bidirectional coupling, and the coherence of spontaneous oscillations can be maximized by tuning the coupling strength. Consistent with previous experimental work, the model demonstrates that dynamical regimes of the hair bundle change in response to variations in the conductances of basolateral ion channels. We show that sensitivity of the hair cell to weak mechanical stimuli can be maximized by varying coupling strength, and that stochasticity of the hair bundle compartment is a limiting factor of the sensitivity.