Bursting behavior

The stochastic behavior of biochemical reactions has been observed in single living cells as well as in in vitro experiments. Sunney Xie and colleagues have observed a stochastic, randomly timed bursting behavior in the production of proteins, i.e., translation of an mRNA [26, 217]. The observed number of the protein molecules produced in each burst, np, follows a geometric distribution,... 

Alonso, A., M.-P. Fame A. Beaudet. 1994. Neurotensin promotes oscillatory bursting behavior and is internalized in basal forebrain cholinergic nemons. J. NeuroscL 14 5778-92. 

RuUcov, N.F. Modeling of spiking-bursting behavior using two-dimensional map. Phys. Rev. E 65, 041922 (2002)... 

Snail RPal bursting neuron A model including a fast sodium current, a delayed rectifier potassium current, a voltage-dependent calcium current, a voltage- and calcium-dependent calcium current, and a leak current was constructed by Berezetskaya et al. [1996] to investigate the bursting behavior of pacemaker cells of the Helix pomatia. 

Figure 12.18 Bursting behavior in (a) the transmembrane potential of a neuron in the crustacean stomatogastric ganglion (Adapted from Sharp, 1994.) (b) two coupled CSTRs, each of whose flow rates is modified according to the iodide concentration in the other reactor. Input concentrations in each reactor [ClOJo = 1 x 10 M, [I ]o = 4.2 X 10 " M. Note the similarity between the neural and chemical traces if one reverses the sign of the potential in one of the recordings. (Adapted from Dolnik and Epstein, 1993.)...

Rinzel (1981) has studied a number of models for bursting behavior and has developed both an intuitive understanding of the origin of this phenomenon and a classification scheme that describes the different ways in which bursting can arise. The essence of his analysis, which is similar in concept to the development of Barkley s model for mixed-mode oscillations that we discussed in section 8.1, rests on identification of a set of slow and a set of fast processes. In neurons, the fast processes are associated with the generation of the action potentials, while the slow processes typically determine the period of the overall oscillation. The membrane potential provides the key link between the two sets of processes. 

A concrete example of a model for neuronal bursting (Plant, 1981) has been analyzed in considerable detail by Rinzel and Lee (1987). The model utihzes the Hodgkin-Huxley model, eqs. (13.3) and (13.4), as the mechanism for action-potential generation and introduces two additional conductances, a calcium channel and a calcium-activated potassium channel, to produce the bursting behavior. The membrane potential is given by... 

Figure 13.9 Bursting behavior in Plant s model for a neuron, eqs. (13.7)-(13.9). (Adapted from Rinzel and Lee, 1987.)...

Fatigue analysis in Division 3 can be done usingthe traditional SN method or the structural stress method (limited to the analysis of welds) only if leak-before-burst behavior can be demonstrated. Otherwise, the fracture mechanics method must be used. 

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