The origin and function of cellular oscillations.
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Biological Clocks↗
Biomedical subjects
P E Rapp
Publications and source records attributed to P E Rapp.
A comparative survey of the function, mechanism and control of cellular oscillators.
This review attempts to survey in a uniform manner the available evidence concerning the generation and behaviour of several well-investigated cellular oscillators. Members of two broad classifications are contrasted: (i) cytoplasmic oscillations, where the periodic phenomena is generated by an instability pathway and (ii) membrane oscillators in which a membrane potential rhythm is generated at the membrane. Interactions between the cytoplasmic and membrane compartments are considered and the effects of these interactions on oscillatory behaviour is discussed. Because of their biological importance and the greater body of experimental results, particular attention is directed to a study of membrane potential oscillations. These systems can be approximately classified in two groups: (i) systems in which a periodic potential results from oscillatory changes in permeability and (ii) systems in which potential oscillations result from the periodic activity of an electrogenic pump. The examples considered include the glycolytic oscillator, oscillations in vein contraction in the slime mould Physarum polycephalum, rhythmic aggregation in Dictyostelium discoideum, neural oscillators, the periodic potential in Purkinje fibres and the sino-atrial node and rhythmic behaviour in smooth muscle. Questions considered include the generation of periodic activity, the modulation of the oscillation by drugs and other metabolic and membrane effectors and the question of the functional role of these oscillations.
Adrenal Cortex↗
An atlas of cellular oscillators.
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Animals↗
Periodic metabolic systems: oscillations in multiple-loop negative feedback biochemical control networks.
For a general multiple loop feedback inhibition system in which the end product can inhibit any or all of the intermediate reactions it is shown that biologically significant behaviour is always confined to a bounded region of reaction space containing a unique equilibrium. By explicit construction of a Liapunov function for the general n dimensional differential equation it is shown that some values of reaction parameters cause the concentration vector to approach the equilibrium asymptotically for all physically realizable initial conditions. As the parameter values change, periodic solutions can appear within the bounded region. Some information about these periodic solutions can be obtained from the Hopf bifurcation theorem. Alternatively, if specific parameter values are known a numerical method can be used to find periodic solutions and determine their stability by locating a zero of the displacement map. The single loop Goodwin oscillator is analysed in detail. The methods are then used to treat an oscillator with two feedback loops and it is found that oscillations are possible even if both Hill coefficients are equal to one.
Feedback↗
Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms.
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Action Potentials↗
Dynamics of brain electrical activity.
In addition to providing important theoretical insights into chaotic deterministic systems, dynamical systems theory has provided techniques for analyzing experimental data. These methods have been applied to a variety of physical and chemical systems. More recently, biological applications have become important. In this paper, we report applications of one of these techniques, estimation of a signal's correlation dimension, to the characterization of human electroencephalographic (EEG) signals and event-related brain potentials (ERPs). These calculations demonstrate that the magnitude of the technical difficulties encountered when attempting to estimate dimensions from noisy biological signals are substantial. However, these results also suggest that this procedure can provide a partial characterization of changes in cerebral electrical activity associated with changes in cognitive behavior that complements classical analytic procedures.
Brain↗
A guide to dynamical analysis.
The number and variety of methods used in dynamical analysis has increased dramatically during the last fifteen years, and the limitations of these methods, especially when applied to noisy biological data, are now becoming apparent. Their misapplication can easily produce fallacious results. The purpose of this introduction is to identify promising new methods and to describe safeguards that can be used to protect against false conclusions.
Animals↗