The relationship of brain activity to conscious intentions is considered on the basis of the functional microstructure of the cerebral cortex. Each ming nerve impulse causes the emission of transmitter molecules by the process of exocytosis. Since exocytosis is a quantal phenomenon of the presynaptic vesicular grid with a probability much less than 1, we present a quantum mechanical model for It based on a tunneling process of the trigger mechanism. Consciousness manifests itself in mental intentions. The consequent voluntary actions become effective by momentary increases of the probability of vesicular emission in the thousands of synapses on each pyramidal cell by quantal selection.
The complex dynamic properties of biological timing in organisms remain a central enigma in biology despite the increasingly precise genetic characterization of oscillating units and their components. Although attempts to obtain the time constants from oscillations of gene activity and biochemical units have led to substantial progress, we are still far from a full molecular understanding of endogenous rhythmicity and the physiological manifestations of biological clocks. Applications of nonlinear dynamics have revolutionized thinking in physics and in biomedical and life sciences research, and spatiotemporal considerations are now advancing our understanding of development and rhythmicity. Here we show that the well known circadian rhythm of a metabolic cycle in a higher plant, namely the crassulacean acid metabolism mode of photosynthesis, is expressed as dynamic patterns of independently initiated variations in photosynthetic efficiency ( PSII) over a single leaf. Noninvasive highly sensitive chlorophyll fluorescence imaging reveals randomly initiated patches of varying PSII that are propagated within minutes to hours in wave fronts, forming dynamically expanding and contracting clusters and clearly dephased regions of PSII. Thus, this biological clock is a spatiotemporal product of many weakly coupled individual oscillators, defined by the metabolic constraints of crassulacean acid metabolism. The oscillators operate independently in space and time as a consequence of the dynamics of metabolic pools and limitations of CO 2 diffusion between tightly packed cells.A current trend in physics and life sciences is the investigation of spatiotemporal patterns that appear in phenomena that were formerly thought to be solely time dependent. Rhythmic phenomena are common in nature and are excellent models for investigation of spatial dynamics because of their regular structure. However, the complex dynamic properties of timing in organisms and biological systems remain a central enigma in biology despite the increasingly precise genetic characterization of oscillating units and their components (1, 2). For example, phase synchronization of predator-prey dynamics in spatially extended ecological systems emerges only when the building blocks are spatially arranged and interrelated by flows of signaling compounds (3). The challenge is to understand how the spatial organization of the components of a system can influence overall temporal development.The circadian rhythm of net CO 2 exchange (JCO 2 ) in crassulacean acid metabolism (CAM) plants in continuous light is regarded as a time-dependent generic model system for exploration of endogenous rhythmicity in a well understood metabolic pathway (4-6). During the normal day͞night cycle, CAM can be divided in four phases (7). In phase I, nocturnal CO 2 fixation by phosphoenolpyruvate-carboxylase (PEPCase) leads to the formation of malic acid that is removed from the site of its formation in the cytoplasm by active accumulation to the central cell vacuole. Malic acid exerts ...
The mechanism of endogenous circadian photosynthesis oscillations of plants performing crassulacean acid metabolism (CAM) is investigated in terms of a nonlinear theoretical model. Unlike previous CAM models containing a discrete element, we use throughout continuous time di¡erential equations which more adequately re£ect the CAM dynamics. By incorporating results from both a complementary and a continuous membrane model, a detailed description of the molecular malate transport in and out of the vacuole through the tonoplast membrane is achieved. Our analysis shows that the membrane e¡ectively acts as a hysteresis switch regulating the oscillations. It thus provides a molecular basis for the circadian clock. The model shows regular endogenous limit cycle oscillations that are stable for a wide range of temperatures, in a manner that complies well with experimental data. The circadian period length is explained simply in terms of the ¢lling time of the vacuole. The results emphasize the central role of membrane dynamics for the generation of circadian oscillations and thus have general relevance for the explanation of biological clocks.
Endogenous free-running regular circadian oscillations of net CO2 exchange in the crassulacean-acidmetabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier de la Bâthie under constant external conditions in continuous light have been shown to change to irregular non-predictable (chaotic) time behaviour as irradiance or temperature are raised above a critical level. A model of CAM has been constructed with pools of major metabolites of varying concentrations, flows of metabolites leading to exchange between pools, metabolite transformations determined by chemical reactions, and feedback regulations. The model is described by a system of coupled non-linear differential equations. It shows stable rhythmicity in normal dark-light cycles and in continuous light and, like the K. daigremontiana leaves in the experiments, a change to chaos as irradiance is increased. The maintenance of endogenous oscillations in the model is brought about by a hysteresis switch or beat oscillator between two stable oscillation modes. In CAM these stable modes are vacuolar malate accumulation and remobilization. The model shows that the physical nature of the beat oscillator in the leaves can be explained by the balance between active and passive transport at the tonoplast.
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