Ca2+ dynamics during membrane excitation of green alga Chara: model simulations and experimental data.

Kinetic investigations of stimulus response coupling in the green alga Chara have revealed that an intermediate second messenger is formed in the process of membrane excitation. This second messenger links electrical stimulation to the mobilization of Ca2+ from internal stores. In the present work, the experimentally based kinetic model, which describes the stimulus-dependent production of the second messenger and Ca2+ mobilization, is combined with a model for inositol 1,4,5-trisphosphate (IP3)-and Ca2+-sensitive gating of a Ca2+-release channel in endomembranes of animal cells. The combination of models allows a good simulation of experimental data, including the all-or-none-type dependence of the Ca2+ response on stimulus duration and complex phase locking phenomena for the dependence of the Ca2+ response on stimulation frequency. The model offers a molecular explanation for the refractory phenomenon in Chara, assigning it to the life time of an inactive state of the Ca2+-release channel. The model furthermore explains the steep dependence of excitation on strength/duration of electrical stimulation as a consequence of an interplay of the dynamical variables in the model.

Day-to-night variations of cytoplasmic pH in a crassulacean acid metabolism plant.

In crassulacean acid metabolism (CAM) large amounts of malic acid are redistributed between vacuole and cytoplasm in the course of night-to-day transitions. The corresponding changes of the cytoplasmic pH (pHcyt) were monitored in mesophyll protoplasts from the CAM plant Kalanchoe daigremontiana Hamet et Perrier by ratiometric fluorimetry with the fluorescent dye 2',7'-bis-(2-carboxyethyl)-5-(and-6-)carboxyfluorescein as a pHcyt indicator. At the beginning of the light phase, pHcyt was slightly alkaline (about 7.5). It dropped during midday by about 0.3 pH units before recovering again in the late-day-to-early-dark phase. In the physiological context the variation in pHcyt may be a component of CAM regulation. Due to its pH sensitivity, phosphoenolpyruvate carboxylase appears as a likely target enzyme. From monitoring delta pHcyt in response to loading the cytoplasm with the weak acid salt K-acetate a cytoplasmic H(+)-buffer capacity in the order of 65 mM H+ per pH unit was estimated at a pHcyt of about 7.5. With this value, an acid load of the cytoplasm by about 10 mM malic acid can be estimated as the cause of the observed drop in pHcyt. A diurnal oscillation in pHcyt and a quantitatively similar cytoplasmic malic acid is predicted from an established mathematical model which allows simulation of the CAM dynamics. The similarity of model predictions and experimental data supports the view put forward in this model that a phase transition of the tonoplast is an essential functional element in CAM dynamics.

Spatiotemporal variation of metabolism in a plant circadian rhythm: the biological clock as an assembly of coupled individual oscillators.

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 (phi(PSII)) over a single leaf. Noninvasive highly sensitive chlorophyll fluorescence imaging reveals randomly initiated patches of varying phi(PSII) that are propagated within minutes to hours in wave fronts, forming dynamically expanding and contracting clusters and clearly dephased regions of phi(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.

Effect of colored noise on networks of nonlinear oscillators.

We discuss noise-induced pattern formation in different two-dimensional networks of nonlinear oscillators, namely a sequence of biochemical reactions and the Lorenz system. The main focus of the work is on the dependence of these patterns on the correlation time (i.e., the color) of exponentially correlated Gaussian noise. It is seen that in the nonchaotic case, the homogeneity (or average cluster size) goes through a minimum with higher correlation time, while in its chaotic regime the Lorenz system shows a higher degree of synchronization when the correlation time of the noise is increased. In order to elucidate the origin of this phenomenon, the effect of colored noise on the individual oscillator is investigated. It is shown that the specific dependence of the network's homogeneity on the noise correlation time arises from an interplay of the collective behavior and the properties of the single oscillators.