Estimating the rate of photorespiration in leaves

The influence of Li⁺ on the circumnutations of hypocotyls of Helianthus annuus L . cv. Californicus was investigated. LiCl at concentration levels from 0 to 40 m M (lethal) was added to intact hypocotyls grown in liquid nutrient medium. The Li⁺ concentration in the hypocotyls was measured by flame photometry. The growth of the hypocotyls was not affected by the LiCl.
Amplitude and frequency of the circumnutations were determined by correlation analysis. The oscillatory pattern of the movements became less regular at concentrations above 10 m M LiCl. The amplitude of the movements was reduced for concentrations above 7 m M LiCl. The frequency of the movements was reduced when LiCl was increased from 0 to 10 m M . Above 10 m M LiCl the frequency of the circumnutations was higher than for control plants. The results showed that circumnutations of sunflower hypocotyls can be added to the group of oscillators in biological organisms that are affected by Li⁺.     

Entrainment of Geotropic Oscillations in Hypocotyls of Helianthus annuus– An Experimental and Theoretical Investigation

The effects of periodically repeated geotropic stimulations (geotropic pulses) on sunflower hypocotyls are studied. The experimental results agree with predictions from a theory for geotropic movements of the hypocotyl. A sunflower hypocotyl performs circumnutations around or across the plumb line with a period of about 2.5 hours. These oscillations can be entrained to periodically repeated geotropic pulses with a period in a region around 2.5 hours. The limits of this “region of entrainment’ for geotropic pulses are studied. In the region of entrainment resonance curves, i.e., the amplitude of the oscillations plotted as a function of the period of the geotropic pulses, are obtained. The phase differences (measured as time differences) between the geotropic pulse rhythms and the resulting oscillations are also studied. Beat phenomena are predicted and recorded outside the region in which the plants can be entrained. The results are discussed in relation to oscillating phenomena of circadian type (i.e., with a period close to 24 hours), and many similarities are pointed out.     

KINETICS OF SUPPRESSION OF CIRCUMNUTATION BY CLINOSTATTING FAVORS MODIFIED INTERNAL OSCILLATOR MODEL

According to a well-conceived gravity-driven model, oscillatory growth movements called circumnutations are produced by a continuing set of gravitational responses with overshoot. In simplest form that model predicts that if the gravity stimulus could be removed completely and abruptly, growth oscillations would damp out within a time less than the period of oscillation. That condition was simulated by imposing on horizontally clinostatted sunflower shoots a unit g centripetal force in the direction that coincided with the plants' morphological axis. Circumnutations proceeded in quantitatively normal manner. By stopping the centrifuge, the plants were subjected abruptly only to clinostat simulated weightlessness. Circumnutations decreased but did not disappear. The half-time for decline to a final low level of activity was about 4-fold the period of oscillation at 1 g—about 8-fold the period at simulated zero g. That slow damping was not consistent with the prediction based on the gravity driven model of circumnutation. The model needs to be revised.     

Short-period circumnutations found in sunflower hypocotyls in satellite orbit. A reappraisal of data from Spacelab-1

We have further analysed data from an experiment performed in satellite orbit, in Spacelab-1. In micro-gravity the hypocotyls of Helianthus annuus, cv. "Teddy Bear", showed short period circumnutations (periods around 30 minutes) as well as the already reported long period nutations (with an average period of about 115 minutes). We applied various types of signal analysis (Fourier and wavelet analysis) to the data series. The long period circumnutations have a larger amplitude than the short term circumnutations. Both short and long period circumnutations exist in one and the same hypocotyl. (This is in contrast to our ground control experiments, where were found only the long-period nutations.) The period of the nutations changed throughout the experiment. These results are extending the conclusions drawn after the Spacelab experiment (Brown et al. 1990). In particular they emphasize the existence of both short- and long-period circumnutations in micro-gravity.     

Circumnutations of Arabidopsis thaliana Seedlings

The hypocotyls of Arabidopsis thaliana seedlings exhibit circumnutations with different frequency ranges. Using a picture-analysis system, two types of oscillations were distinguished, short period (SPN) and long period nutations (LPN). The period of the SPNs is between 20 and 60 min, decreases with increasing temperature (between 20° and 30°C; Q 10 of 2.0) and increases with age. The SPNs changed frequently between circular and pendular movements. The circumnutation usually occurred clockwise, but the direction could change. For SPNs to occur, a minimum growth rate of 0.05 mm/h was required. The period of the LPNs ranged from 1 to 8 h. Peaks occurred around 95 and 200 min. The movements of the LPNs are mostly counterclockwise. The oscillation could change from circular to elliptic or pendular. In contrast to SPNs, LPNs were found also at low growth rates. Under red light and in the strain Landsberg erecta the circumnutations were especially slow. Short and long period oscillations can occur simultaneously or separately in different plants. In cases of simultaneous occurrence the quotient between the period lengths of the LPN and SPN was not constant. The number of occurrences of these frequencies depended on the strain and on external factors such as temperature and light. In continuous bright white light phases of circumnutations alternated with quiescent periods. This behaviour was circadian and correlated with growth bursts.     

Circumnutations of Arabidopsis thaliana Seedlings

The hypocotyls of Arabidopsis thaliana seedlings exhibit circumnutations with different frequency ranges. Using a picture-analysis system, two types of oscillations were distinguished, short period (SPN) and long period nutations (LPN). The period of the SPNs is between 20 and 60 min, decreases with increasing temperature (between 20° and 30°C; Q 10 of 2.0) and increases with age. The SPNs changed frequently between circular and pendular movements. The circumnutation usually occurred clockwise, but the direction could change. For SPNs to occur, a minimum growth rate of 0.05 mm/h was required. The period of the LPNs ranged from 1 to 8 h. Peaks occurred around 95 and 200 min. The movements of the LPNs are mostly counterclockwise. The oscillation could change from circular to elliptic or pendular. In contrast to SPNs, LPNs were found also at low growth rates. Under red light and in the strain Landsberg erecta the circumnutations were especially slow. Short and long period oscillations can occur simultaneously or separately in different plants. In cases of simultaneous occurrence the quotient between the period lengths of the LPN and SPN was not constant. The number of occurrences of these frequencies depended on the strain and on external factors such as temperature and light. In continuous bright white light phases of circumnutations alternated with quiescent periods. This behaviour was circadian and correlated with growth bursts.     

Circadian Modulation of Circumnutation Length, Period, and Shape in Helianthus annuus

Modulation of a turgor-growth movement called circumnutation in sunflower (Helianthus annuus L.) was investigated using a picture analysis system. Two photoperiod conditions were applied: light–darkness conditions (LD) 8:8 and LD 20:10. After about 3 weeks of these regimes, the plants were placed under constant light to determine whether circadian regulation of circumnutation existed or not. The rhythms of movement activity with regard to the trajectory length, period, and shape of individual circumnutations were examined. Data were processed by Fourier spectral analysis. All the parameters, trajectory length, period, and shape, revealed the ability to entrain to the administered daily cycles (16 h or 30 h). We observed diurnal fluctuations of the circumnutation parameters with the phase of the highest trajectory length, the shortest period, and the highest shape coefficient (the most circular form) during the dark period. After the LD–LL transition, the parameters revealed periodicity, which was close to 24 h. After several days of a clear circadian free running rhythm, a gradual decrease of the amplitude of the rhythm was observed. However, the rhythm did not disappear completely. The trajectory length manifested the strongest entrainment; the circumnutation period and the circumnutation shape were less modulated by photoperiod. These findings indicate for the first time that different parameters of circumnutation in sunflower are circadian-regulated rhythms, not solely ultradian as had been thought previously.     

Disturbances of stem circumnutations evoked by wound-induced variation potentials in Helianthus annuus L

The relationship between evoked electrical activity and stem movements in three-week old sunflowers was demonstrated. Electrical potential changes (recorded by Ag/AgCl extracellular electrodes) and time-lapse images (from a top view camera) were recorded and analyzed. A heat stimulus applied to the tip of one of the second pair of leaves evoked a variation potential, transmitted basipetally along one side of the stem. After stimulation, disturbances of circumnutations occurred. They included: changes in the period, disorders in the elliptical shape, and, in some cases, reversion of direction (of movement). We suggest that asymmetrically propagated variation potential induces asymmetric stem shrinking and bending, which strongly disturbs circumnutations. Our results confirm the involvement of electrical potential changes in the mechanism of stem nutations.     

Circumnutations under free-fall conditions in space?

Regular growth movement, so-called circumnutation, of plants and plant organs is a very general phenomenon. The origin of circumnutations is, however, unclear. Three different types of model are discussed in relation to some experimental results on circumnutations. It is suggested that an experiment in space, under free-fall conditions, should be done on different species showing circumnutations in order to discriminate between the models.     

Phase-shift in Geotropical Oscillations - A Theoretical and Experimental Study

Geotropically induced phase-shifts in circumnutations of Heliauthus annuus hypocotyls are studied. - Theoretical deductions from a previously developed theory for geotropical movements are made for the case of a short gravitational stimulation in different phase positions of an oscillating hypocotyl. - Experimental studies are performed to test the theoretical results. - The conclusions are drawn, that the theory mentioned can satisfactorily describe geotropically induced phase-shifts. A comparison with phase-shifts in photoperiodic systems is made.     

Circumnutations of Sunflower Hypocotyls in Satellite Orbit

The principal objective of the research reported here was to determine whether a plant's periodic growth oscillations, called circumnutations, would persist in the absence of a significant gravitational or inertial force. The definitive experiment was made possible by access to the condition of protracted near weightlessness in an earth satellite. The experiment, performed during the first flight of Spacelab on the National Aeronautics and Space Administration shuttle, Columbia, in November and December, 1983, tested a biophysical model, proposed in 1967, that might account for circumnutation as a gravity-dependent growth response. However, circumnutations were observed in microgravity. They continued for many hours without stimulation by a significant g-force. Therefore, neither a gravitational nor an inertial g-force was an absolute requirement for initation or continuation of circumnutation. On average, circumnutation was significantly more vigorous in satellite orbit than on earth-based clinostats. Therefore, at least for sunflower (Helianthus annuus L.) circumnutation, clinostatting is not the functional equivalent of weightlessness.     

An automatic device to record the force necessary to compensate plant movements

A device, which automatically and continuously keeps moving plants in fixed positions, has been constructed. The apparatus is based on optical detection of any movements of the plant organ under study. The plant organ is kept in the desired position by means of wires, and the force necessary to apply to the wires to achieve this is recorded. The force reflects any tendency of the plant organ to move. The system is controlled by an Apple II computer. The device can work in one or two dimensions and record compensation forces in a wide range. In the experiments mentioned below, the magnitude of the forces necessary to keep the plants in a fixed position was of the order of 10^-4N.
Circadian leaf movements of Oxalis regnellii Mig. were studied in the device. The leaf rhythm continued, although the leaflets were clamped and the light input on the leaf therefore constant. Circumnutation of hypocotyls of Helianthus annus L. cv. Californicus were drastically reduced in amplitude when the hypocotyls were kept in vertical position by the wires. Since the gravitropic input signal to this system was zeroed by the equipment, the results demonstrated that in the absence of gravitropic inputs the circumnutation reactions drastically diminish. This confirmed that circumnutations of these hypocotyls are influenced by gravity. Finally, the apparatus was used to study phototropic reactions: By clamping phototropically stimulated coleoptiles of Avena sativa L. cv. Seger no gravitational stimulations were involved and the phototropic reaction without interference from gravity could be studied.     

The effect of lateral illumination on growth oscillations of pine seedling hypocotyls (Pinus silvestris L.)

Phototropic sensitivity of forest wood seedlings to lateral illumination was proposed as an early assay for distinquishing various ecotypes of woody plants of the same species. Statistical analysis showed that results were significantly influenced by heterogenity of experimental material caused by an interference of phototropic movements and natural oscillations of hypocotyl. Both movements of pine seedlings (Pinus silvestris L.) were registered by phase photography and their mechanism was analyzed. The apical part of growing hypocotyl illuminated from above oscillates in a space spiral with frequency 3.3 h at mean growth rate 0.66 mm h^?1. The mean size of spiral amplitudes is 2.9 mm. The oscillation rhythm is disturbed after the lateral illumination and a phase shift was observed as a result. A new oscillation rhythm with frequency 3.9 h and mean growth rate 0.69 mm h^?1 was stabilized after a period of time equal to one nutation turn. Oscillation amplitudes were increased to 4.3 mm. In addition to the radiation intensity the appearance of the phototropic response to light pulse is first of all effected by the actual position of the apical part of hypocotyl in the course of endogenous circumnutations. A uniform plant material for the early assay may be obtained by selection of seedlings which are at the beginning of lateral illumination in the same phase of nutation rhythm. Under such conditions the deviations of longitudinal axis of oscillating spirals characterize the actual phototropic curvature.     

Daily and infradian rhythms of circumnutation intensity in Helianthus annuus

Circumnutation in Helianthus annuus L. was investigated by measurements lasting 4–7 weeks using a picture analysis system. The rhythmicity of circumnutation vigour (intensity) with regard to the trajectory length and period of individual circumnutations were examined. Three photoperiod conditions were applied [light/dark (LD), continuous light (LL) and LD followed by LL]. Data were processed by the Fourier analysis. Statistical analysis included the examination of circumnutation mean frequencies and correlation tests. Both parameters, trajectory length and period, revealed a daily (24 h) modulation in LD with a weak correlation between them, whereas in LL no daily modulation of the parameters was observed. After LD–LL transition, the parameters were gradually losing their daily modulation. Despite a very strong modulation of the trajectory length in LD, the period was quite stable in all groups tested, but only in LD were there no statistical differences in the number of circumnutations per 24 h among the plants studied. LD was concluded to be the strong synchronizer, making the plants circumnutate regularly. Regardless of the presence or absence of daily modulation, the infradian (several and more days long) harmonics of the trajectory length were the same in each group. These findings strongly support the view that circumnutation in sunflower, widely known as an ultradian rhythm, also possesses daily and infradian modulations of its intensity. To the authors' knowledge, this is the first report of circumnutation that was obtained by a picture analysis system in such a large timescale.     

Optimal control of antagonistic muscle stiffness during voluntary movements

This paper presents a study on the control of antagonist muscle stiffness during single-joint arm movements by optimal control theory with a minimal effort criterion. A hierarchical model is developed based on the physiology of the neuromuscular control system and the equilibrium point hypothesis. For point-to-point movements, the model provides predictions on (1) movement trajectory, (2) equilibrium trajectory, (3) muscle control inputs, and (4) antagonist muscle stiffness, as well as other variables. We compared these model predictions to the behavior observed in normal human subjects. The optimal movements capture the major invariant characteristics of voluntary movements, such as a sigmoidal movement trajectory with a bell-shaped velocity profile, an N-shaped equilibrium trajectory, a triphasic burst pattern of muscle control inputs, and a dynamically modulated joint stiffness. The joint stiffness is found to increase in the middle of the movement as a consequence of the triphasic muscle activities. We have also investigated the effects of changes in model parameters on movement control. We found that the movement kinematics and muscle control inputs are strongly influenced by the upper bound of the descending excitation signal that activates motoneuron pools in the spinal cord. Furthermore, a class of movements with scaled velocity profiles can be achieved by tuning the amplitude and duration of this excitation signal. These model predictions agree with a wide body of experimental data obtained from normal human subjects. The results suggest that the control of fast arm movements involves explicit planning for both the equilibrium trajectory and joint stiffness, and that the minimal effort criterion best characterizes the objective of movement planning and control.     

A Theory for Circumnutations in Helianthus annuus

A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material The theory is based on the lateral auxin transport, which arises when a gravitational force component acts on the plant. With a suitable time delay between stimulus and response, oscillations or circumnutations should arise. It is possible to describe these oscillation phenomena by the solutions of a differential equation, derived in this paper. The time delay has a central role in this equation. The time delay is assumed to be identical with the geotropic reaction time for the hypocotyls. The ratio between the periodic time for the circumnutations and the reaction time for geotropic curvatures was found to be approximately constant in the temperature region investigated (namely 15–40°C), which supports the theory. Different methods of recording the circumnutations were used, 8 mm film camera technique being the most frequently employed. The introduction of a weighting function for describing the plants “memory” of the stimulation makes it possible to relate the periodic time of the circumnutations to the reaction time for geotropic curvatures. The necessity of this weighting function as well as of the time delay in the equations is emphasized. An explanation of the “Fünfphasen-bewegungen”, reported in the literature, is presented.     

Endogenous Short Period Rhythms in the Movements of Unifoliate Leaves of Phaseolus angularis Wight

Rhythmic rotational movements with the midvein as the axis have been observed in the unifoliate leaves of Phaseolus angularis Wight grown under controlled environmental conditions with continuous light. The mean period of this movement for all leaves was 53.2 ± 4.3 minutes and remained constant as the leaf matured, except after removal of the apical meristem and emerging trifoliate leaf when the period increased by about 5 minutes. The amplitude of the movement also remained constant as the leaf matured. These rotational movements were pronounced when the leaf blade was in a horizontal position and were not evident during the downward or “sleep” movements of the leaf. This movement began 3 days after leaf unfolding and continued for at least 6 days. It was most pronounced at the time of inflection of the leaf length growth curve after the logarithmic phase of growth.     

Evaluation of the Accuracy of Calculation of the Standard Binding Entropy of Molecules from their Average Mobility in Molecular Crystals

One of the main problems in attempts to predict the binding constants of molecules (or free energies of their binding) is the correct evaluation of configurational binding entropy. This evaluation is possible by methods of molecular dynamics simulation, but these simulations require a lot of computational time. Earlier, we have developed an alternative approach which allows the fast calculation of the binding entropy from summarizing the available data on sublimation of crystals. Our method is based on evaluating the mean amplitude of the movements that are restricted in the bound molecule, e.g., in a crystal, but are not restricted in the free state, e.g., in vapor. In this work, it is shown that the standard entropy of binding of molecules by crystals under standard conditions (1 atm, 25°C) can be assessed rather accurately from geometric and physical parameters of the molecule and the average amplitude of the molecule motions in crystals estimated in our previous work.     

Proton and calcium flux oscillations in the elongation region correlate with root nutation

The involvement of Ca²⁺ and H⁺ flux oscillations in root nutation was studied for decapped roots of corn ( Zea mays L. cv. Aussie Gold) placed horizontally. Net ion fluxes were measured around the elongation and meristematic regions using a microelectrode ion flux measuring system. High correlation between H⁺ flux oscillations and root nutations was found in the elongation region. Two oscillatory components of H⁺ flux, with periods of about 90 min and 7 min, correlated with root circumnutations and micronutations, respectively. The periods of H⁺ flux oscillations and rhythmical root movements in this region could be modified similarly by external factors including pH. In the meristematic region no association between ion flux behaviour and nutation was apparent. Ion flux oscillations and nutations both decreased in amplitude as the growth rate at the measured location decreased. Possible involvement of ion flux oscillations in root circumnutation is discussed. It is concluded that a model involving an internal oscillator must be developed to explain the H⁺ flux involvement in root nutations.