The statistical detection of threshold signals in the retina

1. Photographic records of impulses from single ganglion cells in the cat's retina were made while the retina was stimulated by flashes occurring once a second. Ten flashes at each of several intensities near threshold were used. 2. For the purpose of statistical analysis, the number of impulses (x) falling within a critical period following each flash was used as an index of the response. Histograms of x were plotted and used to calculate rates of transfer of information by the ganglion cell for the case of an ideal experiment, the yes-no choice, in which flashes of intensity I and blanks are to be distinguished. 3. The information rate increased (a) with increasing stimulus intensity and (b) with the number of identical flashes or blanks presented successively in a block. The intensity chosen as threshold by the experimenter, who observed the impulses visually and aurally, corresponded to an average information rate for single flashes of 0.7 bit/flash, compared to the maximum possible rate of 1 bit/flash. A threshold intensity giving 0.4 or more bit/flash, if presented in blocks of six identical flashes, corresponded to 0.95 or more bit/block, or near certainty. Thus the calculation of information rates using the index x provides an estimate of threshold at least as sensitive as those obtained during an experiment, which were made only after observing the responses to five to ten flashes of the same intensity. 4. The index x has statistical properties similar to those of the "index of neural activity" used by Tanner and Swets (1954) in their statistical model of human vision, and represents a possible physical interpretation of their index. However, x gave values (0.5 to 1.5) of the parameter called the slope which were consistently smaller than their values (2.1 to 3.1).     

Suppression of cone signal in the dark-adapted frog retina as indicated by the electroretinogram.

Electroretinogram (ERG) cone acitvity is depressed in the dark-adapted frog retina. The strength of this effect is examined over a large range of flash energy, for 618 nm flashes extending up to about 4 log10 units above the "threshold" (10-25 micron V b-wave) of the cone ERG "released" in the early stage of rapid dark-adaptation (RDA). Cone signal depression is remarkably strong over this flash energy range. The cone ERG is practically absent for flashes up to about I log unit above cone RDA threshold. For stronger flashes, the suppression becomes time-dependent, that is, cone signal is very small for the first few hundred msec. after the flash, cone intrusion then becoming detectable. The results suggest that the cone suppression phenomena arises distally in the retina, probably near the receptor layer, and that cone signal intrusion a few hundred msec. after a strong flash may be due to light-adaptation of rods by the flash itself.     

A statistical analyzer for optic nerve messages

A statistical mathematical model of the discharge in a single optic nerve fiber is proposed, based on a discharge with intervals between impulses distributed independently according to a gamma distribution ("gamma discharge"). A light stimulus distorts the time axis of this discharge according to a "frequency function" which is characteristic of the stimulus. A linear filter is described which calculates the likelihood of a certain stimulus when the nerve fiber message is fed into it. This filter forms the basis of theoretical nerve message analyzers for three visual experiments: (a) The detection of the occurrence of a flash of light of known intensity and time of occurrence, (b) the detection of the time of occurrence of a flash of known intensity, and (c) The estimation of the intensity of a flash occurring at a known time. Possible neural mechanisms in the brain for analyzing optic nerve messages, based on the above mathematical models, are suggested. Changes of excitability or discharge frequency correspond to the output of the likelihood filter. Any such mechanism must be sufficiently plastic to have a response matched to each expected stimuus for most efficient vision near threshold.     

Missing link in firefly bioluminescence revealed: NO regulation of photocyte respiration

Sexual communication in most species of fireflies is a male–female dialogue of precisely timed flashes of bioluminescent light. The biochemical reactions underlying firefly bioluminescence have been known for 30 years and are now exploited in biomedical assays and other commercial applications. Several aspects of flash regulation are also understood: flash rhythm is controlled by a central pattern generator, and individual flashes are neurally triggered, with octopamine serving as the transmitter. The molecular oxygen needed by the biochemical reactants is delivered by a network of tracheal arborizations extending throughout the light organ (lantern). However, the actual means by which oxygen quickly reaches the reactants packaged within specialized photocytes and the specific event(s) triggered by neural action have not been identified; termination of axons away from the photocytes has exacerbated the latter problem. A recent paper( 1 ) by a consortium of cell and evolutionary biologists, however, reports that nitric oxide (NO), manufactured and released in response to neuronal discharge, is the missing link by which neural action in the firefly lantern yields a sudden flash of light. BioEssays 23:992–995, 2001. © 2001 John Wiley & Sons, Inc.     

The Dependence of the Photopupil Response on Flash Duration and Intensity

The changes in pupil size were recorded by infrared pupillographic methods in response to light flashes of different durations and intensities for a 13 degree 34 minute centrally fixated circular field. For such stimuli, the threshold intensities for (rod) vision and for the pupil response were found to be about the same. The response amplitudes were related to the logarithm of the flash energy, the reciprocity law remaining valid up to about one-half second. The curve relating flash energy and pupil response was clearly divisible into two parts commensurate with the duplex character of the human retina. A similar dichotomy appears in curves relating response amplitude to response latency. Since the pupil response is determined by total flash energy, intense long flashes produce larger pupil responses than shorter (and perceptually brighter) ones of the same intensity.     

Flash photolysis of rhodopsin in the cat retina

The bleaching of rhodopsin by short-duration flashes of a xenon discharge lamp was studied in vivo in the cat retina with the aid of a rapid, spectral-scan fundus reflectometer. Difference spectra recorded over a broad range of intensities showed that the bleaching efficacy of high-intensity flashes was less than that of longer duration, steady lights delivering the same amount of energy. Both the empirical results and those derived from a theoretical analysis of flash photolysis indicate that, under the conditions of these experiments, the upper limit of the flash bleaching of rhodopsin in cat is approximately 90%. Although the fact that a full bleach could not be attained is attributable to photoreversal, i.e., the photic regeneration of rhodopsin from its light-sensitive intermediates, the 90% limit is considerably higher than the 50% (or lower) value obtained under other experimental circumstances. Thus, it appears that the duration (approximately 1 ms) and spectral composition of the flash, coupled with the kinetic parameters of the thermal and photic reactions in the cat retina, reduce the light-induced regeneration of rhodopsin to approximately 10%.     

Response entrainment of movement fibers in the optic tract of crayfish

The response properties of jittery movement fibers (JMF) in the crayfish optic tract reacting to a non-moving temporally patterned light were analyzed. The JMFs usually show no response during the regular flickering of stationary light with a flash duration of less than 50 msec when the stimulus frequency is between 4 and 20 per second; however they do respond when the flickering stops if a certain number of flashes have been given. The response appears about 50 msec after the first missing flash, i.e., the latency of the response after the last flash of the train changed from 100 to 300 msec. Thus, the “off” response at the end of the flicker is entrained to the stimulus repetition interval and locked onto the time of the first missing flash. The response of a sustaining fiber to an identical stimulus has quite different features as illustrated in Fig. 2. Some of the fibers show responses to the beginning part of the flicker but not necessarily to each flash, and habituate after several flashes. When a single flash longer than 250 msec is given, the fiber shows an “off” response with about 50 msec latency, as it does to sustained light. Some fibers show a double burst of “off” discharge to single flashes; the first at 50 msec is followed after 120 msec by the second one. However, when the flash duration is between 250 and 50 msec, a single flash elicits little or no response. The latency of the “off” response is as much as 300 msec for short single flashes less than 50 msec. An “on” response to flashes of light is observed when the inter-stimulus interval is more than 5 sec. The responses to the beginning part of flicker train are not simply locked to the just preceding flash except the “on” response to the very first one, but they can be the long latency responses to the flash before that. This response is modified in latency by the succeeding flashes in flicker trains and becomes entrained to the missing flash. Four types of entrainment are classified on the basis of the change in latency from the missing flash with regard to the number of flashes in a train. In most cases, 10 flashes are sufficient to entrain the response to the first missing flash. Non-resposiveness, i.e., habituation, during a regular flicker, may be due to an active inhibitory process, initiated by each succeeding light pulse. The response to the missing flash, therefore results from a disinhibited modified response to the last flash. Some JMFs continue to respond to the flicker even after a considerable number of flashes but only when the repetition interval is about 120 msec corresponding well to the interval of the double burst “off” discharge, thus the JMF has a resonant frequency of about 8 Hz. The JMFs appear to be acting as an irregularity detector in temporal sequence.     

Fusion of influenza virions with a planar lipid membrane detected by video fluorescence microscopy

The fusion of individual influenza virions with a planar phospholipid membrane was detected by fluorescence video microscopy. Virion envelopes were loaded with the lipophilic fluorescent marker octadecylrhodamine B (R18) to a density at which the fluorescence of the probe was self-quenched. Labeled virions were ejected toward the planar membrane from a micropipette in a custom-built video fluorescence microscope. Once a virion fused with the planar membrane, the marker was free to diffuse, and its fluorescence became dequenched, producing a flash of light. This flash was detected as a transient spot of light which increased and then diminished in brightness. The diffusion constants calculated from the brightness profiles for the flashes are consistent with fusion of virus to the membrane with consequent free diffusion of probe within the planar membrane. Under conditions known to be fusigenic for influenza virus (low pH and 37 degrees C), flashes appeared at a high rate and the planar membrane quickly became fluorescent. To further establish that these flashes were due to fusion, we showed that red blood cells, which normally do not attach to planar membranes, were able to bind to membranes that had been exposed to virus under fusigenic conditions. The amount of binding correlated with the amount of flashing. This indicates that flashes signaled the reconstitution of the hemagglutinin glycoprotein (HA) of influenza virus, a well-known erythrocyte receptor, into the planar membrane, as would be expected in a fusion process. The flash rate on ganglioside-containing asolectin membranes increased as the pH was lowered. This is also consistent with the known fusion behavior of influenza virus with cell membranes and with phospholipid vesicles. We conclude that the flashes result from the fusion of individual virions to the planar membrane.     

Female preference for male courtship flashes in Photinus ignitus fireflies

In Photinus fireflies, males produce spontaneous bioluminescentcourtship flashes. Females preferentially respond to particularmale flashes with flashes of their own. This study exploredvariation in female flash responsiveness as a function of maleflash duration, female condition, lantern size, and lanterndistance, as well as the relationship between male characteristicsand spermatophore mass in Photinus ignitus fireflies. We determinedfemale preference by scoring female flash response to simulatedmale flashes and determined variation in overall female flashresponsiveness for laboratory-mated, laboratory-fed, and controlP. ignitus females. Flash duration, lantern size, and body masswere recorded for field-collected males. Males were then matedto determine spermatophore mass. Females exhibited greater preferencefor artificial flashes representing the upper range of conspecificmale flash duration and lantern size as well as flashes producedat a closer distance. Both laboratory-mated and laboratory-fedP. ignitus females showed lower overall responsiveness acrossall flash durations relative to control females that did notmate or feed in the laboratory. Male flash duration predicteda significant proportion of the variation in spermatophore massfor early-season males. These results suggest that female Photinusignitus may prefer long flashes in order to obtain the directbenefit of larger spermatophores and may adjust their overallflash responsiveness as the relative importance of this benefitvarieswith changing female condition.     

Detection of red and green flashes: evidence for cancellation and facilitation.

Green and red flashes of light will differentially stimulate the middle- and long-wavelength sensitive cones. Interaction of cone signals was studied by measuring increment thresholds for combinations of green and red flashes on a yellow adapting field. When the yellow adapting field was at 10.000 trolands (td), green and red incremental flashes (1 degree, 200-msec duration) produced cancellation when presented simultaneously and facilitation when presented sequentially. A green incremental flash (1.15 degrees, 200 msec, 5000-td adaptation field) and red decremental flash, or vice versa, produced facilitation when presented simultaneously. The results can be explained by color-differencing, opponent-mechanisms. The cancellation effect for the simultaneous incremental flashes largely disappeared when the flashes were exposed briefly (10 msec) or reduced in size (0.04 degrees). It is unlikely that the stimuli were exclusively detected by achromatic, luminance channels, as suggested by previous work, since observers could partially distinguish the hue of threshold flashes of 570- and 590-nm light (0.04 degrees, 10 msec) on a bright yellow field.     

Imaging superoxide flash and metabolism-coupled mitochondrial permeability transition in living animals

The mitochondrion is essential for energy metabolism and production of reactive oxygen species (ROS). In intact cells, respiratory mitochondria exhibit spontaneous "superoxide flashes", the quantal ROS-producing events consequential to transient mitochondrial permeability transition (tMPT). Here we perform the first in vivo imaging of mitochondrial superoxide flashes and tMPT activity in living mice expressing the superoxide biosensor mt-cpYFP, and demonstrate their coupling to whole-body glucose metabolism. Robust tMPT/superoxide flash activity occurred in skeletal muscle and sciatic nerve of anesthetized transgenic mice. In skeletal muscle, imaging tMPT/superoxide flashes revealed labyrinthine three-dimensional networks of mitochondria that operate synchronously. The tMPT/superoxide flash activity surged in response to systemic glucose challenge or insulin stimulation, in an apparently frequency-modulated manner and involving also a shift in the gating mode of tMPT. Thus, in vivo imaging of tMPT-dependent mitochondrial ROS signals and the discovery of the metabolism-tMPT-superoxide flash coupling mark important technological and conceptual advances for the study of mitochondrial function and ROS signaling in health and disease.     

Effects of light flashes on the dark closure of Albizzia julibrissin pinnules

An electronic flash unit is used to deliver, at the beginning of a 10 min dark period and within a few ms, large doses of light to Albizzia julibrissin pinnules, to ascertain their effects on the rate of pinnule closing. In a series of alternating light flashes at 710 and 550 nm, the first 710 nm light flash significantly retards closing. A following light flash at 550 nm negates the far-red induced delay. The second 710 nm light flash delays closing less effectively than the first when given within 4 s after the green flash, but is just as effective when given after 30 s. The delay brought about by the second 710 nm light flash is again abolished by a light flash at 550 nm. A light flash at 660 nm has no effect on pinnule closing by itself and is also ineffective in reversing the far-red induced delay. A series of ten 710 nm light flashes becomes most effective in delaying closure when there is a dark interval of one min between flashes. The closing delay induced by a 710 nm light flash escapes reversal by a 550 nm light flash when the dark interval between the two flashes exceeds 2–3 min. A 750 nm light flash has no retarding effect on pinnule closing, but it becomes effective when preceded by a 660 nm or 550 nm light flash. The results obtained are suggested to be due to light absorbed by phytochrome and an unknown photoreceptor with green, far-red photoreversal property.     

Thermoregulatory physiology of menopausal hot flashes: a review

Hot flashes during the climacteric years have long been a frequent clinical complaint, generally considered within the realm of the internist, gynecologist, or endocrinologist. Yet the underlying mechanism of hot flashes remains unknown. Only within the past 10 years has there been significant research on hot flashes as a disturbance of thermoregulation. This paper focuses on thermoregulatory aspects of hot flashes, reviewing current knowledge of the thermoregulatory physiology and endocrinology of hot flashes and discussing future avenues for research. Hot flashes are compared with fever in terms of thermoregulatory changes and speculated mechanisms. Although several substances in the peripheral circulation are found in increased concentrations during hot flashes, none is a trigger for a hot flash. The pattern of hot flash occurrence is striking in its regularity, and the possibility of endogenous rhythmicity is discussed. Recently, investigators have begun to explore a primate model of menopausal hot flashes. These studies are summarized. Finally, the multiple effects of estrogen on various systems of the body and their interrelationships are discussed. An understanding of the mechanism of hot flashes would not only be of importance to women suffering with hot flashes but would further our knowledge of thermoregulatory function and the interactions between thermoregulatory and reproductive systems.     

Flash photography does not induce stress in the Ram cichlid Mikrogeophagus ramirezi (Myers & Harry, 1948) in aquaria

The Ram cichlid Mikrogeophagus ramirezi (Myers & Harry, 1948) was used to examine whether flash photography can be a stressor for fish in aquaria. The point in time of the highest cortisol concentration in whole‐body homogenates was determined by the temporal course of the cortisol response following air exposure as stressor. Thus, the potential stress response to camera flashlight was examined 22 min after exposure to a single flash and after repeated flashes by applying 10 flashes per minute for 8 hr/day over 2 weeks. In both experiments the stress parameters cortisol and glucose were not increased due to exposure to the flash light. In contrast, after a single flash mean cortisol values tended to be lower and mean glucose values were significantly lower than in the control group, and after repeated flashes mean cortisol and glucose values were significantly lower than in the control group. Furthermore, treated fish showed less intraspecific aggressive interactions. These results can be explained by a possible dazzling or irritation of the fish by camera flashes, thus reducing the natural aggressive behaviour and, consequently, the concentration of stress hormones and mobilisation of glucose. In summary, the physiological stress parameters cortisol and glucose do not reveal that flash photography induces stress in M. ramirezi, and, on the contrary, might even reduce stress effects by lowering intraspecific aggressive behaviour of the fish.     

Synergistic Triggering of Superoxide Flashes by Mitochondrial Ca2+ Uniport and Basal Reactive Oxygen Species Elevation

Mitochondrial superoxide flashes reflect a quantal, bursting mode of reactive oxygen species (ROS) production that arises from stochastic, transient opening of the mitochondrial permeability transition pore (mPTP) in many types of cells and in living animals. However, the regulatory mechanisms and the exact nature of the flash-coupled mPTP remain poorly understood. Here we demonstrate a profound synergistic effect between mitochondrial Ca²⁺ uniport and elevated basal ROS production in triggering superoxide flashes in intact cells. Hyperosmotic stress potently augmented the flash activity while simultaneously elevating mitochondrial Ca²⁺ and ROS. Blocking mitochondrial Ca²⁺ transport by knockdown of MICU1 or MCU, newly identified components of the mitochondrial Ca²⁺ uniporter, or scavenging mitochondrial basal ROS markedly diminished the flash response. More importantly, whereas elevating Ca²⁺ or ROS production alone was inefficacious in triggering the flashes, concurrent physiological Ca²⁺ and ROS elevation served as the most powerful flash activator, increasing the flash incidence by an order of magnitude. Functionally, superoxide flashes in response to hyperosmotic stress participated in the activation of JNK and p38. Thus, physiological levels of mitochondrial Ca²⁺ and ROS synergistically regulate stochastic mPTP opening and quantal ROS production in intact cells, marking the flash as a coincidence detector of mitochondrial Ca²⁺ and ROS signals.     

The sensitivity of the labellar sugar receptors of Phormia regina in relation to feeding

The hypothesis that behavioural feeding threshold of P. regina modulates and is modulated by the sensitivity of the labellar contact chemoreceptors is not supported by the examination of individual flies.Sensitivity (number of impulses fired in the first second of stimulation) of the sugar receptors in selected labellar hairs of flies of known age was recorded periodically on a fixed schedule for up to 72 hr. Experimental flies were hand fed 2.0 M fructose once every 24 hr. No correlations between feeding or age and receptor sensitivity were found. Statistically significant changes in firing frequency did occur but were unrelated to feeding and age.The proboscis extension response, on which behavioural threshold measures are based, is known to be triggered by the first few sugar receptor spikes of sufficient frequency. Neither age nor feeding significantly affected the number or frequency of impulses during the first 50 msec of stimulation.     

Abdomen Posture and Flash Gesture Direction in a Female Synchronic Firefly <Emphasis Type="Italic">Photinus carolinus</Emphasis> (Green) (Coleoptera: Lampyridae)

North American Photinus fireflies use bioluminescent flashes to communicate an individual’s species and sex, and to attract potential mates. A female firefly responds to a male firefly’s courtship flash with her own species-specific flash. We used a photic stimulator to produce male-like species-specific P. carolinus LED courtship flashes. These evoked species-specific response flashes from a female. The female’s flashes were preceded by a flash gesture comprising a sequence of abdominal postural adjustments (pitch, roll, and yaw). These gestures changed her lantern’s orientation which, at rest, was downward towards the substrate. Our results demonstrate that these gestures mediate a lateralization of the female’s response flashes towards the direction of the stimulating LED. That is, she directs her response to the left of midline when stimuli are presented from her left, and similarly, she directs her response to the right of midline when stimuli are presented from her right. The directional aspect of the flash gesture adds a new perspective to the complexity of the behaviors associated with flash communication in fireflies. Lateralization of the flash gesture suggests that the female’s visual system processes information about the location of male’s flashes as well as their temporal pattern.     

The induction kinetics of bacterial photophosphorylation. Threshold effects by the phosphate potential and correlation with the amplitude of the carotenoid absorption band shift

1. ATP synthesis (monitored by luciferin-luciferase) can be elicited by a single turnover flash of saturating intensity in chromatophores from Rhodopseudomonas capsulata, Kb1. The ATP yield from the first to the fourth turnover is strongly influenced by the phosphate potential: at high phosphate potential (?11.5 kcal/mol) no ATP is formed in the first three turnovers while at lower phosphate potential (?8.2 kcal/mol) the yield in the first flash is already one half of the maximum, which is reached after 2–3 turnovers.2. The response to ionophores indicates that the driving force for ATP synthesis in the first 20 turnovers is mainly given by a membrane potential. The amplitude of the carotenoid band shift shows that during a train of flashes an increasing ΔΨ is built up, which reaches a stationary level after a few turnovers; at high phosphate potential, therefore, more turnovers of the same photosynthetic unit are required to overcome an energetic threshold.3. After several (six to seven) flashes the ATP yield becomes constant, independently from the phosphate potential; the yield varies, however, as a function of dark time (t_d) between flashes, with an optimum for t_d = 160–320 ms.4. The decay kinetics of the high energy state generated by a long (125 ms) flash have been studied directly measuring the ATP yield produced in post-illumination by one single turnover flash, under conditions of phosphate potential (?10 kcal/mol), which will not allow ATP formation by one single turnover. The high energy state decays within 20 s after the illumination. The decay rate is strongly accelerated by 10^?8 M valinomycin.5. Under all the experimental conditions described, the amplitude of the carotenoid signal correlates univocally with the ATP yield per flash, demonstrating that this signal monitores accurately an energetic state of the membrane directly involved in ATP synthesis.6. Although values of the carotenoid signal much larger than the minimal threshold are present, relax slowly, and contribute to the energy input for phosphorylation, no ATP is formed unless electron flow is induced by a single turnover flash.7. The conclusions drawn are independent from the assumption that a ΔΨ between bulk phases is evaluable from the carotenoid signal.     

Influence of transcranial magnetic stimulation on spike-wave discharges in a genetic model of absence epilepsy

Transcranial magnetic stimulation (TMS) impulses, (0.5 Hz, 3 impulses) were presented at threshold intensity to male WAG/Rij rats. One group received stimuli, which involved motor responses of hindlimbs, rats of the second group received sham stimulation. Electrocorticograms (ECoG) were recorded before and up to 2 hr from the moment of transcranial magnetic stimulation. It was established that such stimulation engendered a reduction of spike-wave discharge (SWD) bursts duration. This effect was most pronounced in 30 min from the moment of cessation of stimulation, when a decrease of 31.4% was noted in comparison with sham-stimulated control group. The number of bursts of spike-wave discharges was reduced, but did not reach significant difference when compared both with pre-stimulative base-line level and with sham-stimulated control rats. Bursts of spike-wave discharges restored up to pre-stimulative level in 90-150 minutes from the moment of cessation of transcranial stimulation. It can be concluded that transcranical magnetic stimulation possessed an ability to engender short-time suppression of bursts of spike-wave discharges in WAG/Rij rats.     

Synthesis and hydrolysis of ATP by intact chloroplasts under flash illumination and in darkness

ATP concentrations were measured in isolated intact spinach chloroplasts under various light and dark conditions. The following results were obtained: (1) Even in darkened chloroplasts and in the absence of exogenous substrates, ATP levels in the chloroplast stroma were significant. They decreased on addition of glycerate, phosphoglycerate or dihydroxyacetone phosphate. When dihydroxyacetone phosphate and oxaloacetate were added together, ATP levels increased in darkened chloroplasts owing to substrate level phosphorylation. (2) Under illumination with saturating single turnover flashes, oxygen evolution in the presence of phosphoglycerate, whose reduction requires ATP, was no lower on a unit flash basis at the low flash frequency of 2 Hz than at higher frequencies. Quenching of 9-aminoacridine fluorescence, which indicates the formation of a proton gradient in intact chloroplasts, decreased with decreasing flash frequencies, until there was no significant fluorescence quenching at a flash frequency of about 2 Hz. In contrast to intact chloroplasts, broken chloroplasts did not phosphorylate much ADP at the low flash frequency of 2 Hz. (3) Flashing at extremely low frequencies (0.2 Hz) caused ATP hydrolysis rather than ATP synthesis in intact chloroplasts. At higher flash frequencies, synthesis replaced hydrolysis. Still, even at high frequencies (10 Hz), the first flashes of a series of flashes given after a long dark time always decreased chloroplast ATP levels.From these results, it is concluded that the enzyme, which mediates ATP synthesis in the light, is inactive in darkened intact chloroplasts. Its light activation can be separated from the formation of the high energy condition, which results in ATP synthesis. After its activation, the enzyme catalyzes a reversible reaction.