Distribution of labelled auxin and derivatives in stem tissues of intact and decapitated broad-bean plants in relation to apical dominance

[³H]-auxin (0.13 to 0.18 nmol) was applied to the apical bud of broadbean plants (Vicia faba L. cv. Aguadulce). After 24 h, the exportation from the donor organ was ended. After 48 h, i.e. 10–15 h after the passage of the [³H]-auxin pulse into the root system, the distribution and the nature of labelled molecules located in the basal part of the stem and in the axillary buds were investigated. Chromatographic analyses concerned both intact plants and plants decapitated 12 h, 24 h or 42 h after the [³H]-auxin application. In intact plants, there was no significant amount of [³H]-auxin in the axillary buds, whose radioactivity was very low compared to the stem tissues. The labelled molecules with the Rf of auxin represented 50% or more of the whole radioactivity of the stem tissues. The distribution of [³H]-auxin was not uniform along the stem. In particular, the cotyledonary node zone, bearing the most inhibited buds, which is known to be an important centre of label retention, contained the highest amounts of labelled auxin both in intact and decapitated plants. The decapitation was quickly followed by a decrease of the [³H]-auxin amount in the stem base more than 15 cm away from the wound, particularly in the scale leaf nodes, whose axillary buds were mainly the ones to grow after relief from apical dominance. The induction of this early decrease was clearly distinct in plants decapitated when auxin exportation from the donor organ was ended.     

The role of hormones in apical dominance. New approaches to an old problem in plant development

The role of hormones in apical dominance has been under investigation with traditional 'spray and weigh' methods for nearly 5 decades. Even though the precision of hormone content analyses in tissue has greatly improved in recent years, there have been no significant breakthroughs in our understanding of the action mechanism of this classical developmental response. Auxin appears to inhibit axillary bud outgrowth whereas cytokinins will often promote it. Conclusive evidence for a direct role of these or other hormones in apical dominance has not been forthcoming. However, promising new tools and approaches recently have begun to be utilized. The manipulation of endogenous hormone levels via the use of transgenic plants transformed with bacterial genes ( iaaM and ipt from Agrobacterium tumefaciens and iaaL from Pseudomonas syringae pv. savastanoi ) has demonstrated powerful effects of auxin and cytokinin on axillary bud outgrowth. Also, possible auxin and cytokinin involvement of rolB and C genes from Agrobacterium rhizogenes whose activity is associated with reduced apical dominance in dicotyledons has received considerable attention. The characterization of unique mRNAs and proteins in non-growing and growing lateral buds before and after apical dominance release is helping to lay the groundwork for the elucidation of signal transduction and cell cycle regulation in this response. The use of auxin-deficient, and auxin/ethylene-resistant mutants has provided another approach for analyzing the role of these hormones. The presumed eventual employment of molecular assay systems (SAUR/GH3 promoters fused with GUS reporter gene) which are presently being developed for analyzing auxin localized in lateral buds will hopefully provide a critical test for the direct auxin inhibition hypothesis.     

Endogenous abscisic acid levels in stems and axillary buds of intact or decapitated broad-bean plants (Vicia faba L.)

Endogenous levels of abscisic acid (ABA) were measured by gas-liquid chromatography (electron capture) in stems and axillary buds of intact or decapitated broad-bean plants ( Vicia faba L. cv. Aguadulce). Endogenous ABA was distributed in the main axis according to a concentration gradient from the apical part of the stem towards the base. Axillary buds contained ABA levels which were from 4 to 9 times higher than those in the corresponding nodes and internodes. Decapitation of the plant was followed within 6 h by a large decrease of ABA levels in all the parts of the main axis. The diminution of ABA content was the most important in axillary buds released from apical dominance. Twenty-four hours after the decapitation, the ABA concentration further decreased in the upper parts of the stem, while no modification was observed in the basal parts of the stem containing the smallest levels of ABA.     

Changes in the ratio of cis-trans to trans-trans abscisic acid during ripening of apple fruits

Immediately after harvest, abscisic acid (ABA) extracted from fruits of the apple cultivar Golden Delicious comprised solely the cis-trans isomer. During postharvest ripening, however, trans-trans ABA accumulated and finally exceeded the level of cis-trans ABA. The two geometrical isomers were separated and identified by high-performance liquid chromatography (HPLC) and combined gas chromatography-mass spectrometry. After purification by HPLC the putative trans-trans isomer yielded considerable quantities of cis-trans ABA, when irradiated with UV light. This isomerization was more rapid than the reverse reaction. The physiological significance of the accumulation of trans-trans ABA is discussed, as well as the applications of these results in the use of trans-trans ABA as an internal standard during the extraction and quantification of ABA from plant tissues.Abbreviations ABA 2-cis-4-trans abscisic acid - t-ABA 2-trans-4-trans abscisic acid - ECD electron capture detector - GC-MS combined gas chromatography-mass spectrometry - HPLC high-performance liquid chromatography - PVP water insoluble polyvinylpyrroli-done - UV ultraviolet     

Axillary bud flowering after apical decapitation in Pharbitis in relation to photoinduction

The flowering response of axillary buds of seedlings of Pharbitis nil Choisy, cv. Violet, was examined in relation to the timing of apical bud removal (plumule including the first leaf or second leaf) before or after a flower-inductive 16-h dark period. When the apical bud was removed well before the dark period, flower buds formed on the axillary shoots that subsequently developed, but when removed just before, or after, the dark period, different results were observed depending on the timing of the apical bud removal and plant age. In the case of 8-day-old seedlings, fewer flower buds formed on the axillary shoots developing from the cotyledonary node when plumules were removed 20 to 0 h before the dark period. When the apical bud was removed after the dark period, no flower buds formed. Using 14-day-old seedlings a similar reduction of flowering response was observed on the axillary shoots developing from the first leaf node when the apical bud was removed just after the dark period. To further elucidate the relationship between apical dominance and flowering, kinetin or IAA was applied to axillary buds or the cut site where the apical bud was located. Both chemicals influenced flowering, probably by modulating apical dominance which normally forces axillary buds to be dormant.     

Effect of apex excision and replacement by 1-naphthylacetic acid on cytokinin concentration and apical dominance in pea plants

As known from literature lateral buds from pea ( Pisum sativum ) plants are released from apical dominance when repeatedly treated with exogenous cytokinins. Little is known, however, about the endogenous role of cytokinins in this process and whether they interact with basipolar transported IAA, generally regarded as the main signal controlling apical dominance. This paper presents evidence that such an interaction exists.
The excision of the apex of pea plants resulted in the release of inhibited lateral buds from apical dominance (AD). This could be entirely prevented by applying 1-naphthylacetic acid (NAA) to the cut end of the shoot. Removal of the apex also resulted in a rapid and rather large increase in the endogenous concentrations of zeatin riboside (ZR), isopentenyladenosine (iAdo) and an as yet unidentified polar zeatin derivative in the node and internode below the point of decapitation. This accumulation of ZR and iAdo, was strongly reduced by the application of NAA. The observed increase in cytokinin concentration preceded the elongation of the lateral buds, suggesting that endogenous cytokinins play a significant role in the release of lateral buds from AD. However, the effect of NAA on the concentration of cytokinins clearly demonstrated the dominant role of the polar basipetally transported auxin in AD. The results suggest a mutual interaction between the basipolar IAA transport system and cytokinins obviously produced in the roots and transported via the xylem into the stem of the pea plants.     

Rapid increases in cytokinin concentration in lateral buds of chickpea (Cicer arietinum L.) during release of apical dominance

We examined the role of cytokinins (CKs) in release of apical dominance in lateral buds of chickpea (Cicer arietinum L.). Shoot decapitation or application of CKs (benzyladenine, zeatin or dihydrozeatin) stimulated rapid bud growth. Time-lapse video recording revealed growth initiation within 2 h of application of 200 pmol benzyladenine or within 3 h of decapitation. Endogenous CK content in buds changed little in the first 2 h after shoot decapitation, but significantly increased by 6 h, somewhat later than the initiation of bud growth. The main elevated CK was zeatin riboside, whose content per bud increased 7-fold by 6 h and 25-fold by 24 h. Lesser changes were found in amounts of zeatin and isopentenyl adenine CKs. We have yet to distinguish whether these CKs are imported from the roots via the xylem stream or are synthesised in situ in the buds, but CKs may be part of an endogenous signal involved in lateral bud growth stimulation following shoot decapitation. To our knowledge, this is the first detailed report of CK levels in buds themselves during release of apical dominance. Received: 12 December 1996 / Accepted: 7 January 1997     

Apical dominance in mulberry (Morus alba): Effects of position of lateral and accessory buds and leaves

Suzuki, T. 1990. Apical dominance in mulberry ( Morus alba ): Effects of position of lateral and accessory buds and leaves. – Physiol. Plant. 78: 468-474.
Removing apical portions of current growth coppice shoots from field-grown, low-pruned stumps of mulberry ( Morus alba L. cv. Shin-ichinose) caused sprouting of one or more upper main buds, almost concurrently with that of accessory buds. However, removal of the new sprouts, including those from accessory buds, slightly enhanced the sprouting of buds immediately below them, and did not affect buds lower down. In contrast, mature leaves inhibited the buds in their axils. Budless, leafy nodes on the upper part of pruned shoots tended to swell after treatment, perhaps due to the accumulation of substances translocated from the roots and possibly from the remaining leaves. Lateral buds at different positions along the shoot differed in their sprouting ability with buds lower on the shoot being more inhibited. This inhibition gradient dissappeared when all coppice shoots on one stump were pruned to the same bud position, suggesting inhibition from neighboring, actively growing shoots. These results demonstrate that acropetal influences are important in bud dominance relationships.     

Estimates of free and bound indole-3-acetic acid and zeatin levels in relation to regulation of apical dominance and tiller release in oat shoots

Oat stem segments containing quiescent lateral (tiller) buds during times of strong apical dominance, and growing buds released from this inhibition, were collected for analysis of native auxin and cytokinins. Free IAA and IAA conjugates were determined by a¹⁴C-IAA and¹⁴C-IBA double isotope dilution assay. Free zeatin (Z), zeatin riboside (Z-r), and their glucoside conjugates were purified from butanol-soluble fractions by means of a cellulose phosphate exchanger and thin-layer chromatography. Hormones were analyzed by gas chromatography and mass spectrometry (GC-MS). Results of these analyses indicate that changes in free and bound IAA within the stem do not correlate well with the release of tiller buds (as brought about by decapitation, gravistimulation, or the emergence of the inflorescence). However, increases in Z-r levels are well correlated with tiller release. The glucoside conjugate of Z-r may act as a storage form of cytokinin in quiescent tiller buds. In light of these results, we find that the auxin-cytokinin ratio in oat stem segments is shifted during tiller     

Glycosylation of free trans-trans abscisic acid as a contributing factor in bud dormancy break

By means of gas-liquid chromatography determination it was found that progress of dormancy break of almond buds is a function of relative proportions of free and glycoside-bound abscisic acid. Successive stages of bud break manifest a marked increase of bound abscisic acid accompanied by a parallel decrease in endogenous levels of the free form. Of the two stereoisomers involved it was found that while the $\text{cis-trans}$ form maintains a more or less stable level throughout, changes were detected primarily in the $\text{trans-trans}$ form. It is thus postulated that the binding of free hormone as well as its total content are of major physiological importance in the process of bud dormancy break.     

Transport and metabolism of labelled abscisic acid in broad-bean plants (Vicia faba L.)

The movement of 2-¹⁴C-abscisic acid applied to a mature leaf of broad-bean plants ( Vicia faba L. cv. Aguadulce) was investigated by liquid scintillation counting and autoradiography. The radioactivity was readily transported into the whole plant by the phloem after 90 min. Thereafter, radioactivity moved towards the upper part of the plant, where it accumulated in the young growing leaves and in the apical bud. During transport, 2-¹⁴C- ABA was slightly metabolized, and a subsequent rapid metabolism occurred in the young leaves of the apical part of the plant and in the axillary buds released from apical dominance in decapitated plants. Transport of exogenous ABA from the apical bud presented the characteristics of a diffusion transport.     

Abscisic acid and apical dominance in Phaseolus coccineus L.

Abscisic acid (ABA) in lanolin, applied to the internode of decapitated runner bean plants enhances the outgrowth of lateral buds. The optimum concentration of the paste is 10^-5 M. The effect of ABA is counteracted by indoleacetic acid (IAA) but not by gibberellic acid (GA₃). There is no effect when ABA is applied to the apical bud or lateral buds of intact plants. However, 13.2 ng given to the lateral buds of decapitated plants stimulate their growth, whereas higher concentrations are inhibitory. Consequently, ABA enhances growth of lateral buds directly, but only when apical dominance is already weakened. The growth of the decapitated 2^nd internode was not affected by ABA. Radioactivity from [2-¹⁴C] ABA, applied to nonelongating 2^nd internode stumps of decapitated runner bean plants moves to the lateral buds, whereas [1-¹⁴C]IAA-and [³H]GA₁-translocation is much weaker. ABA transport is inhibited if IAA or [³H]GA₁ is applied simultaneously. In elongating internodes [¹⁴C]ABA is almost completely immobile. [¹⁴C]IAA-and [³H]GA₁-translocation is not affected by ABA. The amount of radioactivity from labelled ABA, translocated to the lateral buds, is highest during the early stages of bud outgrowth.Abbreviations ABA 2,4-cis, trans-(+)-abscisic acid - GA gibberellic acid - IAA indoleacetic acid - p.l. plain lanolin     

Expression of an mRNA with sequence similarity to pea dehydrin (Psdhn 1) in guard cells of Vicia faba in response to exogenous abscisic acid

The function and location of guard cells uniquely subject them to stress. First, stomatal movements require large fluctuations in the concentration of potassium salts. Second, guard cell inner walls are the first surfaces exposed to evaporation and apoplastic solutes may accumulate there as a result. We have therefore investigated whether guard cells exhibit atypical expression of dehydrin genes because dehydrins accumulate in vegetative tissues in response to water stress. We have also assayed for osmotin mRNA, which is up-regulated in leaves in response to various stresses. mRNA probes for several representative genes were used with RNA extracts from control and water-stressed Vicia faba leaflets. Correlatively, these probes were used with RNA extracts from "isolated' guard cells that had been incubated with combinations of abscisic acid, mannitol and Ca²⁺. (Isolated guard cells are epidermal strips sonicated to destroy cells other than guard cells.) Hybridization with the probe prepared for a dehydrin from Pisum sativum (Psdhn 1) was detected in leaf extracts only if the leaf had been stressed. Similarly, after 1- and 6-h incubations with abscisic acid, isolated guard cells contained an mRNA that hybridized with the probe for Psdhn 1. Appearance of this abscisic acid-dependent mRNA required neither mannitol nor exogenous Ca²⁺. Regardless of the conditions or tissue, no hybridization was detected with the probe against osmotin, but our interpretation of this result is qualified. The simplest conclusion is that atypical expression of dehydrin is not the mechanism by which guard cells cope with their peculiar function and location.     

Apical dominance and the levels of indole acetic acid in Phaseolus lateral buds

Combined gas chromatography-mass spectrometry procedures have been used to establish that the indole acetic acid levels of lateral buds from Phaseolus seedlings rise following removal of the shoot apex.Abbreviations GC gas chromatograph - GC-MS combined gas liquid chromatography mass spectrometry - bis-TMS bis-trimethylsilyl - IAA indole acetic acid - MPM multiple-peak monitoring - MS mass spectrometer - GLC gas liquid chromatography - TLC thin-layer chromatography     

Ethylene, indoleacetic acid and apical dominance in peas: A reappraisal

Decapitation of peas ( Pisum sativum L. cv. Greenfeast) promoted sprouting of the lower buds with the most active growth in the first week occurring in the bud at the lowest fully expanded leaf node. Addition of 3-indolyl acetic acid (IAA; a 0.03 M solution, applied al 10 and 25 μg/plant) inhibited bud outgrowth whether added to the cut stump or injected above or below the lowest leaf node. Ethylene evolution by the nodal region decreased following decapitation, but increased greatly if IAA was added to the cut stump. Ethylene gas (3, 15 and 1 500 ul/l) or the precursor ACC (l-aminocyclopropane-I-carboxylic acid) reduced bud outgrowth while factors which scrub ethylene (mercuric perchlorate). inhibit ethylene synthesis (canaline), or prevent its action (silver nitrate), enhanced bud growth on decapitated plants, It was concluded that auxin-induced inhibition of bud growth through an increase in ethylene synthesis is a more logical hypothesis than the direct inhibition by auxin per se since a) acropetal movement of the inhibitory principle occurred whereas [¹⁴C] IAA movement in stems was basipetal, b) a decline in the levels of ethylene evolution was correlated with bud outgrowth in decapitated plants and c) exogenous application of chemical agents which increase or decrease ethylene level or response lead to correlative decreases or increases in bud outgrowth, respectively.     

The possible roles of nutrient deprivation and auxin repression in apical control

Apical control is the suppression of growth in lower branches by a higher dominant branch or leader shoot. We investigated possible mechanisms involved in this developmental response in three widely diverse species (Japanese morning glory, Ipomoea nil, hybrid poplar, Populus trichocarpa, × P. deltoides, and Douglas-fir, Pseudotsuga menziesii). The following two hypotheses were tested: (1) the mineral nutrient-deprivation hypothesis, which is that the continued growth of the lower branches is repressed by the diversion of nutrients to the upper dominating branch or shoot, and (2) the auxin-repression hypothesis, which is that auxin produced in the upper dominating branch or shoot moves down to the lower branches where continued growth is repressed. The results of experiments involving the manipulation of available nutrients by dominant branch removal and fertilization were consistent with the first hypothesis for morning glory, poplar, and for second- or third flushing of lateral branches in Douglas-fir. The results of the experiments involving auxin (NAA, 1-naphthalene acetic acid) replacement treatments on decapitated shoots bearing growing lateral branches were inconsistent with the second hypothesis in morning glory, poplar and in first-flushing Douglas-fir. However, despite concerns about possible NAA toxic effects, there was evidence of auxin repression of second flushing in Douglas-fir. Overall, the data supported a significant role for nutrient availability but not for auxin repression in apical control of morning glory and poplar. In Douglas-fir, apical control in first-flushing lateral branches from over-wintered buds was largely insensitive to both nutrient availability and auxin repression; however, second flushing was sensitive to both.     

A reappraisal of the role of abscisic acid and its interaction with auxin in apical dominance

BACKGROUND AND AIMS: Evidence from pea rms1, Arabidopsis max4 and petunia dad1 mutant studies suggest an unidentified carotenoid-derived/plastid-produced branching inhibitor which moves acropetally from the roots to the shoots and interacts with auxin in the control of apical dominance. Since the plant hormone, abscisic acid (ABA), known to inhibit some growth processes, is also carotenoid derived/plastid produced, and because there has been indirect evidence for its involvement with branching, a re-examination of the role of ABA in apical dominance is timely. Even though it has been determined that ABA probably is not the second messenger for auxin in apical dominance and is not the above-mentioned unidentified branching inhibitor, the similarity of their derivation suggests possible relationships and/or interactions. METHODS: The classic Thimann-Skoog auxin replacement test for apical dominance with auxin [0.5 % naphthalene acetic acid (NAA)] applied both apically and basally was combined in similar treatments with 1 % ABA in Ipomoea nil (Japanese Morning Glory), Solanum lycopersicum (Better Boy tomato) and Helianthus annuus (Mammoth Grey-striped Sunflower). KEY RESULTS: Auxin, apically applied to the cut stem surface of decapitated shoots, strongly restored apical dominance in all three species, whereas the similar treatment with ABA did not. However, when ABA was applied basally, i.e. below the lateral bud of interest, there was a significant moderate repression of its outgrowth in Ipomoea and Solanum. There was also some additive repression when apical auxin and basal ABA treatments were combined in Ipomoea. CONCLUSION: The finding that basally applied ABA is able partially to restore apical dominance via acropetal transport up the shoot suggests possible interactions between ABA, auxin and the unidentified carotenoid-derived branching inhibitor that justify further investigation.     

Changes in abscisic acid and indole-3-acetic acid in axillary buds of Elytrigia repens released from apical dominance

Growth of axillary buds on the rhizomes of Elytrigia repens (L) Nevski is strongly dominated by the rhizome apex, by mechanisms which may involve endogenous hormones. We determined the distribution of indole-3-acetic acid (IAA) and abscisic acid (ABA) in rhizomes and measured (by gas-chromatography-mass spectrometry) their content in axillary buds after rhizomes were decapitated. The same measurements were also made in buds induced to sprout by removing their subtending scale leaves. The ABA content tended to be higher in the apical bud and in the axillary buds than in the adjacent internodes, and tended to decline basipetally in the internodes and scale leaves. IAA was similary distributed, except that there was less difference between the buds and other rhizome parts. After rhizomes were decapitated, the ABA content of the first axillary bud declined to 20% of that of control values within 24 h, while the IAA content showed no marked tendency to change. The ABA content also declined within 12 h in the first axillary bud after rhizomes were denuded, while the content of IAA tended to increase after 6 h. These changes occurred before the length of the first axillary bud increased 24–48 h after rhizomes were decapitated or denuded. We conclude that the release of axillary buds from apical dominance in E. repens does not require IAA content to be reduced, but is associated with reduced ABA content.     

Free and bound abscisic acid in relation to water potential in aging cotyledons of Lupinus albus

To evaluate the capacity for biosynthesis of abscisic acid (ABA) in the cotyledons of developing plants of Lupinus albus L. (= L. termis Forssk.) cv. Giza 1, and the physiological role which the compound may perform during senescence, the levels of free and bound forms of ABA have been estimated in conjunction with the natural changes in the water potential of the tissues during a period of 18 days after sowing. In the cotyledons of the dry seeds, the bound form of ABA is about three times as abundant as the free form. Peaks of the free ABA occur on days 3 and 8, when the water potential reaches minimum values of –1060 and –950 kPa respectively. Since the concentration of the bound ABA does not drop during days 1–8, it is suggested that the peaks of free ABA are due to synthesis in the expanding cotyledons in response to the two water potential minima. During the post expansion period (days 9–18), free ABA appears to be released from a bound form as a consequence of decreased synthetic activity and increased tissue deterioration. The remarkable increase in the rate of the dry weight loss which immediately follows each peak of ABA suggests the involvement of ABA in the senescence of the cotyledons by speeding up the translocation of nutrients to the developing axis.     

Indole-3-acetic acid transport in apical dominance: a quantitative approach. Influence of endogenous and exogenous IAA apical source on inhibitory power of IAA transport

The relationship between the amount of indole-3-acetic acid transported (IAA transport) through the second node of 7-day-old pea seedlings and the degree of inhibition of axillary bud outgrowth at the same node was studied. For both the endogenous apical IAA source (leaves of apical bud) and the exogenous one (lanolin paste containing 0.25–1.0 mg mL^–1 IAA) the slope of linear dependence between inhibition and IAA transport was similar. However, the same IAA transport induced different inhibitions, which were higher for the endogenous source. Moreover, the apical bud induced higher inhibition at the same level of IAA transport when the 4th leaf was present than when it was absent. Apparently, the source of IAA also may regulate the inhibitory power of IAA transported from it. IAA transport appears to consists of active and slightly active one moving along different pathways.Abbreviations a and b coefficients of linear regression of the type y = a+bx; - confidence level of t-test - ELISA enzyme linked immunosorbent assay - GR_1,2 ^e/d growth rate of the lateral bud of experimental/decapitated (control) pea plants at the first and second days after treatment or decapitation - I degree of inhibition of lateral bud outgrowth - IAA indole-3-acetic acid - L_1,2,3 the lengths of lateral bud at 1, 2 or 3rd day after treatment or decapitation of pea plants - n data number - r correlation coefficient - T amount of IAA transported through the second node of pea plant for 3 hours - TIBA 2, 3, 5-triiodobenzoic acid - t-test statistical test used here to compare slopes of linear regressions (y = a+bx) calculated as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiDaiaabc% cacaqG9aGaaeiiaiaadkgadaWgaaWcbaGaaGymaaqabaGccaqGGaGa% aeylaiaabccacaWGIbWaaSbaaSqaaiaaikdaaeqaaOGaaeiiaiaab+% cacaqGGaWaaOaaaeaacaqGBbaaleqaaOGaaeikaiaabohacaqGLbGa% aeiiaiaadkgadaWgaaWcbaGaaGymaaqabaGccaqGPaWaaWbaaSqabe% aacaqGYaaaaOGaaeiiaiaabUcacaqGGaGaaeikaiaabohacaqGLbGa% aeiiaiaadkgadaWgaaWcbaGaaGOmaaqabaGccaqGPaWaaWbaaSqabe% aacaqGYaaaaOGaaeyxaiaab6caaaa!524A!\[{\text{t = }}b_1 {\text{ - }}b_2 {\text{ / }}\sqrt {\text{[}} {\text{(se }}b_1 {\text{)}}^{\text{2}} {\text{ + (se }}b_2 {\text{)}}^{\text{2}} {\text{]}}{\text{.}}\]