Regeneration of mirror symmetrical limbs in the axolotl

Measurements of tubulin exchange into and from bovine brain microtubules at steady state in vitro were made with 3H-GTP as a marker for tubulin addition to or loss from microtubules. Tubulin has an exchangeable GTP binding site that becomes nonexchangeable in the microtubule. We found that tubulin addition to and loss from microtubules under steady state conditions occurred at equivalent rates, that loss and gain were linear, and that exchange rates (percentage of total tubulin in microtubules lost or gained per hour) were dependent upon microtubule length. Furthermore, we found that podophyllotoxin blocked steady state assembly, but did not alter the rate of steady state tubulin loss. When the assembling microtubule end was pulsed with 3H-GTP at steady state, the label was almost completely retained during a subsequent chase. We conclude that the microtubule assembly-disassembly "equilibrium" is a steady state summation of two different reactions which occur at opposite ends of the microtubule, and that assembly and disassembly occur predominantly and perhaps exclusively at the opposite ends under steady state conditions in vitro.     

Taxol stabilization of microtubules in vitro: dynamics of tubulin addition and loss at opposite microtubule ends

We have investigated the effects of taxol on steady-state tubulin flux and on the apparent molecular rate constants for tubulin addition and loss at the two ends of bovine brain microtubules in vitro. These microtubules, which consist of a mixture of 70% tubulin and 30% microtubule-associated proteins (MAPs), undergo a net addition of tubulin at one end of each microtubule (A end) and a precisely balanced net loss of tubulin at the opposite end (D end) at steady state in vitro. They do not exhibit to a detectable extent the "dynamic instability" behavior described recently for MAP-free microtubules, which would be evident as an increase in the mean microtubule length and a decrease in the number of microtubules in the suspensions [Mitchison, T., & Kirschner, M. (1984) Nature (London) 312, 237-242]. We used a double-label procedure in which microtubules were labeled with tritium and carbon-14 at A ends and carbon-14 at D ends to distinguish the two ends, combined with a microtubule collection procedure that permitted rapid and accurate analysis of retention of the two labels in the microtubules. We found that taxol slowed the flux of tubulin in a concentration-dependent manner, with 50% inhibition occurring between 5 and 7 microM drug. The effects of taxol on the apparent molecular rate constants for tubulin addition and loss at the two microtubule ends were determined by dilution analysis at an intermediate taxol concentration. The results indicated that taxol decreased the magnitudes of the dissociation rate constants at the two ends to similar extents, while exerting little effect on the association rate constants.(ABSTRACT TRUNCATED AT 250 WORDS)     

Stathmin family protein SCG10 differentially regulates the plus and minus end dynamics of microtubules at steady state in vitro: implications for its role in neurite outgrowth

SCG10 (superior cervical ganglia neural-specific 10 protein) is a neuron specific member of the stathmin family of microtubule regulatory proteins that like stathmin can bind to soluble tubulin and depolymerize microtubules. The direct actions of SCG10 on microtubules themselves and on their dynamics have not been investigated previously. Here, we analyzed the effects of SCG10 on the dynamic instability behavior of microtubules in vitro, both at steady state and early during microtubule polymerization. In contrast to stathmin, whose major action on dynamics is to destabilize microtubules by increasing the switching frequency from growth to shortening (the catastrophe frequency) at microtubule ends, SCG10 stabilized the plus ends both at steady state and early during polymerization by increasing the rate and extent of growth. For example, early during polymerization at high initial tubulin concentrations (20 microM), a low molar ratio of SCG10 to tubulin of 1:30 increased the growth rate by approximately 50%. In contrast to its effects at plus ends, SCG10 destabilized minus ends by increasing the shortening rate, the length shortened during shortening events, and the catastrophe frequency. Consistent with its ability to modulate microtubule dynamics at steady state, SCG10 bound to purified microtubules along their lengths. The dual activity of SCG10 at opposite microtubule ends may be important for its role in regulating growth cone microtubule dynamics. SCG10's ability to promote plus end growth may facilitate microtubule extension into filopodia, and its ability to destabilize minus ends could provide soluble tubulin for net plus end elongation.     

Dynamics of Antarctic fish microtubules at low temperatures

The tubulins of Antarctic fishes, purified from brain tissue and depleted of microtubule-associated proteins (MAPs), polymerized efficiently in vitro to yield microtubules at near-physiological and supraphysiological temperatures (5, 10, and 20 degrees C). The dynamics of the microtubules at these temperatures were examined through the use of labeled guanosine 5'-triphosphate (GTP) as a marker for the incorporation, retention, and loss of tubulin dimers. Following attainment of a steady state in microtubule mass at 20 degrees C, the rate of incorporation of [3H]GTP (i.e., tubulin dimers) during pulses of constant duration decreased asymptotically toward a constant, nonzero value as the interval prior to label addition to the microtubule solution increased. Concomitant with the decreasing rate of label incorporation, the average length of the microtubules increased, and the number concentration of microtubules decreased. Thus, redistribution of microtubule lengths (probably via dynamic instability and/or microtubule annealing) appears to be responsible for the time-dependent decrease in the rate of tubulin uptake. When the microtubules had attained both a steady state in mass and a constant length distribution, linear incorporation of labeled tubulin dimers over time occurred at rates of 1.45 s-1 at 5 degrees C, 0.48 s-1 at 10 degrees C, and 0.18 s-1 at 20 degrees C. Thus, the microtubules displayed greater rates of subunit flux, or treadmilling, at lower, near-physiological temperatures. At each temperature, most of the incorporated label was retained by the microtubules during a subsequent chase with excess unlabeled GTP.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mechanism of inhibition of microtubule polymerization by colchicine: inhibitory potencies of unliganded colchicine and tubulin-colchicine complexes.

The tubulin-colchicine binding reaction appears to involve a number of intermediate steps beginning with rapid formation of a transient preequilibrium complex that is followed by one or more slow steps in which conformational changes in tubulin and colchicine lead to formation of a poorly reversible final-state complex. In the present study, we investigated the relative ability of unliganded colchicine and preformed final-stage tubulin-colchicine complex to incorporate at microtubule ends and to inhibit addition of tubulin at the net assembly ends of bovine brain microtubules in vitro. Addition of 0.1 microM final-stage tubulin-colchicine complex to suspensions of microtubules at polymer-mass steady-state resulted in rapid incorporation of one to two molecules of tubulin-colchicine complex per microtubule net assembly end concomitant with approximately 50-60% inhibition of tubulin addition. Incorporation of colchicine-tubulin complex continued slowly with time, without significant additional change in the rate of tubulin addition. In contrast, addition of unliganded colchicine to microtubule suspensions resulted in incorporation of small numbers of colchicine molecules at microtubule ends and inhibition of tubulin addition only after periods of time that varied from several minutes to approximately 20 min depending upon the concentration of colchicine. Inhibition of tubulin addition beginning with unliganded colchicine increased slowly with time, concomitant with increases in the concentration of final-state tubulin-colchicine complex and the amount of colchicine bound per microtubule end. The results indicate that inhibition of tubulin incorporation at microtubule ends is caused by colchicine-liganded tubulin in the form of a final-state complex.(ABSTRACT TRUNCATED AT 250 WORDS)     

Stathmin strongly increases the minus end catastrophe frequency and induces rapid treadmilling of bovine brain microtubules at steady state in vitro

Stathmin is a ubiquitous microtubule destabilizing protein that is believed to play an important role linking cell signaling to the regulation of microtubule dynamics. Here we show that stathmin strongly destabilizes microtubule minus ends in vitro at steady state, conditions in which the soluble tubulin and microtubule levels remain constant. Stathmin increased the minus end catastrophe frequency approximately 13-fold at a stathmin:tubulin molar ratio of 1:5. Stathmin steady-state catastrophe-promoting activity was considerably stronger at the minus ends than at the plus ends. Consistent with its ability to destabilize minus ends, stathmin strongly increased the treadmilling rate of bovine brain microtubules. By immunofluorescence microscopy, we also found that stathmin binds to purified microtubules along their lengths in vitro. Co-sedimentation of purified microtubules polymerized in the presence of a 1:5 initial molar ratio of stathmin to tubulin yielded a binding stoichiometry of 1 mol of stathmin per approximately 14.7 mol of tubulin in the microtubules. The results firmly establish that stathmin can increase the steady-state catastrophe frequency by a direct action on microtubules, and furthermore, they indicate that an important regulatory action of stathmin in cells may be to destabilize microtubule minus ends.     

Determination of the net exchange rate of tubulin dimer in steady-state microtubules by fluorescence correlation spectroscopy

The microtubule cytoskeleton plays an important role in eukaryotic cells, e. g., in cell movement or morphogenesis. Microtubules, formed by assembly of tubulin dimers, are dynamic polymers changing randomly between periods of growing and shortening, a property known as dynamic instability. Another process characterizing the dynamic behaviour is the so-called treadmilling due to different binding constants of tubulin at both microtubule ends. In this study, we used tetramethylrhodamine (TMR)-labeled tubulin added to microtubule suspensions to determine the net exchange rate (NER) of tubulin dimers by fluorescence correlation spectroscopy (FCS) as a measure for microtubule dynamics. This approach, which seems to be suitable as a screening system to detect compounds influencing the NER of tubulin dimers into microtubules at steady-state, showed that taxol, nocodazole, colchicine, and vinblastine affect microtubule dynamics at concentrations as low as 10(-9)-10(-10) M.     

On the nonlinear relationship between the initial rates of dilution-induced microtubule disassembly and the initial free subunit concentration

We have examined the dilution-induced in vitro disassembly kinetics of bovine brain microtubules, initially at steady state, using a wider range of dilutions (2-100-fold) than previously employed. In contrast to earlier results, as well as to the simple nucleation-condensation model for microtubule formation, the initial rate of dimer loss from microtubule ends was not a linear function of the initial concentration of unpolymerized tubulin. Over a 2-20-fold dilution range, plots of the initial rate of dimer loss versus the initial unpolymerized tubulin concentration were approximately linear. However, at greater dilutions, rates of microtubule depolymerization increased nonlinearly. For example, between a 10-fold dilution and a 100-fold dilution, the initial rate of dimer loss for microtubule-associated protein-containing microtubules increased by 300%, rather than a maximum of 11% expected on the basis of a linear rate plot. The nonlinear response was observed for dimer loss from opposite microtubule ends separately and with microtubules containing and lacking associated proteins. Qualitatively similar results were obtained using a wide range of experimental protocols, from which we can reasonably exclude methodological artifact as a basis for the data. We can also reasonably exclude the dissociation of the high molecular weight microtubule-associated proteins 1 and 2 from the microtubules as an explanation for the nonlinearity of the rate plots. The nonlinearity of the rate plots indicates that kinetic constants obtained under nonsteady state conditions of extreme microtubule dilution may not describe the steady state condition accurately.     

Identification of a distinct class of vinblastine binding sites on microtubules

Vinblastine, at concentrations above approximately 1 to 2 microM, causes depolymerization of steady-state bovine brain microtubules in vitro by a fraying of microtubule ends into protofilament-like spirals. Microtubule depolymerization is associated with the binding of vinblastine in approximately molar stoichiometry to tubulin in microtubules with apparent low affinity, as determined by binding experiments with radiolabeled vinblastine and by the ability of vinblastine to inhibit DEAE-dextran decoration of microtubule surfaces. Our data suggest that depolymerization occurs by a propagated mechanism, initially involving binding of vinblastine to a limited number of available sites on microtubule surfaces. This appears to cause loosening of protofilament associations which results in the exposure of new vinblastine-binding sites. Additional vinblastine binding in turn results in further loosening of protofilament associations. Such loosening, when it occurs at microtubule ends, results in protofilament-like splaying and end-wise depolymerization. Microtubule depolymerization appears mechanistically distinct from inhibition of microtubule polymerization by the drug, which is associated with the binding of vinblastine to small numbers of high-affinity binding sites on tubulin at one or both microtubule ends.     

Vinblastine suppresses dynamics of individual microtubules in living interphase cells.

We have characterized the effects of vinblastine on the dynamic instability behavior of individual microtubules in living BS-C-1 cells microinjected with rhodamine-labeled tubulin and have found that at low concentrations (3-64 nM), vinblastine potently suppresses dynamic instability without causing net microtubule depolymerization. Vinblastine suppressed the rates of microtubule growth and shortening, and decreased the frequency of transitions from growth or pause to shortening, also called catastrophe. In vinblastine-treated cells, both the average duration of a pause (a state of attenuated dynamics where neither growth nor shortening could be detected) and the percentage of total time spent in pause were significantly increased. Vinblastine potently decreased dynamicity, a measure of the overall dynamic activity of microtubules, reducing this parameter by 75% at 32 nM. The present work, consistent with earlier in vitro studies, demonstrates that vinblastine kinetically caps the ends of microtubules in living cells and supports the hypothesis that the potent chemotherapeutic action of vinblastine as an antitumor drug is suppression of mitotic spindle microtubule dynamics. Further, the results indicate that molecules that bind to microtubule ends can regulate microtubule dynamic behavior in living cells and suggest that endogenous regulators of microtubule dynamics that work by similar mechanisms may exist in living cells.     

The relative contributions of polymer annealing and subunit exchange to microtubule dynamics in vitro

Microtubules that are free of microtubule-associated protein undergo dynamic changes at steady state, becoming longer but fewer in number with time through a process which was previously assumed to be based entirely on mechanisms of subunit exchange at polymer ends. However, we recently demonstrated that brain and erythrocyte microtubules are capable of joining end-to-end and suggested that polymer annealing may also affect the dynamic behavior of microtubules in vitro (Rothwell, S. W., W. A. Grasser, and D. B. Murphy, 1986, J. Cell Biol. 102:619-627). In the present study, we first show that annealing is a general property of cytoplasmic microtubules and is not a specialized characteristic of erythrocyte microtubules by documenting annealing between tryosinolated and detyrosinolated brain microtubules. We then examine the contributions of polymer annealing and subunit exchange to microtubule dynamics by analyzing the composition and length of individual polymers in a mixture of brain and erythrocyte microtubules by immunoelectron microscopy. In concentrated preparations of short-length microtubules at polymer-mass steady state, annealing was observed to be the principal factor responsible for the increase in polymer length, whereas annealing and subunit exchange contributed about equally to the reduction in microtubule number.     

Mechanism of the microtubule GTPase reaction

The rate of GTP hydrolysis by microtubules has been measured at tubulin subunit concentrations where microtubules undergo net disassembly. This was made possible by using microtubules stabilized against disassembly by reaction with ethylene glycol bis-(succinimidylsuccinate) (EGS) as sites for the addition of tubulin-GTP subunits. The tubulin subunit concentration was varied from 25 to 90% of the steady state concentration, and there was no net elongation of stabilized microtubule seeds. The GTPase rate with EGS microtubules was linearly proportional to the tubulin-GTP subunit concentration when this concentration was varied by dilution and by using GDP to compete with GTP for the tubulin E-site. The linear dependence of the rate is consistent with a GTP mechanism in which hydrolysis is coupled to the tubulin-GTP subunit addition to microtubule ends. It is inconsistent with reaction schemes in which: microtubules are capped by a single tubulin-GTP subunit, which hydrolyzes GTP when a tubulin-GTP subunit adds to the end; hydrolysis occurs primarily in subunits at the interface of a tubulin-GTP cap and the tubulin-GDP microtubule core; hydrolysis is not coupled to subunit addition and occurs randomly in subunits in a tubulin-GTP cap. It was also found that GDP inhibition of the microtubule GTPase rate results from GDP competition for GTP at the tubulin subunit E-site. There is no additional effect of GDP on the GTPase rate resulting from exchange into tubulin subunits at microtubule ends.     

Interaction of vinblastine with steady-state microtubules in vitro

At low concentrations, vinblastine binds rapidly and reversibly to a very limited number of high affinity sites on steady-state bovine brain microtubules (mean K_d, 1.9 × 10^?6m; 16.8 ± 4.3 vinblastine binding sites per microtubule) which appear to be located at one or both ends of the microtubules. At high concentrations, vinblastine binds to a high binding capacity class of sites of undetermined affinity, located on helical strands of protofilaments which form at the ends of depolymerizing microtubules, and/or along the surface of the microtubules. Substoichiometric inhibition of microtubule assembly, which occurs at low vinblastine concentrations, appears to be due to the binding of vinblastine to the high affinity class of sites. Fifty per cent inhibition of tubulin addition to the net assembly ends of steady-state microtubules occurred at 1.38 × 10^?7m-drug, and at this concentration, 1.16 ± 0.27 molecules of vinblastine were bound to the high affinity class of sites. Vinblastine appeared to bind directly to the microtubule ends, and our results indicate that vinblastine inhibits the assembly of steady-state bovine brain microtubules by binding rapidly and with high affinity to one or two molecules of tubulin at the net assembly ends. Splaying and peeling of protofilaments at microtubule ends and the active depolymerization of microtubules occurred only at vinblastine concentrations greater than 1 × 10^?6 to 2 × 10^?6m. This action of vinblastine is associated with and may be due to the binding of vinblastine to the high capacity class of sites. Both actions of vinblastine may be due to the binding of vinblastine to the same binding sites on the tubulin molecule, with the sites exhibiting either a high or low affinity depending upon the location in the microtubule.     

The polarity and stability of microtubule capture by the kinetochore

We have studied the capture of microtubules by isolated metaphase chromosomes, using microtubules stabilized with taxol and marked with biotin tubulin to distinguish their plus and minus ends. The capture reaction is reversible at both the plus and minus ends. The on rate of capture is the same for both polarities but the dissociation rate from the kinetochore is seven times slower with microtubules captured at their plus ends than those captured at their minus ends. At steady state this disparity in off rates leads to the gradual replacement of microtubules captured at their minus ends with those captured at their plus ends. These results suggest that the kinetochore makes a lateral attachment near the end of the microtubule in the initial capture reaction and shows a structural specificity that may be important in proper bipolar attachment of the chromosome to the spindle.     

Dynamics of microtubules bundled by microtubule associated protein 2C (MAP2C)

MAP2C is a microtubule-associated protein abundant in immature nerve cells. We isolated a cDNA clone encoding whole mouse MAP2C of 467 amino acid residues. In fibroblasts transiently transfected with cDNA of MAP2C, interphase microtubule networks were reorganized into microtubule bundles. To reveal the dynamic properties of microtubule bundles, we analyzed the incorporation sites of exogenously introduced tubulin by microinjection of biotin-labeled tubulin and the turnover rate of microtubule bundles by photoactivation of caged fluorescein- labeled tubulin. The injected biotin-labeled tubulin was rapidly incorporated into distal ends of preexisting microtubule bundles, suggesting a concentration of the available ends of microtubules at this region. Although homogenous staining of microtubule bundles with antibiotin antibody was observed 2 h after injection, the photoactivation study indicated that turnover of microtubule bundles was extremely suppressed and < 10% of tubulin molecules would be exchanged within 1 h. Multiple photoactivation experiments provided evidence that neither catastrophic disassembly at the distal ends of bundles nor concerted disassembly due to treadmilling at the proximal ends could explain the observed rapid incorporation of exogenously introduced tubulin molecules. We conclude that microtubules bundled by MAP2C molecules are very stable while the abrupt increase of free tubulin molecules by microinjection results in rapid assembly from the distal ends within the bundles as well as free nucleation of small microtubules which are progressively associated laterally with preexisting microtubule bundles. This is the first detailed study of the function of MAPs on the dynamics of microtubules in vivo.     

Mechanism of GTP hydrolysis at microtubule ends

The kinetics of tubulin subunits incorporation into microtubules and the kinetics of inorganic phosphate release have been measured in parallel. Correlation of the two measurements indicates that the tubulin GTPase activity is due to GTP hydrolysis and exchange at the end of the microtubules. In some cases where the free GTP available in the medium is in-sufficient the rate of GTP hydrolysis is limited by the rate of tubulin-GTP association at the end of the microtubules. The affinity constant of GTP for the microtubule end appears to be 100 times lower than the affinity constant of the tubulin-GTP complex.     

Dietary antioxidant curcumin inhibits microtubule assembly through tubulin binding

Curcumin, a component of turmeric, has potent antitumor activity against several tumor types. However, its molecular target and mechanism of antiproliferative activity are not clear. Here, we identified curcumin as a novel antimicrotubule agent. We have examined the effects of curcumin on cellular microtubules and on reconstituted microtubules in vitro. Curcumin inhibited HeLa and MCF-7 cell proliferation in a concentration-dependent manner with IC(50) of 13.8 +/- 0.7 microm and 12 +/- 0.6 microm, respectively. At higher inhibitory concentrations (> 10 microm), curcumin induced significant depolymerization of interphase microtubules and mitotic spindle microtubules of HeLa and MCF-7 cells. However, at low inhibitory concentrations there were minimal effects on cellular microtubules. It disrupted microtubule assembly in vitro, reduced GTPase activity, and induced tubulin aggregation. Curcumin bound to tubulin at a single site with a dissociation constant of 2.4 +/- 0.4 microm and the binding of curcumin to tubulin induced conformational changes in tubulin. Colchicine and podophyllotoxin partly inhibited the binding of curcumin to tubulin, while vinblastine had no effect on the curcumin-tubulin interactions. The data together suggested that curcumin may inhibit cancer cells proliferation by perturbing microtubule assembly dynamics and may be used to develop efficacious curcumin analogues for cancer chemotherapy.     

In vivo measurement of microtubule dynamics using stable isotope labeling with heavy water. Effect of taxanes

Microtubules are dynamic polymers with central roles in the mitotic checkpoint, mitotic spindle assembly, and chromosome segregation. Agents that block mitotic progression and cell proliferation by interfering with microtubule dynamics (microtubule-targeted tubulin-polymerizing agents (MTPAs)) are powerful antitumor agents. Effects of MTPAs (e.g. paclitaxel) on microtubule dynamics have not yet been directly demonstrated in intact animals, however. Here we describe a method that measures microtubule dynamics as an exchange of tubulin dimers into microtubules in vivo. The incorporation of deuterium ((2)H(2)) from heavy water ((2)H(2)O) into tubulin dimers and polymers is measured by gas chromatography/mass spectrometry. In cultured human lung and breast cancer cell lines, or in tumors implanted into nude mice, tubulin dimers and polymerized microtubules exhibited nearly identical label incorporation rates, reflecting their rapid exchange. Administration of paclitaxel during 24 h of (2)H(2)O labeling in vivo reduced (2)H labeling in polymers while increasing (2)H in dimers, indicating diminished flux of dimers into polymers (i.e. inhibition of microtubule dynamic equilibrium). In vivo inhibition of microtubule dynamics was dose-dependent and correlated with inhibition of DNA replication, a stable isotopic measure of tumor cell growth. In contrast, microtubule polymers from sciatic nerve of untreated mice were not in dynamic equilibrium with tubulin dimers, and paclitaxel increased label incorporation into polymers. Our results directly demonstrate altered microtubule dynamics as an important action of MTPAs in vivo. This sensitive and quantitative in vivo assay of microtubule dynamics may prove useful for pre-clinical and clinical development of the next generation of MTPAs as anticancer drugs.     

Direct observation of steady-state microtubule dynamics

Different types of unusual dynamic behavior have been reported for steady-state microtubules. While almost all earlier reports relied on kinetic measurements of bulk polymerization, we have directly visualized the steady-state addition of subunits to individual microtubules through the use of tubulin derivitized with biotin. Biotinylated tubulin was used both as an internal "seed" for polymerization and as a marker for assembly onto the ends of microtubules composed of purified tubulin. Biotinylated segments were distinguished from unmodified tubulin by double-label immunofluorescence. Microtubule lengths, number concentrations, and segment lengths have been monitored with time at steady state under two buffer conditions. The results indicate that the microtubule steady state under these conditions is a balance between a majority of slowly growing microtubules and a minority of rapidly depolymerizing ones as described by the "dynamic instability" model (Mitchison T., and M. Kirschner, 1984, Nature (Lond.)., 312:232-242). Microtubules show no evidence of treadmilling; instead most show progressive growth off both ends at steady state. Although solvent conditions markedly influence the growth rates, qualitatively the behavior is unchanged.     

Direct observation of microtubule treadmilling by electron microscopy

Using an immunoelectron microscopic procedure, we directly observed the concurrent addition and loss of chicken brain tubulin subunits from the opposite ends of microtubules containing erythrocyte tubulin domains. The polarity of growth of the brain tubulin on the ends of erythrocyte microtubules was determined to be similar to growth off the ends of Chlamydomonas axonemes. The flux rate for brain tubulin subunits in vitro was low, approximately 0.9 micron/h. Tubulin subunit flux did not continue through the entire microtubule as expected, but ceased when erythrocyte tubulin domains became exposed, resulting in a metastable configuration that persisted for at least several hours. We attribute this to differences in the critical concentrations of erythrocyte and brain tubulin. The exchange of tubulin subunits into the walls of preformed microtubules other than at their ends was also determined to be insignificant, the exchange rate being less than the sensitivity of the assay, or less than 0.2%/h.