A radiative transfer modeling approach for accurate interpretation of PAM fluorometry experiments in suspended algal cultures

The results of a numerical study on the simulation of pulse amplitude modulated (PAM) fluorometry within dense suspensions of photosynthetic microorganisms are presented. The Monte Carlo method was used to solve the radiative transfer equation in an algae‐filled cuvette, taking into account absorption, anisotropic scattering, and fluorescence, as well as Fresnel reflections at interfaces. This method was used to simulate the transport of excitation and fluorescence light in a common laboratory fluorometer. In this fluorometer, detected fluorescence originates from a multitude of locations within the algal suspension, which can be exposed to very different fluence rates. The fluorescence‐weighted fluence rate is reported, which is the local fluence rate of actinic light, averaged over all locations from which detected fluorescence originated. A methodology is reported for recovering the fluorescence‐weighted fluence rate as a function of the transmittance of measuring light and actinic light through the sample, which are easily measured with common laboratory fluorometers. The fluorescence‐weighted fluence rate can in turn be used as a correction factor for recovering intrinsic physiological parameters, such as the functional cross section of Photosystem II, from apparent (experimental) values. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1601–1615, 2016     

Kinetic assay of fluorescein mono-beta-D-galactoside hydrolysis by beta-galactosidase: a front-face measurement for strongly absorbing fluorogenic substrates

A novel enzymatic assay method was developed for fluorogenic substrates that have significant intrinsic absorbance and fluorescence under the assay conditions. Fluorescein mono-beta-D-galactoside (FMG) was chosen as the substrate for the fluorescence enzymatic assay because of the high fluorescence of its hydrolytic product (fluorescein) and suitability of being hydrolyzed by beta-galactosidase. The fluorescence-concentration relationships for fluorescein and for FMG in both the right-angle detection mode of a fluorometer and the front-face detection mode of a fluorescence plate reader were exactly established and used to determine the kinetics of the enzyme assay. The results show that only front-face detection in the fluorescence plate reader can overcome the fluorescence concentration quenching that inevitably results from high absorbance by the intrinsically absorbing substrate in the conventional fluorometer, which utilizes right-angle detection. Only with front-face detection was the fluorescent assay of FMG hydrolysis under conditions of high optical density possible. The enzymatic measurements on the fluorescence plate reader were particularly efficient for determination of the enzyme kinetics because of the high rate of data collection. In this assay system, Michaelis-Menten constant Km and enzymatic catalysis rate k2 of FMG were determined as 117.6 microM and 22.7 mumol-(min.mg)-1, respectively. The results and methods described in this paper can be generalized for any assay using a fluorogenic substrate whether or not it has a high background absorbance.     

Measurement of photosynthetic oxygen evolution with a new type of oxygen sensor

We measured the light response curve of photosynthetic oxygen evolution by illuminating a leaf disc in an air-tight windowed chamber. Oxygen production was measured by monitoring the quenching of luminescence of an organometallic ruthenium compound. A photodiode based chlorophyll a fluorometer was used to measure the luminescence intensity. Oxygen evolution measurements with a traditional oxygen electrode gave the same numerical values at different light intensities when the same leaf disk was tested. The quality of the measurement signal of the new method was found to be similar to that obtained with the oxygen electrode method. The new luminescence based system is more stable against electrical disturbances than an oxygen electrode, its response to oxygen pressure changes is very rapid, and the new method allows the same basic equipment to be used for chlorophyll fluorescence and oxygen measurements.     

Fiber-optic fluorometer for microscale mapping of photosynthetic pigments in microbial communities

Microscale fluorescence measurements were performed in photosynthetic biofilms at a spatial resolution of 100 to 200 microm with a new fiber-optic fluorometer which allowed four different excitation and emission wavelengths and was configured for measuring phycobiliproteins, chlorophylls, and bacteriochlorophylls. We present details of the measuring system and describe examples of applications in different microbial communities.     

The use of blue-excitable nucleic-acid dyes for the detection of bacteria in well water using a simple field fluorometer and a flow cytometer

The blue-excitable nucleic acid dyes Coriphosphine O (CPO), YOYO-1, and YOPRO-1 were evaluated to rapidly detect the presence of bacteria in well water samples using a simple field fluorometer (Turner Designs, Sunnyvale, CA, Model 10-AU-005) and a tabletop flow cytometer (Coulter Epics XL). The dyes were first titrated on the Turner Designs Model 10-AU field fluorometer with log-fold dilutions of Esherichia coli, since this organism is the indicator organism for water contamination. A detection limit of 10(4) Colony Forming Units per ml (CFU/ml) was established for YOPRO-1 and 10(5) CFU/ml for YOYO-1. The detection limit with CPO was determined to be 10(7) CFU/ml due to the high background fluorescence of the dye. The dyes were also evaluated with ragweed pollen to gauge the effect of a biological interferent. Ten well-water samples were subsequently analyzed using the technique. The results showed that only YOYO-1 correctly detected all the samples that were positive according to the reference laboratory. YOPRO-1 correctly detected only one of four positive samples. Analysis with the CPO dye was inconclusive due to high background fluorescence. The samples were then subjected to analysis on the flow cytometer. Results obtained with YOYO-1 compared well to those obtained on the fluorometer and by the reference techniques. YOPRO-1 performed better on the flow cytometer than with the simple fluorometer, correctly detecting three of four positive samples. Although the CPO results showed a very slight increase of green fluorescence with positive samples, they were largely indistinguishable from negative samples. This study suggests YOYO-1 could be useful with either a simple fluorometer or with a tabletop flow cytometer in screening water samples for the presence of bacterial contamination.     

Fiber-Optic Fluorometer for Microscale Mapping of Photosynthetic Pigments in Microbial Communities

Microscale fluorescence measurements were performed in photosynthetic biofilms at a spatial resolution of 100 to 200 μm with a new fiber-optic fluorometer which allowed four different excitation and emission wavelengths and was configured for measuring phycobiliproteins, chlorophylls, and bacteriochlorophylls. We present details of the measuring system and describe examples of applications in different microbial communities.     

Modified spectrophotometer for multi-dimensional circular dichroism/fluorescence data acquisition in titration experiments: application to the pH and guanidine-HCI induced unfolding of apomyoglobin.

In a previous paper (Ramsay and Eftink, Biophys. J. 66:516-523) we reported the development of a modified spectrophotometer that can make nearly simultaneous circular dichroism (CD) and fluorescence measurements. This arrangement allows multiple data sets to be collected during a single experiment, resulting in a saving of time and material, and improved correlation between the different types of measurements. The usefulness of the instrument was shown by thermal melting experiments on several different protein systems. This CD/fluorometer spectrophotometer has been further modified by interfacing with a syringe pump and a pH meter. This arrangement allows ligand, pH, and chemical denaturation titration experiments to be performed while monitoring changes in the sample's CD, absorbance, fluorescence, and light scattering properties. Our data acquisition program also has an ability to check whether the signals have approached equilibrium before the data is recorded. For performing pH titrations we have developed a procedure which uses the signal from a pH meter in a feedback circuit in order to collect data at evenly spaced pH intervals. We demonstrate the use of this instrument with studies of the unfolding of sperm whale apomyoglobin, as induced by acid pH and by the addition of guanidine-HCI.     

Kinetic imaging of chlorophyll fluorescence using modulated light

Fluorometers that measure the kinetics of chlorophyll fluorescence have become invaluable tools for determining the photosynthetic performance of plants. Many of these instruments use high frequency modulated light to measure the rate, efficiency and regulation of photosynthesis. The technique is non-invasive and is effective under diverse environmental conditions. Recently, imaging fluorometers have been introduced that reveal variability in photosynthesis over the surface of a leaf or between individual plants. Most imaging instruments depend on continuous light or low frequency modulated light for fluorescence excitation, which imposes serious limitations on measurements of the fluorescence parameters, especially the minimum fluorescence (F₀) and variable fluorescence (F_V). Here, we describe a new instrument that combines the advantage of high frequency modulated light with two-dimensional imaging of chlorophyll fluorescence. The fluorometer produces dynamic images of chlorophyll fluorescence from leaves or plants, providing accurate mapping of F₀ and F_V, and non-photochemical quenching. A significant feature of the instrument is that it can record fluorescence images of leaves in daylight under field conditions. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effect of light intensity on chlorophyll fluorescence in wheat leaves: Application of PAM-fluorometry

Application of pulse-amplitude-modulation (PAM) fluorometers for measuring slow stages of chlorophyll fluorescence induction (CFI) is considered. With an example of Triticum aestuvum L. plants grown under continuous illumination at a photon flux density of 600 μmol/(m² s) photosynthetically active radiation (PAR), the CFI curves were analyzed with leaves of various ages as a function of actinic light intensity. The fluorometer PAM-2100 was applied for measurements of CFI curves. The characteristic peaks of CFI curves in wheat leaves were most conspicuous and had the largest amplitudes at 600–800 μmol/(m² s) PAR, which corresponds to the middle range of actinic light intensities employed in PAM-2100 fluorometers. In plants exposed to favorable and stressful conditions, the developmental stages may proceed at different rates; thus, the comparison of fluorescence parameters for leaves of equal calendar age but having different physiological states may provide ambiguous data. Therefore, the feasibility of recording CFI curves of different types is quite important for rapid diagnostics of the age and state of plant leaves, as well as for adequate physiological conclusions.     

A newly designed microspectrofluorometer for kinetic studies on protein crystals in combination with x-ray diffraction

We present a new design for a fluorescence microspectrophotometer for use in kinetic crystallography in combination with x-ray diffraction experiments. The FLUMIX device (Fluorescence spectroscopy to monitor intermediates in x-ray crystallography) is built for 0 degrees fluorescence detection, which has several advantages in comparison to a conventional fluorometer with 90 degrees design. Due to the reduced spatial requirements and the need for only one objective, the system is highly versatile, easy to handle, and can be used for many different applications. In combination with a conventional stereomicroscope, fluorescence measurements or reaction initiation can be performed directly in a hanging drop crystallization setup. The FLUMIX device can be combined with most x-ray sources, normally without the need of a specialized mechanical support. As a biological model system, we have used H-Ras p21 with an artificially introduced photo-labile GTP precursor (caged GTP) and a covalently attached fluorophore (IANBD amide). Using the FLUMIX system, detailed information about the state of photolyzed crystals of the modified H-Ras p21 (p21(mod)) could be obtained. Measurements in combination with a synchrotron beamline showed significant fluorescence changes in p21(mod) crystals even within a few seconds of x-ray exposure at 100 K.     

Correction for inner filter effects in turbid samples: fluorescence assays of mitochondrial NADH

Fluorescentdeterminations of NADH in porcine heart mitochondria were subject tosignificant errors caused by alterations in inner filter effects duringnumerous metabolic perturbations. These inner filter effects wereprimarily associated with changes in mitochondrial volume andaccompanying light scattering. The observed effects were detected in astandard commercial fluorometer with emission orthogonal to theexcitation light path and, to a lesser extent, in a light path geometrydetecting only the surface fluorescence. A method was developed todetect and correct for inner filter effects on mitochondrial NADHfluorescence measurements that were independent of the optical pathgeometry using an internal fluorescent standard and linearleast-squares spectral analysis. A simple linear correction with theinner fluorescence reference was found to adequately correct for innerfilter effects. This approach may be useful for other fluorescenceprobes in isolated mitochondria or other light-scattering media.

     

Continuous recording of photochemical and non-photochemical chlorophyll fluorescence quenching with a new type of modulation fluorometer

A newly developed fluorescence measuring system is employed for the recording of chlorophyll fluorescence induction kinetics (Kautsky-effect) and for the continuous determination of the photochemical and non-photochemical components of fluorescence quenching. The measuring system, which is based on a pulse modulation principle, selectively monitors the fluorescence yield of a weak measuring beam and is not affected even by extremely high intensities of actinic light. By repetitive application of short light pulses of saturating intensity, the fluorescence yield at complete suppression of photochemical quenching is repetitively recorded, allowing the determination of continuous plots of photochemical quenching and non-photochemical quenching. Such plots are compared with the time courses of variable fluorescence at different intensities of actinic illumination. The differences between the observed kinetics are discussed. It is shown that the modulation fluorometer, in combination with the application of saturating light pulses, provides essential information beyond that obtained with conventional chlorophyll fluorometers.     

Light-induced dynamic changes of NADPH fluorescence in Synechocystis PCC 6803 and its ndhB-defective mutant M55

Blue-green fluorescence emission of intact cells of Synechocystis PCC6803 and of its ndhB-defective mutant M55 was measured with a standard pulse-amplitude-modulation chlorophyll fluorometer equipped with a new type of emitter-detector unit featuring pulse-modulated UV-A measuring light and a photomultiplier detector. A special illumination program of repetitive saturating light pulses with intermittent dark periods (10 s light, 40 s dark) was applied to elicit dynamic fluorescence changes under conditions of quasi-stationary illumination. The observed effects of artificial electron acceptors and inhibitors on the responses of wild-type and mutant M55 cells lead to the conclusion that changes of NAD(P)H fluorescence are measured. In control samples, a rapid phase of light-driven NADP reduction is overlapped by a somewhat slower phase of NADPH oxidation which is suppressed by iodoacetic acid and, hence, appears to reflect NADPH oxidation by the Calvin cycle. Mercury chloride transforms the light-driven positive response into a negative one, suggesting that inhibition of NADP reduction at the acceptor side of PSI leads to reduction of molecular oxygen, with the hydrogen peroxide formed (via superoxide) causing rapid oxidation of NADPH. The new fluorescence approach opens the way for new insights into the complex interactions between photosynthetic and respiratory pathways in cyanobacteria.     

Wavelength-Ratiometric Plasmon Light Scattering-Based Immunoassays

The application of a wavelength-ratiometric plasmon light scattering technique to immunoassays is demonstrated. A model immunoassay for anti-immunoglobulin G (IgG), constructed in gold colloid-modified high-throughput screening wells, was monitored by the changes in the intensity of scattered light (with transmitted light) from gold colloids as a result of antibody–antibody interactions. The quantitative determination of anti-IgG was undertaken by measuring the ratio of intensity of scattered light at both 590 and 500 nm. A white light-emitting diode (LED) and a fiber optic coupled fluorometer was used as an excitation source and the detection system, respectively. The visual confirmation of the quantitative nature of the measurement technique was done by digital photography. A lower detection limit of 0.05 μg/mL for anti-IgG was determined. The wavelength-ratiometric plasmon light scattering technique offers several advantages: (1) light at >500 nm can be used for reduced biological autofluorescence; (2) due to the ratiometric nature of these measurements, the fluctuations in the excitation or ambient light do not perturb the measured signal; and (3) with the addition of automated detection systems, multiple samples in a high-throughput format can potentially be assessed quickly and more efficiently.     

Relationship between Chlorophyll a Concentration,Light Attenuation and Diving Depth of the Southern Elephant Seal Mirounga leonina

Recently, a number of Antarctic marine environmental studies have used oceanographic parameters collected from instrumented top predators for ecological and physical information. Phytoplankton concentration is generally quantified through active measurement of chlorophyll fluorescence. In this study, light absorption coefficient (K_0.75) was used as an indicator of phytoplankton concentration. This measurement, easy to obtain and requiring low electric power, allows for assessing of the fine scale horizontal structuring of phytoplankton. As part of this study, Southern elephant seals (SES) were simultaneously equipped with a fluorometer and a light logger. Along the SES tracks, variations in K_0.75 were strongly correlated with chlorophyll, a concentration measured by the fluorometer within the euphotic layer. With regards to SES foraging behaviour, bottom depth of the seal’s dive was highly dependent on light intensity at 150 m, indicating that the vertical distribution of SES’s prey such as myctophids is tightly related to light level. Therefore, change in phytoplankton concentration may not only have a direct effect on SES’s prey abundance but may also determine their vertical accessibility with likely consequences on SES foraging efficiency.     

Limitations of the pulse-modulated technique for measuring the fluorescence characteristics of algae

Precise measurements of the minimal fluorescence yield (F_o) and maximal fluorescence yield (F_m) of a dark-adapted sample are prerequisites for the quantification of other fluorescence parameters. The pulse amplitude-modulated chlorophyll fluorometer (PAM 101 Chlorophyll Fluorometer, Heinz Walz, Effeltrich, Germany) and saturating pulse technique have frequently been used in measuring F_o and F_m and in resolving the contributions of photochemical and nonphotochemical quenching to the total fluorescence yield. The extent to which instrument-dependent factors may affect the accurate measurement of F_o and F_m is addressed. It is shown that the increase in pulse amplitude-modulated measuring beam intensity at 1.6 and 100 kHz was nonlinear at higher light intensity settings. The implications of this for measurements of F_o (1.6 kHz) and F_m (100 kHz) are discussed. It is also demonstrated that underestimation of F_m may result due to saturation of the PAM 101 photodiode by scattered infrared light associated with intense light pulses. In addition, it is shown how sample-dependent factors may affect measurements of F_o and F_m in samples with low chlorophyll concentrations, in particular, dilute algal suspensions of Phaeodactylum tricornutum and Chlamydomonas reinhardtii. A technique is presented for the accurate measurement of F_o in algal suspensions (<8 μg chlorophyll a mL⁻¹). The importance of examining the saturating pulse transient and F_m level as a function of the damping setting, pulse width, and pulse intensity, and in the presence of 3-(3,4-dichlorophenyl)-1, 1-dimethylurea is discussed.     

A 4-GHz frequency-domain fluorometer with internal microchannel plate photomultiplier cross-correlation

We have developed and tested a multifrequency phase/modulation fluorometer based on the Hamamatsu Model R2024U gatable microchannel plate photomultiplier (MCP-PMT), using internal MCP-PMT cross-correlation. This internal mixing is accomplished by biasing and modulating the gating mesh which is located 0.2 mm behind the photocathode. Near the photocathode center, no high-frequency photocurrent modulation was achieved. Within a circular area near the photocathode edge, however, the R2024U allows accurate phase shift and demodulation measurements up to at least 4.5 GHz, the frequency limit of our PMT-modulation amplifier. By mixing immediately after the photocathode, there is no decrease in the time resolution due to transit time spread, and the MCP has to process only low-frequency signals. This means no low-level high-frequency signal voltages have to be handled in this fluorometer, and the problems of RF shielding become much less critical. Also, the effective output impedance of the PMT has been increased, resulting in a 43-dB increase in the PMT output signal power. In principle, more MCPs could be built into the PMT, allowing an improved fluorescence detection limit. We have used the method of reference fluorophores in order to compensate for pronounced PMT color effects, a wavelength-dependent modulation, and a wavelength-dependent time shift. No color correction is required in the case of time-dependent depolarization. The performance of the instrument was verified by measurements of the intensity decay of perylene, which showed a single-exponential decay, and by measurements of the decay of tryptophan in water, which showed a double-exponential decay, as expected.(ABSTRACT TRUNCATED AT 250 WORDS)     

Biological membrane modeling with a liquid/liquid interface. Probing mobility and environment with total internal reflection excited fluorescence.

Total internal reflection of exciting light, in combination with fluorescence intensity and polarization measurements, was used to selectively study fluorescent compounds adsorbed to the interface region between two immiscible liquids. A fluorometer was constructed which provided excitation at variable angles of incidence and allowed sensitive detection of polarized fluorescence emitted from the interface. The compound 4,4'-bis-1-phenylamino-8-naphthalenesulfonate (bis-ANS) was examined at a decalin/water interface and was found to possess remarkable affinity for the interface region with the bulk of the adsorbed molecule residing in the decalin phase. The adsorbed fluorophore displayed an apparent hindered rotation in the plane of the interface with a rotational diffusion coefficient 3- to 12-fold lower than that expected for bis-ANS in solution. While other dyes examined were not found to be significantly surface active, the addition of cationic surfactant sufficed to induce adsorption of the anionic fluorophore 1-aminonaphthalene-3,6,8-trisulfonic acid. This fluoropore was found to reside in an aqueous environment when bound to the interface, and it also exhibited hindered rotation in the plane of the interface. As the concentrations of the dyes were increased, both adsorbed dyes exhibited polarization reductions consistent with excitation energy transfer. Adsorption of bis-ANS was reversed by addition of bovine serum albumin. The membrane protein cytochrome b5 was found not to bind at the decalin/water interface, indicating that interaction with lipid is required for its adherence to biological membranes.     

How to correctly determine the different chlorophyll fluorescence parameters and the chlorophyll fluorescence decrease ratio R<Subscript>Fd</Subscript> of leaves with the PAM fluorometer

This contribution is a practical guide to the measurement of the different chlorophyll (Chl) fluorescence parameters and gives examples of their development under high-irradiance stress. From the Chl fluorescence induction kinetics upon irradiation of dark-adapted leaves, measured with the PAM fluorometer, various Chl fluorescence parameters, ratios, and quenching coefficients can be determined, which provide information on the functionality of the photosystem 2 (PS2) and the photosynthetic apparatus. These are the parameters F_v, F_m, F₀, F_m′, F_v′, NF, and ΔF, the Chl fluorescence ratios F_v/F_m, F_v/F₀, ΔF/F_m′, as well as the photochemical (q_P) and non-photochemical quenching coefficients (q_N, q_CN, and NPQ). q_N consists of three components (q_N = q_E + q_T + q_I), the contribution of which can be determined via Chl fluorescence relaxation kinetics measured in the dark period after the induction kinetics. The above Chl fluorescence parameters and ratios, many of which are measured in the dark-adapted state of leaves, primarily provide information on the functionality of PS2. In fully developed green and dark-green leaves these Chl fluorescence parameters, measured at the upper adaxial leaf side, only reflect the Chl fluorescence of a small portion of the leaf chloroplasts of the green palisade parenchyma cells at the upper outer leaf half. Thus, PAM fluorometer measurements have to be performed at both leaf sides to obtain information on all chloroplasts of the whole leaf. Combined high irradiance (HI) and heat stress, applied at the upper leaf side, strongly reduced the quantum yield of the photochemical energy conversion at the upper leaf half to nearly zero, whereas the Chl fluorescence signals measured at the lower leaf side were not or only little affected. During this HL-stress treatment, q_N, q_CN, and NPQ increased in both leaf sides, but to a much higher extent at the lower compared to the upper leaf side. q_N was the best indicator for non-photochemical quenching even during a stronger HL-stress, whereas q_CN and NPQ decreased with progressive stress even though non-photochemical quenching still continued. It is strongly recommended to determine, in addition to the classical fluorescence parameters, via the PAM fluorometer also the Chl fluorescence decrease ratio R_Fd (F_d/F_s), which, when measured at saturation irradiance is directly correlated to the net CO₂ assimilation rate (_{P N}) of leaves. This R_Fd-ratio can be determined from the Chl fluorescence induction kinetics measured with the PAM fluorometer using continuous saturating light (cSL) during 4–5 min. As the R_Fd-values are fast measurable indicators correlating with the photosynthetic activity of whole leaves, they should always be determined via the PAM fluorometer parallel to the other Chl fluorescence coefficients and ratios.     

Estimation of chlorophyll content and daily primary production of the major algal groups by means of multiwavelength-excitation PAM chlorophyll fluorometry: performance and methodological limits

The performance and methodological limits of the Phyto-PAM chlorophyll fluorometer were investigated with laboratory grown algae cultures and natural phytoplankton from the rivers Saar and Saale. The Phyto-PAM is a 4-wavelength chlorophyll fluorometer with the functional combination of chlorophyll (Chl) estimation and assessment of photosynthetic activity, both differentiated into the main algal groups. The reliability of fluorescence-based Chl estimation strongly depends on the group specific calibration of the instrument and the resulting chlorophyll/fluorescence (Chl/F) ratios in reference algal cultures. A very high reliability of the Chl estimation was obtained in the case of constant Chl/F-ratios. Algae grown at different light intensities showed marked differences in Chl/F-ratios, reflecting differences in pigment composition and Chl a specific absorption (a*). When the Phyto-PAM was calibrated with laboratory grown diatoms, the Chl a in river grown diatoms was underestimated, due a lower content of accessory pigments and stronger pigment packaging. While this aspect presently limits the application of PAM fluorometry in limnology, this limitation may be overcome by future technical progress in the detection of dynamic changes in Chl/F-ratio via fluorescence-based measurements of the functional PS II absorption cross-section. Practically identical Chl/F-ratios were found for the diatom-dominated waters of the rivers␣Saar and Saale, suggesting that the same instrument calibration parameters may be applied for hydrographically similar surface waters. For this particular case, despite of the present methodological limitations, the potential of PAM fluorometry in limnology could be demonstrated. Light response curves were measured to estimate primary production with a spectrally resolved model in daily courses at two sampling sites. Fluorescence based primary production was closely correlated with measured oxygen evolution rates until midday. In the afternoon, at the water surface the fluorescence approach gave higher␣rates than the measured oxygen evolution. Possible explanations for the observed differences are discussed.