Effects of diurnal fluctuations in light intensity on the efficiency of growth of Skeletonema costatum (Grev.) Cleve (Bacillariophyceae) in a cyclostat

The effects of diurnal variations in light intensity on the biomass characteristics and the efficiency of daily growth of Skeletonema costatum (Grev.) Cleve were evaluated. The relative importance of changes in carbon specific rates of respiration and organic release to the efficiency of growth was determined. Light intensity was either constant at 130 μE · m^?2 · s^?1 during the light period or fluctuated throughout the light period from 500 to 10 μE · m^?2 · s^?1 at rates of either 1 or 12 cycles · day^?1. Total daily light was equivalent for all light regimes at 5.6 E · m^?2 · day^?1.Daily rates of growth remained comparable at ≈ 1 · day^?1 under constant and fluctuating light regimes. Cell size as daily mean carbon · cell^?1, nitrogen · cell^?1 and cellular volume was decreased under diurnally varying light whereas daily mean chlorophyll a · cell^?1 was unaffected.Rates of respiration, organic release and gross production were elevated several fold under diurnally varying light in comparison to constant light. Net growth efficiency decreased from 0.69 under constant light to values of 0.50 and 0.38 under 1 and 12 cycles · day^?1, respectively. Decreased efficiency of growth under diurnally fluctuating light resulted mostly from greater respiratory activity while organic release remained < 10% of gross production. Increased rates of gross production reflected enhancement in the efficiency of carbon fixation with fluctuating light.     

ACTIVE GROWTH OF THE OCEANIC DINOFLAGELLATE CERATIUM TERES IN THE CARIBBEAN AND SARGASSO SEAS ESTIMATED BY CELL CYCLE ANALYSIS1

The growth rate of an oceanic dinoflagellate, Ceratium teres Kofoid, was investigated in the Sargasso and Caribbean Seas from September 1989 to July 1990 using the cell cycle analysis method. Estimated growth rates ranged from 0.29 to 0.58 day^?1 and were 1.5–7.2 times higher than generally accepted rates for oceanic dinoflagellates. The higher rates in this report were mainly due to an improvement in techniques that determine the duration of a terminal cell cycle phase in situ. The day-to-day variation in growth rates was surprisingly small, but, from long-term measurements, a weak correlation was found among temperature, daily irradiance, and seasonal growth rate. The calculated species-specific primary production ranged from 0.5 to 1.8 mg C·m^?2·day^?1, about 1% of the estimated total production. Ceratium teres may be an important carbon source at the base of the grazing food chain.     

Arthrospira platensis biomass with high protein content cultivated in continuous process using urea as nitrogen source

Aims: Arthrospira platensis has been studied for single‐cell protein production because of its biomass composition and its ability of growing in alternative media. This work evaluated the effects of different dilution rates (D) and urea concentrations (N₀) on A. platensis continuous culture, in terms of growth, kinetic parameters, biomass composition and nitrogen removal. Methods and results: Arthrospira platensis was continuously cultivated in a glass‐made vertical column photobioreactor agitated with Rushton turbines. There were used different dilution rates (0·04–0·44 day^?1) and urea concentrations (0·5 and 5 mmol l^?1). With N₀ = 5 mmol l^?1, the maximum steady‐state biomass concentration was1415 mg l^?1, achieved with D = 0·04 day^?1, but the highest protein content (71·9%) was obtained by applying D = 0·12 day^?1, attaining a protein productivity of 106·41 mg l^?1 day^?1. Nitrogen removal reached 99% on steady‐state conditions. Conclusions: The best results were achieved by applying N₀ = 5 mmol l^?1; however, urea led to inhibitory conditions at D ≥ 0·16 day^?1, inducing the system wash‐out. The agitation afforded satisfactory mixture and did not harm the trichomes structure. Significance and Impact of the Study: These results can enhance the basis for the continuous removal of nitrogenous wastewater pollutants using cyanobacteria, with an easily assembled photobioreactor.     

Atmospheric CO2 mole fraction affects stand‐scale carbon use efficiency of sunflower by stimulating respiration in light

Plant carbon‐use‐efficiency (CUE), a key parameter in carbon cycle and plant growth models, quantifies the fraction of fixed carbon that is converted into net primary production rather than respired. CUE has not been directly measured, partly because of the difficulty of measuring respiration in light. Here, we explore if CUE is affected by atmospheric CO₂. Sunflower stands were grown at low (200 μmol mol^?1) or high CO₂ (1000 μmol mol^?1) in controlled environment mesocosms. CUE of stands was measured by dynamic stand‐scale ¹³C labelling and partitioning of photosynthesis and respiration. At the same plant age, growth at high CO₂ (compared with low CO₂) led to 91% higher rates of apparent photosynthesis, 97% higher respiration in the dark, yet 143% higher respiration in light. Thus, CUE was significantly lower at high (0.65) than at low CO₂ (0.71). Compartmental analysis of isotopic tracer kinetics demonstrated a greater commitment of carbon reserves in stand‐scale respiratory metabolism at high CO₂. Two main processes contributed to the reduction of CUE at high CO₂: a reduced inhibition of leaf respiration by light and a diminished leaf mass ratio. This work highlights the relevance of measuring respiration in light and assessment of the CUE response to environment conditions.     

EFFECT OF LIGHT AND TEMPERATURE INTERACTIONS ON GROWTH OF CRYPTOMONAS EROSA (CRYPTOPHYCEAE)1

Cryptomonas erosa Skuja, a planktonic alga, was grown in batch culture at different combinations of light intensity and temperature, under nutrient saturation. Growth was maximal (1.2 divisions · day^?1) at 23.5 C and 0.043 ly · min^?1, declining sharply with temperature (0.025 divisions-day^?1 at 1 C). With decreasing temperature, the cells showed both light saturation and inhibition at much reduced light intensities. At the same time the compensation light intensity for growth declined towards a minimum of slightly above 0.4 × 10^?4 ly · min^?1 (~1 ft-c) at 1 C or <0.1 ly · day^?1 (PAR). Cell division was more adversely affected by low temperature than carbon uptake, and the resulting excess production of photosynthate was both stored and excreted. Extreme storage of carbohydrates resulted in cell volumes and carbon content ca. 22 and 30 × greater, respectively, than the maxima observed for cells incubated in the dark, whereas, at growth inhibitory light levels, as much as 57% of the total assimilated carbon was excreted. A marked increase in cell pigment was observed at the lowest light levels (<10^?3 ly · min^?1), at high temperature. The growth response of C. erosa in culture provides insight into the abundance and distribution of cryptomonads and other small algal flagellates in nature.     

Bacterial metabolism in the River Danube: parameters influencing bacterial production

1. Microbial parameters were determined at five sampling sites in the River Danube up-and downstream of Vienna, Austria, twice monthly over an annual cycle. Bacterial production (BP) was estimated from thymidine and leucine incorporations; additionally, the effect of turbulence on BP and the conversion factors for converting incorporation rates into bacterial cell production were determined using the cumulative approach. 2. BP under turbulent conditions was not significantly different from that under stagnant conditions. For thymidine, a mean annual conversion factor of 3.2 ± 10¹⁸ cells mol^?1 thymidine incorporated was calculated. For leucine, the corresponding factor was 0.07 ± 10¹⁸ cells mol^?1 leucine. Average annual BP calculated by thymidine incorporation was significantly higher than BP calculated from leucine incorporation and ranged from 47.2 to 77.5 μg C 1-^?1 day^?1 depending on the tracer and the conversion factor used. 3. Bacterial growth rates ranged from 0.1 day^?1 during winter to 1.7 day^?1 in the summer. A strong correlation was found between temperature as well as chlorophyll a and bacterial growth when temperature was greater than 5 °C; a major spring phytoplankton bloom at a temperature below 5 °C did not increase BP. 4. Dissolved organic carbon (DOC) concentrations varied between 2 and 7.2 mg C 1-^?1 and comprised between 50 and 92% of the total organic carbon pool in the River Danube, Based on the DOC concentration and an assumed bacterial growth yield of 20% we calculated mean DOC turnover times of around 60 days in the winter and less than 8 days during the summer.     

High rates of net primary production and turnover of floating grasses on the Amazon floodplain: implications for aquatic respiration and regional CO2 flux

We investigated whether rates of net primary production (NPP) and biomass turnover of floating grasses in a central Amazon floodplain lake (Lake Calado) are consistent with published evidence that CO₂ emissions from Amazon rivers and floodplains are largely supplied by carbon from C4 plants. Ground‐based measurements of species composition, plant growth rates, plant densities, and areal biomass were combined with low altitude videography to estimate community NPP and compare expected versus observed biomass at monthly intervals during the aquatic growth phase (January–August). Principal species at the site were Oryza perennis (a C3 grass), Echinochloa polystachya, and Paspalum repens (both C4 grasses). Monthly mean daily NPP of the mixed species community varied from 50 to 96 g dry mass m^?2 day^?1, with a seasonal average (±1SD) of 64±12 g dry mass m^?2 day^?1. Mean daily NPP (±1SE) for P. repens and E. polystachya was 77±3 and 34±2 g dry mass m^?2 day^?1, respectively. Monthly loss rates of combined above‐ and below‐water biomass ranged from 31% to 75%, and averaged 49%. Organic carbon losses from aquatic grasses ranged from 30 to 34 g C m^?2 day^?1 from February to August. A regional extrapolation indicated that respiration of this carbon potentially accounts for about half (46%) of annual CO₂ emissions from surface waters in the central Amazon, or about 44% of gaseous carbon emissions, if methane flux is included.     

KINETICS OF GROWTH AND DEATH IN ANABAENA FLOS-AQUAE (CYANOBACTERIA) UNDER LIGHT LIMITATION AND SUPERSATURATION

The kinetics of population growth and death were investigated in Anabaena flos-aquae (Lyngb.) Bréb grown at light intensities ranging from limitation to photoinhibition (5 W·m⁻² to 160 W·m⁻²) in a nutrient-replete turbidostat. Steady-state growth rate (μ, or dilution rate, D) increased with light intensity from 0.44·day⁻¹ at a light intensity of 5 W·m⁻² to 0.99·day⁻¹ at 20 W·m⁻² and started to decrease above about 22 W·m⁻², reaching 0.56·day⁻¹ at 160 W·m⁻². The Haldane function of enzyme inhibition fit the growth data poorly, largely because of the unusually narrow range of saturation intensity. However, it produced a good fit (P < 0.001) for growth under photoinhibition. Anabaena flos-aquae died at different specific death rates (γ) below and above the saturation intensity. When calculated as the slope of a v_x⁻¹ and D⁻¹ plot, where v_x and D are cell viability (or live cell fraction) and dilution rate, respectively; γ was 0.047·day⁻¹ in the range of light limitation and 0.103·day⁻¹ under photoinhibition. Live vegetative cells and heterocysts, either in numbers or as a percentage of the total cells, showed a peak at the saturation intensity and decreased at lower and higher intensities. The ratio of live heterocysts to live vegetative cells increased with intensity when light was limiting but decreased when light was supersaturating. In cells growing at the same growth rate, the ratio was significantly lower under light inhibition than under subsaturation and the cell N:C ratio was also lower under inhibition. The steady-state rate of dissolved organic carbon (DOC) production increased with light intensity. However, its production as a percentage of the total C fixation was lowest at the optimum intensity and increased as the irradiance decreased or increased. The rate and percentage was significantly higher under photoinhibition than limitation in cells growing at the same growth rate. About 22% of the total fixed carbon was released as DOC at the highest light intensity. No correlation was found between the number of dead cells and DOC.     

Effects of nitrogen on growth and carbohydrate formation in Porphyridium cruentum

The microalga Porphyridium cruentum (Rhodophyta) has several industrial and pharmaceutical uses, especially for its polysaccharide production. This study aimed to investigate the influence of nitrogen levels as reflected by altered N:P ratios on the production and content of biomass and carbohydrate. N:P molar ratios were altered in batch cultures to range from 1.6 to 50 using the Redfield ratio of 1:16 as reference. Algal growth (estimated as final cell number, biomass concentration and maximum specific growth rate) was negatively affected at low N:P ratios. The optimal N:P ratio for growth was identified at 35–50, with specific growth rates of 0.19 day^?1 and maximum cell concentrations of 59·10⁸ cells L^?1 and 1.2 g dry weight of biomass L^?1. In addition, variation in cell size was seen. Cells with larger diameters were at higher N:P ratios and smaller cells at lower ratios. The cellular carbohydrate content increased under reduced nitrogen availability. However, because accumulation was moderate at the lowest N:P ratio, 0.4 g per g dry weight biomass compared to 0.24 at the Redfield ratio of 16:1, conditions for increased total carbohydrate formation were identified at the N:P ratios optimal for growth. Additionally, carbohydrates were largely accumulated in late exponential to stationary phase.     

LIGHT DEPENDENCE OF GROWTH AND PHOTOSYNTHESIS IN PHAEODACTYLUM TRICORNUTUM (BACILLARIOPHYCEAE)1

Phaeodactylum tricornutum Bohlin was maintained in exponential growth over a range of photon flux densities (PFD) from 7 to 230 μmol·m^?2s^?1. The chlorophyll a-specific light absorption coefficient, maximum quantum yield of photosynthesis, and C:N atom ratio were all independent of the PFD to which cells were acclimated. Carbon- and cell-specific, light-satuated, gross photosynthesis rates and dark respiration rates were largely independent of acclimation PFD. Decreases in the chlorophyll a-specific, gross photosynthesis rate and the carbon: chlorophyll ratio and increases of cell- or carbon-specific absorption coefficients were associated with an increase in cell chlorophyll a in cultures acclimated to low PFDs. The compensation PFD for growth was calculated to be 0.5 μmol·m^?2s^?1. The maintenance metabolic rate (2 × 10^?7s^?1), calculated on the basis of the compensation PFD, is an order of magnitude lower than the measured dark respiration rate(2.7 × 10^?6mol O₂·mol C^?1s^?1). Maintenance of high carbon-specific, light-saturated photosynthesis rates in cells acclimated to low PFDs may allow effective use of short exposures to high PFDs in a temporally variable light environment.     

Growth rate correlates negatively with protein turnover in Arabidopsis accessions

Previous studies with Arabidopsis accessions revealed that biomass correlates negatively to dusk starch content and total protein, and positively to the maximum activities of enzymes in photosynthesis. We hypothesized that large accessions have lower ribosome abundance and lower rates of protein synthesis, and that this is compensated by lower rates of protein degradation. This would increase growth efficiency and allow more investment in photosynthetic machinery. We analysed ribosome abundance and polysome loading in 19 accessions, modelled the rates of protein synthesis and compared them with the observed rate of growth. Large accessions contained less ribosomes than small accessions, due mainly to cytosolic ribosome abundance falling at night in large accessions. The modelled rates of protein synthesis resembled those required for growth in large accessions, but were up to 30% in excess in small accessions. We then employed ¹³CO₂ pulse‐chase labelling to measure the rates of protein synthesis and degradation in 13 accessions. Small accessions had a slightly higher rate of protein synthesis and much higher rates of protein degradation than large accessions. Protein turnover was negligible in large accessions but equivalent to up to 30% of synthesised protein day^?1 in small accessions. We discuss to what extent the decrease in growth in small accessions can be quantitatively explained by known costs of protein turnover and what factors may lead to the altered diurnal dynamics and increase of ribosome abundance in small accessions, and propose that there is a trade‐off between protein turnover and maximisation of growth rate.     

PHOSPHATE-LIMITED GROWTH KINETICS OF SELENASTRUM CAPRICORNUTUM (CHLOROPHYCEAE)1

Most theoretical studies of phytoplankton growth in aquatic environments assume that relative nutrient utilization abilities regulate species composition. The steady-state phosphate-limited growth kinetics of Selenastrum capricornutum Printz were examined using continuous cultures to characterize the green alga's ability to compete for orthophosphate (Pi) when Pi limits growth. The maximal specific growth rate for Selenastrum at 20 C was 1.20 day^?1, and the concentration where half maximal growth rate occurs was 40 nM Pi. There was an apparent threshold of 10 nM Pi. Cell yields varied inversely with growth rate; thus ability to utilize Pi could not be characterized in terms of the Monod half-saturation constant and maximal growth rate. Instead, we computed the Pi affinity from steady-state flux vs. external Pi concentrations. This affinity was 2.8 l·mg dry wt^?1· day^?1 for Selenastrum. Kinetic evidence from this study suggests that Selenastrum will not be growth competitive with some other common aquatic heterotrophs and autotrophs when Pi limits microbial growth in lakes.     

EFFECTS OF VARIATIONS IN LIGHT INTENSITY ON THE EFFICIENCY OF GROWTH OF SKELETONEMA COSTATUM (BACILLARIOPHYCEAE) IN A CYCLOSTAT1

The relative importance of respiration and organic carbon release to the efficiency of carbon specific growth of Skeletonema costatum (Grev.) Clave was evaluated over a light range from 1500–15 μE · m^?2· s^?1. Net growth efficiency ranged from 0.45–0.69 with a maximum at 130 μE · m^?2· s^?1. Respiration was 93% or more of the variations in growth efficiency. Organic carbon release ranged from 0–7% of gross production and increased with light intensity. Carbon specific particulate production was a hyperbolic function of incident light intensity and was related exponentially to particulate carbon production per unit chlorophyll a. Full sunlight conditions, 1500 μE · m^?2· s^?1, did not induce photoinhibition of gross production. Variations in the efficiency of growth of S. costatum were minimized over a wide range of light intensities mainly because of variations in cellular pigments which permitted the efficient utilization of available light energy, and a reduction in the losses of carbon which increases the growth rate, possibly as a consequence of the recycling of respired carbon within the cell.     

The interaction of components controlling net phytoplankton photosynthesis in a well-mixed lake (Lough Neagh, Northern Ireland)

The homogeneous distribution of the phytoplankton in a shallow (mean depth 8·6 m) unstratified lake, L. Neagh, Northern Ireland, facilitated the study of the interaction of components controlling gross photosynthesis per unit area. These included the photosynthetic capacity, the phytoplankton content of the euphotic zone, and a logarithmic function describing the effective radiation input. These factors were analysed for two sites, the open lake and Kinnego Bay, which respectively had standing crops of up to 90 and 300 mg chlorophyll a m^?3 and maximum daily rates of gross integral photosynthesis of 11·7 and 15·6 g O₂ m^?2 day^?1. Values are reduced by the high contribution to light attenuation by non-algal sources, which increases at low standing crops particularly in winter, when values of integral photosynthesis decrease to 0·5 g O₂ m^?2 day^?1. This relative change is the result of self-shading behaviour of the phytoplankton altering the crop content of the euphotic zone at different population densities. Changes in the irradiance function, incorporating day length, are largely responsible for the changes in daily rates of integral gross photosynthesis; as daily irradiance is also a determinant of water temperature, it exerts further influence through the photosynthetic capacity which was strongly correlated with temperature. Much of the gain in gross photosynthesis resulting from higher photosynthetic capacity may not be reflected in a higher net column photosynthesis, because of the greater proportional rise in respiration with temperature. The balance in the water column between respiration losses and photosynthetic input may frequently alter since the ratio of illuminated to dark zones is between 1/4 to 1/5 in the open lake, and small shifts in any of the controlling features may result in conditions unfavourable for growth. This is analysed especially for the increase of diatoms in spring, when small modifications of the underwater light field can delay growth.     

OLISTHODISCUS LUTEUS (CHRYSOPHYCEAE). III. UPTAKE AND UTILIZATION OF NITROGEN AND PHOSPHORUS1

Uptake and assimilation of nitrogen and phosphorus were studied in Olisthodiscus luteus Carter. A diel periodicity in nitrate reductase activity was observed in log and stationary phase cultures; there was a 10-fold difference in magnitude between maximum and minimum rates, but other cellular features such as chlorophyll a, carbon, nitrogen, C:N ratio (atoms) · cell^?1 were less variable. K_s values (~2 μM) for uptake of nitrate-N and ammonium-N were observed. Phosphorus assimilated · cell^?1· day^?1 varied with declining external phosphorus concentrations; growth rates <0.5 divisions · day^?1 were common at <0.5 μM PO_4-P. Phosphate uptake rates (K_s= 1.0–1.98 μM) varied with culture age and showed multiphasic kinetic features. Alkaline phosphatase activity was not detected. Comparisons of the nutrient dynamics of O. luteus to other phytoplankton species and the ecological implications as related to the phytoplankton community of Narragansett Bay (Rhode Island) are discussed.     

Productivity and calcification on a coral reef: A survey using pH and oxygen electrode techniques

An instrument package carrying pH and oxygen electrodes and a thermistor was floated across a reef flat at different times of the day and night. The data collected were used to obtain profiles of primary production, respiration, and calcification or solution of reef rock across the transect area. Average rates for these processes across the transect area, and rates at particular points along the transect, were related to light intensity and light response curves were constructed for productivity and calcification. Productivity tended to saturate at high light intensities and the amplitude and shape of the response curve changed with distance from the reef crest. Calcification showed no such saturation. Rates of calcification, and the dependence of calcification on light intensity, increased with distance from the reef crest. Average reef flat gross productivity and net calcification, based on the light response curves were 8.8 g C · m ^?2 · day^?1 and 9.4 g CaCO₃ · m^?2 · day^?1 (3.5 kg · m^?2· yr^?1), and the production: consumption ratio was 1.16:1. These results were obtained in late summer, and are for a cloudless day. The results suggest that the degree of stability in the reef surface, and the amount of disturbance experienced by different reef flat communities, probably exert major controls on reef flat community metabolism.     

The use of the chemostat to study the relationship between cell growth rate, viability, and the effect of interferon on L 1210 cells

Mouse leukemia L 1210 cells were cultivated in the chemostat at growth rates ranging from 0.1 day⁻¹ (population doubling time (T_d) 166.3 h) to 2.0 day⁻¹ (T_d 8.3 h). At growth rates of 1.0 day⁻¹ and above, the viability of the steady-state culture was greater than 99%. However, below 1.0 day⁻¹ there was a progressive decrease in the viability of the culture with decreasing growth rate until a minimum growth rate (0.1 day⁻¹) was reached below which steady-state cultures of L 1210 cells could not be established. Interferon treatment had no effect on the viability (>99%) of L 1210 cells cultivated at fast growth rates in the chemostat, whereas at slow growth rates (0.35 day⁻¹) interferon treatment markedly reduced the viability of the culture, even though the percentage increase in the doubling time of interferon-treated cultures was the same for cells cultivated at both fast and slow growth rates. Thus, although interferon is not directly cytotoxic, it can cause cell death by reducing the rate of cell multiplication below the minimum value compatible with viability.     

An approach to freshwater cyanobacterial production and excretion: tentative application of a deterministic model

The rates of photosynthesis, respiration and carbon excretion by the cyanobacteriumOscillatoria rubescens D.C. were estimated at a range of light intensities between 0 and 60 μE m^?2 s^?1 (μmol photon m^?2 s^?1) using the¹⁴C method. A model of the evolution of cell carbon concentration based on the Hobsonet al. (1976) equations and taking excretion into account is presented. This model predicts that the sum of respiration and excretion rates increases more rapidly with light than the rate of photosynthesis and therefore maximum growth of theO. rubescens strain under study should be obtained at low light intensities, approximately 20 μE m^?2 s^?1 . Light rapidly increases the excretion rate and so induces a deficit in the carbon balance of the cell. In addition, the simultaneous increase in respiration rate, possibly due to photorespiration, contributes to carbon depletion at high irradiances. Thus, this model explains some of our observations, particularly the fact that growth is saturated at lower light intensities than photosynthesis.     

THE ACCLIMATED RESPONSE OF GROWTH,PHOTOSYNTHESIS, COMPOSITION,AND CARBON BALANCE TO TEMPERATURE IN THE PSYCHROPHILIC ICE DIATOM NITZSCHIA SERIATA1

Nitzschia seriata Cleve, a common member of marine bottom ice communities in the Arctic, was grown in unialgal batch cultures to test for compensatory mechanisms for the low temperatures (?1.8° C) typical of its natural habitat. The upper lethal limit for growth was between 12° and 15°C, and the optimum was between 6° and 12° C. The Arrhenius function adequately (R²= 73%) fitted the relationship between growth rate and temperature from – 1.6° up to 10° C, with an average Q₁₀ of 1.9 over the entire range. Light-saturated and light-limited rates of photosynthesis (normalized to chlorophyll a or cell carbon) showed complete compensation from 12° to 4° C. Photosynthetic rates, especially at light saturation, declined rapidly at temperatures below 4° C. Susceptibility to photoinhibition was greatest at the lowest growth temperatures. Cellular composition (chlorophyll a, protein, polysaccharide, and lipid contents) was not systematically related to temperature in any simple way, although cell size (carbon per cell) was maximal at the lowest growth temperature. Dark respiration was unmeasurably low (<0.015 day^?1) at all growth temperatures. The strategy of adaptation in N. seriata may be characterized as optimizing efficiency and compensation, rather than maximization, of growth rate.