Philippa Kaur

For the samples we studied, we found a very good linear correlation (R2 = 0.99, p  More

Meaningless predictors and spatial dependence
The variogram range of the GRF predictors has a strong influence on model validations. Figure 6 shows the increase in the cross-validation (R^2) with increasing ranges for all three study sites. The maximum prediction accuracy is reached when the range of the structurally meaningless predictors (e.g. the GRFs) is similar to the range of the soil properties. This is also the reason why meaningless predictors, with respect to a structural relationship to a soil property, such as photographs of faces or paintings, can produce accurate evaluation statistics.
The effect is more stable when 100 GRFs are used, compared to only 10 GRFs for each range of spatial dependence. That is, when using 100 GRFs, relatively accurate model validations are already reached using lower scale predictors compared to using only 10 GRFs. However, cross-validation accuracy can be relatively high when the variogram ranges of the 10 GRFs are long and thus better resemble the effects of EDFs.
Figure 6

Influence of the variogram ranges of Gaussian Random Fields (GRF) on predictive accuracy. Blue: (R^2) values for models based on 100 GRFs; gold: (R^2) values for models based on 10 GRFs; red: variogram range of the corresponding soil property.

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We can therefore accept the first two hypotheses: using enough but totally meaningless predictors with similar or longer ranges of spatial dependence than that of the response variable, can result in models that produce high predictive accuracies, however, with zero descriptive accuracy. Both, GRFs and EDFs are spatial but not environmental predictors. So, we can “interpolate” with only a few but very large-scale random predictors. But when we interpolate, we cannot interpret. And when the predictors are not completely linear as EDFs, which is the case for GRFs with random meaningless variations between the sample locations, smoothing between the sample points, which is the concept behind interpolation, is not guaranteed. Hence, using GRFs or otherwise meaningless predictors is neither a structural model nor an interpolation model in the classical sense, and therefore must be rejected in principle.
Reference models and prediction accuracy
The prediction accuracies of the different models are presented in Fig. 7. Figure 8 shows the corresponding maps.
Figure 7

Modelling cross-validation accuracies (represented by the coefficient of determination, (R^2)) for all approaches and datasets (GMS: Gaussian mixed scaling, EDF: Euclidean distance fields, GRF: Gaussian random fields models with 100 or 10 predictors).

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Figure 8

Modelling results. The first row shows the reference models (GMS: Gaussian mixed scaling, EDF: Euclidean distance fields). The other three rows show the models based on 100 Gaussian random fields (GRF) with different variogram ranges.

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Generally, the GMS models produced the best results. This could be an effect of the number and structure of the predictors, which is larger compared to the merged restricted GMS + EDF dataset, and thus possibly an effect of overfitting to the dependence structure of the data23.
Models with EDFs generally performed better than models with the restricted GMS. Hence, the spatial dependence of soil properties cannot be described by the constrained GMS dataset. There is an increase in prediction accuracy when using the EDFs together with the restricted GMS dataset (except for the Meuse dataset), which could be an indicator for non-stationarity.
In terms of prediction accuracy, modelling with GRFs produced relatively high predictive accuracies (Fig. 7).
The information horizon—descriptive accuracy and relevance
Generally, the descriptive accuracy is strong if there is a causal relationship25 between the response and a predictor. The descriptive accuracy can also be high if there are associations among variables as usually inferred by statistical analysis, which can suggest potential causal relationships1.
Provided that the relevance of the predictors is given and the algorithm or method to generate the data is valid15, 17, the results of this study indicate that the descriptive accuracy is high if the range of spatial dependence of a predictor is equal or smaller than the range of the response variable. However, predictive accuracy can increase when predictors with longer ranges than the range of the environmental property are included, possibly due to non-stationarities in the environmental process4,26 or effects of anisotropy. Therefore, one should remove only those predictors from multiscale approaches15,17,27,28,29,30 with variogram ranges that are long with respect to the size of the study area and if their information content is below a certain minimum (Fig. 4).
If, on the other hand, predictors show ranges of about the diagonal length of the entire study area, then they resemble the properties of the EDFs (Fig. 5) and their ranges are too long to lend themselves to interpretation. In these cases, predictors behave indistinguishably from purely spatial predictors, although they might still be interpretable in some situations.
In summary, these results confirm our third hypothesis, and show that the primary information horizon is located somewhere between the range of the variogram of the soil property and a certain minimal variation of the predictors across the study site.
Beyond the information horizon—descriptive uncertainty and contextual complexity
We recently showed that when finer to coarser scales are successively removed from a set of all scales of a GMS modelling, prediction accuracy usually remains high, even if only the coarsest scales remain in the model4. In cases where the prediction accuracy decreases, we can assume that (i) structural information is lacking, that (ii) interpolation is not the appropriate method, or that (iii) the spatial dependence of the coarse scale GMS predictors are not suitable for interpolation, e.g. if all these coarse scale predictors only show a trend in one direction, for example in X direction only instead of X and Y direction.
We also found an increase in prediction accuracy beyond the range of the variogram of soil properties in GMS and similar approaches4,15,26, when successively adding coarser scales. There are two explanations. First, not all original terrain properties show exactly the same original scale or range, which is due to the convolution functions and the general approaches to calculate terrain properties (e.g. first and second order derivatives, i.e. slope and curvature). Second, this effect might be related to non-stationarity, where coarse-scale predictors can help to “divide” the study area into zones. We tested this here by combining the restricted set of GMS predictors, which are within the information horizon, with EDFs. In all cases prediction accuracy increased. Hence, there is obviously some spatial dependence present, resulting from predictor interactions on very coarse scales or long ranges, which are beyond the information horizon, inferable by the size of the study area. In these cases, there will be some uncertainty in the descriptive accuracy when using predictors that show information contents below a certain minimum of spatial variation.
Looking specifically at the three study sites we see complex soil property formation processes due to interactions of predictors at different scales. This contextual complexity has to be taken into account when interpreting environmental predictors beyond the information horizon, as discussed above.
In Piracicaba very coarse-scale predictors are important27. The soil formation system, however, is rather simple. It is based on rock formation, strike and dip, and subsequent erosion. In this case coarse scale terrain indicators for aspect are good proxies to differentiate between the two different types of parent material, even though they resemble properties of EDFs. In such cases partial dependence models should be applied to aide interpretation27.
The silt content in Rhine-Hesse is controlled by local silt translocation31, which occurred in the last glacial period of the Pleistocene epoch (Würm glaciation) and which was modulated by interactions of climate and terrain. This can be described in terms of a teleconnected system32 and can be mapped by terrain only, which then serves as a proxy for that system26,27. Similar to Piracicaba, interpretations of predictors with very large ranges and relatively low information content can be reasonable. However, the descriptive uncertainty is higher compared to predictors that fall within the information horizon.
The situation for Meuse is different due to a different dominant process system. The zinc content is driven by flooding events. Therefore, different and more relevant predictors, such as the distance to the river Meuse, should be used in this case9. We see that EDFs perform better compared to the mixed dataset (GMS restricted + EDF). This shows that the multiscale terrain predictors are not relevant, but represent noise, and can therefore serve at most as vague proxies. Another problem resulting in such an effect could be algorithmic issues related to feature selection within the Random Forests model, which in some specific cases might occur in relation to autocorrelated predictors33, or to effects due to fitting noise5.
Interestingly, in all cases the GMS models perform better compared to the mixed dataset (GMS restricted + EDF). This can be either due to a higher number of predictors in the GMS approach or relevant structural predictors beyond the information horizon.
Generally, the interpretation of environmental predictors beyond the edge of the information horizon needs specific care and is afflicted with more uncertainty. More

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Fractional bulk density concept
The first assumption is that soil particles with different sizes contribute to different porosities and water holding capacities in bulk soil. Based on a non-similar media concept (NSMC) defined by Miyazaki49, soil bulk density (ρb) is defined as

$$rho _{{{b}}} = frac{{{M}}}{{{V}}} = tau rho _{{{s}}} left( {frac{{{S}}}{{{{S}} + {{d}}}}} right)^{3}$$
(4)

where M is the mass of a given soil, V is the volume of bulk soil, ρs is soil particle density, and S and d are characteristic lengths of solid phase and pore space, respectively. The parameter τ is a shape factor of the solid phase, defined as the ratio of the substantial volume of solid phase to the volume S3. The value of τ is 1.0 for a cube and π/6 for a sphere. As pointed out by Miyazaki49, these characteristic lengths are not directly measurable but are representative lengths in the sense of the characteristic length in a similar media concept (SMC). Following the approach of NSMC represented by Eq. (4), we conceptually defined the volume of bulk soil as

$$V = frac{{mathop sum nolimits_{{{i } = { 1}}}^{{{n}}} {{m}}_{{{i}}} }}{{{rho }_{{{b}}} }} = frac{{{{m}}_{{1}} }}{{{rho }_{{{{b1}}}} }}{ + }frac{{{{m}}_{{2}} }}{{{rho }_{{{{b2}}}} }}{ + } cdot{mkern -4mu}cdot{mkern -4mu}cdot frac{{{{m}}_{{{n}}} }}{{{rho }_{{{{bn}}}} }}$$
(5)

where mi and ρbi are the solid mass and equivalent bulk density of the ith size fraction of soil particles, respectively. In this study, diameters of the first particle fraction and the last one were assumed to be 1 µm and 1000 µm, respectively8. This equation suggests that different particle size fractions are associated with different equivalent bulk densities due to different contributions of particle arrangement to soil pore space. As a result, the particles with the same size fraction could have different equivalent bulk densities in soils with different textures or after the soil particles are rearranged (e.g., compaction). Figure 4 provides a diagrammatic representation of such fractional bulk density concept for the variation of soil pore volume with soil particle assemblage.
Figure 4

Diagrammatic representation of the fractional bulk density (FBD) model. V and ρb are the volume of bulk soil and the bulk density of whole soil, respectively. mi, and ρbi refer to the solid mass and equivalent bulk density associated with the ith particle-size fractions, respectively.

Full size image

Calculation of volumetric water content
For a specific soil, Eq. (5) means

$${{V}}_{{{{pi}}}} left( { le {{D}}_{{{i}}} } right){{ } = { f}}left( {{{D}}_{{{{gi}}}} {{, M}}_{{{i}}} } right)$$
(6)

where Vpi(≤ Di) denotes the volume of the pores with diameter ≤ Di generated by soil particles with diametes ≤ Dgi in unit volume of soil. Mi is the cumulative mass percentage of the ≤ Dgi particles. Since the pore volume has the maximum value for a given bulk soil and the cumulative distribution of pore volume could be generally hypothesized as a sigmoid curve for most of the natural soils44,45, we formulated Eq. (6) using a lognormal Logistic equation,

$${{V}}_{{{{pi}}}} left( { le {{D}}_{{{{gi}}}} } right) = frac{{{{V}}_{{{{pmax}}}} }}{{1 + kappa left( {{{D}}_{{{{gi}}}} } right)^{{{{b}}_{{{i}}} }} }}$$
(7)

where Vpmax is the maximum cumulative volume of pores pertinent to the particles smaller than or equal to the maximum diameter (Dgmax) in unit volume of soil. In fact, here Vpmax is equal to the total porosity (φT) of soil. Vpi (≤ Dgi) is the volume of the pores produced by ≤ Dgi particles in unit volume of soil, and bi is a varying parameter of increase in cumulative pore volume with an increment of Dgi. By assuming a complete saturation of soil pore space, Eq. (7) changes into

$$theta_{{{i}}} left( { le {{D}}_{{{{gi}}}} } right) = frac{{theta_{{{s}}} }}{{1 + kappa left( {{{D}}_{{{{gi}}}} } right)^{{{{b}}_{{{i}}} }} }}$$
(8)

where θs is saturated volumetric water content calculated with

$$theta_{{{s}}} = left{ {begin{array}{*{20}l} {0.9varphi _{{{T}}} ,} hfill & {~rho _{{{b}}} < 1} hfill \ {varphi _{{{T}}} ,} hfill & {~~rho _{{{b}}} ge 1} hfill \ end{array} } right.$$ (9) $$varphi _{{{T}}} = frac{{rho _{{{s}}} - rho _{{{b}}} }}{{rho _{{{s}}} }}$$ (10) In the above equations, ρbis measured soil bulk density, and ρs is soil particle density (2.65 g/cm3). The empirical parameter κ in Eqs. (7) and (8) is defined as $${{kappa}} = frac{{theta_{{{s}}} - theta_{{{r}}} }}{{theta_{{{r}}} }}$$ (11) where θr is measured residual water content. In this study, θr is set as the volumetric water content at water pressure head of 15,000 cm. The empirical parameter bi is defined as $${{b}}_{{{i}}} = frac{{epsilon }}{{3}}{log}left( {frac{{{theta }_{{{s}}} {{ - omega }}_{{{i}}} {theta }_{{{s}}} }}{{{{kappa omega }}_{{{i}}} {theta }_{{{s}}} }}} right)$$ (12) with ε, a particle size distribution index, calculated with $${varepsilon }; = ;frac{{left( {{{D}}_{{{40}}} } right)^{{2}} }}{{{{D}}_{{{10}}} {{D}}_{{{60}}} }}$$ (13) where D10, D40, and D60 represent the particle diameters below which the cumulative mass percentages of soil particles are 10%, 40%, and 60%, respectively. The parameter ωi is coefficient for soil particles of the ith size fraction, with a range of value between θr/θs and 1.0. By incorporating soil physical properties, ωi can be estimated with $${omega }_{{{i}}} = frac{{{g}}}{{{{1 + kappa }}left( {{{lnD}}_{{{{gi}}}} } right)^{{lambda}} }}$$ (14) where g is regulation coefficient (1.0–1.2). We set it to be 1.2 in this study. λ is the ratio coefficient of particle size distribution fitted using the lognormal Logistic model, $$M_{i} = frac{{M_{T} }}{{1 + eta D_{{gi}} ^{lambda } }}$$ (15) where MT represent the total mass percentage of all sizes of soil particles, and η is a fitting parameter. We set MT = 101 in Eq. (15) for best fit of the particle size distribution. In this study, this continuous function was generated from the discrete data pairs of Dgi and Mi at cutting particle diameters of 1,000, 750, 500, 400, 350, 300, 250, 200, 150, 100, 50, 30, 15, 7.5, 5, 3, 2, and 1 μm. Considering the difference in the upper limits of particle sizes associated with existing datasets of Dgi and Mi, the particle size distribution with the upper limit of 2,000 μm for the Acolian sandy soil and volcanic ash soils in Table 2 was normalized to the case with the upper limit of 1,000 μm using Eq. (3). Table 2 Physical properties of soils used in the study. ρb is bulk density (g/cm3); θr is residual water content (cm3/cm3) at 15,000 cm water pressure head; ε is particle size distribution index. Full size table Calculation of water pressure head To estimate the capillary tube or pore diameter (Di in µm), which was composed of particles with the size of Dgi (µm), Arya and Paris19 developed an expression $${{D}}_{{{i}}} {{ } = { D}}_{{{{gi}}}} left[ {frac{{2}}{{3}}{{en}}_{{{i}}}^{{{{(1 - alpha )}}}} } right]^{{{0}{{.5}}}}$$ (16) where α is the empirical scaling parameter varying between 1.35 and 1.40 in their original model19, but was thought to vary with soil particle size in the optimized model of Arya et al.20. In Tyler and Wheatcraft's model22α is the fractal dimension of the pore. The parameter e is the void rate of entire soil and assumed unchanging with particle size. However, according to Eqs. (5) and (6), e in Eq. (16) should vary with particle size and be replaced by ei, which depends on soil particle sizes. ni is the number of particles in the ith size fraction with a particle diameter (Dgi in μm), assuming that the particles are spherical and that the entire pore volume formed by assemblage of the particles in this class is represented by a single cylindrical pore. The equation for calculating ni is given as19 $$n_{i} = frac{{6m_{i} }}{{rho_{s} pi D_{gi}^{3} }} times 10^{12}$$ (17) where mi is the mass of particles in the ith size fraction of particles. Assuming that soil water has a zero contact angle and a surface tension of 0.075 N/m at 25 °C, the minimum diameter of soil pore (Dmin) was taken to be 0.2 µm in this study, which is equivalent to the water pressure head of 15,000 cm according to Young–Laplace equation. We set this minimum pore size to correspond the minimum particle size (Dgmin = 1.0 µm). The FBD model might thus not apply well to porous media with pores smaller than 0.2 μm. As a result, Eq. (16) can be simplified into the following equation. $${{D}}_{{{i}}} { = 0}{{.2D}}_{{{{gi}}}}$$ (18) The equivalent capillary pressure (ψi in cm) corresponding to the ith particle size fraction can be calculated using $$psi_{{{i}}} = frac{{{3000}}}{{{{D}}_{{{i}}} }} = frac{{{15000}}}{{{{D}}_{{{{gi}}}} }}$$ (19) In Eq. (19), the maximum water pressure head (ψr = 15,000 cm) corresponds to θr and Dgmin (1 μm). The minimum water pressure head (ψ0 = 15 cm) corresponds to θs and Dgmax (1,000 μm). These assumptions were arbitrary and might not be appropriate for some soil types. But these values were used in the study because they approximated the practical range of measurements well. The resulting model of soil water retention Equations 8 and 19 formulate a FBD-based model for estimation of soil water retention curve. To simplify the computation, we incorporated the two equations into the following analytical form, $${theta }; = ;frac{{{theta }_{{{s}}} }}{{{1 + }left( {frac{{{theta }_{{{s}}} - {theta }_{{{r}}} }}{{{theta }_{{{r}}} }}} right)left( {frac{{15,000}}{{psi }}} right)^{{{b}}} }}$$ (20) with the parameter b obtained using $${{b}}; = ;frac{{epsilon }}{{3}}{log}left{ {frac{{{{(theta }}_{{{s}}} - {theta }_{{{r}}} {{)[ln(}}frac{{{15,000}{{.1}}}}{{psi }}{)]}^{{lambda }} - {{(g}} - {{1)theta }}_{{{r}}} }}{{{{g(theta }}_{{{s}}} - {theta }_{{{r}}} {)}}}} right}$$ (21) In Eq. (21), a water pressure head of 15,000.1 cm is employed to consecutively predict the soil water content until the water pressure head of 15,000 cm. Soil dataset Evaluation of the applicability of the proposed modeling procedure required datasets that included soil bulk density, residual water content, and soil particle size distribution covering three particle diameters (D10, D40, and D60) below which the cumulative mass fractions of particles were 10%, 40%, and 60%, respectively. In addition, measured water content and water pressure head were required for the actual retention curve in order to compare with the result of the FBD model. In this study, the soil water retention data of 30 different soils, measured by Yu et al.50, Chen and Wang51, Zhang and Miao52, Liu and Amemiya53, Hayano et al.54, and Yabashi et al.55 were used for model verification (Table 2). The data covered soils in China (such as black soil, chernozem soil, cinnamon soil, brown earth, fluvo-aquic soil, albic soil, red earth, humid-thermo ferralitic, purplish soil, meadow soil, and yellow earth) and soils in Japan (such as volcanic ash soil and acolian sandy soil). The USDA soil taxonomy of these soils was provided in Table 2. The 30 soils ranged in texture from clay to sand and in bulk density from 0.33 g/cm3 to 1.65 g/cm3, which covered a much wider range of soil bulk density than many of the existing models or pedotransfer functions56,57,58,59. Particle size fractions (Dgi) were chosen as the upper limit of the diameters between successive sieve sizes. For the data set in which particle density was not determined, 2.65 g/cm3 was used. More

Lethal toxicity
Living animals are constantly faced with various environmental stresses that challenge their daily lives. Cu is an essential metal that participates in normal physiological process of crustaceans, but several studies have shown that crustaceans are adversely affected when exposed to high concentrations of Cu. LC50 value represents a common point at lethal physiological response to toxicity, which has been well-documented in many crustaceans. For example, the 96-h LC50 value for shrimps of Exopalaemon carinicauda, Echinogammars olivii, Sphaeroma serratum, and Palaemon elegans was 0.712 mg Cu/L, 0.25 mg Cu/L, 1.98 mg Cu/L, and 2.52 mg Cu/L, respectively20,22. In addition, for paddy field crab Paratelphusa hydrodromus and freshwater crab, Barytelphusa cunicularis, the 96-h LC50 values recorded were 15.70 mg Cu/L and 215 mg Cu/L, respectively23,24. Likewise, in freshwater crayfish, Procambarus clarkia, the 96-h LC50 value reached 162 mg Cu/L25. These large variations in sub-lethal effects to Cu toxicity in crustaceans appear to be species specific. In our present study, the 96-h LC50 value for Cu exposure in C. dauricus was 32.5 mg/L, which is much higher than those of the most crustaceans, but this species seems relatively less tolerant to Cu, compared to P. clarkia. This difference may also be attributed to the various biotic and abiotic factors like age, sex, weight, salinity, and temperature, besides the species. For example, Taylor26 compared the 96-h Cu tolerance of Cambarus robustus in Pike Creek and in Wavy Lake and concluded the environment differences could affect population sensitivity to Cu toxicity.
Oxygen consumption rate
The effects of heavy metal on the respiratory rate of marine and estuarine organisms have been well documented. Spicer and Weber27 showed that heavy metal could cause respiratory impairment in crustaceans. The results obtained in the present study confirmed this previous finding. Both acute and sub-chronic Cu exposure induced significant inhibition of OCR in C. dauricus, with the maximum decreases of 48.4% and 57.9%, respectively, compared to the control. Similarly, a declined OCR by heavy metal has been observed in shrimps, including Penaeus indicus19, L. vannamei28, F. paulensis29, and E. carinicauda20, and crabs, including Uca annulipes, U. triangularis30, and Cancer pagarus27, as well as crayfish, P. clarkia25. The levels of inhibition of the respiration rate were mainly dependent on the exposure time and exposure concentration. Those authors assumed that the ultrastructural impairments of gill epithelium were related to the decrease in respiration rate, thereby affecting the oxygen carrying capacity of gills. Besides the cytological damage of gill, heavy metals also inhibit mitochondrial energy production, thereby affecting the key metabolic pathways. By contrast, an increased respiration rate has been detected in freshwater shrimp, Paratya curvirostris21, and lobster Homarus americanus31. The authors argued that it was attributed to an elevated rate of glycolysis, a mechanism of expenditure of energy reserves characteristic of a stress compensation process. In all, the changes of oxygen consumption level were mainly dependent on the time and concentration of exposure to heavy metals.
Ammonia excretion rate
Amino acids are the main sources of ammonia production in vivo. Crustaceans have the ability to regulate the concentration of intracellular free amino acids in order to deal with environmental stress32. In the present study, AER in either acute or sub-chronic Cu exposure showed a declining trend with increasing exposure concentration and time to Cu. A maximum decrease in AER of 79.4% and 70.06%, respectively, were observed respectively after exposure to 16.48 mg/L for 96-h and 2.06 mg/L for 14 days, in comparison to the control (Fig. 1B). In a similar manner, Chinni19 also reported a significant decrease in AER in post larvae P. indicus when exposed to Pb for 30 days. It assumed that such a decrease may be due to reduction in the metabolic rate or an interaction of heavy metal with the pathways for the production of ammonia-N. By contrast, elevations of ammonia excretion in response to heavy metals exposure were reported in other crustaceans. For example, an increase in AER was found in juvenile E. carinicauda after exposure to Zn and Hg20 and in F. paulensis after exposure to Cd and Zn29. It was considered that the gill function was impaired by the metal exposure, resulting in the dysfunction of ammonium excretion control; therefore, outflow of ammonia excretion from the hemolymph to ambient water induced an increased ammonia concentration in the water. In addition, no change in ammonia excretion rate was obtained in Paratya curvirostris after 96-h acute and 10-day sub-chronic Cd stress21. Therefore, the questions of the relationship between heavy metal exposure and ammonia excretion needs to be properly investigated.
Energy metabolism
O:N is a useful value for evaluating the characteristics of nutrients utilized by animals and can provide information on changes in energy substrate utilization under various environmental stresses33,34. Theoretically, pure protein catabolism will produce an O:N ratio of 835, and equal proportions of proteins and lipid results in an O:N of 2436. An O:N ratio higher than 24 indicates an elevation in lipid and carbohydrate metabolisms. In this study, in comparison with the controls, high values of O:N were obtained in individuals of C. dauricus exposed to Cu for 96 h and 14 days (Table 1, Fig. 1C). In generally, protein catabolism for energy is less efficient than lipid/carbohydrate catabolism. A species that relies on lipid and carbohydrate metabolism will likely be able to better meet energy demands of toxicant exposure than a species that principally metabolizes protein. The mean O:N ratio higher than 24 in acute Cu exposure and lower than 24 in sub-chronic exposure (Table 3 and Fig. 1C) indicated the differences in energy utilization strategy in response to two patterns of Cu stress. This could be a mechanism explaining the differences in energetic responses to Cu exposure in C. dauricus, relative to other crustacean species.
Tissues accumulation
Cu is an essential trace element for biological processes, particularly as a component of the respiratory pigment, hemocyanin. The body Cu concentration in decapod crustaceans can be regulated and does not accumulate until certain environmental threshold levels are achieved37. In addition, as an economic species of crustaceans and in relation to food quality and safety assessment, organ-specific accumulation data, especially for the muscle, are markedly required. In this study, tissue-specific bioaccumulation of Cu observed, and the Cu accumulation in hepatopancreas and muscles were highly dependent on water Cu concentration and exposure time (Fig. 2; Fig. 3A, 3B). Hepatopancreas is the organ most associated with the detoxification and biotransformation process and in direct contact with toxicants in water. The hepatopancreas, containing metal-binding protein, is the main target organ for regulating Cu level38. The maximum Cu accumulation was observed in hepatopancreas, which increased 12.7 folds and 31.6 folds after 4-day acute exposure to 16.48 mg Cu/L and chronic 14-day exposure to 4.12 mg Cu/L, respectively, this indicated that C. dauricus had a great potential for rapid accumulation of Cu in fresh waters. The greatest Cu accumulation occurring in hepatopancreas had been reported for the crayfish species, Astacus leptodactylus39 and Procambarus sp.40 as well as for the freshwater prawn, M. rosenbergii38. Although the hepatopancreas could regulate the Cu level in the animal’s body to avoid toxicity and deficiencies, the high level of external water Cu breaks down the regulation of Cu and causes continuous Cu accumulation, which might lead to the loss of muscular control and eventually, death, for crustaceans.
In this study, there was no significant time-dependent trend in the accumulation of Cu in the muscle between 7 and 14 days of Cu stress in the lower concentration of 2.06 mg/L (Fig. 3A), this suggests that C. dauricus was able to regulate Cu in the muscle to a fairly constant level under low Cu exposure concentrations. However, C. dauricus exposed to concentration of 4.12 mg Cu/L showed increased accumulation of Cu in the muscle and the equilibrium of Cu accumulation was not reached at 14 days, which might show that the high level of Cu in the external water breaks down the regulation of Cu and caused a continuous Cu accumulation, leading to its toxicity at high concentration. Similar result had been reported in Procambarus sp.40. The author found that Cu uptake reached a kinetic equilibrium within 10 days of exposure to 0.31 mg Cu/L in five organs (gills, ovaries, exoskeleton, hepatopancreas, and muscles), but Cu was rapidly accumulated in the organs of most Procambarus sp., especially in the hepatopancreas, when exposed to higher concentration of 0.38 mg Cu/L after the 14-d exposure test. However, muscle tissue, as the main edible portion, accumulates Cu at a relatively lower rate (Fig. 2; Fig. 3A) and this is important from the angle of human food quality and safety.
Conclusion
In this study, we observed that the acute and sub-chronic toxicity of Cu had a dramatic impact on the survival, oxygen consumption rate, ammonia excretion rate and bioaccumulation of C. dauricus. C. dauricus mainly took the strategies of inhibiting respiratory metabolism and shifting energy utilization to adapt to copper stress. The C. dauricus had higher concentration-dependent accumulation ability of copper. Our future work will focus on the metabolic characteristics of copper and other heavy metal from the angle of human food safety. Therefore, our studies provided basic information for further understanding of the toxicological responses of this species to trace metals. More

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Phylogenetic analysis and distribution of rhodopsin genes in cyanobacteria
To survey the distribution of rhodopsin genes in cyanobacteria, a sequence homology search was performed using 154 cyanobacterial genomes, including 126 genomes used in a large-scale comparative genomic study of cyanobacteria21 and 28 genomes known to possess rhodopsin genes obtained from a public database. Based on this search, 56 rhodopsin genes in 42 cyanobacterial genomes were identified (Table 1). Stratified by the habitat, the rhodopsin genes were found almost exclusively in freshwater cyanobacteria: 29 in freshwater, 9 in high salinity, 2 in marine, and 2 in NA (not available). There are, however, 9 genomes from a high salinity environment, 8 were from the same site and showed little genetic variation. Phylogenetic analysis of the amino acid sequences of the rhodopsins encoded by the 56 identified genes revealed that the proteins belonged to four known rhodopsin clades: XLR (3 genes), NaR (1 gene), XeR (15 genes), and CyHR (24 genes) and one novel clade (13 genes) (Table 1 and Fig. 1a and Supporting Information Fig. S1); the novel rhodopsin clade consisted entirely of rhodopsin genes from cyanobacterial genomes so we named the clade “cyanorhodopsin” (CyR) (Fig. 1b).
Table 1 Rhodopsin distribution and habitats in cyanobacterial lineage.
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Figure 1

The novel cyanorhodopsin clade. (a) Maximum likelihood tree of amino acid sequences of microbial rhodopsins. Bootstrap probabilities (≥ 50%) are indicated by colored circles. Green branches indicate cyanobacterial rhodopsins, and black branches indicate others. Rhodopsin clades are as follows: NaR (Na+-pumping rhodopsin), ClR (Cl−-pumping rhodopsin), XLR (xanthorhodopsin-like rhodopsin), PR (proteorhodopsin), XeR (xenorhodopsin), DTG-motif rhodopsin, SR (sensory rhodopsin-I and sensory rhodopsin-II), BR (bacteriorhodopsin), HR (halorhodopsin), CyHR (cyanobacterial halorhodopsin), and a novel cyanobacteria-specific clade (yellow shading). (b) Enlarged view of the novel cyanobacteria-specific clade. The three rhodopsins functionally examined in this study are shown in red. The scale bar represents substitutions per site.

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Cyanobacterial nomenclature is based largely on morphological features; therefore, species names often do not reflect their lineage. Therefore, to examine the rhodopsin gene distribution we reconstructed a phylogenomic tree of the 154 cyanobacteria genomes by using conserved phylogenetic marker proteins (120 ubiquitous single-copy proteins). Seven subclades (A–G) were assigned to the phylogenomic tree according to a previous study21, together with information on source environment, morphology, presence or absence of the retinal biosynthetic gene diox1 (carotenoid oxygenase), and genome size (Supporting Information Fig. S2). Almost all of the genomes were found to encode diox1 (152/154), indicating that microbial strains with rhodopsins generally also have the ability to produce retinal. In addition, we found that the rhodopsin-possessing strains were not evenly distributed across the subclades (Supporting Information Fig. S2, Table 1 and Supporting Information Table S1): strains in subclades A, C (mainly marine cyanobacteria with relatively smaller genomes), F, and G did not possess any rhodopsin genes; in contrast, almost all the strains in subclade D did possess rhodopsin genes and subclade B contained all functional types of cyanobacterial rhodopsin detected in this study (Supporting Information Fig. S2 and Table 1). No morphological bias in rhodopsin distribution was observed (Supporting Information Fig. S2).
Amino acid sequences and functions of the rhodopsins in the CyR clade
To examine the functions of the rhodopsins in the CyR clade, a motif sequence containing specific amino acid residues that are crucial for ion transport activity was examined. In BR, the motif corresponds to Asp85BR, Thr89BR, and Asp96BR (DTD) in the third helix (helix C); the Asp85 and Asp96 residues work as proton acceptor and donor, respectively, and Thr89 forms a hydrogen bond with Asp85. Of the 13 rhodopsins in the CyR clade, the DTD motif was detected in 10, whereas the corresponding motif was Asp, Thr, Glu (DTE) in Calothrix sp. NIES-2098, Nostoc sp. RF31Y, and Nostoc sp. 106C (Supporting Information Fig. S3). All of the CyRs included Lys204N2098R in the seventh helix (helix G), which is known to make a Schiff base linkage between the rhodopsin protein moiety and the retinal chromophore in other rhodopsins (Supporting Information Fig. S3). Also, an aspartic acid residue (Asp200N2098R) and two glutamic acid residues (Glu182N2098R and Glu192N2098R), which are classified as a counterion stabilizing the Schiff base and a proton release group, respectively, were conserved in BR and all of the CyRs22,23. Based on this analysis, CyRs were expected to function as light-driven H+ pumps.
Next, to further examine the ion-transporting activities of the CyRs, we heterologously expressed three synthesized rhodopsin genes—N2098R (BAY09002.1), B1401R (WP_074382570.1), and N4075R (GAX43141.1)—in Escherichia coli (see Fig. 1b). Rhodopsin-expressing E. coli cells showed more colors than control vector (pET21a) (Fig. 2a) and protein expressions were detected by western blots using anti-His-tag antibody (Fig. 2b). We examined the light-induced change in the pH of the cell suspension. A light-induced decrease in pH was observed in the suspensions of the cells expressing each of the rhodopsins (Fig. 2c, solid line), and this decrease was almost completely abolished in the presence of the protonophore carbonyl cyanide m-chlorophenylhydrazone (CCCP) (Fig. 2c, broken line). These results showed that N2098R and B1401R transport proton from the cytoplasmic side to the extracellular space. On the other hand, N4075R was thought to act as an outward proton pump, but its activity was smaller than that of the others. Therefore, the possibility of transporting other ions cannot be excluded.
Figure 2

Light-induced changes of the pH of suspensions of Escherichia coli expressing a rhodopsin (N2098R, B1401R, and N4075R) from the novel CyR clade. (a) The pellet color of CyRs. (b) Detection of protein expression of CyRs by western blots using an anti-His-tag antibody. These proteins were expressed in E. coli cells with a His-tag at the C-terminal. The monomer-band of CyRs (around 22 kDa) were quantified using ImageJ software. (c) The changes in pH in the absence (solid line) and presence (broken line) of CCCP are shown. The numbers in parentheses are the pH units of y-axis divisions. All measurements were performed under the dark condition (gray shading) with illumination at 520 ± 10 nm for 3 min (white shading). E. coli cells containing the pET21a plasmid vector alone were simultaneously analyzed as a negative control.

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Spectroscopic characterization of N2098R
To characterize the photochemical properties of the CyRs, we focused on N2098R, a well-expressed, stable rhodopsin. After adaption of purified N2098R to the light or dark condition, the absorption maxima of both adapted samples of N2098R was located at 550 nm (Fig. 3a), which was similar to that of GR but not to that of BR or PR (Table 2)6,16,24.
Figure 3

Absorption spectra and photocycle of N2098R. (a) UV–Vis spectra of N2098R with (green broken line) and without (black solid line) light illumination at 550 ± 10 nm for 10 min. (b) Flash-induced difference absorption spectra of N2098R over a spectral range of 370 to 700 nm and a time range of 0.01 to 977 ms. (c) Detail of flash-induced difference absorption spectra of N2098R over a spectral range of 570 to 680 nm and a time range of 0.01 to 977 ms. (d) Flash-induced kinetic data of N2098R at 405 nm (violet line), 550 nm (green line), 620 nm (orange line), and 645 nm (red line). The gray line represents the absorption changes of pyranine monitored at 450 nm. (e) Detail of flash-induced kinetic data of N2098R at 405 nm (violet line), 550 nm (green line), 620 nm (range line), and 645 nm (red line).

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Table 2 Photochemical properties of light-driven outward proton pump rhodopsins.
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Next, we examined the retinal configuration in N2098R by high-performance liquid chromatography. Both in light- and dark-adapted samples, the isomeric state of retinal was predominantly all-trans (Supporting Information Fig. S4 and Table 2), which was similar to the isomeric state of retinal in PR25 and GR15,26 but different from that in BR (Table 2)27.
Charged residues (e.g., Asp85BR and Lys216BR in BR) are essential for proton transportation by rhodopsins28. We therefore estimated the pKa values of the charged residues in N2098R (i.e., Asp74N2098R and Lys204N2098R) by pH titration and fitted the data using the Henderson–Hasselbalch equation assuming a single pKa; the pKa values of Asp74N2098R and Lys204N2098R were estimated to be  More