# A Novel Algorithm for Predicting Phycocyanin Concentrations in Cyanobacteria: A Proximal Hyperspectral Remote Sensing Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{max}= 620 nm), allophycocyanin (AP) (A

_{max}= 650 nm), and allophycocyanin B (APB) (A

_{max}= 670 nm) [6,7]. Some BG may also contain phycoerythrin (PE) (A

_{max}= 565 nm). These PBPs form a large protein complex which transfers energy primarily to Photosystem II reaction centers. Photosystem I reaction center binds approximately 100 Chl-a, the majority of which serve as antenna pigments for light absorption [5].

_{rs}) spectra for natural water bodies are generally complex because of the presence of many optically active constituents such as Chl-a, carotenoids, total suspended solids (TSS), and Colored Dissolved Organic Matter (CDOM). However, researchers have been reasonably successful in exploiting PC 620 nm absorption feature to develop empirical and semi-empirical models to detect PC as a marker for BG from water bodies [8]. Most research pertaining to the detection and mapping of cyanobacteria from in situ remote sensing spectra have used the absorption and reflectance features from 620 and 650 nm to develop a relationship between R

_{rs}and PC concentrations. To date, three algorithms have been proposed to quantify PC based on its absorption feature at 620 nm: a single band ratio algorithm [9], a semi-empirical algorithm [10] and a nested semi-empirical band ratio algorithm [8].

_{w}) in these infrared bands is greatly reduced due to water absorption and modeling reflectance spectra beyond 750 nm could be accounting for turbidity in the lake caused by algal biomass instead of phycocyanin [12]. Simis et al. [8] developed a semi-empirical algorithm that used the band ratio from 709 nm to 620 nm to estimate PC. They discussed the influence of Chl-a absorption at 620 nm and also included the impact of the variable PC:Chl-a ratio on the performance of the algorithm. They concluded that the model error significantly increased as the PC:Chl-a ratio decreased, providing evidence for the effect of Chl-a absorption at 620 nm.

^{−3}and, can be detected by specific remote sensing instruments with 10 nm spectral resolution and 1000:1 signal-to-noise ratio. They also concluded that the use of 630 nm absorption features in early warning systems for monitoring CHABs is not feasible by remote sensing techniques. Dekker [10] and Schalles and Yacobi [9] have used the reflectance peak between 640 and 660 nm with some success. Unfortunately, there have not been many other studies on the appearance and dynamics of these characteristic reflectance peaks at varying PC concentrations and also when PC is associated with other common optically active pigments like chlorophyll, present in other potential organisms in the environment such as green algae.

## 2. Materials and Methods

#### 2.1. Strains of Cyanobacteria, Green Algae, and Culture Condition

^{−1}s

^{−1}to the mid-to-late exponential phase of growth (OD

_{730}= 0.8–1.5).

#### 2.2. Data Collection

_{λ}) data of the two cyanobacterial species at varying concentrations and also in association with different concentrations of green algae. In the experiments, water samples that were scanned to acquire (ρ

_{λ}) data were prepared as follows. First, 100 mL of an exponential phase culture of a particular BG species was mixed with 500 mL of water for dilution and the dilution sequence was continued by adding 100, 200, and 500 mL of tap water subsequently to achieve the PC concentration levels shown in Table 1.

^{o}field of view (FOV) optical fiber was used to acquire the upwelling radiance (L

_{λ,target}) data of the water samples. The spectroradiometer was calibrated by measuring the upwelling radiance (L

_{λ,cal}) of a Spectralon reflectance standard with 99% reflectance (Labsphere, Inc., North Sutton, NH, USA). ρ

_{λ}was computed using the calibration panel coefficient (cal

_{coeff}) (available in the CALMIT Data Acquisition Program (CDAP; CALMIT, University of Nebraska-Lincoln, NE, USA). ρ

_{λ}data were collected within a range of 400–900 nm with a spectral resolution of 1 nm. The equation used to compute ρ

_{λ}is presented below:

^{−1}with a resolution of 0.1 µg L

^{−1}and linearity with an R

^{2}of 0.9999 relative to serial dilution of rhodamine with solution in the range from 0 to 500 µg L

^{−1}. BGA (PC) sensor for PC measures in a range 0:280,000 cell mL

^{−1}. The resolution of the BGA (PC) sensor is 220 cells mL

^{−1}. Linearity of the BGA (PC) sensor has R

^{2}of 0.99 for serial dilution of rhodamine with solution from 0 to 400 µg L

^{−1}(YSI user's manual). Sensors were calibrated before use as per the instructions in the YSI user manual. However, the readings from YSI sensors are in cells mL

^{–1}, a relative unit, which should be considered as a proxy for PC concentrations or cyanobacterial biomass. In the first experiment (Exp I), measured ranges of Chl-a and PC were 0.7 to 7.8 µg L

^{−1}and 7,050 to 247,960 cells mL

^{−1}, respectively. The same procedure and dilution sequence was repeated in the second experiment (Exp II) on a different day. The measured Chl-a and PC ranges for Exp II were varied from 1.8 to 3.7 µg L

^{−1}and from 506 to 126,570 cells mL

^{−1}respectively.

^{−1}, and 4,095 and 273,883 cells mL

^{−1}respectively. In Exp IV, we studied Anabaena with cell densities ranging from 4,550 to 244,500 cells mL

^{−1}. The descriptive statistics of all experimental data are summarized in Table 1.

**Table 1.**Descriptive statistics of pigment measurements in the four proximal sensing experiments. N refers to the total number of readings acquired. Chl-a data was not acquired in Exp. IV.

Exp. | Pigment | Mean | Std. Dev. | Range | Min | Max | N |
---|---|---|---|---|---|---|---|

I | PC (cells mL^{–1}) | 85529.82 | 75586.96 | 240910.00 | 7050.00 | 247960.00 | 11 |

Chl-a (µg L^{–1}) | 3.40 | 2.39 | 7.10 | 0.70 | 7.80 | 8 | |

II | PC (cells mL^{–1}) | 50409.40 | 41727.17 | 126064.00 | 506.00 | 126570.00 | 20 |

Chl-a (µg L^{–1}) | 2.48 | 0.78 | 1.90 | 1.80 | 3.70 | 5 | |

III | PC (cells mL^{–1}) | 118360.00 | 100771.72 | 269788.00 | 4095.00 | 273883.00 | 12 |

Chl-a (µg L^{–1}) | 13.32 | 7.12 | 19.80 | 2.10 | 21.90 | 12 | |

IV | PC (cells mL^{–1}) | 94137.09 | 76424.23 | 239950.00 | 4550.00 | 244500.00 | 11 |

^{−1}for Synechocystis and 220,000 cells mL

^{−1}for Anabaena; whereas the green algae concentration was increased in sequence for both of the experiments. This was achieved by keeping the Synechocystis or Anabaena at the above described concentration level, while continuing to add Ankistrodesmus in order to increase the Chl-a concentration.

## 3. Results and Discussion

#### 3.1. Analysis of Reflectance Spectra

**Figure 1.**

**(A, B, C)**Percent reflectance spectra of Synechocystis PCC 6803 from Exp I, II, III respectively.

**(D)**Percent reflectance spectra of Anabaena from Exp IV.

#### 3.2. Context for Model Development

^{2}) of 0.96 and 0.97, respectively, in each individual experimental dataset, but they did not perform well during validation with the dataset from Exp IV (Figure 2). We concluded that the performance of existing band ratios are highly dependent of varying chlorophyll-a concentrations, and hence dependant on PC to Chlorophyll ratio. The poor validation result can be explained by analyzing the model calibration plot of both band ratio algorithms (Figure 2A,B). It showed that at the same PC concentration, spectral band ratios $\left({\rho}_{617}^{-1}{\rho}_{654}\right)$ and $\left({\rho}_{620}^{-1}{\rho}_{709}\right)$ (from three different experiments have different trend lines. Hence, it can be concluded that PC is not the only parameter, rather there might be other pigments, most likely Chl-a, that control the reflectance at both 620 and 654 nm. This preliminary research provided the context for studying the dynamics of 620 and 654 nm peaks and their usefulness in band ratio algorithms to quantify PC concentration from remote sensing data.

**Figure 2.**Scatter plots of spectral band ratios such as,

**A.**$\left({\rho}_{617}^{-1}{\rho}_{654}\right)$

**B.**$\left({\rho}_{620}^{-1}{\rho}_{709}\right)$ and

**C.**$\left({\rho}_{600}^{-1}{\rho}_{700}\right)$, versus measured PC concentration (cells mL

^{−1}). Note that the newly developed spectral band ratio (C) has similar trends in all three experiments and outperforms the existing spectral band ratios.

#### 3.3. Usefulness of 654 nm Peak in PC Band Ratio Models

_{rs}peak at 650 nm only appears and can be detected by remote sensing instruments (with 10 nm spectral resolution and 1,000:1 signal-to-noise ratio) when Chl-a concentration reaches 8–10 mg m

^{−3}. However, in a few experiments we observed that the 654 nm peak appeared on the reflectance spectra acquired by USB4000 (sampled at 10 nm spectral resolution with 250:1 signal-to-noise ratio) even when the Chl-a and PC concentration were 0.7 µg L

^{−1}(or 0.7mg m

^{−3}) and 7,050 cells mL

^{−1}, respectively (Figure 3). On the other hand, in another experiment, we did not observe the peak at 654 nm even when the Chl-a and PC concentrations were 7.4 µg L

^{−1}and 21,050 cells mL

^{−1}, respectively. That proved our initial conclusion that the proportion of the concentration of PC to Chl-a controls the appearance of the 654 nm peak.

**Figure 3.**Percent reflectance spectra of Synechocystis and Anabaena showing appearance and dynamics of 650 nm peak at different Chl-a concentrations.

^{−1}and PC concentration was 4,095–21,050 cells mL

^{−1}, the high Chl-a concentration strongly absorbed light at 654nm, thereby lowering the $\left({\rho}_{617}^{-1}{\rho}_{654}\right)$ ratio. Consequently, no peak appeared at 654 nm even if the PC concentration was sufficient enough to form the peak. Hence, two conclusions can be drawn from the experimental data: (1) when Chl-a concentration is ≥2.1 µg L

^{−1}, the 654 nm peak does not appear on the reflectance spectra of BG even with cell concentrations up to 21,050 cells mL

^{−1}, whereas with the prescence of 0.5 µg L

^{–1}of Chl-a and 7,050 cells mL

^{–1}of PC, the 654 nm peak appeas; and therefore the appearance of 654 nm peak is entirely dependent on PC to Chl-a ratio; (2) 654 nm peak is dynamic and influenced by Chl-a, therefore cannot be used in algorithms to predict PC concentrations.

_{654}therefore depends on the concentration of Chl-a, and because of this, the 654 nm peak cannot be accurately used to quantify PC efficiently in the case of variable PC:Chl-a ratios in water.

^{−1}(Figure 4A,B). Movement of the 654 nm peak to 660 nm might be due to absorption by Chl-b which is a major accessory photopigment in green algae. On the other hand, the Chl-a absorption feature blue-shifted from 680 nm to 670 nm at 310 µg L

^{−1}of Chl-a. This blue-shift may be explained by the dominance of scattering by algal cells and fluoresence by Chl-a at 680 nm over absorption at the same wavelength. Thus the ρ

_{678–682}started increasing and the absorption by Chl-a became prominent at 670 nm. This instability of the 654 nm peak with increasing Chl-a and b also points to the lack of utility of this peak in empirical models to quantify PC.

#### 3.4. Model Development and Calibration

**Figure 4.**Effect of varying green algae concentrations on

**(A)**Synechocystis and

**(B)**Anabaena reflectance spectra.

^{2}= 0.97). However, we observed a small nonlinearity between $\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ and measured PC concentration, and therefore the natural logarithm of the same ratio was regressed with the measured PC concentration. The modified version of the new model $\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ was strongly correlated with measured PC concentration (R

^{2}= 0.98) and also showed very strong predictive ability in the validation procedure. In the next step, we extended the model to a different BG species, Anabaena, which was studied in Exp IV to test the applicability of the developed models on other species. Observations from all four experiments were randomly divided into two datasets including one for model calibration (n = 30) and the other for validation (n = 24). The calibration results for both models yielded strong correlation (R

^{2}= 0.95) (Figure 5E, F; Table 2). Calibration results suggest that both the $\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ and $\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ models can be applied to quantify the concentration of different species of cyanobacteria with high accuracy.

**Figure 5.**Calibration scatter plots (PC concentration versus Index) for different band ratio models:

**(A, B, C, D)**data from EXP I, II and III (Synechocystis) and

**(E, F)**data from EXP I–IV (Synechocystis and Anabaena). Coefficients of determinations (R

^{2}) for each model are also reported in corresponding figures. Outer pairs of lines (solid) represent 95% prediction band, inner pairs of lines (dash) represent 95% confidence band and the central solid lines are linear regression fits.

**Table 2.**Model parameters and performance: Intercept (a

_{0}) and slope (a

_{1}) with corresponding standard error of estimate (STE); coefficient of determination (R

^{2}); adjusted coefficient of determination; STE of estimate for linear regression of different models obtained using the calibration dataset.

Band Combination | a_{0} (STE) | a_{1} (STE) | R^{2} | Adj. R^{2} | STE |
---|---|---|---|---|---|

Synechocystis dataset (Exp I, II and III) | |||||

$\left({\rho}_{617}^{-1}{\rho}_{654}\right)$ | 1.0176 (0.0526) | 3.1921 × 10^{−7} (4.3934 × 10^{−7}) | 0.71 | 0.70 | 0.1732 |

$\left({\rho}_{620}^{-1}{\rho}_{709}\right)$ | 0.9270 (0.0365) | 3.8154 × 10^{−6} (3.0458 × 10^{−7}) | 0.88 | 0.87 | 0.1201 |

$\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ | 0.9773 (0.0098) | 2.4985 × 10^{−6} (8.1863 × 10^{−8}) | 0.97 | 0.97 | 0.0323 |

$\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ | −0.0044 (0.006) | 1.9394 × 10^{−6} (5.0150 × 10^{−8}) | 0.98 | 0.98 | 0.0198 |

Synechocystis and Anabaena dataset (Exp I, II, III and IV) | |||||

$\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ | 1.0085 (0.0101) | 2.2589 × 10^{−6} (9.3327 × 10^{−8}) | 0.95 | 0.95 | 0.0387 |

$\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ | 0.0199 (0.0083) | 1.7889 × 10^{−6} (7.616 × 10^{−8}) | 0.95 | 0.95 | 0.0316 |

#### 3.5. Model Validation

^{−1}and 1,140% respectively with a coefficient of determination (R

^{2}) of 0.45. As discussed in earlier sections, the predictive ability of the PC detection band ratio algorithms is significantly dependent on the influence of Chl-a absorption on the selected bands. We believe that the poor accuracy is because the 654 nm peak is strongly affected by Chl-a absorption. Our experimental results show that the 654 nm peak is very sensitive to small changes in Chl-a concentration irrespective of the change in PC concentration.

**Table 3.**Model validation results: root-mean-square-error (RMSE) in cells mL

^{–1}, relative root-mean-square-error (RMS), and coefficient of determination (R

^{2}) are reported for all models.

Band Combination | RMSE | RMS | R^{2} |
---|---|---|---|

Synechocystis data set (Exp I, II and III) | |||

$\left({\rho}_{617}^{-1}{\rho}_{654}\right)$ | 725,709 | 11.4 | 0.45 |

$\left({\rho}_{620}^{-1}{\rho}_{709}\right)$ | 39,168 | 2.35 | 0.70 |

$\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ | 15,260 | 1.01 | 0.94 |

$\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ | 13,885 | 0.69 | 0.95 |

Synechocystis and Anabaena dataset (Exp I, II, III and IV) | |||

$\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ | 19,957 | 1.28 | 0.94 |

$\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ | 19,130 | 2.73 | 0.94 |

**Figure 6.**Validation scatter plots of different models. The solid lines represent the 1-to-1 lines:

**(A,B,C,D)**data from EXP I,II and III (Synechocystis) and

**(E,F)**data from EXP I–IV (Synechocystis and Anabaena). Root-mean-square-error (RMSE) and relative root-mean-square-error (RMS) for each model are also reported. Note that $\left({\rho}_{617}^{-1}{\rho}_{654}\right)$ model predicts many negative values.

^{−1}and RMS of 2350 % (Figure 6B). Our initial observation is that the 620 nm peak is also slightly affected by Chl-a absorption and that this is the cause behind the poor performance of the model. In contrast, our newly developed model $\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ showed promising validation accuracy with an RMSE of 15,260 cell mL

^{−1}and a comparatively low RMS of 101 % (Figure 6B; Table 3). Similarly, the natural logarithmic transformation of our index $\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ yielded very low RMSE of 13,885 cells mL

^{−1}and RMS of 69 % (Figure 6D). Also, both models showed very high R

^{2}of 0.94 and 0.95 respectively. In order to test that the newly developed models are independent of PC species, we performed a validation test on the multiple species dataset (Figure 6E, F). Validation results of newly developed models for the mixed species dataset are summarized in Figure 6E, F and Table 3. RMSE and RMS of the $\left({\rho}_{600}^{-1}{\rho}_{700}\right)$ model are 19,957 cells mL

^{−1}and 128 %, respectively, and similarly the RMSE and RMS of $\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ are 19,130 cells mL

^{−1}and 273 %. The $\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$ model produced slightly lower RMSE but yielded higher RMS. However, the R

^{2}between measured and predicted PC for both models were found to be same (i.e., 0.94).We used PC: Chl-a pigment ratio as a proxy for PC abundance whereas the units of measurement for PC (cells mL

^{−1}) and Chl-a (µg L

^{−1}) were different. Hence the calculated pigment ratio in the residual analysis of all four models carries a pseudo unit (Figure 7).

**Figure 7.**Comparative scatter plots of PC residuals versus PC:Chl-a ratio for four spectral indices such as,

**A.**$\left({\rho}_{617}^{-1}{\rho}_{654}\right)$

**B.**$\left({\rho}_{620}^{-1}{\rho}_{709}\right)$

**C.**$\left({\rho}_{600}^{-1}{\rho}_{700}\right)$, and

**D.**$\left(\mathrm{ln}\left({\rho}_{600}^{-1}{\rho}_{700}\right)\right)$.

**Figure 8.**

**(A, B, C)**3-D surface plots demonstrating the sensitivity of the three indices against Chl-a and PC.

**(D, E, F)**3-D surface plots of residuals, for the three models against Chl-a and PC.

## 4. Conclusions

^{−1}), significantly low RMS (101%) as compared to the existing band ratio algorithms. Natural logarithmic transformation of the new model yielded the lowest RMSE (13,885 cells mL

^{−1}) and RMS (69%) with high coefficient of determination (0.95) between measured and predicted PC concentrations. One reason of the uncertainty observed in the newly developed model could be due to the specific absorption coefficient of PC $\left({a}_{PC}^{*}\right)$ that varies with cell morphology and photo-adaptation [24,25]. Unfortunately this study does not discuss the errors associated with change in $\left({a}_{PC}^{*}\right)$ Rather it discusses the effect of Chl-a as a confounding photo constituent on the performance of model.

## Acknowledgements

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© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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**MDPI and ACS Style**

Mishra, S.; Mishra, D.R.; Schluchter, W.M. A Novel Algorithm for Predicting Phycocyanin Concentrations in Cyanobacteria: A Proximal Hyperspectral Remote Sensing Approach. *Remote Sens.* **2009**, *1*, 758-775.
https://doi.org/10.3390/rs1040758

**AMA Style**

Mishra S, Mishra DR, Schluchter WM. A Novel Algorithm for Predicting Phycocyanin Concentrations in Cyanobacteria: A Proximal Hyperspectral Remote Sensing Approach. *Remote Sensing*. 2009; 1(4):758-775.
https://doi.org/10.3390/rs1040758

**Chicago/Turabian Style**

Mishra, Sachidananda, Deepak R. Mishra, and Wendy M. Schluchter. 2009. "A Novel Algorithm for Predicting Phycocyanin Concentrations in Cyanobacteria: A Proximal Hyperspectral Remote Sensing Approach" *Remote Sensing* 1, no. 4: 758-775.
https://doi.org/10.3390/rs1040758