Kinetic modeling of the synergistic thermal and spectral actions on the inactivation of Cryptosporidium parvum in water by sunlight

Water Research 185 (2020) 116226 Contents lists available at ScienceDirect Water Research journal homepage: www.elsevier.com/locate/watres Kinetic modeling of the synergistic thermal and spectral actions on the inactivation of Cryptosporidium parvum in water by sunlight Ángela García-Gil a , María Jesús Abeledo-Lameiro b , c , Hipólito Gómez-Couso b , c , Javier Marugán a , ∗ a Department of Chemical and Environmental Technology (ESCET), Universidad Rey Juan Carlos, C / Tulipán s/n, 28933 Móstoles, Madrid, Spain b Department of Microbiology and Parasitology, Faculty of Pharmacy, University of Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, A Coruña, Spain c Research Institute on Chemical and Biological Analysis, University of Santiago de Compostela, 15782 Santiago de Compostela, A Coruña, Spain a r t i c l e i n f o Article history: Received 11 May 2020 Revised 20 July 2020 Accepted 23 July 2020 Available online 23 July 2020 Keywords: Solar water disinfection (SODIS) Household water treatment (HWT) Protozoa inactivation Quantum yield Extinction coefficient Water temperature a b s t r a c t Water contamination with the enteroprotozoan parasite Cryptosporidium is a current challenge worldwide. Solar water disinfection (SODIS) has been proved as a potential alternative for its inactivation, especially at household level in low-income environments. This work presents the first comprehensive kinetic model for the inactivation of Cryptosporidium parvum oocysts by sunlight that, based on the mechanism of the process, is able to describe not only the individual thermal and spectral actions but also their synergy. Model predictions are capable of estimating the required solar exposure to achieve the desired level of disinfection under variable solar spectral irradiance and environmental temperature conditions for different locations worldwide. The thermal contribution can be successfully described by a modified Arrhenius equation while photoinactivation is based on a series-event mechanistic model. The wavelength-dependent spectral effect is modeled by means of the estimation of the C. parvum extinction coefficients and the determination of the quantum yield of the inactivation process. Model predictions show a 3.7% error with respect to experimental results carried out under a wide range of temperature (30 to 45 °C) and UV irradiance (0 to 50 W ·m −2 ). Furthermore, the model was validated in three scenarios in which the spectral distribution radiation was modified using different plastic materials common in SODIS devices, ensuring accurate forecasting of inactivation rates for real conditions. ©2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license. ( http://creativecommons.org/licenses/by/4.0/ ) 1. Introduction Water contamination with the enteropathogen Cryptosporidium is a universal challenge ( Efstratiou et al., 2017 ; Hamilton et al., 2018 ; Hofstra and Vermeulen, 2016 ; Karanis et al., 2007 ). Based on WHO reports ( WHO, 2015 ), there were approximately 64 million of estimated cases of illness caused by Cryptosporidium and 35% of them were related to contact with contaminated water sources. Moreover, cryptosporidiosis has a worldwide distribution. In developed countries, prevalence rates range from 0.3 to 54.2%, mainly related to recreational or drinking water ( Abeywardena et al., 2015 ), and reported because of the existence of surveillance systems for routine detection of Cryptosporidium ( Cacciò and Putignani, 2014 ). Furthermore, water bodies may also be contaminated by sewage or effluents from wastewater treatment plants (WWTP), ∗Corresponding author. E-mail address: javier[email protected] (J. Marugán). whose treatments are insufficient to achieve the total removal of Cryptosporidium oocysts ( Nasser, 2016 ; Vermeulen et al., 2019 ). However, the prevalence is assumed to be higher in developing countries ( Putignani and Menichella, 2010 ). In these regions, Cryptosporidium is one of the top three pathogens causing diarrheal disease in children under two years old, and it is responsible for 30–50% of childhood mortality ( Kotloff et al., 2013 ) estimated in 455,0 0 0 deaths in Sub-Saharan region ( Sow et al., 2016 ). The risk of infection by Cryptosporidium through drinking water can be reduced by key intervention methods, such as appropriate selection and protection of the catchment and the installation of an effective filtration step and disinfection by UV-C ( Betancourt and Rose, 2004 ; Swaffer et al., 2018 ). However, developing countries cannot afford the use of advanced technologies and demand lowcost water disinfection processes. Solar water disinfection (SODIS) is a low-cost, easy-to-use and sustainable process to conduct water treatment at the household level. This process is especially interesting for countries where high solar doses are received all around the year. This process, commonly carried out by the expohttps://doi.org/10.1016/j.watres.2020.116226 0043-1354/© 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license. ( http://creativecommons.org/licenses/by/4.0/ ) 2 Á. García-Gil, M.J. Abeledo-Lameiro and H. Gómez-Couso et al. / Water Research 185 (2020) 116226 sure to sunlight of 2 L polyethylene terephthalate (PET) bottles for 6 h, is based on the harmful damage of the UV solar radiation and high temperatures on microorganisms and has been successfully tested for the removal of viruses, bacteria, and protozoa, including Cryptosporidium parvum ( Wegelin et al., 1994 ; McGuigan et al., 2012 ; Gómez-Couso et al., 2012 , 1998 ). At present, SODIS is one of the recommended methods for disinfection of household drinking water ( WHO/UNICEF, 2005 ). Solar inactivation of C. parvum in pure water is dominated by direct endogenous damage caused by UV-B absorption by genome, since the C. parvum action spectrum resembles that of the DNA absorption ( Busse et al., 2019 ; Liu et al., 2015 ). This similarity also confirms the wavelength dependence for the photoinactivation of C. parvum oocysts ( Beck et al., 2015 ; Busse et al., 2019 ; Linden et al., 2001 ) . Recently, Busse et al. (2019) applied the seriesevent model ( Severin et al., 1983 ), that assumes stepwise units of damage until a threshold amount is accumulated, to obtain the relative inactivation constant as a function of wavelength. Actually, the spectral dependence suggests the interest of the potential substitution of PET for other SODIS container materials with higher UV-B transmittance ( García-Gil et al., 2020a ). This work describes for the first time the kinetic modeling of the synergistic effect of the photonic and thermal effects on the inactivation of C. parvum oocysts. The developed model provides an accurate estimation of the required exposure time for the solar inactivation of this protozoon depending on the radiation intensity, available spectral range and water temperature. Application of the model predictions allows the calculation of SODIS treatment time needed to provide safe drinking water from the protozoan point of view, whose higher resistance also ensures the elimination of other less resistant waterborne pathogens. 2. Materials and methods 2.1. Cryptosporidium parvum oocysts Cryptosporidium oocysts were collected from a naturally infected neonatal Friesian-Holstein calf. Concentration (0.04 M phosphate-buffered saline [PBS] pH 7.2 and diethyl ether), purification (discontinuous caesium chloride gradients), quantification (Neubauer haemacytometer) and molecular characterization were performed as previously reported ( Gómez-Couso et al., 2012 ). Briefly, feces were collected from a calf by rectal sampling and stored at 5 °C. Fecal material was then homogenised in 10–20 mL of PBS (0.04 M, pH 7.2), filtered through two sieves (mesh sizes 150 and 45 μm), shaken with diethyl ether (2:1, v/v) and concentrated by centrifugation at 20 0 0 ×g , for 15 min, at 4 °C. The resulting uppermost two layers were removed carefully and discarded, and the sediment was washed with PBS (0.04 M, pH 7.2) by centrifugation at 20 0 0 ×g for 15 min at 4 °C. Cryptosporidium oocysts were purified on discontinuous caesium chloride gradients of 1.05, 1.10 and 1.40 g ·mL −1 by centrifugation at 20 0 0 ×g for 30 min at 4 °C. Finally, the oocysts were counted in a modified Neubauer haemocytometer, with 0.16% malachite green solution as counterstain ( Kilani and Sekla, 1987 ; Lorenzo-Lorenzo et al., 1993 ). The isolate was identified as C. parvum by PCR amplification and sequence analysis of a ≈587-bp fragment of the small subunit rDNA gene (SSUrDNA) ( Ryan et al., 2003 ). 2.1.1. Viability assays The viability of C. parvum oocysts was determined by inclusion/exclusion of the fluorogenic vital dye propidium iodide (PI) and a further modification that includes an immunofluorescence antibody test to verify oocyst identification ( Campbell et al., 1992 ; Dowd and Pillai, 1997 ). Briefly, 200 μL of the sediments were incubated with 15 μL of PI (Sigma-Aldrich, Co., St. Louis, Missouri, USA) working solution [1 mg ·mL −1 in PBS (0.1 M, pH 7.2)] and 15 μL of monoclonal antibodies labelled with fluorescein isothiocyanate (FITC) (AquaGlo TM G/C Direct Test, Waterborne Inc., New Orleans, Louisiana, USA), at 37 °C, for 30 min ( Gómez-Couso et al., 2012 ). Then, the samples were washed three times in PBS (0.04 M, pH 7.2) at 10,0 0 0 ×g , for 5 min at room temperature. Oocysts were identified first under a FITC filter (excitation at 450–480 nm; barrier at 515 nm) before being examined for PI inclusion/exclusion under a PI filter (excitation at 510–550 nm; barrier at 590 nm). The proportions of ruptured (ghost), PI-positive (dead), and PI-negative (viable) oocysts were quantified in an epifluorescence microscope equipped with a Nomarski differential interference contrast, FITC and PI filters (Olympus AX70, Olympus Optical Co., Ltd., Tokyo, Japan). The results are shown as the concentration of PI-negative (viable) oocysts determined for each assay after triplicate counts of more than 100 oocysts. 2.2. Experimental design Three sets of experiments were conducted. In the first set, experiments were carried out at different water temperatures (30, 40, 42, 43, 44, and 45 °C) in the dark to quantify the dark thermal inactivation of C. parvum oocysts. In the second set, inactivation experiments were performed using different UV irradiances (30, 40, and 50 W ·m −2 ) and water temperatures (30, 40, and 44 °C) to determine the contribution of the irradiance effect and its synergistic effect with water temperature. In the third set, experiments for the validation of the developed model predictions were carried out using plastic sheets placed between the illumination source and the water to test the wavelength dependence. Potential materials for the manufacture of SODIS containers ( García-Gil et al., 2020a ) were selected based on their different UV-B transmittances: polyethylene terephthalate (PET), polypropylene (PP) and polymethylmethacrylate (PMMA). For the three scenarios, three experiments were conducted: i) 50 W ·m −2 of UV radiation and 30 °C of water temperature; ii) 50 W ·m −2 and 44 °C; and, iii) 30 W ·m −2 and 44 °C. Table S.1 shows the required treatment time to achieve 1-log reduction (90%) of C. parvum viability. Experiments were carried out in a solar simulator (Atlas Suntest CPS + , ATLAS Material Testing Technology GmbH, Lisengericht, Germany) equipped with a 1100 W air-cooled xenon arc lamp and a combination of filters (Suprax, ATLAS, Material Testing Technology GmbH) to simulate the outdoor solar radiation spectrum. The irradiance was measured with a radiometer PMA2100 fitted with a PMA2107 digital non-weighted UV- A + B Sensor (280–400 nm) (Solar Light® Company, Inc, Glenside, Pennsylvania, USA). An open reaction-jacketed borosilicate beaker (135 ×75 mm) containing 400 mL of distilled water (pH 6.1, conductivity < 10 μS ·cm −1 , organic carbon < 0.5 mg ·L −1 ) was spiked with 75,0 0 0 oocysts ·mL −1 of C. parvum and exposed to artificial solar light at the established intensities of radiation and temperatures for a maximum exposure time of 6 h. The exterior of the reactor was completely black to avoid uncontrolled light reflections and guarantee that only the measured direct radiation participates in the process. In order to maintain the temperature of the water sample during the experiments, the reactor was connected to a refrigerated and heated bath circulator Fisherbrand TM Isotemp TM 4100 R20 (Thermo Fisher Scientific Inc., Waltham, Massachusetts, USA). Constant stirring of 250 rpm was kept during the experiments to ensure a homogeneous concentration of C. parvum oocysts. At different exposure times, 14 mL of the sample was removed and centrifuged at 20 0 0 ×g , 15 °C, for 15 min. The supernatant was discarded, and the sediment thus obtained was resuspended in 500 μL of phosphate buffered saline (PBS) 0.04 M pH 7.2 and used to evaluate the oocyst viability. All tests were performed in duplicate. Á. García-Gil, M.J. Abeledo-Lameiro and H. Gómez-Couso et al. / Water Research 185 (2020) 116226 3 2.3. Kinetic modeling Kinetic parameters were estimated using different datasets obtained for the different submodels after replicated experiments: i) dark thermal inactivation; ii) UV irradiance effect; iii) UV radiationtemperature synergistic effect; and, iv) wavelength-dependent spectral action. 2.3.1. Dark thermal inactivation Experimental data of inactivation in the dark were fitted to a first-order kinetic model ( Eq. (1) and Eq. (2) ): dC dt = −k T ·C (1) ln C C 0 = −k T ·t (2) where C 0 is the initial concentration of the C. parvum (oocysts ·mL −1 ), C is the concentration at a specific time t , and k T is the thermal inactivation kinetic constant. The effect of the water temperature ( T ) on the thermal inactivation kinetic constant ( k T ) was modeled by the Arrhenius equation ( Arrhenius, 1889 ) with a threshold temperature ( Eq. (3) ): k T = k T 0 ·exp −E a T R ·1 T −1 T 0  (3) where k T 0 is the temperature-independent pre-exponential factor, E a T is the activation energy, R is the universal gas constant, and T 0 is the threshold temperature. As Peleg et al. (2012) demonstrated, the threshold temperature can be suppressed, which involves a different value of k T 0 for the same value of k T . However, the present model kept the T 0 as a conceptual threshold to account for the temperature above which the thermal effect is observed. The kinetic parameters of the model ( k T 0 and E a T /R ) have been calculated by minimizing the normalized root mean square error (NRMSE) between the predicted and observed concentration of viable C. parvum oocysts using a constrained nonlinear multivariable optimization algorithm employing the add-in Solver of Excel 2016 software (Microsoft® Corp., Redmond, Washington, USA). 2.3.2. UV irradiance effect The presence of a shoulder in the experimental photoinactivation curves suggests the application of a series-event kinetic model ( Severin et al., 1983 ) to reproduce the experimental data. This model assumes that an event is a unit of damage, and n units of damage must be accumulated to inactivate the microorganisms. Therefore, the inactivation process takes place through a sequence of inactivation levels ( n ). In the population balance of microorganisms at level i (1 ≤i ≤n ), the damaged organisms from the previous level are considered as a source (positive term) and the damaged organisms at the current level are considered as a sink (negative term). This balance is represented by Eq. 4: d C i dt = k RAD ·I ·C i −1 −k RAD ·I ·C i (4) where C i is the concentration of viable C. parvum oocysts (oocysts ·mL −1 ) at level i at a specific time t , C i −1 is the concentration of viable C. parvum oocysts (oocysts ·mL −1 ) at the previous level, k RAD is the photoinactivation constant, and I is the UV irradiance (W ·m −2 ). The values of n and k RAD were calculated minimizing the normalized root mean square logarithmic error (NRMSLE) between experimental and predicted concentrations of viable C. parvum oocysts over time in experiments without thermal effect (30 °C of water temperature) using a constrained nonlinear multivariable optimization algorithm employing the add-in Solver of Excel 2016 software (Microsoft® Corp.). 2.3.3. UV radiation-temperature synergistic effect To account for this synergistic effect in the model, k RAD from Eq. (4) was redefined with the Arrhenius equation ( Eq. (5) ): k RAD = k RA D 0 ·exp −E a RAD R ·1 T −1 T 0  (5) where k RA D 0 is the temperature-independent pre-exponential factor, and E a RAD is the activation energy. The kinetic parameters of the model ( k RA D 0 , E a RAD /R, n , k T 0 and E a T /R ) were recalculated minimizing the NRMSLE between the predicted and observed values of the kinetic constants, using the sequential quadratic programming (SQP) nonlinear optimization tool implemented in GNU Octave platform ( www.octave.org ). The values of the kinetic parameters previously calculated in the previous submodels were used as seeds for the optimization. 2.3.4. Wavelength-dependent spectral action Finally, to describe C. parvum sensitivity to solar inactivation as a function of wavelength, a quantum yield φCP was defined as the ratio between the number of damaged oocysts and the number of absorbed photons. To determine the rate of photon absorption, the absorption spectrum for a single oocyst was defined like Mattle et al. (2015) previously did for adenovirus, MS2, and phiX174 viruses. As Busse et al. (2019) demonstrated, absorption of solar light by C. parvum is dominated by the nucleic acid components, since the action spectrum is similar in shape to the DNA absorption spectrum, with a maximum around 260 nm. The absorbance at 260 nm can be calculated by multiplying the weight of dsDNA in C. parvum by the weight-normalized extinction coefficient of the dsDNA at 260 nm, ɛ CP (260 nm ), reported as 0.020 mL ·μg −1 ·cm −1 ( Gallagher, 2011 ). The weight of the DNA of C. parvum was calculated following data deposited in National Center for Biotechnology Information (NCBI, Reference CM0 0 0429.1) ( National Center for Biotechnology Information, 2020 ) and corresponds to 9.51 ×10 −10 μg. The absorption spectrum for C. parvum was determined by considering the shape of the absorption spectrum of a C. parvum oocyst suspension measured by Busse et al. (2019) and kindly provided by the authors upon request. A 5-point smoothing was applied to the spectrum data in the range from 240 to 400 nm, and the values were normalized to the absorption at 260 nm. The final results of the spectral extinction coefficients of a single C. parvum oocyst, ɛ CP ( λ) (mL ·oocyst −1 cm −1 ) are shown in Table S2. As a result, the photoinactivation kinetic parameter can be expressed according to Eq. (6) : k RAD 0 ·I = φCP · λ ε CP ( λ) ·I ( λ) ·λ h ·c ·dλ(6) where λ h ·c (photon ·J −1 ) converts the energy units of the spectral irradiance, I ( λ), to the photonic units, where h is the Planck’s constant and c is the speed of light in vacuum. The value of the quantum yield, φCP , can be calculated by resolution of Eq. (6) . 3. Results and discussion 3.1. Dark thermal inactivation Data from experiments in dark conditions were evaluated at water temperatures commonly achieved during solar exposure of water (30, 40, 42, 43, 44, and 45 °C). Experimental results shown in Fig. S1 confirm a noticeable effect of temperature, the experiment at 30 °C being the only case in which inactivation did not happen. For this reason, the threshold temperature of the Arrhenius equation ( T 0 in Eq. (3) ) was set to 30 °C (303 K). The experimental results (two replicates in all cases) were fitted to a firstorder kinetic model ( Eq. (1) ), and the values of the kinetic constant 4 Á. García-Gil, M.J. Abeledo-Lameiro and H. Gómez-Couso et al. / Water Research 185 (2020) 116226 were used to calculate the provisional values of the thermal kinetic parameters ( k T 0 = 1.12 ×10 −4 h −1 and E a T /R = 4.37 ×10 5 K, NRMSE = 8.59%). These parameters will be refined later with the complete set of experimental data, using these provisional values as seeds. Predicted results of the thermal inactivation are also shown in Fig. S1. Some reports found no effects on C. parvum survival for water temperatures up to 40 °C ( Liu et al., 2015 ). However, other publications suggested that the viability of C. parvum decreases progressively for temperatures in the range from 30 to 50 °C due to the melting point of the fatty acids and hydrocarbons present in the oocyst wall and the increase in the metabolic activity ( Fayer and Nerad, 1996 ; Jenkins et al., 2010 ; King et al., 2005 ; Peng et al., 2008 ). Furthermore, temperatures above 37 °C can induce the phenomenon of spontaneous excystation of C. parvum oocysts, making their survival impossible in the absence of a host ( Gómez- Couso et al., 2009 ; Smith et al., 2005 ). However, these phenomena do not necessarily follow a pure Arrhenius behavior, what can explain the small deviations observed in experiments at 40 and 42 °C. 3.2. UV irradiance effect Data from C. parvum inactivation experiments under illumination (UV irradiance of 30, 40, and 50 W ·m −2 ) at a temperature of 30 °C to neglect thermal effects were fitted to a series-event model ( Eq. (4) ). Calculation of the kinetic parameters ( n = 8 and k RAD = 4.05 ×10 −2 m 2 ·W −1 ·h −1 ) was carried out by fitting the experimental data with an NRMSLE of 2.44% (see Fig. S2.1). The direct coupling of the dark thermal inactivation model with the UV irradiance model failed to predict the inactivation of C. parvum at temperatures higher than 30 °C (Figs. S2.2 and S2.3) with a global value of NRMSLE = 17.9%. The predictions clearly underestimate the experimental data, showing a higher error for higher temperatures, which supports the existence of a synergy between the thermal and photonic inactivation processes. The existence of a strong synergistic effect between the optical and thermal processes to inactivate microorganisms is well known ( McGuigan et al., 1998 ; Wegelin et al., 1994 ) and has been modeled for bacteria and viruses ( Castro-Alférez et al., 2017 ; García-Gil et al., 2020b ). 3.3. UV radiation-temperature synergistic effect The synergistic effect was included in the model through the temperature dependence of the kinetic constant of the series-event model according to the modified Arrhenius equation, using again a value of 30 °C (303 K) for the temperature threshold ( T 0 ). All the kinetic parameters were recalculated using as seeds the provisional values in the previous submodels. The global fitting of the whole experimental data set for the complete range of irradiances and temperatures provides the values of the final kinetic parameters: n = 7, k RAD 0 = 2.97 ×10 −2 m 2 ·W −1 ·h −1 , E a RAD /R = 6.90 ×10 4 K, k T 0 = 4.19 ×10 −5 h −1 , and E a T /R = 5.06 ×10 5 K with an NRMSLE of 3.68% ( Figs. 1.1 , 1.2 , 1.3 , and 1.4 ). In this case, whereas the predictions of the dark thermal inactivation and the photoinactivation at 30 °C are very similar, the prediction of the photoinactivation at higher temperatures improves significantly. 3.4. Wavelength-dependent spectral action The developed model, which considers the synergistic effect between the UV irradiance and temperature and the independent thermal effect, succeeds in reproducing the C. parvum inactivation using a light source with the solar spectrum. However, for the same global UV irradiance, if the spectral distribution of the radiation changes, the effective damage can also dra- Fig. 1.1. Observed inactivation profiles of C. parvum oocysts in distilled water after exposure to different temperatures in dark conditions and predictions with the synergistic UV radiation-temperature model. Fig. 1.2. Observed photoinactivation profiles of C. parvum oocysts in distilled water after exposure at 30 °C to different intensities of solar radiation and predictions with the synergistic UV radiation-temperature model. matically change. The wavelength-dependent spectral contribution needs to be modeled to predict the inactivation in solar disinfection containers with different transmission spectra. As suggested by Mattle et al. (2015) , the inactivation rate can be calculated by multiplying the quantum yield, the concentration of microorganisms, and the volumetric rate of photon absorption (calculated as the integration in wavelength of the spectral microorganism extinction coefficient by the spectral irradiance for each wavelength). Table S2 shows the C. parvum extinction coefficients ( ɛ CP ( λ)) (calculated in this work) and the spectral irradiance ( I ( λ)) from 280 to 400 nm for a global UV ( I ) of 50 W ·m −2 . Following Eq. (6) , the quantum yield for C. parvum inactivation with the solar simulator spectrum was calculated as φCP = 3.94 ×10 −7 oocysts damaged per absorbed photon, indicating that C. parvum is more resistant to direct inactivation than viruses such as phiX174, MS2, and adenovirus (1.4 ×10 −2 , 2.9 ×10 −3 , and 2.5 ×10 −4 virus in- Á. García-Gil, M.J. Abeledo-Lameiro and H. Gómez-Couso et al. / Water Research 185 (2020) 116226 5 Fig. 1.3. Observed photoinactivation profiles of C. parvum oocysts in distilled water after exposure at 40 °C to different intensities of solar radiation and predictions with the synergistic UV radiation-temperature model. Fig. 1.4. Observed photoinactivation profiles of C. parvum oocysts in distilled water after exposure at 44 °C to different intensities of solar radiation and predictions with the synergistic UV radiation-temperature model. activated per absorbed photon, respectively) ( Mattle et al., 2015 ). In any case, it is important to notice the critical role of the calibration of the spectroradiometer used to measure the emission of the incident radiation, especially in the UVB range. For instance, in the case of the MS2 virus different values of the quantum yield can be found in the literature: 2.07 ×10 −3 , 2.9 ×10 −3 and 2.56 ×10 −4 viruses inactivated per absorbed photon for García- Gil et al. (2020b) , Mattle et al. (2015) and Silverman et al. (2019) , respectively. The reason for these apparent discrepancies is the high sensibility of the results to the experimental data provided by the spectroradiometer. Basically, each quantum yield value worked well in the framework of the spectral measurements from which it was derived. In this sense, the use of quantum yields reported in the literature should be carefully selected and the calculation for each specific device is always recommended. 3.5. Validation of the model The developed model is able to predict the inactivation of C. parvum oocysts depending on the water temperature, irradiance, and spectral distribution of the incident light, allowing the estimation of the required inactivation times for different locations around the world. Additionally, the model has also a particular strength: the capability of estimating required solar exposure time when solar water disinfection is performed in containers made of any material with a known transmission spectrum. To validate this strength, experiments were carried out using plastic materials of different UV-B transmittance: PET, PP, and PMMA and combining two levels of global UV irradiance (30 and 50 W ·m −2 ) and water temperature (30 and 44 °C) in three experiments (the experiment with the lowest values of both variables was neglected). Figs. 2.1 , 2.2 , and 2.3 show the comparison between the observed and the predicted inactivation profiles of C. parvum oocysts versus the exposure time for the PET, PP, and PMMA scenarios. Considering the fully predictive nature of the model inactivation curves (they are not fitting results), the agreement can be considered very good, with values of NRMSLE of 5.54, 5.72, and 11.68% for PET, PP, and PMMA, respectively. The results can be easily interpreted based on the different UV transmission of the materials: 1%, 44%, and 57% in the global UV-B range, and 59%, 60%, and 86% in the UV-A range, for PET, PP, and PMMA, respectively. The radiation transmitted and the C. parvum extinction coefficients versus wavelength are shown in Fig. 3 (data in Table S2). As can be observed, the UV-B is the critical region in which the C. parvum absorption mainly overlaps with the spectrum of the incident radiation, and therefore the UV- B transmission will be very significant in the C. parvum photoinactivation. However, as shown Fig. 3 , the emission of the solar simulator overestimates the irradiance of the standard AM 1.5 solar spectrum, especially in the 280–300 nm range where the process is very sensitive. Consequently, under real sunlight, PP and PMMA would be expected to perform slightly worse. For the PP and PMMA scenarios, the photoinactivation is possible being higher for the plastic with the higher transmission (PMMA). The thermal effect and the irradiance effect can be observed in both cases for experiments at the same global UV irradiance and the same water temperature, respectively. In the case of PET, plastic that essentially does not transmit UV-B radiation, the thermal contribution is almost the only damage source in pure water, achieving at simple sight the same disinfection rate for different values of global UV irradiance (model predictions for 30 and 50 W ·m −2 at 44 °C seem to be the same). The type of photodamage can be direct or indirect ( Nelson et al., 2018 ). Direct damage is due to the absorption of radiation by genome (DNA in this case) and is mainly initiated by photons in the UV-B range. The indirect damage is caused when an external or internal photosensitizer, that can absorb UV-B radiation as well as UV-A and visible radiation, produces photo-produced reactive intermediates (PPRI) that damage the microorganisms ( i.e. reactive oxidative species (ROS)) ( Nelson et al., 2018 ). The absence of external sensitizers (experiments carried out in distillate water) and the negligible inactivation with only UV-A and visible radiation at low temperature (PET scenario at 30 °C) leads to think that C. parvum cannot be damage by endogenous indirect damage produced by internal photosensitizers. However, King et al., 2010 were unable to readily detect cyclobutane pyrimidine dimers formation or DNA damage in oocysts exhibiting similar or greater levels of inactivation by solar UV but they proved that solar UV radiation induces sporozoite membrane depolarization, resulting in reduced cellular ATP and increased cytosolic calcium, accompanied by a reduction in the internal granularity of sporozoites, indicative of apical organelle discharge and sporozoite exocytosis, resulting in a significant reduction in the ability of sporozoites to attach and invade host cells. 6 Á. García-Gil, M.J. Abeledo-Lameiro and H. Gómez-Couso et al. / Water Research 185 (2020) 116226 Fig. 2.1. Observed and predicted inactivation profiles of C. parvum oocysts in distilled water after exposure at different combinations of intensities of solar radiation and temperatures during the experiments of validation using polypropylene (PP) to modify the spectral distribution of radiation. Fig. 2.2. Observed and predicted inactivation profiles of C. parvum oocysts in distilled water after exposure at different combinations of intensities of solar radiation and temperatures during the experiments of validation using polymethylmethacrylate (PMMA) to modify the spectral distribution of radiation. Other authors confirm that the presence of natural organic matter (NOM), one of the known photosensitizers, did not improve the inactivation, likely due to the resistance of the thick oocyst wall to exogenous inactivation ( Liu et al., 2015 ). Furthermore, in the case of using high volume containers, the damage produced by the external PPRI can be completely overshadowed by the role of the sensitizers as attenuators of radiation ( García-Gil et al., 2020c ). Moreover, only for the temperature higher than 30 °C, the thermal effect is noticeable. These facts confirm two things: the threshold on the thermal inactivation set to 30 °C and the dominant mechanism of C. parvum photoinactivation by the direct damage caused by the UV-B photons’ absorption by DNA. Thus, it also means that the solar water disinfection of C. parvum in common containers of Fig. 2.3. Observed and predicted inactivation profiles of C. parvum oocysts in distilled water after exposure at different combinations of intensities of solar radiation and temperatures during the experiments of validation using polyethylene terephthalate (PET) to modify the spectral distribution of radiation. Prediction profiles for 44 °C are practically equal (gray and blue lines). PET with pure water is practically possible because of thermal inactivation, however, reached temperature during solar water disinfection easily rises up to 30 °C ( Dejung et al., 2007 ; Gómez- Couso et al., 2010 ). In the present study, the survival of C. parvum oocysts were determined by the inclusion/exclusion of the fluorogenic vital dye PI, an indicator of the integrity and permeability of the oocyst wall ( Campbell et al., 1992 ) which may be affected during SODIS procedures ( McGuigan et al., 2006 ). This staining method is quick, simple, non-expensive and provides useful information in studies on the influence of environmental factors/pressures, as the temperature and radiation, on the survival of Cryptosporidium spp. oocysts. However, this technique overestimates the oocyst infectivity in comparison with cell culture methods and bioassays in murine models ( Adeyemo et al., 2018 ; Robertson and Gjerde, 2007 ) providing a safety margin in the water treatment by SODIS, which will benefit the microbiological quality of the treated water and in protecting consumer health. Moreover, it should be considered that in those geographical regions where the WHO recommends the use of SODIS as an alternative method of disinfection to guarantee the safety of water destined for human consumption, the levels of water turbidity varied widely. Depending on weather conditions and time of collection, the turbidity of water in some areas can vary between 5 and 20 0 0 NTU daily ( Joyce et al., 1996 ). Laboratory experiments have shown that in water samples of turbidity higher than 200 NTU, less than 1% of the total incident ultraviolet light (UV) penetrates further than a depth of 2 cm from the surface ( Joyce et al., 1996 ). In this case, the role of temperature in the inactivation of C. parvum oocysts is more crucial and, therefore, the viability values determined by the inclusion/exclusion of fluorogenic vital dyes will be very similar to the infectivity values detected using a murine model or a cell culture. Also, in a previous study in which the combined effects of solar radiation intensity, water turbidity and exposure time on the survival of C. parvum oocysts during simulated SODIS exposure were investigated, it was showed that only in those cases in which the infectivity was not 100%, the values of oocyst viability obtained by the inclusion/exclusion of PI were slightly higher than the Á. García-Gil, M.J. Abeledo-Lameiro and H. Gómez-Couso et al. / Water Research 185 (2020) 116226 7 Fig. 3. Extinction coefficient of C. parvum (left axis) and spectral irradiance of the solar simulator and transmitted by PMMA, PP, and PET plastics (right axis). Inset: Details of the UV-B region. corresponding values obtained with a neonatal murine model ( Gómez-Couso et al., 2009 ). 4. Conclusions A novel comprehensive kinetic model for the inactivation of C. parvum in clear water by solar light has been developed. The model considers the solar irradiance, water temperature, the photonic-thermal synergistic effect, and the specific sensibility of C. parvum to the spectral distribution of radiation. A threshold temperature of 30 °C is considered in the model for the dark thermal inactivation of C. parvum , being this process especially significant above 40 °C. UV radiation also leads to the inactivation , being the efficacy strongly affected by the spectral distribution of the incident light, as C. parvum inactivation in mainly driven by photons in the UV-B range. The quantum yield of the photonic process has been calculated from experimental data and the spectral extinction coefficients of C. parvum has been also determined. These values reflect the strong sensitivity of the process to the spectral distribution of the incident light, in agreement with the biological mechanism of Cryptosporidium oocyst inactivation based on the direct absorption of photons by the nucleic acids. The joint action of temperature and radiation leads to a strong synergistic effect that improves the efficacy of the process. The incorporation of this synergistic effect in the model gives very meaningful predictions with an average fitting error of the experimental data of only 3.7%. Finally, the predictions of this comprehensive model have been successfully validated with experimental data from three different scenarios of variable temperature and spectral transmission in the UV range. Predictions of solar inactivation using PET, PP, and PMMA materials led to errors of 5.5, 5.7, and 11.7%, respectively. Therefore, the developed model constitutes a powerful tool for the predictive evaluation of C. parvum inactivation rate under different solar spectral irradiance and environmental temperature conditions for any location worldwide. Applications range from the estimation of the natural inactivation in the environment to the technical design of solar water disinfection processes for drinking water supply, including the spectral transmission of the materials. However, because SODIS procedures can be implemented in different geographical regions, it is recommended to carry out experiments in order to adjust the model to local conditions. Supplementary Information Experimental data and predictions for dark thermal inactivation; experimental data and predictions for the thermal-radiation additive model; spectral extinction coefficients of C. parvum ; spectral emission from the solar simulator and transmitted radiation through sheets of different plastics materials. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge the financial support of the European Union’s Horizon 2020 research and innovation program under WATERSPOUTT H2020-Water-5c-2015 project (GA 688928) and under PANIWATER project (GA 820718), jointly funded by the European Commission and the Department of Science and Technology of India (DST). Ángela García Gil also acknowledges Técnicas Reunidas for the economic support to finance her scholarship in Residencia de Estudiantes and Spanish Ministry of Education for her FPU grant (FPU17/04333). The authors would like to thank the glass-blowing staff of the RIAIDT-USC for technical advice and Mr. Martin Vincent and Dr. Tracy Morse for the supply of the PMMA and PP plastic materials. The authors also thank Prof Ernest R. 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