Light distribution and spectral composition within cultures of micro-algae: Quantitative modelling of the light field in photobioreactors

Abstract

Light, being the fundamental energy source to sustain life on Earth, is the external factor with the strongest impact on photosynthetic microorganisms. Moreover, when considering biotechnological applications such as the production of energy carriers and commodities in photobioreactors, light supply within the reactor volume is one of the main limiting factors for an efficient system. Thus, the prediction of light availability and its spectral distribution is of fundamental importance for the productivity of photo-biological processes. The light field model here presented is able to predict the intensity and spectral distribution of light throughout the reactor volume based on the incident light and the spectral characteristics of the photosynthetic microorganism. It takes into account the scattering and absorption behaviour of the micro-algae, as well the adaptation of the biological system to different light intensities. Although in the form exposed here the model is optimized for photosynthetic microorganism cultures inside flattype photobioreactors, the theoretical framework is easily extensible to other geometries. Our calculation scheme has been applied to model the light field inside Synechocystis sp. PCC 6803 wild-type and Olive antenna mutant cultures at different cell-density concentrations exposed to white, blue, green and red LED lamps, delivering results with reasonable accuracy, despite the data uncertainties. To achieve this, Synechocystis experimental attenuation profiles for different light sources were estimated by means of the Beer-Lambert law, whereby the corresponding 1 downward irradiance attenuation coefficients K d (λ) were obtained through inherent optical properties of each organism at any wavelength within the photosynthetically active radiation band. The input data for the algorithm are chlorophyll-specific absorption and scattering spectra at different mean acclimatisation irradiance values for a given organism, the depth of the photobioreactor, the cell-density and also the intensity and emission spectrum of the light source. In summary, the model is a general tool to predict light availability inside photosynthetic microorganism cultures and to optimize light supply, in respect to both intensity and spectral distribution, in technological applications. This knowledge is crucial for industrial-scale optimisation of light distribution within photobioreactors and is also a fundamental parameter for unravelling the nature of many photosynthetic processes.

Contribution to the modelling of the light field distribution within Synechocystis sp. PCC 6803 cultures and its influence on cellular photosynthesis processes

“…Indeed, this is the first work where experimental data corresponding to a system with a slower-than-exponential light decay have been benchmarked with in silico results. By updating the previous exponential-type published model Fuente et al (2017) with Mittag-Leffler functions, accurate results are obtained. In fact, this framework generalisation allows the estimation of the light field at any cell density and optical depth inside a PBR for photosynthetic microorganism cultures acclimated to a given irradiance.…”

“…To this purpose, measured inherent optical properties altogether with the depth of the photobioreactor, the cell-density and also the intensity and emission spectrum of the light source have to be taken into account. Following this strategy, classical Lambert-Beer law predictions are available as described in a previous modelling work Fuente et al (2017). In the present manuscript, such modelling framework has been upgraded with Mittag-Leffler functions to improve its predictability capacity.…”

“…To predict the light field within the culture, we utilised a published light model Fuente et al (2017) that takes into account Inherent Optical Properties (IOPs) Preisendorfer (1961). This mathematical structure was afterwards updated Fuente et al (2018) by replacing the Lambert-Beer law with the Mittag-Leffler (ML) equation in order to improve the model accuracy for very low intensities because at light depleted conditions, radiation decay deviates from the pure exponential case.…”

“…In order to assess the package effect, several cell properties are necessary. Such quantities, which will be described in the following, were gathered in the growth and optical conditions outlined in a previous work Fuente et al (2017). First, the measured mean external diameter of the cell d is 2.3 µm and the chlorophyll mass per cell c accounts for 30 fg.…”

“…Light decay in photosynthetic cultures is due to absorption and scattering phenonema Mishchenko (2014b), can be described using inherent optical properties of the suspension Preisendorfer (1961) and by solving a self-consistency problem between average irradiance inside the whole volume and the average PAR downward attenuation coefficient, as both magnitudes depend on each other. In this regard, a modelling approach was recently proposed Fuente et al (2017), where the remaining light given as a PAR integrated irradiance value at different depths from the emission lamp within Synechocystis sp. PCC 6803 (hereafter referred to as Synechocystis) cultures was in silico estimated.…”