Predicting microalgae growth

Ward Blanken^{a,⁎} , P. Richard Postma^{a} , Lenneke deWinter^{a} , René H.Wijffels^{a,b }, Marcel Janssen^{a,⁎}

"Please note that this page is a prototype. Its purpose is to demonstrate the concept of an interactive publication.

Henceforth it is incomplete. Only the section "2. Theory" has been partially developed."

**Publication:**

Algal Research, Elsevier

Journal homepage: www.elsevier.com/locate/algal
Algal Research 14 (2016) 28–38

DOI: doi:10.1016/j.algal.2015.12.020

**Article history:**

Received 30 August 2015

Received in revised form 22 December 2015

Accepted 31 December 2015

Available online 8 January 2016:

A generally applicable kineticmodel is presented to predict light limited microalgal growth. This model combines a
mathematical description for photoautotrophic sugar production with a description for aerobic chemoheterotrophic
biomass growth. The model is based on five parameters which are directly measurable but were obtained from
literature for the purpose of this study. The model was validated for Chlorella sorokiniana with 52 experiments derived
from eight publications and for Chlamydomonas reinhardtii with 32 experiments derived from seven publications.
The specific growth rate was initially predicted with a mean absolute percent error (MAPE) of 34–36%.
The low accuracy is most likely caused by simplifications in the lightmodel and inaccurate parameter estimations.
When optimizing the light model per experimental dataset, a 1–2% MAPE was obtained. When optimizing input
parameters separately from the light model, a 2–18% MAPE was realized. After validating this model on batch
data, we conclude that this model is a reliable engineering tool to predict growth in photobioreactors provided
the light field is accurately measured or calculated.

© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(https://creativecommons.org/licenses/by/4.0/).

**Keywords:** Photosynthesis, Microalgae, Light limited, Growth model, Productivity prediction

Please note that this page is a prototype. It's purpose is to demonstrate the concept of an interactive publication.

Henceforth it is incomplete. Only the section "2. Theory" has been partially developed.

All of the sugar that is used for aerobic chemoheterotrophic biomass
growth is produced by photoautotrophic sugar production. In our model,
the photoautotrophic sugar production is represented by coupling photosynthesis
and the Calvin–Benson cycle. Hereby, it is assumed that all
energy generated in the form of ATP and NADPH during photosynthesis
is used in the Calvin–Benson cycle to incorporate CO^{2} into triose sugars.

Calvin-Benson cycle

ATP = Adenosine Tri-Phosphate

The rate of photoautotrophic sugar production is dependent on light intensity (Eq. (1)). This equation is equivalent to the model of Jassby and Plattwhich is based on a hyperbolic tangent function [7]. The original equation proposed by Jassby and Platt has been rewritten to make sugar as the end product of photosynthesis (Eq. (4)). In Eq. (1), the parameter alpha (α) describes the initial slope of the curve which levels off to the maximal specific sugar production (qs,m). Please note that α can also be expressed as the product of the sugar yield on photons and the specific light absorption coefficient (Eq. (2)) which is in accordance with the approach of Geider [16]. Eq. (3) depicts the relation to calculate the specific photon absorption rate based on the light intensity and the specific light absorption coefficient. By incorporating Eqs. (2) and (3) into Eq. (1), the sugar production rate (Eq. (4)) becomes a function of the maximal specific sugar production (qs,m), the specific photon absorption rate (qph), and the sugar yield on photons (Ys/ph) which are process parameters or measurable characteristics of the microalgae. Variable qph thus replaces Iph in the Jassby & Platt model, and this is practical for the integration of the light model within the growth model, which will be discussed later.

\[q_{s}=q_{s,m}.tanh(\frac{α.I_{ph}}{q_{s,m}})\]

(1)

q_{s}= sugar rate in mol (cmol s)^{−1}

q_{s,m}= maximal specific sugar production (cmol s)^{−1}

tanh=frite

α(alpha) = initial slope of PI curve / product of the sugar yield on photons / specific light absorption coefficient

I_{ph}= light in mol-photon (m^{2} s)^{−1}

PI = photosynthetic irradiance

q

tanh=frite

α(alpha) = initial slope of PI curve / product of the sugar yield on photons / specific light absorption coefficient

I

PI = photosynthetic irradiance

\[α=Y_{s/ph}.a_x\]

(2)

\[q_{ph}=I{ph}.a_x\]

(3)

\[q_s=q_{s,m}.tanh(\frac{q_{ph}.Y_{s/ph}}{q_{s,m}})\]

(4)

The sugar produced in the light reaction is exploited as a fundament for newbiomass and is oxidized in the mitochondria to obtain extra energy that is necessary to support growth related processes and cell maintenance. This partitioning of sugar between anabolic and catabolic reactions can be described using Pirt's Law (Eq. (5)) [8] which states that a small amount of substrate (sugar) is continuously consumed for maintenance (ms). The remaining sugar is available for growth (μ) resulting in new biomass according to a constant biomass yield on sugar (Yx/s), which indirectly implies that a fixed amount of sugar is respired per carbon mol-x (cmol-x) produced. The validity of adopting Pirt's description for partitioning of photosynthetically derived energy has been established for several microalgae species [17,18]. Please note that the specific sugar production rate (qs) in Eq. (5) is predicted employing Eq. (4). To summarize, a typical photosynthesismodel is combined with the classical aerobic chemoheterotrophic growth model of Pirt to predict the specific growth rate of microalgae (Eq. (5)).

White board

Light attenuation within a microalgae suspension in flat plate photobioreactors is described based on the Lambert–Beer Law which states that the attenuation of light over distance is proportional to the light intensity itself with the proportionality constant being the volumetric absorption coefficient. The latter is the product of the specific light absorption coefficient (ax) and the biomass concentration (Cx).

White Board

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