Enhanced Algal Photosynthetic Photon Efficiency by Pulsed Light
Yair Zarmi, Jeffrey M. Gordon, Amit Mahulkar, Avinash R. Khopkar, Smita D. Patil, Arun Banerjee, Badari Gade Reddy, Thomas P. Griffin, Ajit Sapre
iiScience
Article
Enhanced Algal Photosynthetic Photon Efficiencyby Pulsed Light
Yair Zarmi, JeffreyM. Gordon, AmitMahulkar, AvinashR. Khopkar, SmitaD. Patil, ArunBanerjee, BadariGade Reddy,Thomas P. Griffin,Ajit Sapre [email protected]
HIGHLIGHTS
Sizable enhancement ofalgal photosyntheticphoton efficiency at highlight intensityExtensive experimentalevidence from new andrevisited experimentsModel based on photonarrival statistics accountsfor all experimentalobservationsThe key is synchronizingbiological and photonictimescales via pulsed light
Zarmi et al., iScience ,101115May 22, 2020 ª ll OPEN ACCESS
Science
Article
Enhanced Algal Photosynthetic PhotonEfficiency by Pulsed Light
Yair Zarmi, * Jeffrey M. Gordon,
Amit Mahulkar, Avinash R. Khopkar, Smita D. Patil, Arun Banerjee, Badari Gade Reddy, Thomas P. Griffin, and Ajit Sapre SUMMARY
We present experimental results demonstrating that, relative to continuousillumination, an increase of a factor of 3–10 in the photon efficiency of algal photo-synthesis is attainable via the judicious application of pulsed light for light inten-sities of practical interest (e.g., average-to-peak solar irradiance). We also proposea simple model that can account for all the measurements. The model (1) reflects theessential rate-limiting elements in bioproductivity, (2) incorporates the impact ofphoton arrival-time statistics, and (3) accounts for how the enhancement in photonefficiency depends on the timescales of light pulsing and photon flux density. Thekey is avoiding ‘‘clogging’’ of the photosynthetic pathway by properly timing thelight-dark cycles experienced by algal cells. We show how this can be realizedwith pulsed light sources, or by producing pulsed-light effects from continuous illu-mination via turbulent mixing in dense algal cultures in thin photobioreactors.
INTRODUCTION
Background and Motivation
The quest to improve the bioproductivity of algae is largely prompted by their value for biofuels, nutritionalsupplements, and pharmaceuticals (Borowitzka and Moheimani, 2013). Previous investigations havefocused on (1) trying to improve the efficiency with which the photosynthetic apparatus can exploit incidentphotons as well as (2) more efficiently distributing those photons among the algae in a photobioreactor(Tennessen et al., 1995; Gebremariam and Zarmi, 2012; Greenwald et al., 2012; Zarmi et al., 2013; Gordonand Polle, 2007; Abu-Ghosh et al., 2015).Algae exhibit maximal conversion efficiency at photon flux densities I that are below ! m E/(m -s), de-noted by I in Figure 1 (1 E h ! m E/(m -s)), which is notachieved by cultivating algae under continuous light, where a progressively increasing fraction of the photonsabove intensity I are dissipated as I increases. A pivotal question, then, is to what extent this inefficiency canbe surmounted by illumination with pulsed (rather than continuous) light.The consensus from an extensive literature on algal photobioreactor performance has been that pulsedlight cannot lead to higher bioproductivity (Schulze et al., 2020; Graham et al., 2017). In these studies, how-ever, the biomass production rate was taken as the average over the entire cycle time, i.e., over both lightand dark periods. Results from pulsed-light experiments were compared against those under continuouslight of the same cycle-average photon flux density, and not the instantaneous intensity of the pulsed light,such that the number of photons impinging on the culture over an extended period of time was the samefor both the pulsed and continuous light protocols.Comparisons were sometimes generated for continuous-light intensities I < I , where maximal efficiency isachieved, so, intrinsically, no improvement was possible with pulsed light. Other studies used cycle andpulse times that are well beyond the values where efficiency enhancements are possible (Schulze et al.,2020; Graham et al., 2017; Combe et al., 2015). And publications depicting pulsed-light experiments whereenhancements in photosynthetic efficiency could have been deduced are sparse and do not explicitly notethe improvements (Vejrazka et al., 2011, 2012, 2013, 2015; Simionato et al., 2013). Department of Solar Energyand Environmental Physics,Jacob Blaustein Institutes forDesert Research, Ben-GurionUniversity of the Negev, SedeBoqer Campus 8499000,Israel School of Mechanical andChemical Engineering,University of WesternAustralia, Perth WA, 6009,Australia Reliance Industries Ltd.,Mumbai, MH, India Present address:Breakthrough EnergyVentures, Boston, MA, USA Lead Contact*Correspondence:[email protected]://doi.org/10.1016/j.isci.2020.101115 iScience , 101115, May 22, 2020 ª ll OPEN ACCESS he purpose of this article is to show how such previous misconceptions can be resolved and, in theprocess, to present and analyze extensive experimental measurements showing how algal photosyntheticefficiency per photon, in particular at the light intensities required for high biomass generation rates, canbe enhanced severalfold relative to continuous illumination via the judicious application of pulsed light.
Basic Trends in Bioproductivity ( P - I Curves)
The performance of algal photobioreactors is commonly plotted as bioproductivity P versus I (Figure 1). P may be the dry biomass production rate (e.g., g dry wt./(m -s)) (Mann and Myers, 1968; Molina-Grima et al.,2000; Chisti, 2007), or the O production rate (e.g., mol/(m -s)) (Chalker et al., 1993; Geider and Osborne,1992). Once I exceeds I min below which algal respiration dominates (the light compensation point), P in-creases linearly until, over a range of flux densities above I , P grows sublinearly and then plateaus (Fig-ure 1A). Bioproductivity per photon is P/I (Figure 1B). As I min is invariably far smaller than I values of practicalinterest, P/I remains essentially constant at its maximum value up to around I , and then decreases with I .For pulsed light, each cycle has an irradiation duration T pulse and a dark period T dark . In the presentationthat follows, I consistently refers to the instantaneous photon flux density, be it for continuous or pulsedlight. To evaluate P per photon , one must take into account the number of photons (per unit area) thathit the photosynthetic apparatus during a pulse ( I , T pulse ). Hence, for comparisons with continuous lightdata, P / I must be computed only for the time of exposure to light pulses, rather than the full cycle time. Figure of Merit: Relative Photon Efficiency
To compare between pulsed and continuous light operation, we define relative photon efficiency h ph as: h ph = ! Average biomass generated per photonin pulsed regime "
Average biomass generated per photonunder continuous light operation " : (Equation 1a) Assuming the number of photons reaching the reaction centers is proportional to T pulse , we re-express h ph as: h ph = ! Average biomass generated in one cycle T pulse " Average biomass production rateunder continuous illumination " : (Equation 1b) Equation 1b constitutes a good approximation for h ph (in the statistical sense) as long as the number ofphotons hitting a reaction center during T pulse is sufficiently longer than the average time between thearrival of consecutive photons. For example, for I = 1,000 m E/(m -s) and an effective photon absorptioncross-section A of 1 nm , the average time between photon arrivals is 1.66 ms. Effective absorption cross-section refers to a characteristic value for each reaction-center antenna responsible forphotochemical conversion in Photosystem II (PS II). Extensive measurements have established a value of
Figure 1. Key Trends in Algal Photobioreactor Performance (A) Biomass production rate per unit time and per unit area, P , as a function of instantaneous photon flux density. Undercontinuous light, the instantaneous and time-averaged photon flux densities are identical. For pulsed light, however, I instantaneous refers to its value only during T pulse , which is why P can be noticeably greater under pulsed light.(B) The corresponding variation of P/I (biomass production per photon ) with instantaneous photon flux density. ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article he order of 1 nm , which, depending on algal strain and photo-acclimation, can vary from about half thatvalue up to several square nanometers (de Wijn and van Gorkom, 2001; Zou and Richmond, 2000;Simionato et al., 2011; Bonente et al., 2012; Gris et al., 2014; Ley and Mauzerall, 1982; Klughammer andSchreiber, 2015; Osmond et al., 2017; Murphy et al., 2017; Koblı´zek et al., 2001). In contrast, the measuredcross-section of a single chlorophyll molecule is ! (Ley and Mauzerall, 1982). However, the effec-tive absorption cross-section A for each reaction center antenna, which comprises of the order of hundredsof chlorophyll molecules, is commensurately larger (Ley and Mauzerall, 1982; Klughammer and Schreiber,2015; Osmond et al., 2017; Murphy et al., 2017; Koblı´zek et al., 2001; Greenbaum, 1988).Exploiting the statistics of photon arrival times, we will show below that, for I = 1,000 m E/(m -s) and A = 1 nm , T pulse should be longer than ! I = 250 m E/(m -s), T pulse should be longerthan !
10 ms. If, on the other hand, T pulse is short relative to the average photon arrival time, then Equa-tion 1b is not a suitable expression for h ph and must be revised. Absolute photon efficiency can vary notice-ably with reactor temperature, reactor chemistry, algal strain, and light intensity. However, the primary aimhere is demonstrating how properly chosen pulsed-light protocols can boost photon efficiency relative tocontinuous illumination. Hence relating to relative photon efficiency permits a meaningful comparisonamong previous studies and against the measurements reported below.
Deducing Photon Efficiency Enhancements from Prior Studies
Published data for pulsed-light experiments where it is possible to rigorously deduce enhancements in h ph are scarce, and do not explicitly articulate them. The publications for which the reported data permit one toascertain such improvements are: (Vejrazka et al., 2011, 2012, 2013, 2015; Simionato et al., 2013).From the data in Vejrazka et al. (2011, 2012, 2013, 2015), h ph z T pulse = 1 ms and T dark = 9 ms at I = 1,000 m E/(m -s). From the data in Simionato et al. (2013), h ph z T pulse = 11 ms and T dark = 22 ms at I = 350 m E/(m -s), with h ph z
10 for T pulse = 10 ms and T dark = 90 ms at I = 1,200 m E/(m -s). Both are elaborated in the following discussion. RESULTS
New Experimental Measurements of Marked Increases in h ph under Pulsed Light Our experimental methods are summarized in Transparent Methods of the Supplemental Information,including the definition of specific growth rate m . The normalized m plotted in Figure 2 is defined so asto permit comparisons between pulsed and continuous illumination experiments, equal to the productof (1) average biomass production rate over a long time and (2) ( T pulse + T dark )/ T pulse . Hence the normalized m is the average biomass produced in one cycle divided by T pulse .Notable aspects of our results are summarized in Figure 2. Figure 2A highlights that at I = 1,000 m E/(m -s):(1) h ph is enhanced by a factor of !
3, (2) h ph increases and peaks as T dark lengthens, (3) an optimal T dark Figure 2. Measured Normalized Specific Growth Rate
As a function of: (A) T dark for pulsed light with I = 1,000 m E/(m -s) at T pulse = 5, 10, and 15 ms and (B) I for both continuousirradiation and pulsed light. Vertical bars indicate G ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article xists beyond which h ph decreases, and (4) the highest h ph is achieved for shorter pulses and lessens as T pulse is increased beyond !
10 ms. Figure 2B shows the dependence of h ph on I .The existence of an optimal dark time may be understood by considering extreme cases. (1) For very short T dark , there is not enough time to process all plastoquinones ( PQ s) the reduction of which forms an essentiallink in the photosynthetic chain, including the PQ pool, which refers to whether the PQ molecules exist in anoxidized or reduced state (see Figure 3). In this limit, h ph is close to its value under continuous illumination.(2) For excessive T dark , PQ s may decay or the system may revert to respiration.Our highest h ph was achieved for T dark = 200–300 ms. The measurements of Simionato et al. (2013) spanned T dark = 22–900 ms. In the experiments of Vejrazka et al. (2011, 2012, 2013, 2015), much shorter pulses (1 ms)and dark times (9 ms) were applied. The magnitude of the average T dark in the thinnest and most efficientturbulent dense-culture flat-plate photobioreactors reported in Qiang et al. (1998a, 1998b) and Richmondet al. (2003) was 200–400 ms. In no prior investigation did the authors search for an optimal T dark . We as-sume in our model that there is a dark time over which all PQ s reduced during a pulse are exploited forbiomass production. The Model and the Rate-Limiting Process
Our model for the rate-limiting step of PS II, sandwiched between ultra-fast photochemical processes andfar longer chemical processing in Photosystem I (PS I), is sketched in Figure 3. Biomass generation is treatedas proportional to the number of charges delivered to PS I by re-oxidation of PQ s at Cytb f and subsequentproduction processes, with two photons being required for the reduction of one PQ .The model allows for the confluence of three factors: (1) the potential to avoid ‘‘clogging’’ of the photosyn-thetic pathway inherent to continuous irradiation by proper timing of the light-dark cycles, (2) the state ofthe PQ pool, and (3) photon arrival-time statistics. We proceed by presenting the ideas incorporated in themodel, followed by demonstrating that the results of Vejrazka et al. (2011, 2012, 2013, 2015) and Simionatoet al. (2013) and our new data can all be accounted for by the model with reasonable values for the param-eters A , PQ pool size N pool , and delivery time t del . ‘‘Bottleneck’’ Timescale and P-I
Curves
Experiments indicate that the transition from linearity to saturation in algal
P-I curves ( I = I in Figure 1) oc-curs in the range I = 150–300 m E/(m -s). Our measurements plotted in Figure 4 below provide one suchexample. This transition can be related to timescales of physiological relevance. For example, for A = 1 nm , a photon is then absorbed, on average, every 10 to 5 ms. So with two photons being requiredto reduce one PQ (Figure 3), an average of 20 to 10 ms is needed. If A is doubled, then the requisite time ishalved to 10 to 5 ms. Thus, the transition to saturation occurs when the average PQ reduction time is of theorder of 10 ms. At higher I (the saturation branch of the P-I curve) the average PQ reduction rate is clearlyfaster.Saturation suggests there is a timescale of the same order of magnitude in the subsequent stage of theproduction process, which constitutes a ‘‘bottleneck.’’ Indeed, it has been recognized that once a PQ isreduced, its delivery time t del to the next processing stage is !
10 ms (Diner and Mauzerall, 1973; Mauzeralland Greenbaum, 1989; Joliot and Joliot, 2008; Govindjee et al., 2010; Hasan and Carmer, 2012; Green-baum, 1979), so that the average charge delivery rate to Cytb f (from PSII) on the saturation branch ofthe P-I curve should be 1/ t del . Figure 3. Schematic of the Rate-Limiting Step in Algal Bioproductivity as Implemented in Our Model ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article nsuing production stages have processes with timescales at least one order of magnitude greater( R P , based on the argument that if they gave rise toa bottleneck effect, then the transition to saturation in the P-I curve would occur at roughly 10 times lowervalues of I . In fact, the same bottleneck effect characterizes the rates of O generation (a direct product ofPS II) and biomass generation (a product of processes beyond PS II).In view of the fact that the only observed bottleneck is a timescale related to the rate of reduction of PQ s,we adopt the hypothesis that the biomass production rate is proportional to the rate of reduction of PQ s byPS II to the following production stages. PQ Pool and Pulsed-Light Operation
Prior studies have estimated the size of the PQ pool in PS II as N pool z !
7, com-pounded by evidence that there may be a distribution of N pool (Simionato et al., 2013; Greenbaum, 1979;McCauley and Melis, 1986; Guemther et al., 1988; Hemelrijk and van Gorkom, 1996; Cleland, 1998). Thispool enables PS II to store the energy extracted from the dissociation of up to N pool water molecules (drivenby the absorption of up to 2 , N pool photons) by twice reducing each available PQ .To appreciate the influence of N pool on h ph , we first consider continuous irradiation. Along the linear part ofa P-I curve in Figure 1A, each electron from PQ is delivered to the next electron carrier, so that PQ poolsaturation does not impact performance. Once I > I , the PQ reduction rate exceeds the electron deliveryrate. Hence, almost immediately after irradiation begins, the PQ pool is saturated, and excess photons arenot utilized as all the charge carriers are occupied. Because PQ reduction rate increases with I, whereas thedelivery rate is approximately independent of I , photon efficiency decreases with I .Now consider pulsed operation at I instantaneous > I (Figure 1). During the pulse, some reduced PQ s maydeliver charges to the subsequent stage. Concurrently, additional PQ s get reduced in the pool,because the PQ re-oxidation rate is slower than the reduction rate. If the light pulse ends just whenthe PQ pool has been reduced, namely, before ‘‘clogging’’ begins, and if the system is then givenenough dark time to process all the PQ s reduced during the pulse and/or in the pool, then all ab-sorbed photons can be exploited, and a correspondingly higher h ph can be attained (modulo lossesthat may occur during T dark ).There is direct experimental evidence, not just correlative evidence, supporting the assumption about howthe state of the PQ pool and its saturation affect photosynthetic dynamics (Joliot and Joliot, 1984a, 1984b,1992; Joliot, 2003; Rokke et al., 2017; Suslichenko and Tikhonov, 2019). There is comparable additional ev-idence for the influence of the PQ pool on photosynthetic efficiency from investigations of direct hydrogenproduction (rather than biomass generation) from algae (Greenbaum, 1979) where the same rate-limitingsteps in PS II dominate photosynthetic yield. Figure 4. Comparison of Model Predictions for a
P-I
Curve against Our Measurements for Continuous Illumination
Vertical bars indicate G ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article hoton Arrival-Time Statistics
Photon arrival-time statistics are governed by a Poisson distribution: P ð D t Þ = t e $ D t = t ; (Equation 2) where D t is the time between the arrival of two consecutive photons and t is the average of D t , which for thePoisson distribution is equal to the standard deviation. Note that this is not a narrow distribution centeredon its average with a small standard deviation.For example, consider A = 1 nm . At I = 2,000 m E/(m -s), 1,204 photons/s are absorbed on average, so theaverage time gap between two consecutive photons is 0.83 ms, with a standard deviation of 0.83 ms.Except for the effect of the 0.2 ms timescale, photon arrival statistics do not affect photon efficiency undercontinuous light, because averaging over long times depends only on the average photon arrival rate, towhich I is proportional. However, once light pulses as short as several milliseconds are considered, the sta-tistics of photon arrival times plays a progressively important role in the PQ reduction rate. The 0.2-ms Timescale and Its Influence at High Light Intensity or Short Pulse Length
The excitation of a reaction center by a single photon, leading to the reduction of a QA , is estimated torequire ! QA , it cannot processadditional photons. Hence, if a second photon hits the reaction center within less than 0.2 ms, it is unuti-lized. This timescale plays a significant role at high photon flux densities ( R m E/(m -s)), as well as atlower flux densities under short pulses of the order of 1 ms.Under continuous light, the loss of a second photon in a consecutive pair, which arrives within less than0.2 ms after the first photon, is small compared with the losses owing to ‘‘clogging.’’ For example, with I = 2,000 m E/(m /s) and A = 1 nm , the fraction of lost second photons is 11%, whereas the loss owing tothe slowness of PQ re-oxidation is ! A or I is doubled, then the loss amounts to ! ! A or I increases the loss to 31%. Statistics of PQ s under Pulsed-Light Operation The aforementioned observations, compounded with the experimental findings of de Wijn and van Gor-kom (2001), Zou and Richmond (2000), Simionato et al. (2011), Bonente et al. (2012), Gris et al. (2014),Ley and Mauzerall (1982), Klughammer and Schreiber (2015), Osmond et al. (2017), Murphy et al. (2017),and Koblı´zek et al. (2001) lead us to propose that biomass generation is proportional to the number of PQ s delivered to the ensuing production processes. h ph calculated from the model is then h ph = ! Average number of PQ s reoxidized at cyt b f in one flash T pulse " Average reoxidation rate of PQ at cytb funder continuous illumination ! = ! Average number of PQ s reoxidized at cytb f in one flashT pulse " % t del (Equation 3) Owing to the statistical nature of photon arrival times, the number of PQ s re-oxidized under pulsed-lightoperation is a random variable with an average and a standard deviation. The average varies in a non-trivialmanner with T pulse and the reduced state of the PQ pool. The standard deviation is large for short pulsesand diminishes as T pulse is increased. When a distribution of PQ pool sizes is incorporated, as T pulse isincreased, pools with a larger number of PQ s allow for the reduction of a larger number of PQ s and theirsubsequent re-oxidation during T pulse . The effect of this possibility is demonstrated in the following discus-sion. Under continuous light, averaging over long exposure times smoothes out the fluctuations owing tophoton statistics. By contrast, under short pulses, the measurements have significant statistical fluctuations,especially in measurements that do not extend over a long time. ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article onfirming Model Validity for Continuous-Illumination Performance
Before embarking upon comparisons of model predictions against data from pulsed-light experiments, wemust ensure that the model can predict
P-I curves under continuous illumination. Our measured
P-I curve ispresented with our model calculation in Figure 4. The detailed computational procedure is described laterin the discussion. The values of the biological parameters chosen were: A = 1 nm , N pool = 7, and t del = 10 ms. The small effect of respiration at very low I was not incorporated considering the error barson the data, i.e., the light compensation point was taken as I min z PQ re-oxidation at Cytb f. Assuming that the biomass production rate isproportional to the latter, the experimental and computed curves ought to be proportional to one another: P Biomass = C % ð PQ reoxidation rate Þ (Equation 4) with a least-squares fit yielding C = 1.956. Simple Average Model
Description
Assuming a single value for N Pool , we approximate N g , the number of PQ s reduced per pulse, by N g = n T pulse $ : (Equation 5) Here, n is the rate of photons hitting the reaction center (photons/ms), given by n = % I $ $ $ Av & % A $ $ & ; (Equation 6) where I is in m E/(m -s), Av is Avogadro’s number (6.02 ), A is in nm , and T pulse is in ms. When T pulse exceeds the PQ reduction time, the number of PQ s reduced during the pulse is approximately n re $ oxidizedo = T pulse $ t del : (Equation 7) The number of PQ s reduced during the pulse and not re-oxidized immediately is then: n additional = N g $ n re $ oxidizedo = ! n o $ t del " T pulse (Equation 8) which are stored in the PQ pool as long as it is not full. The number of additional (reduced) PQ s should notexceed the maximum allowed pool size: n additional % N Pool T pulse % N Pool ð n = $ = t del Þ h T Maxpulse : (Equation 9) If T pulse does not obey Equation 9, then the PQ pool is completely reduced at the end of the pulse, andsome photons are wasted. Hence, the total number of PQ s re-oxidized during a pulse and the ensuing T dark is given by n re $ oxidized = n o T pulse ; T pulse % T maxpulse T pulse t del + N pool ; T pulse > T maxpulse (Equation 10) which yields an expression for h ph (from Equation 3): h ph = ð n = Þ t del ; T pulse % T Maxpulse + N pool % t del $ T pulse & ; T pulse > T Maxpulse : (Equation 11) How T pulse Affects h ph Equation 11 shows the importance of selecting T pulse appropriately. For T pulse < T Maxpulse , h ph is constant. For T pulse > T Maxpulse , h ph diminishes as T pulse is increased, illustrated in Figure 5. For A = 1 nm , a delivery time(bottleneck) of 10 ms, and N Pool = 7, one finds from Equations 6 and 9: I = ; m E $% m $ s & : n = :
602 photons $ ms ; T maxpulse = :
81 msI = ; m E $% m $ s & : n = :
204 photons $ ms ; T maxpulse = :
34 ms : (Equation 12) ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article s long as T pulse does not exceed these maximal values, all reduced PQ s are re-oxidized during the darkperiod. Hence, using Equation 11: h ph = ð n = Þ t del : (Equation 13) The prediction is then h ph = 3, which is the same value obtained in the new experimental results reportedhere, as well as in the data of Vejrazka et al. (2011), both at the same I value and both with pulse times notexceeding that of Equation 12. Estimating Effective Absorption Cross-Section A Consider the results of Simionato et al. (2013) for I = 1,200 m E/(m -s). The observed time-averaged biomassproduction rates under continuous light and under a pulsed regime of { T pulse = 10 ms, T dark = 90 ms} areclose to one another. Using Equation 3, one finds that this implies h ph = 10. In terms of Equation 11, thismeans that for every PQ re-oxidized under continuous light (roughly one every 10 ms), 10 PQ s are re-oxidized in one pulsed cycle. Based on Equation 7, roughly 1 PQ is re-oxidized during the pulse. To obtain h ph of order 10, the PQ pool must be able to store 9 PQ s. Equation 9 then yields n additonal = = ð n = $ = t del Þ T pulse : (Equation 14) For T pulse = t del = 10 ms, Equation 14 yields n = 2 photons/ms. Equation 6 then requires A = 2.77 nm .Changing t del within a reasonable range (5 ms % t del %
15 ms) does not significantly modify the resultingvalue of A . Comparison of Model Predictions against Our Measurements
Figure 6 summarizes comparisons between our measurements and the simple average model. For the casewith T pulse = 150 ms and T dark = 250 ms, where the predicted trend is opposite to that of the data, we showin the Supplemental Information (Figures S1 and S2) how the trend can be predicted by the model if (1)photo-acclimation can cause a reduction of A as well as a lessening of N pool as I is increased (de Wijnand van Gorkom, 2001; Zou and Richmond, 2000; Simionato et al., 2011; Bonente et al., 2012; Gris et al.,2014) or (2) there is a distribution of N pool (Guemther et al., 1988; Hemelrijk and van Gorkom, 1996; Cleland,1998). Comparison of Model Predictions against Data with Pulse Times R
10 ms
The values for h ph deduced from the data of Simionato et al. (2013) are plotted in Figure 7. They correspondto a different algal strain and different photobioreactor conditions compared with the ones reported here.A larger A value was necessary for the model to yield good agreement ( A z ), but is within the rangereported in the literature (de Wijn and van Gorkom, 2001; Zou and Richmond, 2000; Simionato et al., 2011;Bonente et al., 2012; Gris et al., 2014). Figure 5. Calculated h ph versus Pulse Duration At two values of photon flux density (from Equation 11). A = 1 nm , N Pool = 7, and t del = 10 ms. ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article omparison of Model Predictions against Data with Very Short Pulse and Cycle Times
The data reported in Vejrazka et al. (2011) were for a pulsed regime with T pulse = 1 ms, T dark = 9 ms, and I = 1,000 m E/(m -s), for which a measured h ph z A = 1 nm , Equation 6 yields n = 0.6 photons/ms, hence an average PQ reduction rate of 0.3 molecules/ms. As all the PQ s are re-oxidized during a pulsed cycle, a delivery time of t del = 10 ms yields a computed value of h ph z
3, in agree-ment with the data. However, the dynamics are more complicated because T pulse is much shorter than t del ,a point explored in the subsequent discussion. Uncertainties and Limitations
Values of A , t del , and N pool were not reported in the previous studies from which h ph could be estimated fromtheir data (Vejrazka et al., 2011, 2012, 2013, 2015; Simionato et al., 2013). Moreover, it remains to be establishedwhether such parameters depend on photo-acclimation. This is important because, in our experiments, algaewere photo-acclimated to each separate pulsed regime. Nevertheless, the non-negligible variations of thevalues of these parameters can be appraised from several prior studies (de Wijn and van Gorkom, 2001; Zouand Richmond, 2000; Simionato et al., 2011; Bonente et al., 2012; Gris et al., 2014; Ooms et al., 2016) and typi-cally vary from one determination to another by no more than a factor of 2–3 (as opposed to an order of magni-tude). The more important variances are in other phenomena and parameters; hence we do not attempt to findbest-fit values for this parameter set. Rather, we try to demonstrate that the simple picture of rate-limitingbehavior depicted in Figure 3, combined with the average photon arrival times, can account for a wide rangeof measurements of h ph in pulsed versus continuous irradiation experiments.The simple average model does not take into account that the numbers of PQ s reduced and stored areintegers. Hence, the model will generate an error that may be large when the number of PQ s reducedper pulse is small, which can stem from very short pulses, low I , small A, and/or small N pool . Second, this Figure 6. Measured and Calculated h ph h ph versus (A) T pulse at I = 1,000 m E/(m -s) (at the optimal T dark ) and N pool = 7, t del = 10 ms, A = 1 nm for model calculations; (B) I for T pulse = 10 ms, T dark =290 ms; and (C) I for T pulse = 150 ms, T dark = 250 ms. Vertical bars indicate G Figure 7. Comparison of Simple Average Model Predictions for h ph against Data with Pulse Times R
10 ms
Calculated values show the sensitivity to the assumed t del . (A) For two pulse durations at a relatively low I = 350 m E/(m -s). (B) Forthree pulse durations at an intermediate I = 1,200 m E/(m -s). The vertical bars of G ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article ersion of the model cannot account for the effect of photon arrival-time statistics or the existence of a PQ pool size distribution on the statistical fluctuations in PQ reduction rates, and hence cannot provide an es-timate of standard deviations. These limitations call for a full statistical analysis. Full Statistical Analysis
Model Details
A random sequence of photon arrivals times was prepared. The program then counted how many PQ s arereduced from pairs of photons during a pulse, how many of them are re-oxidized to deliver charges to the nextstage of the production process during the pulse ( n ( reoxidized )), and how many remain reduced in the PQ pool.The second in a pair of consecutive photons is lost if the time between photon arrivals is smaller than 0.2 ms.Both photons are lost if all the PQ s are already reduced. At the end of the pulse, the program generates:1 The number of reduced PQ s in the pool: n ð kept Þ .2 The number of PQ s re-oxidized during a full cycle of duration T pulse + T dark : n ð reoxidized Þ = n ð reoxidized during flash Þ + n % kept & (Equation 15) ð lost Þ .Similar runs for very long times generated the same quantities for continuous light. The output yields theaverage rate of PQ re-oxidation, < r ( re-oxidized) > Continuous . For a given light intensity and parameter set ( I , A , t del , N Pool ), the average h ph was computed as: h ph = C n ð reoxidized Þ flash D $ T flash C r ð reoxidized Þ continuous D : (Equation 16) The program also computed the standard deviation around this average.In addition, the program generated the probability distributions of n ( kept ), n ( re-oxidized ), and n ( lost ).Representative results are presented in the Supplemental Information (Figure S3). To check the sensitivityof the statistical results to sample size, computations were performed over 10 , 10 , and 10 reaction cen-ters. The program generated the average and standard deviation of the desired quantities (SupplementalInformation). The values obtained with different sample sizes did not vary in a statistically significantmanner. Hence, we computed all results for a sample of 10 reaction centers. Comparisons between Predictions of the Full Statistical Model against Our Data
Our data and the corresponding model predictions in Figure 8 highlight the sensitivity of h ph to I and T pulse . The standard deviations noted for the calculated results derive from the inherent variance Figure 8. Comparisons of Model Predictions Against Data for h ph For (A) I = 200, 500, and 1,000 m E/(m -s), at T pulse = 10 ms and T dark = 290 ms; (B) T pulse = 5, 10, and 15 ms, at I = 1,000 m E/(m -s). The vertical bars of G ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article ssociated with photon arrival-time statistics. For the relatively long T pulse = 150 ms, the predicted trend isopposite to that of the data even when the effect of photon arrival-time statistics is accounted for.Different choices of model parameters could reduce the discrepancy, but could not eliminate it. In theSupplemental Information (Figure S4), we show that the discrepancy can be remedied by taking into ac-count the possibility that A and N pool may vary owing to photo-acclimation or to the existence of a distri-bution of PQ pool size. Comparisons between Predictions of the Full Statistical Model against Data with Pulse Times R
10 ms
An additional comparison, based on the experimental results from Simionato et al. (2013), is offered in Fig-ure 9 where a larger but reasonable value of A was again necessary to achieve reasonable agreement. Analysis with Data with Ultra-Short Pulses and Dark Times
Values of T pulse shorter than t del pose an intriguing challenge, because there are situations where, on average, noteven a single photon impinges upon A within the pulse duration. Of particular interest are the data from Vejrazkaet al. (2011) with T pulse = 1 ms and T dark = 9 ms (at I = 1,000 m E/(m -s)), for which one can deduce that h ph z T dark = 9 ms is substantially shorter than the dark times employed in all other experiments for which adequatedata were available to perform the analyses ( T dark = 200–300 ms in our measurements, and T dark = 20–900 msin those of Simionato et al., 2013). It will now be shown that convolving the shortness of T pulse (1 ms) with photonarrival-time statistics leads to an effective T dark that may be substantially longer than the nominal 9 ms.For I = 1,000 m E/(m -s) and A = 1 nm , the average arrival time between consecutive photons is 1.66 ms.This corresponds to a probability of 0.45 for one photon arriving during a pulse. The probability of receivingtwo photons in two consecutive pulses is then 0.205. This means that, typically, two photons will be ab-sorbed by cross-section A in two consecutive pulses only once every 5 rounds of two pulses, namely, every100 ms.Another possible scenario is cross-section A absorbing two photons at least 0.2 ms apart in one pulse, with0.2 ms being the shortest rate-limiting timescale of interest. The probability for such an event is 0.075.Hence, it occurs, on average, every 13 cycles, amounting to an effective T dark > 100 ms. Using the detailedstatistical analysis to compute the average number of PQ s reduced per photon, we find that events solely ofthis kind yield h ph = 2.52, with a large standard deviation. Within the statistical error bars, this is consistentwith the data.In the more probable scenario of only one photon being absorbed during a pulse, a singly reduced PQ molecule ( QA - ) is generated. Its lifetime determines the probability of its surviving the long effective Figure 9. Comparisons of Model Predictions against Data for h ph For (A) ( T pulse , T dark ) = (11 ms, 22 ms), and ( T pulse , T dark ) = (33.33 ms, 66.67 ms), at a relatively low value of I = 350 m E/(m -s);(B) ( T pulse T dark ) = (10 ms, 20 ms), ( T pulse , T dark ) = (20 ms, 180 ms), and ( T pulse , T dark ) = (100 ms, 900 ms) at I = 1,200 m E/(m -s).The vertical bars of G ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article ark time, of the order of 100 ms, so as to be affected by a second photon, completing the generation of thedoubly reduced PQ molecule ( QB $ ) required for biomass production. In view of the fact that the effectiveT dark is an order of magnitude longer than the nominal dark time of 9 ms, the data analyzed here appear toindicate that the lifetimes of QA - and QB $ must be long enough to survive these long effective dark timesto which absorption cross-section A is exposed.The short 1-ms pulse also points to the importance of photon arrival statistics. Consider a longer T pulse , e.g.,5 ms. The probability of A = 1 nm receiving a single photon is then 0.95, and the probability of receivingtwo photons at least 0.2 ms apart is 0.70. Therefore, most reaction centers would receive two photons in asingle pulse under this parameter set. Effects of PQ Pool Size Distribution and Photo-acclimation
Information about the existence of a distribution of PQ pool sizes is scant. For the data published to date(Hemelrijk and van Gorkom, 1996; Cleland, 1998), we found that a normal probability distribution providesa good fit: P ð N Pool Þ = ffiffiffiffiffiffiffiffiffiffiffiffiffiffi p s p e $ð NPool $ C NPool D Þ s (Equation 17) where < N Pool > is the average pool size and s is the standard deviation. A fit to the results of Hemelrijk andvan Gorkom (1996) yields < N Pool > = 6–7 with s = 1–3.For the relatively long T pulse = 150 ms, the data (Supplemental Information) show h ph decreasing with I ,whereas the model predicts the opposite trend. However, the model assumed a fixed PQ pool size. Forsuch long pulses, h ph becomes particularly sensitive to N Pool , because the number of PQ s reduced perpulse is large. The ability to store most or all of the reduced PQ s depends on whether N Pool varies with I and/or whether there is a distribution of pool sizes. The capability of the model to account for the correctbehavior is presented in the Supplemental Information (Figures S5 and S6). DISCUSSION
Translating Higher Photon Efficiency to Increased Bioproductivity
The enhanced h ph in pulsed-light experiments comes at the price of low time-averaged bioproductivity.Designing photobioreactors for ultra-high bioproductivity is challenging, but solutions are possible,e.g., opto-mechanically manipulating the distribution of light input such that delivered photons are notwasted while each reactor is exposed to the requisite light-dark cycles.Another direction is inducing suitably turbulent mixing in dense cultures under continuous irradiationwhereby effective light-dark cycles are experienced by algal cells. This was achieved in Qiang et al.(1998a, 1998b) and Richmond et al. (2003), where turbulent mixing was induced by gas bubbles fed atthe bottom of a thin vertical channel illuminated on both sides with continuous halogen-lamp light at I = 250–4,000 m E/(m -s). Culture densities were so high that the photic zone was only ! /s, ensuring that the average time spent by cells in the photic zone was oforder ! effective light pulse delivered a small number of photons to cross-section A . Hence, despite nominallycontinuous irradiation, ‘‘clogging’’ in PS II could be avoided. The cells then spent ! P-I curve was avoided, while photon efficiency was raised, with no signs of photo-inhibi-tion. The paucity of any evidence of photo-inhibition at such high light intensities accentuates the fact thatphoto-inhibition is determined by cumulative photon absorption, which can be maintained sufficientlysmall by applying intense light pulses for only a small fraction of the cycle time, be it with properly pulsedlight-emitting diodes or via suitable turbulent mixing of the algal culture. In these experiments, P exceededthe rates obtained in standard reactors by a factor of ! I was increased to 4,000 m E/(m -s), P grew almost linearly with I , with an absolute (time- ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article veraged) photon efficiency of 15% (based on photosynthetically active radiation), which is close to thethermodynamic limit (Gordon and Polle, 2007).We have presented data from pulsed-light experiments on algal photobioreactors, complemented by sim-ple physical arguments rooted in photon arrival-time statistics, to substantiate significant increases in therelative photon efficiency of algal photosynthesis. The key is identifying the principal rate-limiting photo-synthetic step in PS II, and imposing a judiciously chosen pulsed-light regime for a given photon fluxdensity, so as to attain the necessary synchronization of biological and photonic timescales. The enhance-ment in relative photon efficiency varies from a factor of 3 (from our own measurements and deduced fromprior studies) to a factor of 10 (deduced from published data).This enhancement does not automatically enable the practical attainment of higher bioproductivity in ascalable cultivation device, for which skillful optical, mechanical, and hydrodynamic design of photobior-eactors is required. Indeed, previous investigations (Qiang et al., 1998a, 1998b; Richmond et al., 2003) real-ized the commensurate improvement in bioproductivity via a combination of turbulent mixing, densecultures, and thin reactors. The challenge of engineering feasible photobioreactors that can achieve thisobjective, be they driven by solar or artificial light, is delegated to future research efforts. (The use of arti-ficial light should be viewed as sustainable provided the electricity source derives from renewables such assolar, wind, or hydroelectric.)We have identified the associated timescales, as well as an understanding of how synchronization betweenthe pulsed-light regime and biological timescales can lead to markedly enhanced photon efficiency.
Limitations of the Study
Our experimental and modeling results prompt fundamental questions in algal research, for which exper-imental results are needed before properly optimized reactors can be designed. These issues subsume:Photo-acclimation: How does algal performance depend on acclimation to pulsed-light regimes (in partic-ular on millisecond timescales, including the dependence on instantaneous photon flux density)? Howdoes A , as well as the size and distribution of N pool , vary with these pulsed regimes and with light intensity?Optimal dark time: The basis for quantifying the optimal dark time under pulsed light is not yet understoodand requires detailed study. Increasing bioproductivity by following each pulse with a sufficiently long darktime was proposed (Abu-Ghosh et al., 2015), but the dark times in that study were too short for the dramaticpotential improvement in photon efficiency depicted here to be observed.Long timescales characterizing post-PS II processes: These long timescales do not appear to affect the P-I curve. Is it because these processes are endowed with large buffers for storing intermediate products or isit because there are parallel-processing elements in ensuing stages? PQ pools: Their size and possible size distribution need to be ascertained.Genetic intervention: To what extent can it further improve photon efficiency via modification of effectiveabsorption cross-section A and PQ pool size? For example, our model predicts that increasing A can in-crease h ph proportionately for commensurately modified pulse regimes, with genetic intervention alreadyhaving demonstrated the ability to moderate A (Melis et al., 1998, 1999; Polle et al., 2002, 2003; Kirst andMelis, 2014), whereas increasing PQ pool capacity should not impact h ph but would affect the tolerance tohigh light intensity and would allow for a wider range of pulse-time duration. METHODS
All methods can be found in the accompanying Transparent Methods supplemental file.
SUPPLEMENTAL INFORMATION
Supplemental Information can be found online at https://doi.org/10.1016/j.isci.2020.101115. ll OPEN ACCESS iScience , 101115, May 22, 2020 iScience Article
CKNOWLEDGMENTS
Y.Z. and J.M.G. express appreciation for financial support for this research from Reliance Industries Ltd.J.M.G. gratefully acknowledges the hospitality and support of the Institute of Advanced Studies of the Uni-versity of Western Australia during the writing of this paper. The RIL authors gratefully acknowledge Srid-haran Govindachary for his technical input about the photosynthetic process.
AUTHOR CONTRIBUTIONS
Y.Z.: conceptualization, investigation, visualization, methodology, validation, formal analysis, writing, re-view & editing; J.M.G.: conceptualization, investigation, visualization, methodology, validation, formalanalysis, writing, review & editing; A.M.: investigation, methodology, data curation, formal analysis, writing,review & editing; A.R.K.: conceptualization, validation, resources, supervision, writing, review & editing;S.D.P.: investigation, data curation, methodology, writing, review & editing; A.B.: conceptualization, vali-dation, writing, review & editing; B.G.R.: investigation; T.P.G.: conceptualization, project administration,writing, review & editing; A.S.: conceptualization, funding acquisition, writing, review & editing.
DECLARATION OF INTERESTS
The authors have no conflict of interest to declare.
Received: February 13, 2020Revised: April 7, 2020Accepted: April 26, 2020Published: May 22, 2020
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Science, Volume Supplemental InformationEnhanced Algal Photosynthetic PhotonEf fi ciency by Pulsed Light Yair Zarmi, Jeffrey M. Gordon, Amit Mahulkar, Avinash R. Khopkar, Smita D. Patil, ArunBanerjee, Badari Gade Reddy, Thomas P. Grif fi n, and Ajit Sapre upplemental Information Results when N pool and A can vary For the case with T pulse = 150 ms and T dark = 250 ms (Fig. S1a), the predicted trend is opposite to that of the data. Whereas the measured η ph decreases as I is increased, the model predicts an increase in η ph (Eq. (11)). The predicted increase is predicated on both A and N pool having constant values. However, photo-acclimation can cause a reduction in A and N pool as I is increased (de Wijn and van Gorkom, 2001; Zou and Richmond, 2000; Simionato et al., 2011; Bonente et al., 2012; Gris et al., 2014). Figure S1b illustrates that the correct trend can be attained if it is assumed that photo-acclimation induces changes in A and N Pool as I is increased (Table S1 lists values that are reasonable based on prior measurements, but do not signify actual observed parameters). Fig. S1. Related to Fig. 6c. (a) Measured and calculated (Eq. (11)) η ph vs. I for T pulse = 150 ms, T dark = 250 ms (same as Fig. 6c where the standard deviations and number of replications for the measured points are noted). (b) Modification of model predictions of part (a) when model parameters vary with I owing to photo-acclimation as in Table S1. The data points are the same as in part (a). Figure S2a shows model predictions when a distribution of N pool is accounted for (Eq. (17)), with average < N pool > = 7 and standard deviation σ = 2. Figure S2b shows the same data but with model calculations that allow for the effect of photo-acclimation on A and N pool as listed in Table S2. The effect of photon arrival time statistics has been incorporated. Fig. S2. Related to Fig. 6c. Dependence of η ph on I at the relatively long T pulse = 150 ms. The measured data and their standard deviations are the same as in Fig. S1. Model predictions account for (i) a distribution of N pool , and (ii) the possible impact of photo-acclimation on A and N pool . Vertical bars for the model (computed) results correspond to the inherent standard deviations associated with photon-arrival statistics, as elaborated in the text. Figure S3 further sharpens this point with a comparison between data from (Simionato et al., 2013) and model predictions when a distribution of N pool is accounted for. In all these computations with the full statistical model, each reaction center was randomly assigned a value of N pool using the probability density of Eq. (17). Fig. S3. Related to Fig. 7. Comparison of data from (Simionato et al., 2013) against model predictions for the dependence of η ph on T pulse at (a) low and (b) intermediate I values. The theory accounts for a distribution of N pool . The vertical bars of ±1 standard deviation about the average: (i) were taken from (Simionato et al., 2013) for the measured data, for 3 replications, and (ii) correspond to the inherent standard deviations associated with photon-arrival statistics for the model (computed) results, as elaborated in the text. able S1. Related to Fig. 6c. Parameter values used for the model predictions in Fig. S1, based on the possible impact of photo-acclimation. I ( µ E/(m -s) A (nm ) N Pool
200 4 10 500 2 7 1000 1 5 Table S2. Related to Fig. 6c. Parameter values for model calculations in Fig. S2, accounting for the possible effect of photo-acclimation. I ( µ E/(m -s)) A (nm ) N Pool
200 4 9 500 2 7 1000 1 5
Full statistical analysis Sample distributions are presented in Fig. S4 for I = 1000 µ E/(m -s), A = 1 nm , T pulse = 10 ms, τ del = 10 ms and N Pool = 7. Figure S4a reflects the fact that the number of photons absorbed during the pulse is small. The average number of photons hitting A = 1 nm during a 10 ms pulse is 6.02. The actual number varies randomly from one reaction center to another, depending on the randomly varying time gaps between photons. Hence, the probability of fully reducing the PQ pool is negligible, as is the probability of losing a large number of photons. Fig. S4. Related to Fig. 8. Probability distribution for the number of (a) PQ s stored in the pool, (b) photons lost by the end of a 10 ms pulse, (c) PQ s reduced over a cycle with T pulse = 10 ms and a sufficiently long dark time. The situation is quite different for long pulses. Examples are presented in Figs. S5 and S6 for I = 1,000 µ E/(m -s), A = 1 nm , τ del = 10 ms and N Pool = 7, but with a longer T pulse = 150 ms. Owing to the long pulse time, the probability that the PQ pool is completely reduced at the end of the pulse is high (Fig. S5a). The high number of lost photons (Fig. S6) is a consequence of the fact that the PQ pool is fully reduced shortly after the start of the pulse, so that many photons are lost due to reduced charge carriers. Fig. S5. Related to Fig. 6c. Probability distribution for (a) the number of PQ s reduced in the pool at the end of a 150 ms pulse and (b) the number of PQ s re-oxidized by the end of a cycle with T pulse = 150 ms and a sufficiently long dark time. Fig. S6. Related to Fig. 6c. Probability distribution for the number of photons lost during a 150 ms pulse. Using the approach of the simple average model, Eq. (5) yields the number of reduced PQ s to be 45. Of these, 15 are re-oxidized during the pulse (Eq. (7)), from which 7 PQ s can stay reduced. Hence, 22 PQ s can be re-oxidized during one cycle. The statistics of photon arrival times, combined with the losses owing to the 0.2
20 40 60 80 100 n ( lost ) s time scale, reduce this number to an average of 20.63, in which case η ph = 20.63/( T pulse ⋅ τ del ) = 20.63/(150 ⋅
10) = 1.375.
Transparent Methods
We used a locally isolated strain of the
Nanochloris species (which is a green microalgae) from our repository, cultivated in urea-phosphoric acid medium (urea 214 ppm and phosphoric acid 31 ppm, prepared in artificial seawater 4% by weight) and maintained at 27 ° C and 300 µ E/(m -s), at an optical density of 2 in a 500 ml flask. Biomass growth curves were generated using a Multi-Cultivator MC 1000-OD of Photon Systems Instruments (PSI, Czech Republic), comprising 8 test-tubes, each holding 70 ml of algal culture, and immersed in a water bath maintained at 35 ° C. Dilute algal cultures were used (density 17-30 mg/l, i.e., 0.05 OD, < 10% light attenuation), to ensure that all cells experienced essentially the same light intensity. pH was maintained at 7.0 by sparging humidifed air with 2% CO at an air flow rate of 1 VVM (70 ml/min). Each test tube was irradiated by its own cool-white LED array. For pulsed-light experiments, four PSI light sources (Model SL-3500, with an LC-100 PSI light controller) permitted independently tuning the irradiation and dark times from 1 ms to 999 ms. Our small glass reactors had optical path 3 cm, width 10 cm and height 15 cm. An operating height of 10 cm was used, so the total fluid volume was 300 ml. For both continuous and pulsed irradiation, LEDs were controlled such that the instantaneous photon flux density for photosynthetically-active radiation at the surface of the culture was 1000 µE/(m -s), measured using Apogee Instruments’ quantum meter model MQ-200. The 13 cm ×
13 cm LED panel was sited less than 1 cm from the reactor. Light intensity was measured at the center of each of 9 equal-area regions comprising the reactor’s illuminated surface, and the reported I = 1,000 µ E/(m -s) represents the average over these 9 sections. Growth was measured over an illumination period of 6 hours, followed by a period of 6 hours of dark time, after which a fresh run was started, with these cycles repeated for 24 hours. Each day, the culture was harvested and brought to the desired starting operating optical density of 0.08, measured at a wavelength of 750 nm at the start ( OD ) and end of irradiation ( OD ) to get specific growth rate µ over time t : ! = ' /%& ) * ..