Hydromechanical stress in shake flasks: correlation for the maximum local energy dissipation rate

Shake flasks are widely used in biotechnological process research. Bioprocesses for which hydromechanical stress may become the rate controlling parameter include those where oils are applied as carbon sources, biotransformation of compounds with low solubility in the aqueous phase, or processes employing animal, plant, or filamentous microorganisms. In this study, the maximum local energy dissipation rate as the measure for hydromechanical stress is characterized in shake flasks by measuring the maximum stable drop size. The theoretical basis for the method is that the maximum stable drop diameter in a coalescence inhibited liquid/liquid dispersion is only a function of the maximum local energy dissipation rate and not of the dispersing apparatus. The maximum local energy dissipation rate is obtained by comparing the drop diameters in shake flasks to those in a stirred tank reactor. At the same volumetric power consumption, the maximum energy dissipation rate in shake flasks is about 10 times lower than in stirred tank reactors explaining the common observation of considerable differences in the morphology of hydromechanically sensitive cells between these two reactor types. At the same volumetric power consumption, the maximum local energy dissipation rate in baffled and in unbaffled shake flasks is very similar. A correlation is presented to quantify the maximum local energy dissipation rate in shake flasks as a function of the operating conditions. Non-negligible drop viscosity may be considered by known literature correlations. Further, from dispersion experiments a critical Reynolds number of about 60,000 is proposed for turbulent flow in unbaffled shake flasks.     

Fabrication and use of a transient contractional flow device to quantify the sensitivity of mammalian and insect cells to hydrodynamic forces

A microfluidic device was fabricated via photolithographic techniques which can create transient elongational and shear forces ranging over three orders of magnitude while still maintaining laminar flow conditions. The contractional fluid flow inside the microfluidic device was simulated with FLUENT (a computational fluid dynamics computer program) and the local deformation forces were characterized with the scalar quantity, local energy dissipation rate. The sensitivities of four cell lines (CHO, HB-24, Sf-9, and MCF7) were tested in the device. The results indicate that all four cell lines are able to withstand relatively intense energy dissipation rates (up to 10(4)-10(5) kW/m(3)), which is orders of magnitude higher than the maximum local energy dissipation rates generated by impellers in bioreactors, but comparable to that associated with small bursting bubbles. While the concept that suspended animal cells are relatively robust with respect to purely hydrodynamic forces in bioprocess equipment is well known, these results quantitatively demonstrate these observations.     

A critical assessment of the impact of mixing on dilution refolding

Refolding often presents a bottleneck in the generation of recombinant protein expressed as inclusion bodies. Few studies have looked at the effect of physical factors on the yield from refolding steps. Refold reactors typically operate in fed-batch mode with a slow injection rate. This paper characterizes mixing in a novel reactor, and seeks to relate the conditions of mixing to native lysozyme yields after refolding. A novel twin-impeller system incorporating a mini-paddle impeller located in the vicinity of the injection point was used to increase the local levels of energy dissipation experienced by the injected material, and to improve refolding yields. Mixing only affected yields during and immediately after denatured protein addition. Analysis of lysozyme refolding yield, under a variety of conditions, revealed that dispersive mixing affected the yield. The beneficial effect of the mini-paddle impeller in providing a source of localized energy dissipation was limited to conditions where the bulk impeller intensity was low. The effects appeared to become more significant when injection times were longer, because of increased exposure of the injected material to the energy dissipation of the mini-impeller. The results suggest that for fed-batch protein refolding systems, where mixing has been shown to be a critical factor, the local energy dissipation experienced in the vicinity of the injection point is critical to the refolding yields.     

Characterization of hydromechanical stress in aerated stirred tanks up to 40 m<Superscript>3</Superscript> scale by measurement of maximum stable drop size

Background

Turbulence intensity, or hydromechanical stress, is a parameter that influences a broad range of processes in the fields of chemical engineering and biotechnology. Fermentation processes are often characterized by high agitation and aeration intensity resulting in high gas void fractions of up to 20% in large scale reactors. Very little experimental data on hydromechanical stress for such operating conditions exists because of the problems associated with measuring hydromechanical stress under aeration and intense agitation.

Results

An indirect method to quantify hydromechanical stress for aerated operating conditions by the measurement of maximum stable drop size in a break-up controlled dispersion was applied to characterize hydromechanical stress in reactor scales of 50 L, 3 m³ and 40 m³ volume with a broad range of operating conditions and impeller geometries (Rushton turbines). Results for impellers within each scale for the ratio of maximum to specific energy dissipation rate ? based on measured values of maximum stable drop size for aerated operating conditions are qualitatively in agreement with results from literature correlations for unaerated operating conditions. Comparison of data in the different scales shows that there is a scale effect that results in higher values for ? in larger reactors. This behavior is not covered by the classic theory of turbulent drop dispersion but is in good agreement with the theory of turbulence intermittency. The data for all impeller configurations and all aeration rates for the three scales can be correlated within ±20% when calculated values for ? based on the measured values for d_max are used to calculate the maximum local energy dissipation rate. A correlation of the data for all scales and all impeller configurations in the form ??=?2.3?(?_unaerated)^0.34?(D_R)^0.543 is suggested that successfully models the influence of scale and impeller geometry on ? for aerated operating conditions.

Conclusions

The results show that besides the impeller geometry, also aeration and scale strongly influence hydromechanical stress. Incorporating these effects is beneficial for a successful scale up or scale down of this parameter. This can be done by applying the suggested correlation or by measuring hydromechanical stress with the experimental method used in this study.

     

Ultra scaledown to predict filtering centrifugation of secreted antibody fragments from fungal broth

Extracellularly expressed anti-hen egg lysozyme single-chain antibody fragments (scFv) produced by Aspergillus awamori were recovered using filtering centrifugation. Two filtering centrifuges with 0.5- and 30-L capacities were used to represent laboratory- and pilot-scale equipment, respectively. Critical regime analysis using the computational fluid dynamics (CFD) technique provided information about the local energy dissipation rates in both units. Experimental data indicated loss of scFv activity for energy dissipation rates above about 2.0 x 10(4) W kg(-1). This loss of activity increased in the presence of gas-liquid interfaces during filtering centrifugation. An ultra scaledown filtering centrifuge with a maximum working volume of 35 mL was designed to mimic the operating conditions identified by the critical regime analysis for the laboratory- and pilot-plant-scale units. The recovered scFv activity levels and the separation performance of the three units were comparable when operated at equal maximum energy dissipation rates.     

Can plant oncogenes inhibit programmed cell death? The rolB oncogene reduces apoptosis-like symptoms in transformed plant cells

The rolB oncogene was previously identified as an important player in ROS metabolism in transformed plant cells. Numerous reports indicate a crucial role for animal oncogenes in apoptotic cell death. Whether plant oncogenes such as rolB can induce programmed cell death (PCD) in transformed plant cells is of particular importance. In this investigation, we used a single-cell assay based on confocal microscopy and fluorescent dyes capable of discriminating between apoptotic and necrotic cells. Our results indicate that the expression of rolB in plant cells was sufficient to decrease the proportion of apoptotic cells in steady-state conditions and diminish the rate of apoptotic cells during induced PCD. These data suggest that plant oncogenes, like animal oncogenes, may be involved in the processes mediating PCD.     

Dependence of photosynthesis and energy dissipation activity upon growth form and light environment during the winter

Two very distinctive responses of photosynthesis to winter conditions have been identified. Mesophytic species that continue to exhibit growth during the winter typically exhibit higher maximal rates of photosynthesis during the winter or when grown at lower temperatures compared to individuals examined during the summer or when grown at warmer temperatures. In contrast, sclerophytic evergreen species growing in sun-exposed sites typically exhibit lower maximal rates of photosynthesis in the winter compared to the summer. On the other hand, shaded individuals of those same sclerophytic evergreen species exhibit similar or higher maximal rates of photosynthesis in the winter compared to the summer. Employment of the xanthophyll cycle in photoprotective energy dissipation exhibits similar characteristics in the two groups of plants (mesophytes and shade leaves of sclerophytic evergreens) that exhibit upregulation of photosynthesis during the winter. In both, zeaxanthin + antheraxanthin (Z + A) are retained and PS II remains primed for energy dissipation only on nights with subfreezing temperatures, and this becomes rapidly reversed upon exposure to increased temperatures. In contrast, Z + A are retained and PS II remains primed for energy dissipation over prolonged periods during the winter in sun leaves of sclerophytic evergreen species, and requires days of warming to become fully reversed. The rapid disengagement of this energy dissipation process in the mesophytes and shade sclerophytes apparently permits a rapid return to efficient photosynthesis and increased activity on warmer days during the winter. This may be associated with a decreasing opportunity for photosynthesis in source leaves relative to the demand for photosynthesis in the plant's sinks. In contrast, the sun-exposed sclerophytes – with a relatively high source to sink ratio – maintain PS II in a state primed for high levels of energy dissipation activity throughout much of the winter. Independent of whether photosynthesis was up- or downregulated, all species under all conditions exhibited higher levels of soluble carbohydrates during the winter compared to the summer. Thus downregulation of photosynthesis and of Photosystem II do not appear to limit carbohydrate accumulation under winter conditions. A possible signal communicating an altered source/sink balance, or that may be influencing the engagement of Z + A in energy dissipation, is phosphorylation of thylakoid proteins such as D1.This revised version was published online in October 2005 with corrections to the Cover Date.     

Prediction of mechanical damage to animal cells in turbulence

In previous work a model was proposed for estimation of disruption of animal cells in turbulent capillary flows using information about the hydrodynamics, and cell mechanical properties determined by micromanipulation. The model assumed that the capillary flow consists of a laminar sublayer and a homogeneous turbulent region, and within the latter eddies of sizes similar to or smaller than the cells interact with those cells, causing local surface deformations. The proposed mechanism of cell damage was that such deformations result in an increase in membrane tension and surface energy, and that a cell disrupts when its bursting membrane tension and bursting surface energy are exceeded. The surface energy of the cells was estimated from the kinetic energy of appropriate sized eddies. To test the model, cells were disrupted in turbulent flows in capillaries at mean energy dissipation rates ranging from 800 to 2×10⁴ Wkg^–1. The model assumed that the specific lysis rate is almost independent of the number of passes, which was verified by the experimental data. The implication was that despite the damage the cell mechanical properties did not change markedly during multiple recirculations through the capillaries. On average the model underestimated the cell disruption by about 15%. Although the model gave reasonably good predictions, it lacks proper explanation of the independence of the specific lysis rate on the number of passes. In this paper it is shown that this problem can be resolved in principle by consideration of the localisation of the energy dissipation in turbulent capillary flows. The necessity of further modelling of cell-turbulence interactions is demonstrated.     

Effects of small scale fluid motion on bacterial growth and respiration

1. Laboratory experiments were conducted to investigate the effect of small‐scale turbulent motion on the growth and respiration of bacteria in an oscillating grid apparatus. The experiments were performed under a range of energy dissipation levels similar to those occurring in freshwater systems. 2. The results showed that small‐scale turbulent motion does have an effect on bacterial growth and respiration. A higher gradient in the dissolved oxygen time series, higher 5‐day biochemical oxygen demand values, increased bacterial abundance, increased bacterial specific respiration, higher bacterial growth rate and increased nutrient uptake were all observed when the energy dissipation rate in the water column was increased. 3. This has implications for traditional laboratory procedures that are used to characterise bacterial metabolic rates under stagnant fluid‐flow conditions, such as biochemical oxygen demand (BOD), which would be influenced by the effects of the small‐scale fluid motion inherent in aquatic environments. According to our results, BOD values in natural systems experiencing fluid motion would be higher than traditional bottle‐derived rates.     

The fluid dynamic and shear environment in the NASA/JSC rotating-wall perfused-vessel bioreactor

The rotating-wall perfused-vessel (RWPV) bioreactor, used for both microgravity and Earth-based cell science experiments, is characterized in terms of the fluid dynamic and fluid shear stress environment. A numerical model of the flow field is developed and verified with laser Doppler velocimeter measurements. The effects of changes in operating conditions, including rotation rates and fluid perfusion rates, are investigated with the numerical model. The operating conditions typically used for ground-based experiments (equal rotation of the inner and outer cylinders) leads to flow patterns with relatively poor mass distribution characteristics. Approximately 50% of the inlet-perfused fluid bypasses the bulk of the fluid volume and flows to the perfusion exit. For operating conditions typical in microgravity, small differential rotation rates between the inner and outer cylinders lead to greatly improved flow distribution patterns and very low fluid shear stress levels over a large percentage of the fluid volume. Differences in flow patterns for the different operating conditions are explored. Large differences in the hydrodynamic environments for operating conditions typical of true microgravity and ground-based "microgravity simulations" are demonstrated.     

Effects of paddle impeller geometry on power input and mass transfer in small-scale animal cell culture vessels

Process scaleup for stirred-tank animal cell cultures such as suspension and microcarrier cultures often begins at the bench scale in small spinner vessels. In order to initiate process development under the proper conditions, it is essential to know the physical conditions under which the cells are grown. In this article, power inputs and surface oxygen transfer rates to culture medium in 500-mL Corning spinner vessels were determined as a function of the impeller geometry, impeller height, and agitation speed. The results obtained indicate that power dissipation dependency differs from literature correlations and may compromise scale up at constant power input from these vessels. These results are of general utility to researchers using small-scale vessels.     

Estimation of disruption of animal cells by turbulent capillary flow

Disruption of animal cells in turbulent capillary flows has been predicted from a model of cell-hydrodynamic interactions using cell mechanical properties determined by micromanipulation. Eddies of sizes similar to or smaller than the cells are presumed to interact with those cells, causing local surface deformations. The proposed mechanism of cell damage is that such deformations result in an increase in membrane tension and surface energy and that a cell disrupts when its bursting membrane tension and bursting surface energy are exceeded. The surface energy of the cells is estimated from the kinetic energy of appropriately sized eddies. To test the model, cells were disrupted in turbulent flows in capillaries at mean energy dissipation rates up to 2 x 10(4) m(2)/s(3). In all cases the model underestimated the cell disruption by about 15%. Such good agreement implies that the approach of the model to the complicated phenomena of cell turbulence interactions is reasonable. (c) 1993 John Wiley & Sons, Inc.     

Computational fluid dynamics analysis of mixing and gas–liquid mass transfer in wave bag bioreactor

Single use bioreactors provide an attractive alternative to traditional deep-tank stainless steel bioreactors in process development and more recently manufacturing process. Wave bag bioreactors, in particular, have shown potential applications for cultivation of shear sensitive human and animal cells. However, the lack of knowledge about the complex fluid flow environment prevailing in wave bag bioreactors has so far hampered the development of a scientific rationale for their scale up. In this study, we use computational fluid dynamics (CFD) to investigate the details of the flow field in a 20-L wave bag bioreactor as a function of rocking angle and rocking speed. The results are presented in terms of local and mean velocities, mixing, and energy dissipation rates, which are used to create a process engineering framework for the scale-up of wave bag bioreactors. Proof-of-concept analysis of mixing and fluid flow in the 20-L wave bag bioreactor demonstrates the applicability of the CFD methodology and the temporal and spatial energy dissipation rates integrated and averaged over the liquid volume in the bag provide the means to correlate experimental volumetric oxygen transfer rates (k_La) data with power per unit volume. This correlation could be used as a rule of thumb for scaling up and down the wave bag bioreactors.     

The xanthophyll cycle and sustained thermal energy dissipation activity in Vinca minor and Euonymus kiautschovicus in winter

The influence of low temperature on the operation of the xanthophyll cycle and energy dissipation activity, as ascertained through measurements of chlorophyll fluorescence, was examined in two broad-leaved evergreen species, Vinca minor L. and Euonymus kiautschovicus Loessner. In leaves examined under laboratory conditions, energy dissipation activity developed more slowly at lower leaf temperatures, but the final, steady-state level of such activity was greater at lower temperatures where the rate of energy utilization (through photosynthetic electron transport) was much lower. The rate at which energy dissipation activity increased was similar to that of the de-epoxidation of violaxanthin to antheraxanthin and zea-xanthin at different temperatures. However, leaves in the field examined prior to sunrise on mornings following cold days and nights exhibited a retention of antheraxanthin and zeaxanthin that was associated with sustained decreases in photosystem II efficiency. We therefore suggest that this phenomenon of ‘photoinhibition’ in response to light and cold temperatures during the winter results from sustained photoprotective thermal energy dissipation associated with the xanthophyll cycle. Such retention of the de-epoxidized components of the xanthophyll cycle responded to day-to-day changes in temperature, being greatest on the coldest mornings (when photoprotective energy dissipation might be most required) and less on warmer mornings when photosynthesis could presumably proceed at higher rates.     

Death mechanisms of animal cells in conditions of intensive agitation

The question is addressed as to whether cells which are subject to high-energy dissipation rates in agitated bioreactors show an apoptotic response. Murine hybridoma cells in batch culture were agitated in bench-scale (1-L) bioreactors without gas sparging. At an energy dissipation rate of 1.5 W m(-3) there was no apparent damage. At 320 W m(-3) cell viability declined, and increasing proportions of the dead cells displayed the morphological features of apoptosis, but necrosis also remained as a significant mechanism of death. When cells were subjected to the intensive energy dissipation rate of 1870 W m(-3) in a bioreactor without gas headspace, the cell number dropped by 50% within 2 h and a subpopulation of smaller-sized cells emerged. This excluded trypan blue but showed some apoptotic characteristics such as reduced and condensed DNA content and low F-actin content. The incidence of apoptotic activity was further demonstrated by the appearance of numerous apoptotic bodies. Analysis of the cell cycles of both small and normal size populations indicated that greater proportions of S and G2 cells had become apoptotic and there was evidence of preferential survival of G1 cells. It is suggested that two mechanisms of cell death are apparent in hydrodynamically stressful situations, but their relative expression depends on the energy dissipation rate.     

Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics

Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network’s structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.     

Patch choice and population size

The distribution of animals between feeding patches has been the subject of considerable theoretical and empirical investigation. When all animals are equal and fitness is well represented by intake rate, the ideal free distribution requires the animals to be distributed in such a way as to equalize intake rate in each feeding patch. We refer to this as the equal rates policy. This approach ignores the effect of stochasticity in the food supply on starvation. It also ignores predation. An alternative approach is based on the assumption that each animal tries to minimize its death rate. An optimal policy now involves making decisions about which patch to use on the basis of the current level of energy reserves. We investigate a simple model of population dynamics in which over-winter mortality is either derived from animals adopting the equal rates policy or the optimal state-dependent policy to decide between two feeding patches. We show that the state-dependent policy results in a larger equilibrium population size than the equal rates policy. This difference can be considerable when the foraging environment is very stochastic. Furthermore, the state-dependent policy may result in a viable equilibrium population when the equal rates policy does not. The equilibrium under the state-dependent policy may be less stable than that under the equal rates policy. We identify conditions under which the state-dependent policy results in approximately equal intake rates on the two feeding patches. Levels of mortality as a result of predation are investigated. We show that, under some circumstances, the proportion of mortality that is due to predation may decrease as the predation pressure increases.     

ACCLIMATION OF EMILIANIA HUXLEYI (PRYMNESIOPHYCEAE) TO PHOTON FLUX DENSITY1

Growth rate, pigment composition, and noninvasive chl a fluorescence parameters were assessed for a noncalcifying strain of the prymnesiophyte Emiliania huxleyi Lohman grown at 50, 100, 200, and 800 μmol photons·m^?2·s^?1. Emiliania huxleyi grown at high photon flux density (PFD) was characterized by increased specific growth rates, 0.82 d^?1 for high PFD grown cells compared with 0.38 d^?1 for low PFD grown cells, and higher in vivo chl a specific attenuation coefficients that were most likely due to a decreased pigment package, consistent with the observed decrease in cellular photosynthetic pigment content. High PFD growth conditions also induced a 2.5‐fold increase in the pool of the xanthophyll cycle pigments diadinoxanthin and diatoxanthin responsible for dissipation of excess energy. Dark‐adapted maximal photochemical efficiency (F_v/F_m) remained constant at around 0.58 for cells grown over the range of PFDs, and therefore the observed decline, from 0.57 to 0.33, in the PSII maximum efficiency in the light‐adapted state, (F_v′/F_m′), with increasing growth PFD was due to increased dissipation of excess energy, most likely via the xanthophyll cycle and not due to photoinhibition. The PSII operating efficiency (F_q′/F_m′) decreased from 0.48 to 0.21 with increasing growth PFD due to both saturation of photochemistry and an increase in nonphotochemical quenching. The changes in the physiological parameters with growth PFD enable E. huxleyi to maximize rates of photosynthesis under subsaturating conditions and protect the photosynthetic apparatus from excess energy while supporting higher saturating rates of photosynthesis under saturating PFDs.     

Effect of agitation intensities on fungal morphology of submerged fermentation

Both parallel fermentations with Aspergillus awamori (CBS 115.52) and a literature study on several fungi have been carried out to determine a relation between fungal morphology and agitation intensity. The studied parameters include hyphal length, pellet size, surface structure or so-called hairy length of pellets, and dry mass per-wet-pellet volume at different specific energy dissipation rates. The literature data from different strains, different fermenters, and different cultivation conditions can be summarized to say that the main mean hyphal length is proportional to the specific energy dissipation rate according to a power function with an exponent of -0.25 +/- 0.08. Fermentations with identical inocula showed that pellet size was also a function of the specific energy dissipation rate and proportional to the specific energy dissipation rate to an exponent of -0.16 +/- 0.03. Based on the experimental observations, we propose the following mechanism of pellet damage during submerged cultivation in stirred fermenters. Interaction between mechanical forces and pellets results in the hyphal chip-off from the pellet outer zone instead of the breakup of pellets. By this mechanism, the extension of the hyphae or hair from pellets is restricted so that the size of pellets is related to the specific energy dissipation rate. Hyphae chipped off from pellets contribute free filamentous mycelia and reseed their growth. So the fraction of filamentous mycelial mass in the total biomass is related to the specific energy dissipation rate as well.To describe the surface morphology of pellets, the hyphal length in the outer zone of pellets or the so-called hairy length was measured in this study. A theoretical relation of the hairy length with the specific energy dissipation rate was derived. This relation matched the measured data well. It was found that the porosity of pellets showed an inverse relationship with the specific energy dissipation rate and that the dry biomass per-wet-pellet volume increased with the specific energy dissipation rates. This means that the tensile strength of pellets increased with the increase of specific energy dissipation rate. The assumption of a constant tensile strength, which is often used in literature, is then not valid for the derivation of the relation between pellet size and specific energy dissipation rate. The fraction of free filamentous mycelia in the total biomass appeared to be a function of the specific energy dissipation in stirred bioreactors. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 715-726, 1997.     

Leaves of Japanese oak (Quercus mongolica var. crispula) mitigate photoinhibition by adjusting electron transport capacities and thermal energy dissipation along the intra-canopy light gradient

We investigated the morphological and physiological acclimation of leaves grown within a canopy of Japanese oak tree (Quercus mongolica var. crispula) in terms of the susceptibility to photoinhibition under various growth light conditions. The maximum rates of photosynthesis (P(max) ) and electron transport (ETR(max) ) were higher in mature leaves grown under stronger light with higher area-based leaf nitrogen (N) content closely associated with higher leaf mass per area. The net photosynthetic (P(n) ) and electron transport (ETR) rates corresponding to the daily peak photosynthetic photon flux density (PPFD(max) ) during leaf maturation were almost comparable to P(max) and ETR(max) , respectively. Conversely, P(n) and ETR at the daily average PPFD (PPFD(avg) ) were substantially low in shade-grown leaves when compared with P(max) and ETR(max) . The susceptibility to photoinhibition at PPFD(max) , i.e. at sunflecks for the shade-grown leaves, was assessed by the rate of excess energy production. Although sun leaves showed higher rates of electron transport and thermal energy dissipation than shade leaves under PPFD(max) conditions, the rate of excess energy production was almost constant across shade to sun leaves. The shade leaves of the Japanese oak grown within a crown were suggested to adjust their N investment to maintain higher photosynthetic capacities compared with those required to maximize the net carbon gain, which may facilitate the dissipation of the excessive light energy of sunflecks to circumvent photoinhibition in cooperation with thermal energy dissipation.