Advanced search
Publication Cover
Biofuels Volume 5, 2014 - Issue 1
Submit an article Journal homepage
535
Views
31
CrossRef citations to date
0
Altmetric
Perspective

Mathematics for streamlined biofuel production from unicellular algae

Martin A Bees Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK. [email protected]
&
Ottavio A Croze Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge, CB2 3EA, UK; Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge, CB3 0HE, UK
Pages 53-65 | Published online: 09 Apr 2014

References

  • Chisti Y. Biodiesel from microalgae. Biotechnol. Adv.25(3),294–306 (2007).
  • Scott SA, Davey MP, Dennis JS et al. Biodiesel from algae: challenges and prospects. Curr. Opin. Biotechnol.21(3),277–286 (2010).
  • Stephenson AL, Kazamia E, Dennis JS, Howe CJ, Scott SA, Smith AG. Life-cycle assessment of potential algal biodiesel production in the United Kingdom: a comparison of raceways and air-lift tubular bioreactors. Energy Fuels24,4062–4077 (2010).
  • García-González M, Moreno J, Manzano JC, Florencio FJ, Guerrero MG. Production of Dunaliella salina biomass rich in 9-cis-β-carotene and lutein in a closed tubular photobioreactor in batch culture. J. Biotechnol.115(1),81–90 (2005).
  • Melis A, Happe T. Hydrogen production. Green algae as a source of energy. Plant Physiol.127(3),740–748 (2001).
  • Williams CR, Bees MA. Mechanistic modelling of sulfur-deprived photosynthesis and hydrogen production in suspensions of Chlamydomonas reinhardtii. Biotechnol. Bioeng. doi: 10.1002/bit.25023 (2013) (Epub ahead of print).
  • Greenwell HC, Laurens LML, Shields RJ, Lovitt RW, Flynn KJ. Placing microalgae on the biofuels priority list: a review of the technological challenges. J. R. Soc. Interface7(46),703–726 (2010).
  • Huesemann MH, Van Wagenen J, Miller T, Chavis A, Hobbs S, Crowe B. A screening model to predict microalgae biomass growth in photobioreactors and raceway ponds. Biotechnol. Bioeng.110(6),1583–1594 (2013).
  • James SC, Boriah V. Modeling algae growth in an open-channel raceway. J. Comput. Biol.17(7),895–906 (2010).
  • James SC, Janardhanam V, Hanson DT. Simulating pH effects in an algal-growth hydrodynamics model. J. Phycol.49(3),608–615 (2013).
  • Stephenson AL, Dennis JS, Howe CJ, Scott SA, Smith AG. Influence of nitrogen-limitation on the production of Chlorella vulgaris of lipids for biodiesel feedstocks. Biofuels1(1),47–58 (2010).
  • Wager H. On the effect of gravity upon the movements and aggregation of Euglena viridis, Ehrb., and other micro-organisms. Philos. Trans. R. Soc. Lond. B Biol. Sci.201,333–390 (1911).
  • Melis A, Zhang L, Forestier M, Ghirardi M, Seibert M. Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green alga Chlamydomonas reinhardtii. Plant Physiol.122(1),127–136 (2000).
  • Kosourov S, Makarova V, Fedorov AS, Tsygankov A, Seibert M, Ghirardi ML. The effect of sulfur re-addition on H2 photoproduction by sulfur-deprived green algae. Photosynth. Res.85(3),295–305 (2005).
  • Croft MT, Warren MJ, Smith AG. Algae need their vitamins. Eukaryot. Cell5(8),1175–1183 (2006).
  • Hill NA, Pedley TJ. Bioconvection. Fluid Dyn. Res.37(1–2),1–20 (2005).
  • Croze OA, Ashraf EE, Bees MA. Sheared bioconvection in a horizontal tube. Phys. Biol.7,046001 (2010).
  • Bees MA, Croze OA. Dispersion of biased swimming micro–organisms in a fluid flowing through a tube. Proc. R. Soc. A466(2119),1067–1070 (2010).
  • Croze O, Sardina G, Ahmed M, Bees MA, Brandt L. Dispersion of swimming algae in laminar and turbulent channel flows: theory and simulations. J. R. Soc. Interface10(81),20121041 (2013).
  • Smayda TJ. Harmful algal blooms: their ecophysiology and general relevance to phytoplankton blooms in the sea. Limnol. Oceanogr.42,1137–1153 (1997).
  • Kessler JO. Gyrotactic buoyant convection and spontenous pattern formation in algal culture. In: Non-equilibrium Cooperative Phemomena in Physics and Related Fields. Verlarde MG (Ed.). Plenum, NY, USA, 241–248 (1984).
  • Fouchard S, Pruvost J, Degrenne B, Titica M, Legrand J. Kinetic modeling of light limitation and sulfur deprivation effects in the induction of hydrogen production with Chlamydomonas reinhardtii: part I. Model development and parameter identification. Biotechnol. Bioeng.102(1),232–245, (2009).
  • Kessler JO. Hydrodynamic focusing of motile algal cells. Nature313(5999),218–220 (1985).
  • Kosourov S, Tsygankov A, Seibert M, Ghirardi M. Sustained hydrogen photoproduction by Chlamydomonas reinhardtii: effects of culture parameters. Biotechnol. Bioeng.78(7),731–740 (2002).
  • Pedley TJ, Kessler JO. Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech.24(1),313–358 (1992).
  • Lauga E, Powers TR. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys72,096601 (2009).
  • Guasto JS, Rusconi R, Stocker R. Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech.44,373–400 (2012).
  • Platt JR. “Bioconvection Patterns” in cultures of free-swimming organisms. Science133(3466),1766–1767 (1961).
  • Bees MA, Hill NA. Wavelengths of bioconvection patterns. J. Exp. Biol.200(10),1515–1526 (1997).
  • Williams CR, Bees MA. A tale of three taxes: photo-gyro-gravitactic bioconvection. J Exp. Biol.214(Pt 14),2398–2408 (2011).
  • Kessler JO. Individual and collective fluid dynamics of swimming cells. J. Fluid Mech.173,191–205 (1986).
  • Pedley TJ, Kessler JO. A new continuum model for suspensions of gyrotactic micro-organisms. J. Fluid Mech.212,155–182 (1990).
  • Bees MA. Non-Linear Pattern Generation in Suspensions of Swimming Micro-Organisms [PhD thesis]. University of Leeds, Leeds, UK (1996).
  • Bees MA, Hill NA. Linear bioconvection in a suspension of randomly swimming, gyrotactic micro-organisms. Phys. Fluids10(8),1864–1998 (1881).
  • Bees MA, Hill NA. Non-linear bioconvection in a deep suspension of gyrotactic swimming micro-organisms. J. Math. Biol.38(2),135–168 (1999).
  • Ghorai S, Hill NA. Development and stability of gyrotactic plumes in bioconvection. J. Fluid Mech.400,1–31 (1999).
  • Ghorai S, Hill NA. Gyrotactic bioconvection in three dimensions. Phys. Fluids19(5),054107 (2007).
  • Harashima A, Watanabe M, Fujishiro I. Evolution of bioconvection patterns in a culture of motile flagellates. Phys. Fluids31(4),764–775 (1988).
  • Hillesdon AJ, Pedley TJ. Bioconvection in suspensions of oxytactic bacteria: linear theory. J. Fluid Mech.324(1),223–259 (1996).
  • Metcalfe AM, Pedley TJ. Bacterial bioconvection: weakly nonlinear theory for pattern selection. J. Fluid Mech.370(1),249–270 (1998).
  • O’Malley S, Bees MA. The orientation of swimming biflagellates in shear flows. Bull. Math. Biol.74(1),232–255 (2011).
  • Bees MA, Hill NA, Pedley TJ. Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows. J. Math. Biol.36(3),269–298 (1998).
  • Hill NA, Bees MA. Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow. Phys. Fluids14,2598–2605 (2002).
  • Willams CR, Bees MA. Photo-gyrotactic bioconvection. J. Fluid Mech.678,41–86 (2011).
  • Bearon R. Helical swimming can provide robust upwards transport for gravitatic single-cell algae; a mechanistic model. J. Math. Biol.66,1341–1359 (2013).
  • Durham WM, Kessler JO, Stocker R. Disruption of vertical motility by shear triggers formation of thin phytoplankton layers. Science323,1067–1070 (2009).
  • Durham WM, Climent E, Stocker R. Gyrotaxis in a steady vortical flow. Phys. Rev. Lett.106,238102 (2011).
  • Bearon RN, Grünbaum D. Bioconvection in a stratified environment: experiments and theory. Phys. Fluids18(12),127102 (2006).
  • Hardin G. The competitive exclusion principle. Science131,1292–1297 (1960).
  • Fogg GE, Thake B. Algae Cultures and Phytoplankton Ecology, 3rd Edition. The University of Wisconsin Press, Ltd, WI, USA, 269 (1987).
  • Massie TM, Blasius B, Weithoff G, Gaedke U, Fussmann GF. Cycles, phase synchronization, and entrainment in single-species phytoplankton populations. Proc. Natl Acad. Sci. USA107,4236–4241 (2010).
  • Croft MT, Lawerence AD, Raux-Deery E, Warren MJ, Smith AG. Algae acquire vitamin b12 through a symbiotic relationship with bacteria. Nature438,90–93 (2005).
  • Fergola P, Cerasuolo M, Pollio A, Pinto G, DellaGreca M. Allelopathy and competition between Chlorella vulgaris and Pseudokirchneriella subcapitata: experiments and mathematical model. Ecol. Modell.205,875–214 (2007).
  • Flynn KJ, Fielder J. Changes in intracellular and extracellular amino acids during the predation of the chlorophyte Dunaliella primolecta by the heterotrophic dinoflagellate Oxyrrhis marina and the use of the glutamine/glutamate ratio as an indicator of nutrient status in mixed populations. Mar. Ecol. Prog. Ser.53,117–127 (1989).
  • Elbrächter M. On population dynamics in multi-species cultures of diatoms and dinoagellates. Helgoländer wiss. Meeresunters.30,192–200 (1977).
  • Proctor VW. Studies of algal antibiosis using Hematococcus and Chlamydomonas. Limnol. Oceanogr.2,125–139 (1957).
  • Kroes HW. Growth interactions between Chlamydomonas globosa snow and Chlorococcum ellispoideum. Limnol. Oceanogr.16,869 (1971).
  • Gaffron H, Rubin J. Fermentative and photochemical production of hydrogen in algae. J. Gen. Physiol.26,219–240 (1942).
  • Cao H, Zhang L, Melis A. Bioenergetic and metabolic processes for the survival of sulfur-deprived Dunaliella salina (Chlorophyta). J. Appl. Phycol.13(1),25–34 (2001).
  • Zhang L, Melis A. Probing green algal hydrogen production. Philos. Trans. R. Soc. Lond. B Biol. Sci.357(1426),1499–1507 (2002).
  • Ghirardi ML, Zhang L, Lee J et al. Microalgae: a green source of renewable H2. Trends Biotechnol.18(12),506–511 (2000).
  • Happe T, Hemschemeier A, Winkler M, Kaminski A. Hydrogenases in green algae: do they save the algae’s life and solve our energy problems? Trends Plant Sci.7(6),246–250 (2002).
  • Fouchard S, Hemschemeier A, Caruana A et al. Autotrophic and mixotrophic hydrogen photoproduction in sulfur-deprived Chlamydomonas cells. Appl. Environ. Microbiol.71(10),6199–6205 (2005).
  • Hemschemeier A, Fouchard S, Cournac L, Peltier G, Happe T. Hydrogen production by Chlamydomonas reinhardtii: an elaborate interplay of electron sources and sinks. Planta227(2),397–407 (2008).
  • Scoma A, Giannelli L, Faraloni C, Torzillo G. Outdoor H2 production in a 50-l tubular photobioreactor by means of a sulfur-deprived culture of the microalga Chlamydomonas reinhardtii. J. Biotechnol.157,620–627 (2012).
  • Degrenne B, Pruvost J, Titica M, Takache H, Legrand J. Kinetic modeling of light limitation and sulfur deprivation effects in the induction of hydrogen production with Chlamydomonas reinhardtii. Part II: definition of model-based protocols and experimental validation. Biotechnol. Bioeng.108(10),2288–2299 (2011).
  • Yildiz JP, Davies FH, Grossman AR. Characterization of sulfate transport in Chlamydomonas reinhardtii during sulfur-limited and sulfur-sufficient growth. Plant Physiol.104(3),981–987 (1994).
  • Droop MR. On the definition of the x and q in the cell quota model. J. Mar. Biolog. Assoc. UK39,203 (1979).
  • Duysens LNM. The flattening of the absorption spectrum of suspensions, as compared with that of solutions. Biochim. Biophys. Acta19,1–12 (1956).
  • Hill NA, Häder DP. A biased random walk model for the trajectories of swimming micro-organisms. J. Theor. Biol.186,503–526 (1997).
  • Vladimirov VA, Wu MSC, Pedley TJ, Denissenko PV, Zakhidova SG. Measurement of cell velocity distributions in populations of motile algae. J. Exp. Biol.207(7),1203–1216 (2004).
  • Drescher K, Leptos KC, Goldstein RE. How to track protists in three dimensions. Rev. Sci. Instrum.80,014301 (2009).
  • Cerbino R, Trappe V. Differential dynamic microscopy: probing wave vector dependent dynamics with a microscope. Phys. Rev. Lett.100,188102 (2008).
  • Wilson LG, Martinez VA, Schwarz-Linek J et al. Differential dynamic microscopy of bacteria mobility. Phys. Rev. Lett.106,018101 (2011).
  • Martinez VA, Besseling R, Croze OA et al. Differential dynamic microscopy: a high-throughput method for characterizing the motility of microorganisms. Biophys. J.103,1637–1647 (2012).
  • Berne BJ, Pecora R. Dynamic Light Scattering. John Wiley, NY, USA (1976).
  • Taylor GI. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R Soc. Lond. A Maths Phys. Sci.219,186–203 (1953).
  • Taylor GI. The dispersion of matter in turbulent flow through a pipe. Proc. R Soc. Lond. A Maths Phys. Sci.223,446–468 (1954).
  • Aris R. On the dispersion of a solute in a fluid flowing through a tube. Proc. R Soc. Lond. A Maths Phys. Sci.235,67–77 (1956).
  • Bearon RN, Bees MA, Croze OA. Biased swimming cells do not disperse in pipes as tracers: a population model based on microscale behaviour. Phys. Fluids24,122012 (1902).
  • Bees MA, Mezic I, McGlade J. Planktonic interactions and chaotic advection in langmuir circulation. Math. Comput. Simul.44,527–544 (1998).
  • Reigada R, Hillary RM, Bees MA, Sancho JM, Sagués F. Plankton blooms induced by turbulent flows. Proc. R. Soc. Lond. B Biol. Sci.270,875–880 (2002).
  • Fisher HB. Longitudinal dispersion and turbulent mixing in open-channel flow. J Fluid Mech.5,59–78 (1973).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.