Expanded and Practical Use of Logistic Equations in Eco-Toxicity Evaluation: Cases of Lethal Metal Toxicity Curves in Green Paramecia with Minimal-Sized Experiments
Hiroshi Takaichi and Tomonori Kawano
The University of Kitakyushu
1-1 Hibikino, Wakamatsu-ku, Kitakyushu 808-0135, Japan
In ecological systems, living organisms are surrounded by a number of chemicals, among which certain portion may be toxic to organisms. Therefore, from the environment-centric point of view, importance of accurate eco-toxicological analyses is increasing day-by-day. Eco-toxicity responses in animals and other organisms against chemicals can be scored by several parameters such as median lethal concentration (LC50) and median lethal dose (LD50), for examples. In the present study, we attempted to perform simulations of eco-toxicological nature of given chemicals based on limited data size (showing apparently incomplete curves of toxicity response) through model experiments performed with green paramecia (Paramecium bursaria) exposed to toxic metal ions, by using practically re-arranged logistic equation and Hill-type equations with an aid by graphical elucidation of Gauss-Newton algorithm determining the constants and/or coefficients.
-  P. Turchin, ”Does population ecology have general laws?,” Oikos, Vol.94, pp. 17-26, 2001.
-  P.-F. Verhulst, “Notice sur la loi que la population poursuit dans son accroissement,” Correspondance Mathématique et Physique, Vol.10, pp. 113-121, 1838.
-  P.-F. Verhulst, “Recherches mathématiques sur la loi d’accroissement de la population,” Nouveaux Mémoires de l’Académie Royale des Sciences et Belles-Lettres de Bruxelles, Vol.18, pp. 1-42, 1845.
-  A. G. McKendrick and M. K. Pai,“XLV. The Rate of Multiplication of Micro-organisms: A Mathematical Study,” Proc. of the Royal Society of Edinburgh, Vol.31, pp. 649-653, 1912.
-  R. Pearl and L. Reed, “On the rate of growth of the population of the United States,” Proc. Natl. Acad. Sci. U.S.A., Vol.6, pp. 275-288, 1920.
-  G. F. Gause, “The struggle for existence,” The Williams & Wilkins, Baltimore, 1934.
-  T. Kosaka, “Life cycle of Paramecium bursaria syngen 1 in nature,” J. Protozool, Vol.38, pp. 140-148, 1991.
-  W. Reisser, “Basic mechanisms of signal exchange, recognition, specificity, and regulation in endosymbiotic systems,” Algae and Symbioses: Plants, Animals, Fungi, Viruses, Interaction Explored (W. Reisser ed.), Biopress, Bristol, pp. 657-674, 1992.
-  T. Kawano, T. Kadono, T. Kosaka, and H. Hosoya, “Green paramecia as an evolutionary winner of the oxidative symbiosis: A hypothesis and supportive data,” Z. Naturforsch, Vol.59c, pp. 538-542, 2004.
-  T. Takahashi, M. Yoshii, T. Kawano, T. Kosaka, and H. Hosoya, “A new approach for the assessment of acrylamide toxicity using a green paramecium. Toxicol,” in Vitro, Vol.19, pp. 99-105, 2005.
-  T. Kadono, K. Uezu, T. Kosaka, and T. Kawano, “Altered toxicities of fatty acid salts in green paramecia cultured in different waters,” Z. Naturforsch., Vol.61c, pp. 541-547, 2006.
-  K. Goto, C. Lin, T. Kadono, M. Hirono, K. Uezu, and T. Kawano, “Eco-toxicity of a soap component (sodium oleate) and a synthetic detergent cocktail using green paramecia assayed in natural water samples from East Asia,” J. Environ. Engin. Manag., Vol.17, pp. 377-383, 2007.
-  K. Goto, T. Kadono, K. Yokawa, and T. Kawano, “Model toxicity assay for amino acid derivatives using green paramecia: Comparison of natural amino acids and N-acetylated non-protein amino acids,” Curr. Topic Peptide Protein Res., Vol.12, pp. 29-34, 2011.
-  K. Goto, H. Takaichi, and T. Kawano, “Learning from the eco-toxicology of fire-fighting foams in aquatic organisms: Altered eco-toxicity of sodium alkyl sulfonates in green paramecia and medaka fish maintained in in different waters,” J. Disaster Res., Vol.10, pp. 604-612, 2015.
-  T. Kawano, “Use of swimming cells of green paramecia for detection of toxic rare earth ions at lethal and sub-lethal concentration,” Adv. Mater. Res., Vol. 875-877, pp. 2229-2237, 2014.
-  V. I. Yukalov, E. P. Yukalova, and S. Sornette, “Punctuated evolution due to delayed carrying capacity,” Physica, Vol.D238, pp. 1752-1767, 2009.
-  M.Tanaka, Y. Ishizaka, H. Tosuji, M. Kunimoto, N. Nishihara, T. Kadono, T. Kawano, T. Kosaka, N. Hosoya, and H. Hosoya, “A new bioassay system for detection of chemical substances in environment using green paramecia,” Paramecium bursaria, Environmental Chemistry – Green Chemistry and Pollutants in Ecosystems (Eds., E. Lichtfouse, J. Schwarzbauer, and D. Robert), Springer-Verlag, Berlin. pp. 673-680, 2005.
-  N. Miyoshi, T. Kawano, M. Tanaka, T. Kadono, T. Kosaka, M. Kunimoto, T. Takahashi, and H. Hosoya, “Use of Paramecium species in bioassays for environmental risk management: determination of IC50 values for water pollutants,” J. Health Sci. Vol.46, pp 429-435, 2003.
-  OECD, “Test guideline No. 201: Alga, growth inhibition test,” OECD Guideline for testing chemicals. OECD, 1984.
-  H. Okamura, R. Luo, I. Aoyama, and D. Liu, “Ecotoxicity assessment of the aquatic environment around Lake Kojima,” Japan. Environ. Toxicol. Water Quality, Vol.11, pp. 213-221, 1998.
-  I. C. Mori, C. K. Arias-Barreiro, A. Koutsaftis, A. Ogo, T. Kawano, K. Yoshizuka, S. H. Inayat-Hussain, and I. Aoyama,“Toxicity of tetramethylammonium hydroxide to aquatic organisms and its synergistic action with potassium iodide,” Chemosphere, Vol.120, pp. 299-304, 2014.
-  S. Goutelle, M. Maurinc, F. Rougier, X. Barbaut, L. Bourguignona, M. Ducher, and P. Maire, “The Hill equation: a review of its capabilities in pharmacological modeling,” Fund. Clin. Pharmacol., Vol.22, pp. 633-648, 2008.
-  K. Nagasawa, J. Iwase, D. Comparini, and T. Kawano, “Empirical and simulative evaluations of white fluorescence-type light emitting diodes as algal growing light sources based on the photosynthetic oxygen evolution by Synechocystis spp. PCC6803,” Environ. Cont. Biol., Vol.53, pp. 169-173, 2015.
-  A. D. Jasby and T. Platt,“ Mathematical formulation of the relationship between photosynthesis and light for phytoplankton,” Limnol. Oceanogr. Vol.21, pp. 540-547, 1976.
-  T. Kawano, T. Kosaka, and H. Hosoya, “Impact of a sulfonylureic herbicide on growth of photosynthetic and non-photosynthetic protozoa,” Environmental Chemistry – Green Chemistry and Pollutants in Ecosystems (Eds., E. Lichtfouse, J. Schwarzbauer, and D. Robert), Springer-Verlag, Berlin, pp. 495-504, 2005.
-  R. M. F. Bezzerra, I. Fraga, and A. A. Dias, “Utilization of integrated Michaelis-Menten equations for enzyme inhibition diagnosis and determination of kinetic constants using Solver supplement of Microsoft Office Excel,” Computer Methods and Programs in Biomedicine, Vol.109, pp. 26-31, 2013.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.