Statistical diagnostic tests of residuals from the Gompertz model used in the fitting of the growth of <i>E. coli</i> measured using a real-time impedimetric biosensor
AbstractThe development of in situ sensor for measuring bacterial concentrations in biotechnology and the health sciences would allow real-time monitoring of the concentration of bacteria. Kim et al  has developed such a method using impedance spectroscopy, and was able to measure in realtime the concentration of E. coli at 0.01 MHz frequency using impedance changes. We modeled the growth kinetics using several nonlinear regression methods and discovered that the modified Gompertz model is the best model for the growth of the bacterium . It is well known that nonlinear regression of a data and further statistical analysis to find the best model relies on the facts that the residuals (difference between observed and predicted data) followed a normal or Gaussian distribution and that the data must be free of outliers. If all of these assumptions are satisfied, the test is said to be robust. In this work we perform statistical diagnostics to the residuals to satisfy the requirements above and found that removal of an outlier allows the residuals to conform to all of the requirements above. The results indicated that remodelling of the Gompertz model using the new set of data should be carried out.
Kim YH, Park JS, Jung HI. An impedimetric biosensor for
real-time monitoring of bacterial growth in a microbial
fermentor. Sensor Actuat B-Chem. 2009; 138:270–277.
Shukor MS, Shukor MY. Modeling the growth kinetics of E.
coli measured using real-time impedimetric biosensor.
Nanobio Bionano. 2014; 1:52-57.
Dweik M, Stringer RC, Dastider SG, Wu Y, Almasri M,
Barizuddin S. Specific and targeted detection of viable
Escherichia coli O157:H7 using a sensitive and reusable
impedance biosensor with dose and time response studies.
Talanta. 2012; 94:84–89.
Ward AC, Connolly P, Tucker NP. Pseudomonas
aeruginosacan be detected in a polymicrobial competition
model using impedance spectroscopy with a novel biosensor.
PLoS ONE. 2014; 9.
Zwietering MH, Wit JCD, Cuppers HGAM, Riet KV.
Modeling of bacterial growth with shifts in temperature. Appl
Environ Microb. 1994; 60:204–213.
Ricker WE. 1979. 11 Growth Rates and Models. p. 677.
Gompertz B. On the nature of the function expressive of the
law of human mortality, and on a new mode of determining
the value of life contingencies. Philos Trans R Soc London.
Richards FJ. A flexible growth function for empirical use. J
Exp Bot. 1959; 10:290–300.
Schnute J. A versatile growth model with statistically stable
parameters. Can J Fish Aquat Sci. 1981; 38:1128–40.
Baranyi J. Mathematics of predictive food microbiology. Int J
Food Microbiol. 1995; 26:199–218.
Bertalanffy LV. 1951. Heoretische Biologie, Zweiter Band:
Stoffwechsel,Wachstum. A FranckeAG Verlag, Bern,
Switzerland; p. 418.
Buchanan RL, Golden MH. Model for the non-thermal
inactivation of Listeria monocytogenes in a reduced oxygen
environment. Food Microbiol. 1995; 12:203–212.
Huang L. Optimization of a new mathematical model for
bacterial growth. Food Control. 2013; 32:283–288.
Abd Rachman AR, Halmi MIE, Shukor MY. Amplification of
new isolated luciferase gene from marine Photobacterium
strain MIE by using specific PCR. J Environ Microbiol
Toxicol. 2014; 2:35–7.
Motulsky HJ, Ransnas LA. Fitting curves to data using
nonlinear regression: a practical and nonmathematical review.
FASEB J Off Publ Fed Am Soc Exp Biol. 1987; 1:365–374.
Grubbs F. Procedures for detecting outlying observations in
samples. Technometrics. 1969; 11:1–21.
Kolmogorov A. Confidence limits for an unknown
distribution function. Ann Math Stat. 1941; 12:461–463.
Smirnov N. Table for estimating the goodness of fit of
empirical distributions. Ann Math Stat. 1948; 19:279–281.
Royston P. Wilks-Shapiro algorithm. Appl Stat. 1995; 44:R94.
D’Agostino RB. 1986. Tests for Normal Distribution. In:
D’Agostino RB, ed. Stephens MA, Goodness-Of-Fit
Techniques. Marcel Dekker
Draper NR, Smith H. 1981. Applied Regression Analysis.
Wiley, New York;
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