Modelling the growth kinetics of <i>E. coli</i> measured using real-time impedimetric biosensor

  • Mohd Shukri Shukor Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, UPM 43400 Serdang, Selangor, Malaysia.
  • Mohd Yunus Shukor Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, UPM 43400 Serdang, Selangor, Malaysia.


The development of in situ sensor for measuring bacterial concentrations in fermenter would allow real-time monitoring of the concentration of bacteria. Kim et al [1] has developed such a method using impedance spectroscopy, and was able to measure in real-time the concentration of E. coli at 0.01 MHz frequency using impedance changes. In this work we used several mathematical models of bacterial growth kinetics such as logistic, Gompertz, Richards, Schnute, Baranyi-Roberts, Von Bertalanffy, Buchanan three-phase and the Huang models to model the resulting bacterial growth curve from Kim et al. The Buchanan three-phase model was chosen as the best model based on statistical tests such as root-mean-square error (RMSE), adjusted coefficient of determination (R2), bias factor (BF), accuracy factor (AF) and corrected AICc(Akaike Information Criterion). Parameters obtained from the growth fitting exercise were maximum specific growth rate (μmax), lag time (λ) and maximal number of cells achieved per droplet (Ymax) with values of 0.67±0.086 (h-1), 2.45±0.24 (h) and 20.26±0.038 (ln cell no/ml), respectively. The parameters obtained from fitting the bacterial growth curve using this model can be used for further modeling and optimization exercises for identifying key optimal parameters for improving the sensitivity of the biosensor.


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(1):270–277.

Baranyi J. Mathematics of predictive food microbiology. Int J

Food Microbiol. 1995; 26(2); 199–218.

Halmi MIE, Shukor MS, Johari WLW, Shukor MY. Evaluation

of several mathematical models for fitting the growth of the

algae Dunaliella tertiolecta. Asian J Plant Biol. 2014; 2(1):1–6.

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(3):e91732.

Zwietering MH, Wit JCD, Cuppers HGAM, Riet KV.

Modeling of bacterial growth with shifts in temperature. Appl

Environ Microb. 1994; 60(1):204–213.

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.

; 115:513–85.

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; 38:1128–1140.

Bertalanffy LV. 1951. Heoretische Biologie, Zweiter Band:

Stoffwechsel, Wachstum. Ed: Francke A & Verlag AG, 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.

Snedecor GW, Cochran WG. 1980. Statistical methods. 7th ed.

Ames Iowa: Iowa State University Press.

Akaike H. New look at the statistical model identification.

IEEE Trans Automat Contr. 1974; 19:716–23.

Burnham KP, Anderson DR. Model Selection and

Multimodel Inference: A Practical Information-Theoretic

Approach. Springer Science & Business Media; 2002. 528.

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.

McMeekin TA, Ross T. Predictive microbiology: Providing a

knowledge-based framework for change management. Int J

Food Microbiol. 2002; 78:133–153.

López S, Prieto M, Dijkstra J, Dhanoa MS, France J. Statistical

evaluation of mathematical models for microbial growth. Int J

Food Microbiol. 2004; 96:289–300.