EXPERIMENTAL PROPOSAL

CREATING AND TESTING A MATHEMATIC MODEL TO PREDICT GROWTH CURVES OF

E. COLI AFTER EXPOSURE TO ELEVATED TEMPERATURES

Team 3March 31, 2014

Problem statement The purpose of this study is to

create and validate a mathematical model of a growth curve of bacterial behavior after thermal shock at various temperatures

Facts about E. Coli Escherichia coli (E. coli) is a type of

bacteria commonly found in the intestinal tracts of large mammals

The growth and decay rate are also affected by: Temperature Initial concentration of bacteria Presence of antibacterial substances pH levels Oxidation reduction potential

Facts about E. Coli In our experiment, we demonstrate how

the growth curve is affected by thermal shock

E. Coli grows well between 21oC to 50oC with an optimum at about 37oC .

E. coli can divide every 20 minutes At temperatures of 0°C (32°F) E. coli

are unable to divide, keeping the population stable

E. coli is killed above 70°C (160°F)

Growth Curve of E. coli

Lag phase: the population remains temporarily unchanged

Log phase: the cells divide at a constant rate depending on temperature conditions

Stationary phase: the population growth is limited by temperature Death phase: the number of cells decreases

The E.coli Growth Curve

Hypothesis

The growth curves of colonies shocked at temperatures (45-650C) demonstrate longer lag times but accelerated exponential growth when compared to a control grown at 37°C

Mathematic model to predict growth curve

WE WILL APPLY THIS EQUATION TO CREATE THE GROWTH CURVE MODEL[17]

(1- NMIN /N)C

Where: (Nmin) = minimum

population of E.coli (Nmax) = maximum

population of E.coli r = Temperature-

dependent constant C= Adjustment factor N= number colonies at

time t

Experimental Design

Materials and EquipmentSpectrophotometer and cuvettesInoculation Loop 1000μL and 100μL micropipettesBeakers and hot plates Incubator (37oC) Reagents:

Distilled water and deionized water Culture of E.Coli Nutrient broth as a food source

Experimental Setup

Thermal Shock: Initially raise bacterial environment

temperature to 450C, 550C, 600C, and 700C Growth continued at 370C after thermal shock Control group grown at 370C

Measure growth Create a concentration ladder Measure cloudiness in a test tube as the

number of cells increase (turbidity) using a spectrophotometer

Data Analysis

Mintab and MATLAB software Plot mathematical growth curve and

experimental growth curves Regression analysis

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