Line 117: | Line 117: | ||
<h3>Estimating Model Parameters from Experimental Measurements</h3> | <h3>Estimating Model Parameters from Experimental Measurements</h3> | ||
− | <p>Two parameters relating to the Monod equation, the maximum specific growth rate | + | <p>Two parameters relating to the Monod equation, the maximum specific growth rate μ, and the saturation constant Ks are estimated graphically. These graphical methods are based on our readings of the literature [1, 3]. First, the cell growth described in equation 16, the Monod equation, is linearized similar to a linearization of the Michaelis-Menten equation. </p> |
\[\dfrac {1}{\mu} = \frac {K_s}{\mu_m}.\frac{1}{S}+\frac{1}{\mu_m} \] | \[\dfrac {1}{\mu} = \frac {K_s}{\mu_m}.\frac{1}{S}+\frac{1}{\mu_m} \] | ||
<p>Where </p> | <p>Where </p> | ||
\[ \frac{1}{\mu} = \frac{X}{\frac{dX}{dt}} \] | \[ \frac{1}{\mu} = \frac{X}{\frac{dX}{dt}} \] | ||
− | This takes the form of a double-reciprocal Line-Weaver Burk plot of 1/μ vs 1/S. From the slope and intercept of this plot, model parameters μ and Ks are estimated. The graph below shows the estimated parameters derived from the experimental data for the genetically modified yeast and wild type yeast in a glucose substrate (YPD yeast media). | + | <p>This takes the form of a double-reciprocal Line-Weaver Burk plot of 1/μ vs 1/S. From the slope and intercept of this plot, model parameters μ and Ks are estimated. The graph below shows the estimated parameters derived from the experimental data for the genetically modified yeast and wild type yeast in a glucose substrate (YPD yeast media). </p> |
<p> </p> | <p> </p> | ||
<p>Figure 1 Double-reciprocal Line-Weaver Burk plot for Cell Growth </p> | <p>Figure 1 Double-reciprocal Line-Weaver Burk plot for Cell Growth </p> |
Revision as of 04:35, 18 October 2016
.MathJax nobr>span.math>span{border-left-width:0 !important};
Here is some filler text.
Mathematical Modeling
Model Formulation
Cell Growth
Substrate Utilization
Product Formation
Monod Equation for Limited-Substrate Growth
Michaelis-Menten Kinetics for Enzymatic Reactions
Model Simulation with MATLAB
Estimating Model Parameters from Experimental Measurements
Two parameters relating to the Monod equation, the maximum specific growth rate μ, and the saturation constant Ks are estimated graphically. These graphical methods are based on our readings of the literature [1, 3]. First, the cell growth described in equation 16, the Monod equation, is linearized similar to a linearization of the Michaelis-Menten equation.
\[\dfrac {1}{\mu} = \frac {K_s}{\mu_m}.\frac{1}{S}+\frac{1}{\mu_m} \]Where
\[ \frac{1}{\mu} = \frac{X}{\frac{dX}{dt}} \]This takes the form of a double-reciprocal Line-Weaver Burk plot of 1/μ vs 1/S. From the slope and intercept of this plot, model parameters μ and Ks are estimated. The graph below shows the estimated parameters derived from the experimental data for the genetically modified yeast and wild type yeast in a glucose substrate (YPD yeast media).
Figure 1 Double-reciprocal Line-Weaver Burk plot for Cell Growth
To check our work, we also used a simpler method, a plot of the log ratios of cell concentrations against time. This method applies to the exponential phase of growth and is useful for getting an estimate of μ from the slope of the graph, according to Equation 8. The log plots are shown below. The figure also captures a summary Table of model parameters.
Figure 2 Log plot of exponential cell growth to estimate the maximum specific cell growth rates for the genetically modified and wild type yeast in a glucose substrate, and the genetically modified yeast in starch substrate. The Table summarizes the model parameters from the two graphical methods. The growth yield Yx/s is obtained from the experimental measurements; calculated as the ratio of the differences between cell densities and glucose concentration for two time points, at time zero and the time point corresponding to the end of exponential growth
Future Modeling
References
1. Shuler, M. L., & Kargi, F. (2002). Bioprocess engineering: Basic concepts, Chapter 4 and Chapter 6. Upper Saddle River, NJ: Prentice Hall.
2. Zangirolami, T.C., Carlsen, M., Nielsen, J., & Jørgensen, S.B.. (2002). Growth and enzyme production during continuous cultures of a high amylase-producing variant of Aspergillus Oryzae. Brazilian Journal of Chemical Engineering, 19(1), 55-68
3. Wang, L., D. Ridgway, T. Gu and M.Y. Murray, 2009. Kinetic modeling of cell growth and product formation in submerged culture of recombinant Aspergillus niger. Chem. Eng. Com., 196:481-490.
4. Akpa J (2012) Modeling of a Bioreactor for the Fermentation of Palm wine by Saccaharomyce cerevisiae (yeast) and lactobacillus (bacteria). Bioresource Technology 3: 231-240.