University of Virginia iGEM 2015

Modeling

Modeling is a major component of our project since in the scope of this project, the direct effect of the transformed E. coli strain on reducing glycemic spikes cannot be tested in animal models, e.g. Rattus norvegicus. Instead, we will model the theoretical decrease in blood sugar levels based on data obtained from experiments that are performed in liquid solutions containing various concentrations of glucose and/or fructose. Thus, our first modeling goal is to predict the usefulness of our system and guide our experimental design, troubleshooting and future potential improvements. In addition, since our project is related to health and would need to be orally taken to be effective, safety concerns should also be counted for. Thus, our second modeling goal is to show the degree of possible horizontal gene transfer between our modified E. coli and endogenous gut flora.

First Part: Modeling the efficacy of our design

Uptake of the sugar by the transformed strain

The uptake of the sugar is the cornerstone of the design. It is modeled as a function of promoter strength and concentration of free sugars. Thus we can find the range of uptake that is most physiologically reasonable and back-calculate the strength of the promoter to achieve the desired level of sugar uptake. Since the relative strength of the promoter family J23100 (Anderson, 2006) has been characterized, we could determine which promoter from the family is optimal based on our model. The model is made to fit data obtained from characterization process.

Modeling of the glgC and sacB function

Conversion of simple sugars into complex saccharides is modeled as a function of simple sugar concentrations and expression level of the enzymes, glgC and sacB. The concentration profile of complex sugars is modeled as a function of free sugar concentrations inside cells, expression level of the genes and time. The cell death and release of the sugars will relate to concentration profile of complex sugars. The model will be used to estimate the input, the released complex sugars, for the model of reabsorption.

Glycogen concentration is measured by absorbance. Because the recommended wavelength by the assay kit manufacturer is 570. Based on wavelength/absorbance plot provided by the manufacturer, we determined that the out of the wavelength filters that we have, the 540 nm is most ideal. So we used the absorbance measured at 540 nm to reproduce a plot.

Reabsorption of complex saccharides by the human body

Previous study has suggested that high molecular weight levan is digested into low molecular weight product and free fructose by gastric juice but not pancreatic enzymes (Yamamoto et al., 1999). Thus once inside the small intestine, the levan will not be digested and will reach the colon and be excreted out of the human body. Thus we only need to model the digestion and absorption of glycogen. Recently, a physiological model of intestinal absorption of glucose has been developed, and specifically the Ra has been estimated as a function of the amount of glucose in the gut (Man, Camilleri, & Cobelli, 2006):

Because the enzyme responsible for the breakdown of polysaccharides, pancreatic alpha-amylase (AMY2A), has been well-characterized (Narimasa, Tatsuo, Mitsutaka, & Toshio, 1979), we can use Equation 2 (Butterworth, Warren, & Ellis, 2011) to estimate the amount of glucose from the amount of glycogen.

The total amount (mass) of glucose can be assumed to equal the total amount of glycogen when all glycogen is depleted. Then, we can model the function of our transformed strain inside small intestine as a three-step linear process, where the free sugars are first taken by the bacteria, then polymerized inside the bacteria and then released after about 2 hours. The Ra will be compared with the Ra estimated without our device to quantify the effectiveness of our device to delay and reduce PPG level. Additionally, we can constrain our model to achieve an ideal Ra and solve for the parameters such as promoter strength of the two devices.

Second Part: Modeling the rate of horizontal gene transfer

Horizontal gene transfer between our modified E. coli and indigenous gut flora is something we must address as a safety concern. The most rapid means of horizontal gene transfer in bacteria is through the shuttle of plasmids. Transfer of plasmids occurs at about 1*10^-9 (ml cell^-1 h^-1, ref). And the number of E. coli is decreasing (as determined by the growth assay). Thus the total number of transferred plasmid within one load could be modeled as an ODE. The number is calculated to be #, given the SacB could kill #% of the cells after 2 hrs.

Ideally, we could transform our modified E. coli with a circuit composed of a consensus E. coli promoter, GFP, a consensus ASF 361 promoter and RFP. If we measure the expression level of GFP and RFP in the E. coli and ASF 361 respectively and get distinct FU readings, we could use a flow cytofluorometer to find out the specific plasmid transfer rate of our modified E. coli to a representative of the indigenous gut flora. However, we did not have the time to complete this experiment.