Team:GeorgiaTech/Systems Modeling

• 800 mV electric potential drop of 4 electrons  generates  5.12 x 10-19 Joules   
• 70% of electrons enter AOX pathway
• Assume time scale of ATP cycle to calculate power
• Power generated per cell is 1.6 x 10-13 Watt

II) Heat transfer in liquid culture:

• Simplifying Assumptions

1.Liquid solution can be assumed water
2.Complete insulation
3.Heat accumulation within system
4.Homogeneous mixture
5.No work done on or performed by the system

• Density of bacterial culture can vary by 2 orders of magnitude
• Temperature of system can be raised by 1K in 4 – 40 min.

III) Heat transfer in bacterial colony (analytical solution)
Assumptions:
1.  Petri dish is completely insulated, and kept at 288K
2.  Ambient temperature is 288K
3.  Conduction through E. coli is similar to that in water
4.  Constant coefficients for conductivity in both media, constant convective coefficient for air
5.  Aspect ratio : width of colony >> height of colony
Required : Insert Diagram of ecoli on agar (green outlines)
Required: Insert slides titled (steady state temperature profile for agar and ecoli)
Solving for boundary conditions:
1. Heat flux at the E. coli - air boundary was equal to the convective heat flux ( x = 0 )
2. Heat flux and temperature were equated at E. coli - agarose boundary ( X = d )

The following information was also known:

• Q: volumetric flow of heat generated by Ecoli
• k : conductive coefficient of water at 288K
• h : convective coefficient of air at 288K
• Tambient: 298 K
• Measurements of height of colony and agarose
• C2 = Te , Temperature at Ecoli- air boundary (unknown)

3) We solved for boundary conditions by solving two temperature profile  equations simultaneously in MATLAB
Required: Slide in MATLAB
SLIDE DESCRIPTION: This figure shows the temperature profile of bacteria and the solid growth media as a function of height. In E. coli, temperature drops quadratically, and it drops linearly in agarose. This is because of the heat generation term included within the Poisson equation developed to describe heat transfer in E. coli. The total drop of temperature at steady state across the height of bacterial colony and agarose is approximately 0.1 K.

IV) Heat transport in bacterial colony 2D and 3D (using COMSOL)
Required: slide on 2d comsol
Required: slide on 3d comsol
SLIDE DESCRIPTION: This figure as well as the previous were developed in COMSOL. They depict 2D and 3D heat transfer in bacterial colony and agarose. The difference between peak temperatures in both scenarios did not differ by more than 0.006K which indicates that a 2D control volume may provide sufficiently accurate representation for heat transport modeling. In a 2D control volume, heat is transferred radially to the environment. If high aspect ratio is implemented, as in case of a uniform stretch of bacterial colony formed on a petri dish, then 1D control volume will be sufficient.

V) Conclusions:

• Within solution 1K change in temperature in 4 – 40 minutes.

• On agar, steady state temperature profile derived analytically matches closely with those found computationally using COMSOL.

• Using 1D control-volume is a good assumption, since 3D temperature profile was not considerably different.

• Derived analytically and computationally, the change in temperature due to AOX expression should be approximately 0.1 K (on solid growth media).

• Due to better accumulation of energy in liquid media, characterization of heat production may be more accessible using a liquid culture.

• A highly sensitive (at least 0.1K) thermal imaging camera will be essential for measuring heat production of bacterial colony in both liquid and solid growth media