Team:GeorgiaTech/Systems Modeling

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Modeling Bacterial Heat Production Due to AOX Pathway

AOX pathway is responsible for thermogenesis in various organisms. But to what extent it would be responsible for heat production in genetically engineered bacteria remains an interesting question. Georgia Tech modeling team aimed at theorizing an answer to this question using both analytical and computational methods. The primary goal was to suggest a calorimetric technique with optimal sensitivity, as well as to compare heat transfer in liquid culture and bacterial colonies.

Heat Transfer Modeling Aims

The following models were devised:

I. Rate of heat production via AOX pathway

II. Heat transfer in liquid culture

III. Heat transfer in bacterial colony (analytical solution 1D)

IV. Heat transfer in bacterial colony (computational solution 2D and 3D)

I) Calculations for rate of heat production in E. coli:

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

Figure 1. 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)

Figure 2.

Figure 3.

Figure 2 and 3 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

@@ Line 94: / Line 94: @@
      <td bgcolor="#964141" width="900"><font color="#FFFFFF" size=4><p><center>Heat Transfer Modeling Aims</font></center></p>
 <center><p><strong>The following models were devised:</strong></p>
-<p><strong>I. Rate of heat production via AOX pathway</strong></p>
+<p>I. Rate of heat production via AOX pathway</strong></p>
 <p><strong>II. Heat transfer in liquid culture </strong></p>
 <p><strong>III. Heat transfer in bacterial colony (analytical solution  1D)</strong></p>
-<p><strong>IV. Heat  transfer in bacterial colony (computational solution 2D and 3D)</strong></p></center>
+<p><strong>IV. Heat  transfer in bacterial colony (computational solution 2D and 3D)</p></center>
-<p><strong>I) Calculations for rate of heat production in E. coli:</strong></p>
+<p>I) Calculations for rate of heat production in E. coli:</strong></p>
 <font color="#FFFFFF"><ul>
    <li>800 mV electric potential drop of 4  electrons  generates  5.12 x 10-19 Joules    </li>
    <li>70% of electrons enter AOX pathway</li>
    <li>Assume time scale of ATP cycle to calculate  power </li>
-   <li><strong>Power  generated per cell is 1.6 x 10-13 Watt</strong></li>
+   <li>Power  generated per cell is 1.6 x 10-13 Watt</li>
 </ul>
 <p><strong>II) Heat transfer in liquid  culture:</strong></p>
@@ Line 116: / Line 116: @@
 <ul>
    <li>Density of bacterial culture can vary by 2  orders of magnitude</li>
-   <li><strong>Temperature  of system can be raised by 1K in 4 – 40 min. </strong></li>
+   <li>Temperature  of system can be raised by 1K in 4 – 40 min. </li>
 </ul>
 <p><strong>III) Heat transfer in bacterial colony (analytical solution)</strong><br />