# Measurement

###### A Novel Approach to Measure

### Achievement

- Develop a new measurement approach to determine the carbon fixation ability of each strain
- Estimate the carbon fixation amount with our experiment result

### The Xylose Utilization Index (XUI)

In the total solution experiment,
we strive to measure the carbon fixation amount of each sample.
After reading numerous publications,
we found out that previous researches determine the efficiency of carbon fixation
via measuring the decrease of carbon dioxide concentration in the closed system or
measure
the weight percentage of ^{14}C radioisotope in the dry cell.
However, due to biosafety constrain of our lab, we can barely use the radioisotope.
Measuring the decrease of carbon dioxide concentration in the closed system is also
impractical for us since we have too much test samples.
A new method to measure multiple samples in the short period of time is developed
by our team.
We are able to evaluate the fixation efficiency of each sample with optical density
O.D. 600 and
xylose consumption. We have measure various construction to prove that the enzyme
of our construction
is necessary for carbon fixation.

The test samples below were incubated in a modified M9 medium which substitutes xylose for glucose. 1/1000 of Luria-Bertani (LB) medium was added to support trace elements. Since the concentration of LB medium is too low, it doesn’t contribute to the carbon source of the bacteria.

We defined a new index, Xylose Utilization Index (XUI), to describe the potential of carbon fixation. We can compare this index of each strain to find out the strain that has highest capacity of carbon fixation.

To define the XUI, we firstly made two assumptions:

- O.D. 600 of the sample has linear relationship to dry cell weight (biomass). Optical density is frequently used as a means of describing the cell density in the broth. We measured the dry cell weight of samples in different O.D. value and discovered that it has linear relationship. We conclude that we can utilize O.D. value to estimate the dry cell weight. 1 O.D. of BL21 (DE3) strain per litre yields the dry cell weight of 0.8 gram.
- The elemental formula of
*E. coli*should be fixed or varies within a small range. Although the formula may have variations in different growth condition, we assume that such error can be ignore during the following calculation.

Fig 1. shows the dry cell weight of BL21 (DE3) incubated in modified M9 xylose medium. A linear relationship between O.D. and dry cell weight is observed.

Combining these two assumptions, we can conclude that in a fixed O.D. 600 value, the composite weight of carbon is also fixed. Thus, O.D. 600 can be considered equivalent to carbon weight of the bacteria.

After these two assumptions,
the XUI is designed to evaluate the carbon fixation ability of each strain.
The definition of the index is xylose consumption over O.D. 600.
O.D. 600 measurement can be viewed as the weight of carbon of the bacteria.
The index shows the ratio of xylose consumption per biomass.
For wild type *E. coli*, it only consumes xylose (the sole carbon source
provided by the medium)
as its carbon source. Although some native *E. coli* pathway may utilize CO_{2}
(such as lipid synthesis), the amount is too small to be considered.
As for engineered strain, carbon dioxide can be utilized as its carbon source.
By producing same amount of carbon biomass, it requires less xylose.
We can thus compare the XUI of each strain to determine the strain that fix carbon.
The less the XUI in the sample, the more possibility that it fix carbon.

$${XUI = {{xylose \ consumption \ (g/l)} \over {O.D. 600}}}$$

We use the XUI to compare the carbon fixation efficiency of each strain and prove the function of each system. For the experiment result, please view the Result(hyperlink) page.

### Carbon Fixation amount estimation

To find out how much and how efficient genetically engineered *E.
coli* can fix
carbon dioxide, we use the material balance concept to evaluate the heterotrophic
CO_{2} fixation process.
Consider a system composed of a single component, the general material balance can
be written as:
$${\{Input\ to\ the\ system\}\ –\ \{Output\ to\ the\ system\}\ =\
\{Accumulation\ in\ the\ system\}}$$
A system can be defined as an arbitrary portion of a process considered for
analysis,
in which in this case, is an engineered carbon capturing *E. coli*.

The engineered *E. coli* BL21 (DE3) is cultured in M9 medium with formula
adjusted so that xylose is the sole carbon source. The aforementioned M9 Medium
contains
4 (g/l) xylose and 1/1000 LB medium (the carbon consumed from LB medium can be
ignored). By applying the law of conservation of mass, which states that mass
may neither be created nor destroyed, the material balance for carbon in an
engineered *E. coli* may simply be written as
$${\{C_{CO_2}\ in\}\ +\ \{C_{xylose}\}\ -\ \{C_{CO_2}\ out\}\ -\ \{C_{waste}\}\
=\ \{C_{biomass}\}...(1)}$$
Considering the difficulties in measuring carbon in *E. coli* metabolic
waste and
that C_{waste} would be positive, the equation reduces to
$${\{C_{CO_2}\ in\}\ -\ \{C_{CO_2}\ out\}\ ≥\ \{C_{biomass}\}\ -\
\{C_{xylose}\}...(2)}$$
Let {C_{CO2} net}= {C_{CO2} in} - {C_{CO2}
out}, equation (2) further simplifies to
$${\{C_{CO_2}\ net\}\ ≥\ \{C_{biomass}\}\ -\ \{C_{xylose}\}...(3)}$$
If C_{waste} is very small and negligible, we can obtain the net amount
of carbon
dioxide fixed over time. If, on the contrary, C_{waste} cannot be
neglected,
equation (3) allows us to estimate the minimum net amount of carbon dioxide
fixed.

C_{biomass} can be calculate by multiplying O.D. 600 to DCW and mass
percent of carbon in *E. coli* biomass. The O.D. 600 of engineered *E.
coli* is
measured after a 12-hour cultivation and the result obtained is 0.45O.D. . Yin
Li et al. reported that dry cell weight (DCW) of *E. coli* is
$${0.35g\over L ∙ 𝑂.𝐷. 600}$$
, determined by experiment. *E. coli* biomass contains 48% of carbon by
mass.
$${C_{biomass}\ =\ 0.4511\ ×\ 0.35\ ×\ 48\%}$$
$${=\ 0.0758\ g/L}$$

On the other hand, C_{xylose} can be calculated by multiplying the
amount of
xylose consumed per unit volume of broth to the mass percent of carbon in
xylose. Xylose consumption is calculated by using a DNS kit that measures the
concentration of reducing sugar and the result obtained is 0.1723g of xylose
consumed per liter of M9 medium. Carbon mass percentage of xylose
is 40%.
$${C_{xylose}\ =\ 0.1723\ ×\ 40\%\ =\ 0.0689\ g/L}$$
By equation (3)
$${C_{CO_2\ net}\ =\ 0.0758\ -\ 0.0689}$$
$${=\ 0.0069\ g/L}$$
Since the *E. coli* has been cultured for 12 hours, we can calculate the
rate of
carbon fixation by
$${Rate\ of\ carbon\ fixation\ =\ {𝐶_{𝐶𝑂_2\ 𝑛𝑒𝑡}\over 12}}$$
$${=\ {0.0069\over 12}}$$
$${=\ 0.575\ {mg\over L ∙hr}}$$
To find out how much carbon in biomass comes from the carbon in CO2 captured by the
heterotrophic microbes, we can divide equation (3) by the mass percentage of carbon
in biomass:

$${{{ \{ CO_{2 net}} \} \over \{ {C_{biomass}} \} } \geq {1 - { \{ {C_{xylose}} \} \over \{ {C_{biomass}} \} }}}$$

We can thus calculate the ratio with our experiment results:

$${{Ratio \ of \ carbon \ in \ CO_2 \ fixed \ to \ carbon \ in \ biomass} = {1 -{0.0689 \over 0.0758}} = 9.1 \%}$$

### References

- Gong, F., Liu, G., Zhai, X., Zhou, J., Cai, Z., & Li, Y. (2015).
Quantitative analysis of an engineered CO
_{2}-fixing*Escherichia Coli*reveals great potential of heterotrophic CO_{2}fixation. Biotechnology for Biofuels,8(1). doi:10.1186/s13068-015-0268-1 - Stockar, U. V., & Liu, J. (1999). Does microbial life always feed on negative entropy? Thermodynamic analysis of microbial growth. Biochimica Et Biophysica Acta (BBA) - Bioenergetics,1412(3), 191-211. doi:10.1016/s0005-2728(99)00065-1