I'm working with the following equation:
$$MU=1000\gamma k [ONPG] \delta \frac{1}{V} \frac{N_z}{N_{cells}}$$
To which I would am trying to get to the following:
$$MU \times mL \times min \times 0.5=\frac{N_z}{N_{cells}}$$
The paper this is based off is called "Comparison and Calibration of Different Reporters for Quantitative Analysis of Gene Expression" if anyone would like some further context (p539). They define the following:
$$\gamma=\frac{0.0045}{\mu M_{ONP}}\times \frac{1.7mL}{1.4mL}=\frac{0.0055}{\mu M_{ONP}}=\frac{5500}{M_{ONP}}$$
$$k=\frac{138\times 10^6 M_{ONP}}{min} \times M_{LacZ} \times M_{ONPG} $$
$$[ONPG]=1.86mM$$
$$\delta=\frac{8.9\times 10^8}{mL}$$
$$V=1.2mL$$
So putting this all together using the first equation I get:
$$MU=1000\times \frac{5500}{M_{ONP}} \times \frac{138\times 10^6 M_{ONP}}{min} \times M_{LacZ} \times M_{ONPG} \times 1.86mM \times \frac{8.9\times 10^8}{mL} \times \frac{1}{1.2mL} \frac{N_z}{N_{cells}}$$
After cancelling $M_{ONP}$ and combining the first set of numbers:
$$MU=759\times10^{12} \times \frac{1}{min} \times M_{LacZ} \times M_{ONPG} \times 1.86mM \times \frac{8.9\times 10^8}{mL} \times \frac{1}{1.2mL} \frac{N_z}{N_{cells}}$$
Moving over $min$ and combining $mL$:
$$MU \times min =759\times10^{12} \times M_{LacZ} \times M_{ONPG} \times 1.86mM \times \frac{7.42\times 10^8}{mL^2} \times\frac{N_z}{N_{cells}}$$
Moving over one $mL$ and combining the rest of the numbers:
$$MU \times min \times mL=11\times10^{12} \times M_{LacZ} \times M_{ONPG} \times M \times \frac{1}{mL} \times\frac{N_z}{N_{cells}}$$
Now I am stuck with three concentrations ($M$), another $mL$ and a number that is no where near $0.5$. Does anyone have any ideas? Thanks!
