Table 1.

A Summary of the Analytically Derived Expressions Used to Analyze Experimental Results

Comparison of Virological Assay Analyses
Assay (parameter)	Standard Method	New Method
Plaque (N0)	${\hat{N}}_0=D^{d_c}\left(\frac{1}{T}\sum _{t=1}^T{P}_{d_c,t}\right)$	$0=\sum _{d=d_c}^{d_{\text{max}}}\sum _{t=1}^T\frac{M\text{exp}\left(-\frac{{\hat{N}}_0}{QM{D}^d}\right)-M+P_{d,t}}{QM{D}^d\left[1-\text{exp}\left(-\frac{{\hat{N}}_0}{QM{D}^d}\right)\right]}$
		Initial guess: ${\hat{N}}_0^{\text{init}}=-QM{D}^d\text{ln}\left(1-\frac{1}{MT}\sum _{t=1}^T{P}_{d_c,t}\right)$
Endpoint dilution (N0)	RM: ${\text{log}}_{10}\left({\hat{N}}_0\right)=d_{50\text{\%}}+\frac{E_{d_{50\text{\%}}}-0.5T}{E_{d_{50\text{\%}}}-E_{d_{50\text{\%}}+1}}$	$0=\sum _{d=1}^{d_{\text{max}}}\frac{E_d-T+T\text{exp}\left(-\frac{{\hat{N}}_0}{Q{D}^d}\right)}{Q{D}^d\left[1-\text{exp}\left(-\frac{{\hat{N}}_0}{Q{D}^d}\right)\right]}$
	SK: ${\text{log}}_{10}\left({\hat{N}}_0\right)=d_{100\text{\%}}-\left[\frac{1}{2}-\sum _{d=d_{100\text{\%}}}^{d_{\text{max}}}\frac{E_d}{T}\right]{\text{log}}_{10}D$	Initial guess: ${\hat{N}}_0^{\text{init}}=\frac{-Q{D}^{d_c}}{2}\text{ln}\left[\left(1-\frac{E_{d_c}}{T}\right){\left(1-\frac{E_{d_c+1}}{T}\right)}^D\right]$
Luciferase reporter $\left(\mu =\frac{N}{M}\right)$	$\hat{\mu }=\frac{1}{L_{0}MT}\sum _{t=0}^T{L}_t^{\text{data}}$	$0=\frac{1}{T}\sum _{t=0}^T{L}_t^{\text{data}}-L_0{f}_{\text{max}}M{e}^{-\hat{\mu }}\sum _{r=0}^{N_0}\frac{r{\hat{\mu }}^r}{\left(K+r\right)r!}$
		Initial guess: ${\hat{\mu }}^{\text{init}}=\frac{1}{L_{0}MT}\sum _{t=0}^T{L}_t^{\text{data}}$

For virus quantification assays, such as the plaque and endpoint dilution assays, one typically wishes to estimate the number of initial viral particles N₀. For luciferase reporter infectivity assay, the ratio μ = N/M is desired. Our improved parameter estimation methods are listed next to standard methods currently used.