vFitness: a webbased computing tool for improving estimation of in vitro HIV1 fitness experiments
 Jingming Ma^{1}Email author,
 Carrie Dykes^{2},
 Tao Wu^{1},
 Yangxin Huang^{3},
 Lisa Demeter^{2} and
 Hulin Wu^{1}
https://doi.org/10.1186/1471210511261
© Ma et al; licensee BioMed Central Ltd. 2010
Received: 7 January 2010
Accepted: 18 May 2010
Published: 18 May 2010
Abstract
Background
The replication rate (or fitness) between viral variants has been investigated in vivo and in vitro for human immunodeficiency virus (HIV). HIV fitness plays an important role in the development and persistence of drug resistance. The accurate estimation of viral fitness relies on complicated computations based on statistical methods. This calls for tools that are easy to access and intuitive to use for various experiments of viral fitness.
Results
Based on a mathematical model and several statistical methods (leastsquares approach and measurement error models), a Webbased computing tool has been developed for improving estimation of virus fitness in growth competition assays of human immunodeficiency virus type 1 (HIV1).
Conclusions
Unlike the twopoint calculation used in previous studies, the estimation here uses linear regression methods with all observed data in the competition experiment to more accurately estimate relative viral fitness parameters. The dilution factor is introduced for making the computational tool more flexible to accommodate various experimental conditions. This Webbased tool is implemented in C# language with Microsoft ASP.NET, and is publicly available on the Web at http://bis.urmc.rochester.edu/vFitness/.
Background
The replication rate (or fitness) between viral variants has been investigated in vivo [1, 2] and in vitro [3–7] for human immunodeficiency virus (HIV). The lack of a consensus on how to measure fitness makes it difficult to determine if the replication capacity is important in disease progression. An accurate method to calculate fitness along with an easy to use tool will be valuable to virologists who study virus fitness.
Although the importance of HIV fitness in disease progression is unknown, the fitness itself plays an important role in drug resistance [8]. In order to develop a better understanding of viral fitness, Marée et al. proposed a mathematical model to describe the dynamics of viral competition between a wildtype virus and a mutant virus, and presented a formula to calculate the relative fitness 1+s based on data collected from two time points during the course of the experiment [6]. Here, s is the selection coefficient [9]. If there are more than two time points, investigators must choose a pair of time points for the calculation of relative fitness, and the formula does not provide a way to obtain a more accurate estimation over all the observed data. Bonhoeffer et al. proposed a more complicated approach for estimation of viral fitness from timeseries data [3] based on the work of Marée et al [6]. Most recently, Wu et al. combined a mathematical model and statistical methods for estimation of virus fitness in growth competition assays [7], which is more in line with population biologist's definition of fitness [9] than the work of Marée et al. [6].
In this paper, we present a Webbased computing tool based on linear regression methods for improving the estimation of in vitro HIV1 virus fitness measured by the growth competition experiment [7]. We will briefly describe the methods and models used in this computing tool, including the growth competition experimental design, a differential equation model, the leastsquares regression, and the linear regression with measurement error. Then we will describe software specifications, like the graphic user interface for the estimation, and dilution factors for various experiments. With the data from two experiments of in vitro HIV1 growth competition assay, we use this Webbased tool to estimate the fitness parameters and compare the estimation results with twopoint calculations used in previous studies. The Webbased tool is implemented in C# with Microsoft ASP.NET. We also implemented validation controls into the web interface to help users input the correct data. The twopoint calculation of virus fitness is also provided in this tool for the purpose of comparison.
Implementation
Growth Competition Assay of HIV1
A growth competition assay developed by Dykes et al. is used here to measure HIV1 replication fitness by using flow cytometry to determine the relative proportion of test (mutant) and reference (wildtype) viruses [4]. PM1 cells were infected with two virus stocks, each virus expressed a unique marker for expression that is detected on the surface of the infected cell. After 1 hour incubation at 37°C, unbound viruses were washed out with phosphatebuffered saline (PBS). Cells were then seeded in medium and cultured at 37°C. Half of the culture was removed and fresh medium were added in the culture on day 3, 4, 5, and 6. Cells removed from culture were stained with antibodies specific to the markers for infection, and fixed before analysis by flow cytometry. The numbers of wildtype or mutant infected cells are calculated by multiplying the percentage of cells determined by flow cytometry with the absolute number of viable cells in the culture measureed by automated cell counting.
Modeling
where s is the selection coefficient [9].
Linear Regression
Multiple data points
where two variables m_{ j }and w_{ j }form a linear relationship. Therefore, we know that the parameter p can be estimated by linear regression with the observed values of wildtype infected cells and mutant infected cells. Similarly, we can use the linear regression method to get the estimations for parameters r and d. Finally, the relative fitness 1+s can be estimated by exp(d) as indicated in Eq.(6). The following sections will briefly list two linear regression methods, the leastsquares approach and the measurement error models, which will be used in our computation tool.
Leastsquares approach
Linear regression with measurement errors
For most biologists who are interested in virus fitness, using those formulas to calculate the regression coefficient would be cumbersome, timeconsuming, and impractical. Therefore, we developed a Webbased computing tool, vFitness. Investigators can use different statistical methods to improve the estimation of viral fitness.
Software Development
Web application
We have implemented a Webbased computing tool in C# language with ASP.NET under Microsoft .NET Framework, which provides a means to program Web pages on the Web server facilities of Internet Information Services (IIS). The code of this computing tool runs on the server machine, and investigators can use their web browser to estimate fitness.
Graphic user interface
This computing tool provides the graphic user interface forinvestigators to estimate the relative fitness in competitionexperiments. Investigators just need to type in the observed valuesfor wildtype infected cells and mutant infected cells in therequired format (values delimited by comma), along with theparameters (δ_{m}, δ_{w}). Then, the estimation of virus fitness can be easily obtained by submitting the calculation request. This computing tool also provides the validation controls to help users to input correct values for calculation. Four types of validation controls (Range, Compare, RequiredField, RegularExpression) have been used to verify the input values. For example, an error message will show up if the observations of T_{m} are not delimited by commas. The server code also verifies the input values for error checking. One validation is to make sure that the number of timepoints is equal to the number of observations.
Dilution factor
Since the experimental design involves replacing half the culture with fresh media at each time point, we developed the graphic interface to accommodate the half dilution in growth competition assays and the other dilutions as well.
For an in vitro growth competition assay with a half dilution [4, 6], half the medium is taken out from the culture for counting and then thrown away at each time point. The observed data are the data from the half volume. So, the total infected cells in the initial culture would be two times the observed data, which results in a dilution factor of 2. The calculation model here is based on the total number of infected cells relative to the initial culture. The only exception is the estimation of parameter d, which depends on the ratio of two observations T_{m} and T_{w} at the same timepoint in Eq.(5). Two examples of the dilution factor are given as follows,

If the half dilution is taken at every time point of Day 3, 4, and 5, the corresponding dilution factors would be 2, 4, and 8;

If one third of testing medium is taken away for counting at each time point of Day 3, 4, 5, and 6, the dilution factors would be 3, 4.5 (or 9/2), 6.75 (or 27/4), and 10.125 (or 81/8).
Missing data
If a dataset is missing at one time point, we can ignore it andcontinue to estimate fitness parameters with the rest of data. Forexample, if the data from Day 4 of a 5day experiment on Days 3, 4,5, 6, and 7 (half dilution at each time point) was missing, thedilution factors from Day 3 to Day 5 would be 2 to 8 since anadditional dilution was made on Day 4.
Note that the above case is different from the case of four observations at Day 3, 5, 6, and 7, in which no dilution takes place on Day 4 and the dilution factors are still 2, 4, 8, and 16.
Software deployment
This Webbased computing tool has been deployed on a server computer where the Windows 2003 operating system is running. The web server must run IIS (Internet Information Services), FrontPage Server Extensions and must have the .Net Framework installed. This computing tool can be freely used on the Web at http://bis.urmc.rochester.edu/vFitness/.
Results
HIV1 replication fitness experiments
Observation of infected cells in AT1WT/AT2V106I fitness test
Number of infected cells  Day 3  Day 4  Day 5  Day 6 

T _{w}  62,169  161,525  1,293,863  823,368 
T _{m}  284,200  410,025  4,955,738  5,325,275 
Observation of infected cells in AT1WT/AT2Y188C fitness test
Number of infected cells  Day 3  Day 4  Day 5  Day 6 

T _{w}  47,469  140,175  831,250  645,299 
T _{m}  199,369  334,863  1,323,350  1,408,831 
Fitness estimation by statistical methods
Fitness estimation from AT1WT/AT2V106I experiment
Method  p(SD)  r(SD)  d(SD)  1 + s 

LS  0.9988 (0.0831)  0.9970 (0.106)  0.1157 (0.353)  1.1226 
MEr  1.0023 (0.0835)  1.0026 (0.107)  
MEv  0.9974 (0.0836)  0.9945 (0.107)  
AM  1.1862  1.6546  0.1157  1.1226 
Fitness estimation from AT1WT/AT2Y188C
Method  p(SD)  r(SD)  d(SD)  1 + s 

LS  0.8532 (0.0471)  0.8104 (0.0557)  0.2181 (0.271)  0.8040 
MEr  0.8543 (0.0471)  0.8119 (0.0558)  
MEv  0.8486 (0.0476)  0.8029 (0.0567)  
AM  0.9838  1.0787  0.2181  0.8040 
Estimation with missing data
Parameter p estimation with missing data in AT1WT/AT2Y188C
Missing data  LS  MEr  MEv  AM 

on Day 4  0.8612  0.8620  0.8551  1.0756 
on Day 5  0.8773  0.8784  0.8677  0.8645 
Comparison with twopoint calculation
Parameter p based on twopoint calculations
Pair of timepoints  Day 3 & 4  Day 3 & 5  Day 3 & 6  Day 4 & 5  Day 4 & 6  Day 5 & 6 

AT1WT/AT2V106I  0.7261  0.9673  1.0563  1.1256  1.2329  1.7069 
AT1WT/AT2Y188C  0.7521  0.8152  0.8943  0.8635  0.9770  1.3360 
Conclusions
We have developed a Webbased computing tool for improving the estimation of HIV1 fitness. The tool is based on a mathematical model and linear regression methods which use multiple measurements over time. Two experiments of HIV1 fitness were completed in this study using growth competition (one with AT2V106I mutant virus, and the other with AT2Y188C mutant virus), and the experimental data has been applied to evaluate the fitness estimation by this Webbased computing tool. The leastsquares approach and measurement error models fit the fitness estimation of HIV1 growth competition, even when data points are missing. It provides an easy way to get a more accurate estimation by using all observations in a fitness experiment.
For comparison, this computing tool also provides the twopoint calculation used in the previous studies. Our data has shown that the calculation of the fitness parameter can be very different depending on the pair of time points chosen. Therefore, using all time points to calculate fitness will incorporate the variability from day to day. This computing tool is implemented in C# with Microsoft ASP.NET. The tool provides a graphic user interface and validation controls. Introducing the dilution factor makes it more adaptable to different experimental designs. In this study we competed mutant and wildtype viruses. However, it can be used with any two competing strains of virus by letting W represent one of the strains. This computing tool can be freely used on the Web at http://bis.urmc.rochester.edu/vFitness/.
Availability and requirement
Project name: vFitness
Project home page: http://bis.urmc.rochester.edu/vFitness/
Operating system: Platform independent, Web application
Program language: C# with ASP.NET
Any restrictions to use by nonacademics: license needed
Declarations
Acknowledgements
The authors are grateful for financial support from NIH/NIAID R01 AI041387, R01 AI065217, R01 AI087135, R21 AI078842, P30 AI078498, N01 AI50020, N01 AI50029, N01 AI70008, HHSN272200900041C, and University of Rochester Center for AIDS Research.
Authors’ Affiliations
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