# Integrated modeling and experimental approach for determining transcription factor profiles from fluorescent reporter data

- Zuyi Huang
^{1}, - Fatih Senocak
^{1}, - Arul Jayaraman
^{1}Email author and - Juergen Hahn
^{1}Email author

**2**:64

**DOI: **10.1186/1752-0509-2-64

© Huang et al; licensee BioMed Central Ltd. 2008

**Received: **21 March 2008

**Accepted: **17 July 2008

**Published: **17 July 2008

## Abstract

### Background

The development of quantitative models of signal transduction, as well as parameter estimation to improve existing models, depends on the ability to obtain quantitative information about various proteins that are part of the signaling pathway. However, commonly-used measurement techniques such as Western blots and mobility shift assays provide only qualitative or semi-quantitative data which cannot be used for estimating parameters. Thus there is a clear need for techniques that enable quantitative determination of signal transduction intermediates.

### Results

This paper presents an integrated modeling and experimental approach for quantitatively determining transcription factor profiles from green fluorescent protein (GFP) reporter data. The technique consists of three steps: (1) creating data sets for green fluorescent reporter systems upon stimulation, (2) analyzing the fluorescence images to determine fluorescence intensity profiles using principal component analysis (PCA) and K-means clustering, and (3) computing the transcription factor concentration from the fluorescence intensity profiles by inverting a model describing transcription, translation, and activation of green fluorescent proteins.

We have used this technique to quantitatively characterize activation of the transcription factor NF-κB by the cytokine TNF-α. In addition, we have applied the quantitative NF-κB profiles obtained from our technique to develop a model for TNF-α signal transduction where the parameters were estimated from the obtained data.

### Conclusion

The technique presented here for computing transcription factor profiles from fluorescence microscopy images of reporter cells generated quantitative data on the magnitude and dynamics of NF-κB activation by TNF-α. The obtained results are in good agreement with qualitative descriptions of NF-κB activation as well as semi-quantitative experimental data from the literature. The profiles computed from the experimental data have been used to re-estimate parameters for a NF-κB model and the results of additional experiments are predicted very well by the model with the new parameter values. While the presented approach has been applied to NF-κB and TNF-α signaling, it can be used to determine the profile of any transcription factor as long as GFP reporter fluorescent profiles are available.

## Background

Systems Biology seeks to develop models for describing cellular behavior on the basis of regulatory molecules such as transcription factors and signaling kinases. The control of gene expression by transcription factors is an integral component of cell signaling and gene expression regulation [1, 2]. Different transcription factors exhibit different expression and activation dynamics, and together govern the expression of specific genes and cellular phenotypes [3]. An important requirement for the development of these signal transduction models is the ability to quantitatively describe the activation dynamics of transcriptions so that parameters can be estimated for model development. The activation of transcription factors under different conditions have been conventionally monitored using protein binding techniques such as electrophoretic mobility shift assay or chromatin immunoprecipitation [4]. While these techniques provide snapshots of activation at a small set of single time points, they can yield only qualitative or semi-quantitative data at best. This approach also requires the use of multiple cell populations for each time point at which transcription factor activation is to be measured, and often, the true dynamics of transcription factors are not captured due to limited sampling points and frequencies. Hence, these methods are not ideal for investigating time-dependent activation of transcription factors in a quantitative manner.

In this study, we use an integrated modeling and experimental strategy for deriving transcription factor activation rates from GFP-based fluorescent reporter systems. Using GFP reporter data for the activation of the transcription factor NF-κB by the cytokine TNF-α, (Figure 1C), we demonstrate that NF-κB activation dynamics can be accurately determined from GFP reporter profiles. The quantitative data that is determined from the presented approach can be used to update models of signal transduction pathways. This is illustrated by first developing a model describing TNF-α signal transduction based upon the models presented by Rangamani and Sirovich [10] and Lipniacki et al. [11] and then re-estimating model parameters. In a final modeling step, the most important parameters of the model are estimated from the data obtained in this work. The presented approach is not limited to NF-κB and can be used to determine the activation profile of any transcription factor as long as GFP reporter fluorescent profiles are available.

## Methods

### Reagents

All cell culture reagents including, Dulbecco's modified Eagle's Medium (DMEM, 4.5 g/L glucose), Bovine serum (BS) were purchased from Hyclone (Logan, UT). Human insulin and penicillin/streptomycin were purchased from Sigma (St. Louis, MO).

### Cell culture

The generation of a NF-κB reporter cell line has been described earlier [5]. Briefly, a reporter plasmid containing 4 tandem repeats of the NF-κB DNA binding sequence upstream of the CMV-minimal promoter and a 2 h half-life variant of the enhanced green fluorescence protein (d2EGFP) was stably introduced into H35 rat liver hepatoma cells by electroporation and selected based on neomycin resistance. Reporter cells were grown in DMEM supplemented with 10% v/v BS, penicillin (200 U/ml), and streptomycin (200 μg/ml).

### Reporter gene assays

H35-NF-κB cells were grown in 6-well tissue culture dishes (Corning, NY) to ~70% confluence prior to the experiment. Reporter cells were stimulated for 30 minutes, 2 hours, and 4 hours or continuously with either 10 ng/mL or 25 ng/ml TNF-α (R&D Systems). All experiments were run in triplicate.

### Fluorescence microscopy

GFP measurements were made using a Axiovert 200 M fluorescence microscope (Zeiss, Thornwood, NY). Cell culture dishes were placed in a controlled environment chamber in the microscope and maintained at 37°C and 10% CO_{2} throughout the experiment. Multiple imaging locations (3 per culture well) were randomly selected and the positions marked before the addition of TNF-α using the 'mark and find' feature of the using the Zeiss AxioVision imaging software. Fluorescence and phase contrast images were obtained at the marked positions throughout the duration of the experiment using a 20X objective every hour for 16 h using an AxioCam MrM digital camera.

### Image Analysis

*M*(

*i*,

*j*,

*k*) refer to the position of a particular pixel on the image, i.e., the

*i*-th row and

*j*-th column, and the third dimension refers to the red (

*k*= 1), green (

*k*= 2), or blue (

*k*= 3) value of the pixel. It is required to transform this three dimensional tensor,

*M*, to a two-dimensional matrix,

*X*:

Principal component analysis can be performed on *X* to determine pixels with similar brightness in the images [12]:

*X* = *TP*^{T}+*E*

*T*is the score matrix,

*P*is the loading matrix, and

*E*is the residual between the actual image data and the reconstruction by PCA. The columns of

*P*represent principle components of the image data matrix, while the columns of

*T*are the projections of the image data matrix onto the principle components. An illustration of the data and the first principal component (PC1) is shown in Figure 2. The projection of a point onto PC1 can be used as a measure for clustering the pixel brightness into different sets via K-means clustering. Figure 3 illustrates the procedure of fluorescent cell searching based on K-mean clustering and PCA. In an initial step PCA is used to divide the pixels of the image into two clusters based upon their projection onto PC1. K-means clustering iteratively updates the pixels and centroids of the two clusters until the sum of distances from all the pixels in each cluster is minimized. The cluster with the larger variation is divided in a next step. The centroids of the two new clusters, which are determined by PCA, and the centroid of the un-divided cluster are used as the initial centroids of the three clusters for K-means clustering, which then sorts the pixels of the image belonging to one of the three clusters. This procedure can be repeated until any number of desired clusters is obtained. The clusters with higher fluorescent intensity are considered to represent the cells which show a significant level of fluorescence. Once the cell region has been determined it is possible to compute the average fluorescence intensity by the following formula:

*I*_{f,k}refers the fluorescent intensity of the *k*_{th} pixel in a fluorescent cell region, *I*_{b,k}refers the fluorescent intensity of the *k*_{th} pixel belonging to the background, *N*_{
f
}is the total number of pixels in the fluorescent cell region, *N*_{
b
}is the total number of pixels in the background. For a RGB image, the fluorescent intensity *I* is defined as the sum of the values of red and green and blue of each pixel. The reason for subtracting the intensity of the pixels representing the background is to reduce measurement noise due to brightness variations.

### Model Development

_{t}from Lipniacki et al.'s model. The rationale behind this assumption is that c-IAP and cgen

_{t}are both involved in transcription of DNA.

*C*

_{NF-κB}is the concentration of activated NF-κB in the nucleus,

*m*is the mRNA concentration,

*n*is the concentration of GFP, and

*f*corresponds to the concentration of activated GFP. The values of the parameters shown in equation (5) are given in Table 1. The procedure for estimation of

*C*is described below.

Parameters for the model shown in equation (5).

Parameter | Value | Parameter | Value |
---|---|---|---|

| 373 1/hr |
| 0.347 1/hr |

| 0.45 1/hr |
| 108 nM |

| 780 1/hr |
| 5 nM |

| 0.5 1/hr |
| 0 nM |

The experimental measurements consist of the fluorescence intensity, *I*, as seen on the images which is directly proportional to the concentration of activated green fluorescent protein:

*f* = Δ*I*

where Δ is the ratio between activated GFP and computed fluorescence intensity.

As *I* can be obtained from the fluorescence images that have been processed by the procedures described in the image analysis section, the dynamics of NF-κB can be computed by solving an inverse problem involving equations (5).

## Results

*C*

_{NF-κB}from the fluorescence intensity profile

*I*. This analytical solution treats equation (5) as a static nonlinearity

*f*(

*s*) as a function of

*u*(

*s*):

*u*(

*s*), we opted for

*u*(

*s*) represents a concentration profile of

*C*

_{NF-κB}that shows damped oscillatory behavior as has been reported in the literature [13]. Substituting equation (10) into equation (9) and performing an inverse Laplace transform results in:

where *A*_{1}, *A*_{2}, *A*_{3}, *A*_{4}, *A*_{7}, and *ϕ* are constants with the values given in 'Additional file 2'.

*ε*,

*ω*

_{ n }and

*T*

_{ α }are estimated by fitting

*f*(

*t*) to the experimental data for each experiment. The concentration of NF-κB is then given by:

The values of *C* from equation (7) and Δ from equation (6) only need to be estimated once and can be assumed to be constant for all future experiments. We have chosen the concentration profile for NF-κB as reported in the paper by Hoffman et al. [13], which corresponds to a stimulation with 10 ng/ml of TNF-α, as the input, and have estimated *C* and Δ from experimental data that we have collected for stimulation with 10 ng/ml of TNF-α. The value of *C* was determined to be 108 nM and Δ was found to be equal to 2.5562 × 10^{4}. It should be noted that some of the data derived from a stimulation with 10 ng/ml of TNF-α was used for determining these parameter values, while other data points will be used for testing model. Figure 7A shows the fit of equation (11) to the data generated by this experiment.

*C*and Δ are constant for these experiments, however, the values for

*ε, ω*

_{ n }and

*T*

_{ α }are estimated separately for each data set. The corresponding concentration profiles for NF-κB, as computed by equation (12) are shown in Figure 8. It can be seen that stimulation with higher concentrations of TNF-α results in larger long-term concentrations of NF-κB as well as in higher peak concentrations. One important aspect of this procedure is that the data obtained is quantitative (i.e., numerical values of the NF-κB profile at each time point are obtained) and not merely qualitative.

*c*

_{3},

*k*

_{1p}, and

*k*

_{ r }are good candidates for estimation. Nonlinear least square routines in MATLAB were then used to estimate these three parameters. The estimated values were found to be 0.0104, 0.0740 and 2.50, respectively. Since the data derived from the stimulation with 10 ng/ml of TNF-α was not used for estimating these parameters, this data set can be used for validating the accuracy of the updated model. Figure 9 shows the model prediction for 10 ng/ml of TNF-α together with the experimental results derived from the described image analysis procedure. It can be concluded that the updated model predicts experimental data very well.

## Discussion

In this study, we have demonstrated that transcription factor activation profiles can be quantitatively extracted from fluorescence reporter data. The proposed approach was effective in deriving transcription factor activation rates from GFP profiles generated from NF-κB reporter cells stimulated with 10 – 50 ng/mL of TNF-α, a concentration range that is commonly used in cell culture experiments [5, 14] and reported to result in strong activation of NF-κB [8]. However, predicting NF-κB activation at lower concentrations of TNF-α (< 10 ng/mL) was not as effective due to low levels of GFP signal. This is evident from Figure 7B which shows a better correlation between the model and experimental data at higher (13 and 19 ng/mL) than at lower (6 ng/mL) TNF-α concentrations. Therefore, while our method is effective for moderate-to-high levels of activation, further improvement (e.g., in the image analysis methods) is needed to increase the GFP signal/noise ratio for effectively predicting profiles of low abundance transcription factors.

Another discrepancy between the model and experimental data is predicting long-term NF-κB activation profiles. The data in Figure 7B shows that fluorescence decreases after ~11 h even though the stimulus (TNF-α) is continually present, with the decrease being more pronounced at the higher concentrations. However, this decrease is not reflected in Figure 7B which shows NF-κB levels being constant beyond 11 h as the assumed model structure from equation (10) cannot represent this decrease. It is possible to postulate a different profile for the transcription factor, resulting in differences in equation (10), e.g., one that can reflect such a decrease. However, it is not clear if the decrease in fluorescence observed after ~11 h of stimulation results from experimental artifacts (i.e., fluorescence photobleaching and cell death arising from cells being repeatedly exposed to UV light for imaging) or is a real biological phenomenon (i.e., consequence of change in gene expression arising due to constant stimulation with TNF-α). A better understanding of long-term activation is needed to evaluate this behavior.

It should also be noted that the model describing the activation of NF-κB by TNF-α is not required for deriving NF-κB profiles from GFP profiles. However, use of the 1^{st} principles model enables us to estimate model parameters using the data and thereby refine the model describing activation of NF-κB by TNF-α, so as to develop a systems level understanding of TNF-α signaling. In this paper, we have utilized the fact that a considerable body of literature is present on TNF-α induction of NF-κB activation. Previously developed models and experimental data [13] suggest that NF-κB exhibits oscillatory behavior upon exposure to TNF-α. However, our overall approach for deriving transcription factor activation profiles is also valid for other transcription factors where the activation profile is not well characterized. In such cases, it will be necessary to assume different transcription factor activation profiles and verify the model prediction by comparing the predicted fluorescence intensity profiles with the experimental data.

In summary we have developed a methodology for quantitatively determining transcription factor profiles. This technique makes use of fluorescence microscopy images from a GFP reporter system for transcription factor activation and involves solving an inverse problem to determine the transcription factor profile from the fluorescence intensity dynamics. Data generated by this method can then be used to estimate parameters for signal transduction pathway models. This technique was applied to the activation of NF-κB by TNF-α, however, it can be used to determine transcription factor profiles for any system where limited qualitative knowledge about the transcription factor dynamics exists.

## Declarations

### Acknowledgements

The authors gratefully acknowledge partial financial support from the National Science Foundation (Grant CBET# 0706792) and the ACS Petroleum Research Fund (Grant PRF# 48144-AC9).

## Authors’ Affiliations

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