Bioinformatics Advance Access originally published online on September 16, 2008
Bioinformatics 2008 24(22):2639-2640; doi:10.1093/bioinformatics/btn494
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tCal: transcriptional probability calculator using thermodynamic model
College of Biological Sciences, China Agricultural University.
*To whom correspondence should be addressed.
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ABSTRACT |
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Summary: Thermodynamic model has been proposed as a realistic model of gene transcriptional regulation in bacteria, in which transcription probability calculation is based on physical interpretation of biological knowledge. We extend the published results in this area, and derive a relatively new model which could serve as a generalized form of previous results. To facilitate the application in gene network modeling studies, we implement our model in a Python module, ‘tCal’. With minimum programming efforts, user can use tCal to build transcription units, and either compute the transcription probabilities, or construct SBML models of regulatory networks.
Availability: tCal module and its online version can be found at: http://bioinformatics.cau.edu.cn/tCal.
Contact: zhensu{at}cau.edu.cn
Supplementary information: Supplementary data are available at Bioinformatics online.
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1 INTRODUCTION |
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Gene transcriptional regulation is one fundamental aspect of cellular activity, and detailed understanding has been achieved for the transcription pathway in bacteria (Browning et al., 2004). Modeling of this process is a key issue in computational biology and serves a fundamental basis for systems biology. The thermodynamic model is promising for this task, as it utilizes statistical mechanics to interpret experimental knowledge on bacterial transcriptional regulation, with some assumptions and simplification. This subject has been thoroughly described in recent papers (Buchler et al., 2003; Bintu et al., 2005a). Compared with empirical models, its major advantage is rational and rigorous quantitation of gene transcription probability under regulation, especially complex combinatorial regulation governed by multiple regulators. Bintu et al. (2005a) presented various formulas to compute transcriptional probability under combinatorial regulation, with emphasis on dual-regulator cases. Such results can be directly applied in modeling of such specific cases of bacterial gene transcription (Bintu et al., 2005b). However, in application it is cumbersome to choose correct formula for the transcriptional regulation system under study from a pool of complete formula set, which is yet to be established. Here by adding some plausible extensions to the modeling assumptions, a single formula is derived to calculate transcriptional probability. We show that our result could serve as a general form for many of the formulas presented in Bintu et al. (2005a), and has the potential to fit all simple combinatorial regulation schemes. To facilitate its application in gene regulatory network modeling studies, we implement the result in a Python programming module. In the following, we will briefly describe our model and usage of the module.
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2 RESULT |
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Our improvement to the model is based on the work of Bintu et al. (2005a), and here we will discuss the different assumptions we use. To calculate transcriptional probability under the thermodynamic model, it needs to sum the Boltzmann factors of all possible binding events to compute RNA polymerase (RNAP) specific-binding probability. This requires enumeration of all combinations of binding sites in the regulatory region (2s combinations from s binding sites). We use the ‘group interaction energy’
g to characterize the interaction between binding proteins, and the Boltzmann weight e–g/kBT reflects the likelihood of the co-binding event to happen. Negative g is assigned for the group of attracting binding proteins and positive g for the group of repelling ones. For those binding events that are unlikely to happen (e.g. co-binding of two proteins with overlapping binding sites), they could be marked as ‘forbidden’ during the configuration process to escape probability computation, as shown below. A single formula is thus derived to fit for all regulatory configurations. The detailed derivation process is described in the supplementary document, and the regulation factor Freg (Bintu et al., 2005a) is shown here, which is the most important component of probability formula: |
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rijd=
–
is the binding energy of regulator i at binding site j, compared with this regulator's background binding energy. rip is the interaction energy between regulator i with RNAP. The summation 
g and (g+gp) are performed for any groups of interactive regulators in the current binding state, g is the group interaction energy of the regulators and gp is their interaction energy with RNAP as a whole.
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3 APPLICATION |
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Above model is implemented in a Python module named ‘tCal’, which should run on any platforms with Python interpreter installed. With tCal, user can easily build and configure transcription models of target genes. As an example, we use tCal to model nine typical cases of transcription regulation in which target gene expression is controlled by two regulators with one binding site for each. The cases are categorized by regulator type (by row) and interaction between regulators (by column). Modeling results are presented as 3D-plots of the transcription probability fold change against regulator abundance (Fig. 1). Choice of the parameter values (Table 1) are based on the ‘benchmark’ energy values used in Bintu et al. (2005a). We use
g=0 to denote the independent regulation, which could be either due to inability of regulators to interact, or sufficient spacing between binding sites, and g<0 to denote the cooperative regulation, and g>0 for the repelling regulation. From the result, the cooperative regulation (C2 and C8) show significant synergistic effects when both regulators are abundant, compared with the independent regulation (C1 and C7). Such result displays characteristics of logical AND/OR operators, and is in accordance with those obtained by individual formulas (Bintu et al., 2005b). C4 and C5 show mixed effect of repressor and activator with equal DNA-binding strength (rd=–8kBT), which have not been discussed before. In C4, the repressor fails to inhibit transcription with a large amount of activator molecules in presence, due to the high likelihood of activator binding when repressor is not binding specifically. To achieve dominant effect of repression, either the binding strength of repressor needs to outweigh that of activator, or in case of equal binding strength, the repressor has to be able to ‘silence’ activator, as is demonstrated by C5. In this case, two regulators have great potential to associate (g=–8kBT), which leads to transcriptional repression (total interaction energy with RNAP: rAp+rBp+gp=6kBT). In C3, C6 and C9, two binding sites overlap and the co-binding events take high energy (g=10kBT). As from the probability plots, the failure of co-binding has very little effect compared with independent cases (C1, C4, C7), which indicates that the regulator co-binding contributes little in independent cases. Besides, excluding co-binding events (marked as forbidden) will produce very similar results as C3, C6, and C9 (data not shown). In general, our model is applicable to simple regulation schemes in which the mechanisms are clear and are covered by the assumptions. The transcription units as used in Figure 1 can be coupled to compose regulatory network. To facilitate interaction with other systems biology softwares, the SBML-format models can be created using tCal's formula export method. Using Python API of libsbml (Bomstein et al., 2008), the exported formula can be used to create ‘RateRule’ instance which is essential for creating SBML models. Demonstration programs for such purposes along with a short tutorial are also available on tCal's distribution website.
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Funding |
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TOPABSTRACT1 INTRODUCTION2 RESULT3 APPLICATIONFundingACKNOWLEDGEMENTSREFERENCES |
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National Basic Research Program of China (grant no. 2006CB100100).
Conflict of Interest: none declared.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 RESULT3 APPLICATIONFundingACKNOWLEDGEMENTSREFERENCES |
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The authors wish to thank three anonymous reviewers for their critical comments.
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FOOTNOTES |
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Associate Editor: John Quackenbush
Received on July 2, 2008; revised on August 27, 2008; accepted on September 12, 2008
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REFERENCES |
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TOPABSTRACT1 INTRODUCTION2 RESULT3 APPLICATIONFundingACKNOWLEDGEMENTSREFERENCES |
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Browning DF, et al. The regulation of bacterial transcription initiation. Nat. Rev. Microbiol. (2004) 2:1–9.[Medline]
Buchler NE, et al. On schemes of combinatorial transcription logic. Proc. Natl Acad. Sci. USA (2003) 100:5136–5141.
Bintu L, et al. Transcriptional regulation by the numbers: models. Curr. Opin. Genet. Dev. (2005a) 15:116–124.[CrossRef][Web of Science][Medline]
Bintu L, et al. Transcriptional regulation by the numbers: applications. Curr. Opin. Genet. Dev. (2005b) 15:125–135.[CrossRef][Web of Science][Medline]
Bomstein BJ, et al. LibSBML: an API library for SBML. Bioinformatics (2008) 24:880–881.
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