Statistical mechanical model of coupled transcription from multiple promoters due to transcription factor titration - PubMed (original) (raw)

Statistical mechanical model of coupled transcription from multiple promoters due to transcription factor titration

Mattias Rydenfelt et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan.

Abstract

Transcription factors (TFs) with regulatory action at multiple promoter targets is the rule rather than the exception, with examples ranging from the cAMP receptor protein (CRP) in E. coli that regulates hundreds of different genes simultaneously to situations involving multiple copies of the same gene, such as plasmids, retrotransposons, or highly replicated viral DNA. When the number of TFs heavily exceeds the number of binding sites, TF binding to each promoter can be regarded as independent. However, when the number of TF molecules is comparable to the number of binding sites, TF titration will result in correlation ("promoter entanglement") between transcription of different genes. We develop a statistical mechanical model which takes the TF titration effect into account and use it to predict both the level of gene expression for a general set of promoters and the resulting correlation in transcription rates of different genes. Our results show that the TF titration effect could be important for understanding gene expression in many regulatory settings.

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Figures

FIG. 1

FIG. 1

(Color online) States and weights for three studied promoter architectures (a) simple repression, (b) repression with looping, and (c) repression exclusively due to looping. The last two promoter architectures differ only by the addition of two states to the exclusive looping architecture (third and eighth from the top), corresponding to RNAP and the main operator being simultaneously bound.

FIG. 2

FIG. 2

(Color online) Repression through DNA looping. The repressor binds to the main and auxiliary operators simultaneously looping the intervening DNA.

FIG. 3

FIG. 3

(Color online) Fold change as a function of repressor copy number (R) for gene copy numbers N = 1 (solid line), N = 10 (dashed line), and N = 100 (dotted line) for three different promoter architectures: (a) simple repression, (b) repression with looping, and (c) exclusive looping repression. For these plots we used operator binding energy −17.3 kB T (equivalent to the strongest known lac operator Oid [21]), the number of nonspecific sites as the genome length of E. coli (NN S = 5 × 106), number of RNAP P = 1000, and the looping energy Δ_F_loop = 10 kB T [2]. The RNAP promoter binding energy is assumed to be weak (p ≪ 1) [21,76].

FIG. 4

FIG. 4

(Color online) Fold change of a simple repressor with gene copy number N = 10 for three different TF binding site strengths, with strengths chosen to correspond to the range observed for real repressors. Stronger repressor binding leads to a steeper response in fold change around R ≈ N. The RNAP promoter binding energy is assumed to be weak (p ≪ 1), and the number of nonspecific sites NN S = 5 × 106.

FIG. 5

FIG. 5

(Color online) Effect of TF sequestration on fold change. (a) A repressor can bind to a reporter construct located in a single copy on the chromosome or to a binding site on a multicopy plasmid which leads to no gene expression. (b) Fold change of a simple repressor for different repressor binding site strengths, where the TF is subject to sequestration from 100 nonfunctional binding sites (Δ_εpl_ = −15 kBT). If the sequestration sites are much stronger than the simple repressor operator, the fold change remains constant until these sites have been filled. The RNAP promoter binding energy is assumed to be weak (p ≪ 1), and the number of nonspecific sites NN S = 5 × 106.

FIG. 6

FIG. 6

(Color online) Correlation coefficient between transcription rates of two equally strong promoters PA,PB for a single RNAP molecule (P = 1), as a function of probability pA = pB of one of the promoters being bound.

FIG. 7

FIG. 7

(Color online) States and weights for the simple activation regulatory motif [2].

FIG. 8

FIG. 8

(Color online) Two simple activators regulated by the same TF.

FIG. 9

FIG. 9

(Color online) Correlation coefficient between transcription rates of two positively regulated genes on a plasmid, as a function of (a) number of plasmids, (b) RNAP-activator interaction energy εap, (c) activator operator strength Δ_εad_, and (d) promoter strength Δ_εpd_. For fixed parameter values we use number of nonspecific sites NN S = 5 × 106, 10 plasmids, operator strength Δ_εad_ = −17.3 kBT, promoter strength Δ_εpd_ = −5 kBT, and interaction energy between TF and RNAP εad = −7 kBT.

FIG. 10

FIG. 10

(Color online) (a) Fold change in the simple repression architecture for fixed (N = 10) or Poisson distributed (mean N̄ = 10) promoter copy number. (b) Fold change in the exclusive looping repression architecture for fixed (N = 100) or Poisson distributed (mean N̄ = 100) promoter copy number. For these plots we use operator binding energy −17.3 kBT, looping energy 10 kBT, and number of nonspecific sites NN S = 5 × 106. The RNAP promoter binding energy is assumed to be weak.

FIG. 11

FIG. 11

(Color online) Correlation coefficient between transcription rates of two positively regulated genes located on 20 plasmids, as a function of number of TFs. Three different Gaussian TF copy number distributions are considered with standard deviations σ=0,12A,A. TF fluctuations constitute extrinsic noise, affecting expression of both genes, that hides the anticorrelation in transcription rates due to promoter entanglement. As parameter values we choose number of RNAP P = 1000, nonspecific sites NN S = 5 × 106, 20 plasmids, operator strength Δ_εad_ = −17.3 kBT, promoter strength Δ_εpd_ = −5 kBT, and interaction energy between TF and RNAP εad = −7 kBT.

FIG. 12

FIG. 12

(Color online) States and transition rates in a the simple repression architecture with no RNAP present. The rates correspond to “per molecule” rates, i.e., the total probability flux into the right, repressed state, is given by RkRonP(0).

FIG. 13

FIG. 13

(Color online) Fold change as a function of repressor copy number in the simple repression (formula image), repression with looping (formula image), and repression exclusively due to looping (formula image) promoter architecture, for N = 10 promoter copies. Solid lines correspond to thermodynamic model predictions and markers Gillespie simulated data. Here we use the parameters: kRon=1.0,kRoff=0.15(simplerepression),kRoff=0.075(looping),kRNAPon=3.0×10-5,kRNAPoff=1, _k_loop = 1, and _k_unloop = 6.8 × 10−4 in arbitrary inverse time units, chosen according to Eqs. (59), (60), (64). The standard deviations, acquired from three separate runs, are smaller than the marker size. Since the rates only enter as ratios in the state probabilities we use this freedom to set larger of the two rates to 1. As initial condition we set all promoters to the empty state, G = 10, RNAP copy number P = 1000, and repressor copy number R indicated by the x axis.

FIG. 14

FIG. 14

(Color online) States and transition rates in a simplified version of the repression with looping promoter architecture, with no RNAP and where the auxiliary operator is not allowed to be bound individually.

FIG. 15

FIG. 15

(Color online) Simple activation promoter architecture in the weak promoter approximation, neglecting RNAP binding to the empty promoter.

FIG. 16

FIG. 16

Correlation coefficient between transcription rates of two positively regulated genes on a plasmid (copy number N = 10) as a function of activator copy number. The solid line corresponds to thermodynamic model prediction, and dots correspond to Gillespie simulated data. Here we use the parameters: kAon=1.0,kAoff=0.15,kRNAPon=3.0×10-5,kRNAPoff=1,kRNAP∗on=0.033, and kRNAP∗off=1 in arbitrary inverse time units, chosen according to Eqs. (59), (60), and (69). The standard deviations, acquired from three separate runs, are smaller than the marker size. Since the rates only enter as ratios, we use this freedom to set the larger of the two rates to 1. As initial condition we set all promoters to the empty state, _G_1 = _G_2 = 10, RNAP copy number P = 1000, and activator copy number A indicated by the x axis.

FIG. 17

FIG. 17

(Color online) Transcription factor (TF) copy number vs number of binding sites, using two different protein censuses of E. coli. Protein copy numbers were determined using mass spectrometry [62] and fluorescence [7]. The number of binding sites was obtained from RegulonDB [24]. The solid line marks the boundary between depletable TFs (more binding sites than TF copies) and nondepletable (more TF copies than binding sites). For TFs forming dimers (e.g., CRP, Fis, GalR), this boundary is replaced by the dashed line. Due to incomplete knowledge about the E. coli regulatory system we expect the number of binding sites to be underestimated, and hence more TFs might belong to the depletable category than shown in the figure.

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References

    1. Buchler NE, Gerland U, Hwa T. Proc Natl Acad Sci USA. 2003;100:5136. - PMC - PubMed
    1. Bintu L, Buchler NE, Garcia HG, Gerland U, Hwa T, Kondev J, Phillips R. Curr Opin Genet Dev. 2005;15:116. - PMC - PubMed
    1. Bintu L, Buchler NE, Garcia HG, Gerland U, Hwa T, Kondev J, Kuhlman T, Phillips R. Curr Opin Genet Dev. 2005;15:125. - PMC - PubMed
    1. Buchler N, Louis M. J Mol Biol. 2008;384:1106. - PubMed
    1. Burger A, Walczak AM, Wolynes PG. Proc Natl Acad Sci USA. 2010;107:4016. - PMC - PubMed

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