Transcription: Pausing and Backtracking: Error Correction Mamata Sahoo and Stefan Klumpp Theory and Bio-systems group, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany
Transcription ◮ Transcription is the efficient regulatory process in cells,organisms and tissues → Control the complex form of gene expression. ◮ what happens? ◮ The genetic information → stored in DNA → RNA transcript. ◮ How? ◮ Transcription → RNA polymerase moves along the length of a DNA template by a single base pair per stochastic nucleotide addition → creating a complementary RNA.
Transcriptional pausing ◮ 1 Heterogeneity in transcription rate → Transcription is not continuous ⇒ interrupted by pausing events. ◮ Pauses:RNAP gets halt for times → forms inactive configuration. ◮ 2 Two general classes of Pauses → most frequent. 1 K. Adelman et al., PNAS 99 , 13538(2002) 2 I.Artsimovitch et al., PNAS 97 , 7090(2000)
Backtracking during transcription: Backtracking pauses ◮ 3 Backtracking occurs in three phases. ◮ Phase 1: Backtracking ◮ Phase 2: Sliding → diffusional in nature. ◮ Phase 3: Recovery of transcription 3 J.W. Shaevitz, et al., Nature 426 , 684(2003)
Questions Addressed? ◮ What happens to the transcription → pause and backtracking ? ◮ Pauses have negative effect on transcription ⇒ High transcription rate requires the pausing events to be suppressed. ◮ Backtracking pauses → automatically suppressed by the trailing RNAP from behind. However, backtracking is required for the error correction and further recovery of transcription. ◮ Making a pause → creating an error, Cleaving the transcript → Correcting the error. ◮ Questions?? ◮ What fraction of errors are corrected?? ◮ How the efficiency of error correction limited controlled?? ◮ How the accuracy can be improved??
Model studied for transcription D D D k c D 1 D k c k c ′ ǫ α p ǫ ǫ ǫ
Transcription with pausing and backtracking 0.012 without Pausing 0.01 with pause+backtracking P=0.0 0.008 P=0.00007 D 1 =0.28, D=0.07 P=0.0007 K c =0.07 P=0.007 0.006 J 0.004 0.002 0 α 0 0.02 0.04 0.06 0.08 0.1 ◮ Both initiation and elongation limited. ◮ 4 Low density and maximal current phase. ◮ At high transcription intiation rate → transcription starts limiting by elongation. ◮ Strongly affected by pausing events → elongation limited regime. ◮ Suppresses ⇒ with pausing and backtracking. 4 L.B. Shaw, et al., Phys.Rev.E 68 , 021910(2003)
Single RNAP transcription: Efficiency of error correction (fec) D D D 1 D k c ′ ǫ p k c ǫ ǫ ǫ P ∞ m = 1 K c P m ◮ Efficiency of error correction, fec = P ∞ m = 1 K c P m + ǫ 1 P m − 1 1 ◮ For single RNAP transcription, fec = ǫ 1 1 + P ∞ m = 1 Kc Pm ◮ Following the relation, fec = K c a K c a + ǫ 1 ( 1 − a ) ; ( 4 D 2 + K 2 a = ( 1 + K c 1 � 2 D ) − c + 4 K c D − 4 DD 1 ) . 2 D � = ( 1 + K c 2 D ) − K c ( 1 + 4 D K c ) (for D = D 1 ) . 2 D
Fec with diffusive rate ( D ) 1 D 1 =0.28, D=0.007 D 1 =0.28, D=0.07 K c =0.07 0.9 D 1 =0.28, D=0.2 D 1 =0.28, D=0.4 0.8 0.7 fec 0.6 0.5 0.4 0.3 0 0.025 0.05 0.075 α 0.1 0.125 0.15 0.175 0.2 ◮ Fec is also both initiation and elongation limited. ◮ Increase of D affect strongly in the elongation limited regime. ◮ Strong diffusivity suppresses the error correction ⇒ RNAP spends much time in diffusive manner in any of the backtracked sites.
Fec with backward stepping rate( D 1 ): Single RNAP and Multi-RNAP transcription 1 1 0.9 0.9 α=0.0 0.8 K c =D=0.07 0.8 α=1.0 α=0.0 K c =D/10=0.007 0.7 α=1.0 0.7 0.6 0.6 fec fec 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0 0.1 0.2 0.3 D 1 0.4 0.5 0.6 D 1 ◮ Fec in multi-RNAP transcription is always reduced comparatively with single-RNAP transcription ⇒ Lack of free spaces that restricts diffusion of backtracked RNAP. ◮ The difference is strongly affected for higher D 1 regime. ◮ Further increase of K c reduces the difference between both cases ⇒ Push back effect of the trailing RNAP from behind in the multi-RNAP transcription.
Fec with the cleavage rate( K c ):Single-RNAP and Multi-RNAP transcription 1 1 α=0.0 0.8 0.8 D 1 =0.28, D=0.07 α=1.0 α=0.0 D=D 1 =0.07 α=1.0 0.6 0.6 fec fec 0.4 0.4 0.2 0.2 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 K c 0.4 0.5 0.6 K c ◮ Fec for single-RNAP transcription is always above the fec for multi-RNAP transcription ⇒ Available free spaces for error correction. ◮ Fec for multi-RNAP transcription is always reduced ⇒ Dense traffic effect. ◮ Error correction in multi-RNAP case is improved for higher K c . Further improvement is achieved with increase in D 1 .
Fec with both cleavage rate( K c ) and backward stepping rate( D 1 ) α=0.0 α=1.0 D 1 0.1 0.1 0.01 0.01 0.01 0.1 0.01 0.1 K c ◮ Fec is strongly controlled both by D 1 and K c . ◮ Error correction → Strongly improved increasing both by backward stepping rate, D 1 and cleavage rate, K c .
Fec with distance(L) between an active RNAP and a paused RNAP 1 0.9 0.8 Simulation Analytical 0.7 0.6 fec 0.5 D1=D=K c =0.07 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 L ◮ fec ( L ) = fec single max { 1 − exp ( − ( L / L 0 )) } ◮ Approximation: L 0 = K c . ǫ ◮ Gap distribution, P ( L ) = ( α ǫ ) L . ǫ )( ǫ − α ◮ fec increases with the distance: More free space available for error correction. ◮ Larger gap size ⇒ Better error correction.
Efficiency of error correction:Multi-RNAP transcription 1 D=D 1 =K c =0.07 Simulation 0.9 Analytical 0.8 0.7 α c =0.04 0.6 fec 0.5 0.4 α c =0.08 0.3 0.2 0.1 0 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 α ◮ Analytical results valid for low value of α ⇒ Semianalytical. ◮ The deviation starts from the crictical value, α c = 0 . 04 where the density starts saturating. ◮ Beyond α c , the error correction may depend on other parameters.
Summary ◮ Transcription rate → suppressed both by pausing and backtracking (reduced saturated density effect). ◮ We exactly calculate the efficiency of error correction for a single-RNAP and multi-RNAP transcription in a semi-analytical way. ◮ Error correction can be strongly improved by increasing both the backward stepping rate and the transcript cleavage rate.
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