Polymerase chain reaction (PCR)-generated DNA fragment of appY upstream regulatory region (from position -260 up to position -60, respectively, to appY ATG codon) was inserted into the reporter vector pPF1 at the BglII restriction site. Oligonucleotides used for amplification:

appY_For _BglII 5${}^{\prime }$ GCAAGATCTTTCAGGTGCGTTGTAGTGAG

appY_Rev _BglII 5${}^{\prime }$ ACAAGATCTTAATCAGGATGATGTGCAT

PCR products were purified in 4.5% Polyacrylamide Gel (PAAG), pPF1 vector, and DNA fragments were subjected to restriction using endonuclease BglII (NEB, Ipswich, MA, USA), separated in 1% agarose and purified using Cleanup Standard kit (Evrogen, Moscow, Russia). T4 DNA ligase (NEB) was used for ligation, the reaction was carried out according to manufacturer protocol (0.1 pmol of DNA fragment and 0.05 pmol of linearized plasmid were taken into reaction in total volume 20 µL). A ligation mixture was used for the transformation of competent E.coli K12 MG1655 cells prepared as described in [18]. Bacterial colonies after transformation were selected by fluorescence of Egfp and mCherry. Primers used for PCR assumed the probability of insertion in opposite orientations. The orientation and quality of inserts were confirmed by sequencing the resulting plasmids using primers specific for mCherry and Egfp genes (mCherry 5${}^{\prime }$ AGCGCATGAACTCCTTGATG) and Egfp 5${}^{\prime }$ GTCCAGCTCGACCAGGATG). Plasmids corresponding to constructions appY_Red (Red) and appY_Green (Green) (Fig. 1) with confirmed sequence were used for transformation of E.coli K12 MG1655, purified from cultures using Plasmid Miniprep kit (Evrogen) and stored for subsequent experiments (transformation of E.coli K12 MG1655 for transcription starts mapping and colonies fluorescence assay).

To determine transcription start sites within appY regulatory region analyzed in this study primer extension reaction was carried out. E.coli K12 MG1655 cells transformed by the derivatives of pPF1 plasmid were grown on Lysogeny broth (LB) medium in the presence of kanamycin (40 µg/mL) and harvested at OD${}_{600}$ = 0.6. Total RNA was isolated with an ExtractRNA kit (Evrogen). RNA concentration was measured spectrophotometrically using NanoDrop1000 (Thermo Scientific, Wilmington, DE, USA). RNA integrity was estimated in denaturating 1.5% PAAG in the presence of 8M urea. ${}^{32}$P-labeled oligonucleotides were prepared using T4 polynucleotide kinase (NEB) according to manufacturer protocol. A total of 20 µg of RNA and 4 pmol of ${}^{32}$P-labeled oligonucleotide primer were taken for the reaction of reverse transcription with MuLV Reverse Transcriptase (Evrogen). The reaction was performed at 43 ℃ in conditions specified by the manufacturer. cDNA was precipitated by a 10-fold volume of N-butanol. Reaction products were separated in 6% PAAG and 8M urea and exposed with X-Ray Retina film. Guanine-specific hydrolysis of PCR fragments obtained with oligonucleotide pairs mCherry*/Egfp and mCherry/Eegfp* using Green plasmid as a template was carried out according to [18]. For the construction of plasmid Red, oligonucleotides mCherry* (5${}^{\prime }$ AGCGCATGAACTCCTTGATG) and Egfp* (5${}^{\prime }$ GTCCAGCTCGACCAGGATG) were used for mapping of Transcription Start Site (TSS) in sense and antisense directions, respectively. For the construction of plasmid Green, Egfp* and mCherry* radiolabeled primers respectively reflect direct and antisense transcription.

Transcriptional activity was assessed by the level of fluorescence of transformant colonies when grown on LB agar medium in the presence of 50 µg/mL kanamycin for 14 hours. Fluorescence of E. coli cell colonies transformed with plasmid constructions was recorded using a Leica DM 6000B microscope (lot number 289896, Leica Microsystems, Wetzlar, Germany). Images were obtained in the “Fluorescence” mode, and the choice of filters for emission excitation and radiation detection was set at settings “Cubes”: “GFP” (excitation in the region 488 $\pm$ 25 nm, emission 500–550 nm) and “N21” (excitation in the region of 515–550 nm, emission in the region of 580–590 nm).

Image processing was carried out using the ImageJ program (ver. 153t, National Institutes of Health, Bethesda, MD, USA) [19]. To perform this, we used the algorithm of threshold selection of cell colonies (whole spots) in the image, followed by the calculation of the average intensity of pixels in the selected areas. Sample sizes were 16 spots for Egfp protein and 15 spots for mCherry. To correctly estimate the amount of synthesized fluorescent proteins, we took into account the difference in the brightness of the glow of red and green proteins. Thus, according to the data of [20], the luminescence brightness of Egfp proteins is 33.54, and that of mCherry proteins is 15.84. Then the intensity of fluorescent luminescence can be expressed through the number (N) of proteins and their brightness ($\alpha$) as follows:

(1)$$I_i={\alpha }_i{N}_i,i=Egfp,mCherry.$$

If we go to the new variables describing the amount of proteins in brightness units as follows: $N_i^{{}^{\prime }}={\alpha }_{mCherry}{N}_i$, then for the new variables, the following is true:

(2)$$N_{Egfp}^{{}^{\prime }}={\displaystyle \frac{{\alpha }_{mCherry}}{{\alpha }_{Egfp}}}{I}_{Egfp},$$ $$N_{mCherry}^{{}^{\prime }}=I_{mCherry},$$

where ${\alpha }_{Egfp}=33.54$ and ${\alpha }_{mCherry}=15.84$. Such variables allow us to correctly estimate the number of fluorescent proteins on the scale of the intensity of the glow of mCherry proteins in colonies of transformed cells.

When conducting model studies, we took into account that the Red and Green constructions contain three genes separated by three intermediate regions. There are six regions in total. To model the internal mobility of each of these regions, a modified Englander model [16] that was based on the assumption that angular displacements of the nitrous bases make the main contribution to the formation of DNA open states was used. The model neglects the contribution of other internal movements involved in the formation of open states, such as transverse and longitudinal movements of nucleotides. Unlike the model originally proposed by Englander [21], the modified model took into account the angular deviations of the bases in both the coding and complementary chains, and also took into account the effects of dissipation and the action of constant torsion moment M${}_{\tau }$:

(3)$$I_{n,1}{\displaystyle \frac{d^2{\phi }_{n,1}(t)}{d{t}^2}}-K_{n,1}^{{}^{\prime }}[{\phi }_{n+1,1}(t)-2{\phi }_{n,1}(t)+{\phi }_{n-1,1}(t)]$$ $$+k_{n,1-2}{R}_{n,1}(R_{n,1}+R_{n,2})\sin {\phi }_{n,1}\left(t\right)-k_{n,1-2}{R}_{n,1}{R}_{n,2}\sin ({\phi }_{n,1}(t)-{\phi }_{n,2}(t))$$ $$=-{\beta }_{n,1}{\displaystyle \frac{d{\phi }_{n,1}\left(t\right)}{dt}}+M_{\tau },$$

(4)$$I_{n,2}{\displaystyle \frac{d^2{\phi }_{n,2}(t)}{d{t}^2}}-K_{n,2}^{{}^{\prime }}[{\phi }_{n+1,2}(t)-2{\phi }_{n,2}(t)+{\phi }_{n-1,2}(t)]$$ $$+k_{n,1-2}{R}_{n,2}\left(R_{n,1}+R_{n,2}\right)\sin {\phi }_{n,2}(t)-k_{n,1-2}{R}_{n,1}{R}_{n,2}\sin ({\phi }_{n,2}(t)-{\phi }_{n,1}(t))$$ $$=-{\beta }_{n,2}{\displaystyle \frac{d{\phi }_{n,2}\left(t\right)}{dt}}+M_{\tau },n=1,2,\mathrm{\dots }N.$$

Here ${\phi }_{n,i}(t)$ is the angular deviation of the n-th nitrogenous base of the i-th chain; I${}_{n\mathrm{,}i}$ is the moment of inertia of the base; R${}_{n\mathrm{,}i}$ is the distance from the center of mass of this base to the sugar-phosphate backbone; $K{}^{\prime }{}_{n,i}=K{R}_{n,i}^2$; K is a constant characterizing the stiffness (tensile strength) of the sugar-phosphate backbone; ${\beta }_{n,i}=\alpha R_{n,i}^2$; $\alpha$ is the dissipation coefficient; $k_{n,1-2}$is a constant characterizing the interaction between complementary bases within the n-th pair; M${}_{\tau }$ is the constant torsion moment; i = 1, 2; n =1, 2, …N; N is the total number of pairs of nitrogenous bases. It is assumed that the length of the modeled region is sufficiently large, and the effects at the ends of the region can be neglected.

To simplify Eqns. 3,4, the coefficients of the equations were averaged inside the region under consideration:

(5)$${\overline{I}}_1{\displaystyle \frac{d^2{\phi }_{n,1}(t)}{d{t}^2}}-{\overline{K}}_1^{{}^{\prime }}[{\phi }_{n+1,1}(t)-2{\phi }_{n,1}(t)+{\phi }_{n-1,1}(t)]$$ $$+{\overline{k}}_{1-2}{\overline{R}}_1({\overline{R}}_1+{\overline{R}}_2)\sin {\phi }_{n,1}-{\overline{k}}_{1-2}{\overline{R}}_1{\overline{R}}_2\sin ({\phi }_{n,1}(t)-{\phi }_{n,2}(t))$$ $$=-{\overline{\beta }}_1{\displaystyle \frac{d{\phi }_{n,1}\left(t\right)}{dt}}+M_{\tau },$$

(6)$${\overline{I}}_2{\displaystyle \frac{d^2{\phi }_{n,2}(t)}{d{t}^2}}-{\overline{K}}_2^{{}^{\prime }}[{\phi }_{n+1,2}(t)-2{\phi }_{n,2}(t)+{\phi }_{n-1,2}(t)]$$ $$+{\overline{k}}_{1-2}{\overline{R}}_2({\overline{R}}_1+{\overline{R}}_2)\sin {\phi }_{n,2}(t)-{\overline{k}}_{1-2}{\overline{R}}_1{\overline{R}}_2\sin ({\phi }_{n,2}(t)-{\phi }_{n,1}(t))$$ $$=-{\overline{\beta }}_2{\displaystyle \frac{d{\phi }_{n,2}\left(t\right)}{dt}}+M_{\tau },$$

where

(7)$${\overline{I}}_i=I_A{C}_{A,i}+I_T{C}_{T,i}+I_G{C}_{G,i}+I_C{C}_{C,i},$$ $${\overline{R}}_i=R_A{C}_{A,i}+R_T{C}_{T,i}+R_G{C}_{G,i}+R_C{C}_{C,i},$$ $${\overline{K}}_i^{{}^{\prime }}=K_A^{{}^{\prime }}{C}_{A,i}+K_T^{{}^{\prime }}{C}_{T,i}+K_G^{{}^{\prime }}{C}_{G,i}+K_C^{{}^{\prime }}{C}_{C,i},$$ $${\overline{k}}_{1-2}=k_{A-T}\left(C_{A,1}+C_{T,2}\right)+k_{G-C}\left(C_{G,1}+C_{C,2}\right),$$ $${\overline{\beta }}_i={\beta }_A{C}_{A,i}+{\beta }_T{C}_{T,i}+{\beta }_G{C}_{G,i}+{\beta }_C{C}_{C,i}.$$

Here $C_{j,i}=N_{j,i}/N$ is the concentration of bases of the j-th type in the considered region of the i-th chain; $N_{j,i}$ the number of bases of the j-th type in this region; N is the total number of bases in the region; j = A, T, G, C, i = 1, 2.

Assuming that the solutions of Eqns. 5,6 are sufficiently smooth functions, we rewrote Eqns. 5,6 in the continuum approximation as follows:

(8)$${\overline{I}}_1{\phi }_{1,tt}-{\overline{K}}_1^{{}^{\prime }}{a}^2{\phi }_{1,zz}+{\overline{k}}_{1-2}{\overline{R}}_1\left({\overline{R}}_1+{\overline{R}}_2\right)\sin {\phi }_1-{\overline{k}}_{1-2}{\overline{R}}_1{\overline{R}}_2\sin ({\phi }_{1,}-{\phi }_2)=-{\overline{\beta }}_1{\phi }_{1,t}+M_{\tau },$$

(9)$${\overline{I}}_2{\phi }_{2,tt}-{\overline{K}}_2^{{}^{\prime }}{a}^2{\phi }_{2,zz}+{\overline{k}}_{1-2}{\overline{R}}_1({\overline{R}}_1+{\overline{R}}_2)\sin {\phi }_2-{\overline{k}}_{1-2}{\overline{R}}_1{\overline{R}}_2\sin ({\phi }_2-{\phi }_1)=-{\overline{\beta }}_2{\phi }_{2,t}+M_{\tau },$$

where a is the distance between the nearest base pairs.

Further, we took into account the features of the distribution of interactions within the DNA molecule: the presence of “weak” hydrogen bonds between nitrogenous bases within complementary pairs and “strong” valence interactions along the sugar-phosphate chains. This property of the DNA molecule made it possible, as a first approximation, to transform two coupled Eqns. 8,9 into two independent equations:

(10)$${\overline{I}}_1{\phi }_{1,tt}-{\overline{K}}_1^{{}^{\prime }}{a}^2{\phi }_{1,zz}+{\overline{k}}_{1-2}{\overline{R}}_1^2\sin {\phi }_1=-{\overline{\beta }}_1{\phi }_{1.t}+M_{\tau },$$

(11)$${\overline{I}}_2{\phi }_{2.tt}-{\overline{K}}_2^{{}^{\prime }}{a}^2{\phi }_{2,.zz}+{\overline{k}}_{1-2}{\overline{R}}_2^2\sin {\phi }_1=-{\overline{\beta }}_2{\phi }_{2,t}+M_{\tau }.$$

Thus, the original problem was divided into two independent problems. The first was related to Eqn. 10, which models the angular deviations of nitrogenous bases in the coding chain. The second problem was with Eqn. 11, which described the angular deviations of nitrogenous bases in the complementary chain.

In a particular case, when the effects of dissipation and the action of a constant torsion moment are small (${\overline{\beta }}_1\cong 0$ and $M_{\tau }\cong 0)$), Eqns. 10,11 take the form of classical sine-Gordon equations:

(12)$${\overline{I}}_1{\phi }_{1,tt}-{\overline{K}}_1^{{}^{\prime }}{a}^2{\phi }_{1,zz}+{\overline{k}}_{1-2}{\overline{R}}_1^2\sin {\phi }_1=0,$$

(13)$${\overline{I}}_2{\phi }_{2.tt}-{\overline{K}}_2^{{}^{\prime }}{a}^2{\phi }_{2,.zz}+{\overline{k}}_{1-2}{\overline{R}}_2^2\sin {\phi }_1=0.$$

One-soliton solutions of these equations—kinks—found by analytical methods have the following form:

(14)$${\phi }_{k,1}(z,t)=4arctg\{\exp [({\overline{\gamma }}_1/{\overline{d}}_1)(z-{\upsilon }_{k,1}t-z_{0,1})]\},$$

(15)$${\phi }_{k,2}(z,t)=4arctg\{\exp [({\overline{\gamma }}_2/{\overline{d}}_1)(z-{\upsilon }_{k,2}t-z_{0,2})]\}.$$

Here, $v_{k,i}$ is the kink velocity in the coding (i = 1) or complementary (i = 2) chains; ${\overline{\gamma }}_i={\left(1-v_{k,i}^2/{\overline{C}}_i^2\right)}^{-\frac{1}{2}}$ is the Lorentz factor; ${\overline{C}}_i={\left({\overline{K}}_i^{\prime }{a}^2/{\overline{I}}_i\right)}^{1/2}$ is the sound velocity in the i-th chain; ${\overline{V}}_i={\overline{k}}_{1-2}{\overline{R}}_i^2$; ${\overline{d}}_i={\left({\overline{K}}_i^{\prime }{a}^2/{\overline{V}}_i\right)}^{1/2}$ is the size of the i-th kink; $z_{0,i}$ is the coordinate of the i-th kink at the initial moment of time; i is the chain number, i = 1, 2.

The total energy and rest energy of the i-th kink are determined by the following formulas:

(16)$${\overline{E}}_i={\overline{\gamma }}_i{\overline{E}}_{0,i},$$

(17)$${\overline{E}}_{0,i}=8\sqrt{{\overline{K}}_i^{{}^{\prime }}{\overline{V}}_i}.$$

In the case of low velocities ${\upsilon }_{k,i}\ll {\overline{C}}_i$, Eqn. 16 can be rewritten as follows:

(18)$${\overline{E}}_i=8\sqrt{{\overline{K}}_i^{{}^{\prime }}{\overline{V}}_{i,}}\cdot {\overline{\gamma }}_i\cong {\overline{E}}_{0,i}+\frac{{\overline{m}}_i{\upsilon }_{k,i}^2}{2},$$

where ${\overline{m}}_i=\frac{{\overline{E}}_{0,i}}{2{\overline{C}}_i^2}$ is the mass of the i-th kink. The form of Eqn. 18 explains why DNA kinks are often considered quasiparticles with a certain mass, velocity, and energy.

Section 3.2.1 presents a preliminary analysis of the kink behavior based only on the analysis of the form of the energy profiles of the coding and complementary sequences of the Red or Green constructions.

In the general case $({\overline{\beta }}_1\ne 0,M_{\tau }\ne 0)$, Eqns. 10,11 are solved by us numerically using the difference scheme described in [15]. The results obtained are presented in Section 3.2.2 in the form of kink trajectories.

tfaX/appY intergenic interval represents one of 78 genomic loci of E.coli chromosome oversaturated by potential promoters predicted using PlatProm software (http://www.mathcell.ru/model6.php?l=en) [13] that assumes specific structural properties of this region and its intrinsic capacity to respond to DNA conformational rearrangements including transcription-coupled changes in superhelical state. In our previous work, we found that two primary promoters mapped in the regulatory region between positions -260 and -61 with respect to appY ATG are active [12], though only one orientation of the fragment of interest in the reporter vector was studied. Here, we compared transcription activity in two constructions representing the same genomic region placed in inverted positions relative to the same plasmid environment. In both genetic constructions obtained after the transformation of E.coli K12MG1655 cells, TSSs were mapped using primer extension reaction with oligonucleotides specific for EGFP and mCherry genes. Despite the orientation of the insert, the same TSSs are revealed in the direction of the appY gene at the position -81 relative to the initiation codon, as well as in the opposite antisense direction at the position -148 (Fig. 2). Thus, the capacity of the insert to initiate bidirectional transcription remains conserved and provided by two promoters located back-to-back in the region under study.

The nucleotide sequences of the studied E. coli DNA fragments in the Red and Green constructions and reviled TSS are shown in Fig. 3A,B, respectively. It turned out that in the region under study, one main promoter on each of the strands works (Fig. 2). For the coding strand in Red and Green constructions, the start of RNA synthesis is at position -81 relative to the start of the appY gene (promoter P1 in Fig. 3C). This prevalent promoter is characterized by almost perfect -10 and -35 consensus hexamers (TATAAA and TTGCAA), though separated by non-optimal spacer 22 bp in length. On the complementary strand, transcription is initiated from position -148 (promoter P2 in Fig. 3C), having the context of -10 and -35 regions TTTAAG and TTGCAA, respectively, and separated by 16 bp. Promoter P2 possessing fewer conservative hexamers -10 and -35 exhibits low activity as compared to P1 (Fig. 2). When the orientation of the studied fragment is changed (Green construction), the promoters maintain their location in the sequence but move from one strand to the other (Fig. 3D).

Transformant colonies and their fluorescence levels are shown in Fig. 4A,D. It can be seen from these figures that in cells transformed with both variants of the plasmid, synthesis of both the Egfp protein and mCherry is observed. This suggests that transcription initiation is possible both on the coding strand of the appY gene and on its complementary strand. In the case of Red and Green, transcription is observed in both directions, but the transcriptional activity in these two cases is different. From diagrams in Fig. 4B,E, it can be seen that in the case of Red, the brightness of the luminescence of cells containing red proteins is significantly (p 0.001) higher than the brightness of cells containing green proteins. In the case of Green, the opposite picture is observed. The brightness of the glow of red and green proteins is different [20]. Diagrams that take this difference into account are shown in Fig. 4C,F. From these diagrams, it can be seen that in the case of Red, more red protein is synthesized, and in the case of Green, more green.

From the diagrams presented in Fig. 4, it can be observed that in the case of Red construction, the height of the red column in the diagram shown in Fig. 4C is significantly (p 0.001) higher than the height of the green column. In the case of Green construction, the height of the green column shown in Fig. 4F is significantly (p 0.003) higher than the height of the red column. This indicates that in both cases, the P1 promoter is more active than the P2 promoter. In addition, comparing promoter activity in Red and Green constructions, it can be seen that the P1 promoter decreases (Fig. 4C, mCherry; Fig. 4F, Egfp) and the P2 promoter increases (Fig. 4C, Egfp; Fig. 4F, mCherry) its functional activity when the orientation of the fragment is changed.