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. 2019 Oct 31;10(4-5):187–194. doi: 10.1080/21541264.2019.1682454

Change in inorganic phosphate physical state can regulate transcription

Max E Gottesman a, Arkady Mustaev b,✉
PMCID: PMC6948957  PMID: 31668122

ABSTRACT

Inorganic phosphate (Pi), a ubiquitous metabolite, is involved in all major biochemical pathways. We demonstrate that, in vitro, MgHPO4 (the intracellular Pi form) at physiological concentrations can exist in a metastable supersaturated dissolved state or as a precipitate. We have shown that in solution, MgHPO4 strongly stimulates exonuclease nascent transcript cleavage by RNA polymerase. We report here that MgHPO4 precipitate selectively and efficiently inhibits transcription initiation in vitro. In view of the MgHPO4 solubility and in vitro sensitivity of RNA synthesis to MgHPO4 precipitate, at physiological concentrations, MgHPO4 should cause a 50–98% inhibition of cellular RNA synthesis, thus exerting a strong regulatory action. The effects of Pi on transcription in vivo will, therefore, reflect the physical state of intracellular Pi.

KEYWORDS: precipitated magnesium phosphate, RNA polymerase, initiation, inhibition

Introduction

RNA polymerase (RNAP) transfers genetic information from DNA to messenger RNA in the course of transcription. This multi-step process [1,2] includes: (i) promoter recognition by RNAP holoenzyme (ii) initiation of RNA synthesis; (iii) elongation of RNA transcripts and (iv) termination, with release of full-size RNA transcript.

Initial binding of RNAP holoenzyme to the promoter is followed by melting of the DNA double helix. Melting enables RNA synthesis using one of the DNA strands as template. Short RNA oligonucleotides, synthesized in the transcription initiation complex (TIC) at the beginning of the transcription cycle, readily dissociate from the active centre, thus allowing RNA re-synthesis in cycles of abortive initiation. This process can repeat many times before the enzyme escapes to elongation, releasing σ subunit in the process of promoter clearance. After promoter clearance, the RNA/DNA/RNAP ensemble is dramatically stabilized as a ternary elongation complex (TEC). Advancement of TEC along the template, albeit processive, is frequently delayed by pausing. Some pauses are due to backtracking, that is, back-translocation of transcribing RNAP [3,4]. Backtracking unwinds the downstream edge of the RNA:DNA hybrid. The disengaged RNA 3′ segment occludes the active centre and prevents transcript elongation. This segment can be hydrolytically removed through RNAP endonuclease activity, which is greatly stimulated by bacterial factors GreA and GreB [5–7] and eukaryotic factor TFIIS [8], thus enabling transcript elongation from newly formed 3ʹ end. RNAP is also able to eliminate the 3′ terminal RNA residue in pretranslocated TEC by exonucleolytic cleavage [9].

Transcription is a highly regulated process (for review see [10–12]). To understand these regulatory mechanisms, we must elucidate how RNAP catalysis is altered by regulatory agents. These can be divided into i) protein factors, and ii) small molecules (e.g., cellular metabolites) that interfere with or enhance transcription. Representatives of the first class are more common, whereas there are few examples of cellular metabolites that directly target RNAP. Our in vitro data suggest that transcription can also be regulated by a novel mechanism through a change in the physical state of a cellular metabolite.

Inorganic phosphate, Pi, plays central roles in many cellular reactions [13–16]. Pi attachment to biomolecules mediates major cellular processes including differentiation, proliferation, cell death and survival, cell mobility as well as cell metabolism, intracellular signaling and energetics. Pi also serves as a buffering agent in mammalian cells and is a major component of bone and membranes. Depending on the organism, its functional state, and external conditions, among other considerations, intracellular Pi concentrations can vary over a wide range, ~5–100 mM [17,18]. Pi regulates RNA synthesis through association with protein factors that alter transcription from certain promoters by interacting with DNA [19,20].

At physiological pH, simple Pi salts are highly water-soluble. Thus, Na2HPO4 is soluble to ~0.5 M at ambient temperature. However, the intracellular Pi form, MgHPO4, is poorly soluble at ~ 1.5 mM. Considering the high intracellular concentrations of Pi and Mg2+ and their ~1 mM complex formation constant, the bulk of intracellular Pi must exist as a precipitated complex with Mg2+. However, we demonstrated that the solubility equilibrium for MgHPO4 requires prolonged incubation to establish, so that the kinetic solubility of MgHPO4 formed in situ by mixing Na2HPO4 and MgCl2 is much greater than its equilibrium solubility (see below). This permits formation of a metastable supersaturated solution, which could persist in the cell.

As we have shown previously [21], dissolved MgHPO4 stimulates exonuclease nascent transcript cleavage by RNA polymerase nearly 2000-fold through engaging a Mg2+ ion in catalysis and activating an attacking water molecule at the RNAP active centre. Here we find that as a precipitate, MgHPO4 strongly inhibits initiation of RNA synthesis in vitro. These distinct activities of the compound in different physical states suggest that MgHPO4 could play a regulatory role in vivo. How it affects transcription in vivo would depend critically on its physical state in the cell.

Results

Determination of kinetic solubility of MgHPO4

In experiments exposing an RNAP transcription initiation complex to MgHPO4, we noticed an inhibition of RNA synthesis initiation that depended on how the compound was prepared. MgHPO4 is poorly soluble in water. However, if prepared by mixing K2HPO4 with MgCl2, MgHPO4 starts to precipitate from a concentration of 20 mM (of each component) only after prolonged incubation at 20°C. This observation suggested that MgHPO4 kinetic solubility was much higher than thermodynamic solubility. Therefore, to determine kinetic MgHPO4 solubility, we generated MgHPO4 by mixing the starting compounds at various concentrations. As seen from Figure 1, at concentrations 30 and 40 mM of each reactant, MgHPO4 started to precipitate immediately, while at 20 mM, the solution remained transparent for many hours, suggesting that at this concentration MgHPO4 formed a metastable supersaturated solution. Remarkably, the kinetic solubility of MgHPO4 exceeds its equilibrium solubility at least 13-fold.

Figure 1.

Figure 1.

Determination of the kinetic solubility for MgHPO4. The turbidity of MgHPO4 solutions generated by mixing the equivalent amounts of K2HPO4 and MgCl2 at indicated concentrations.

Effect of MgHPO4 on promoter-initiated full-size RNA synthesis

As seen in Figure 2(b) soluble MgHPO4 had little effect on RNA synthesis initiated from the T7A2 promoter template (slots 1–5). However, if added as a precipitate, the compound significantly inhibited transcription at concentrations >2.5 mM (lanes 6–10; Figure 2(c)). The principal effect of insoluble MgHPO4 was a general inhibition of RNA synthesis. In addition, RNA product distribution was affected. Increasing precipitated MgHPO4 concentration significantly reduced the amount of 23 nt run-off transcript, but was less inhibitory on the synthesis of abortive 4–9 nt RNA products. The size-distribution within the latter group of products was similarly affected by precipitated MgHPO4, resulting in the shift to smaller RNAs. Overall inhibition of RNA synthesis could be explained by disintegration of the RNAP open promoter complex, whereas the second effect – a relative increase in shorter transcripts at elevated [MgHPO4] – could be due to interference with RNA elongation. Notably, we observed extended RNA products whose size, about 50 nt, exceeded that of the 23 nt template. Most likely, these products are generated upon template switching by RNAP [22]. The template switch RNA’s are decreased by both soluble and precipitated MgHPO4.

Figure 2.

Figure 2.

Effect of dissolved and precipitated MgHPO4 on transcription from T7A2 promoter. (a). The scheme of the assay. (b). effect of various MgHPO4 forms on promoter-initiated RNA synthesis. (c) Scans of the slots 6, 8–10 of B.

Inhibitory effect of precipitated MgHPO4 is not promoter-specific

We then asked if RNA synthesis inhibition by MgHPO4 precipitate was promoter-specific. To this end, we repeated the experiments with the T7A1 and ribosomal rrnB1 promoters. As seen in Figure 3, RNA synthesis was inhibited to the same extent on all templates, and is thus not promoter-specific.

Figure 3.

Figure 3.

Effect of precipitated MgHPO4 on transcription from various promoters.

Note the sharp drop off in RNA synthesis at 10 mM MgHPO4; we discuss this point below.

Precipitated MgHPO4 inhibits promoter-directed abortive dinucleotide synthesis

If RNA synthesis is initiated in the presence of an incomplete set of NTP substrates, stalled RNA products are released, and the initiation complex undergoes multiple abortive cycles. We tested the effect of precipitated MgHPO4 on abortive dinucleotide synthesis of pppGpC from GTP and [α-32P]CTP at the T7A2 promoter. As seen in Figure 4, dinucleotide formation was also significantly inhibited. The response of this RNAP activity to precipitated MgHPO4 was as robust as in the previous assay. This result is thus consistent with the proposal that precipitated MgHPO4 disrupts an initiating RNAP complex.

Figure 4.

Figure 4.

Effect of precipitated MgHPO4 on abortive dinucleotide synthesis from the T7A2 promoter. (a). Reaction scheme. (b). Autoradiogram of the reaction mixture products after TLC separation. (c). Quantification of the results of B.

Precipitated MgHPO4 does not significantly affect RNA elongation from a preformed TEC

To explore the effect of MgHPO4 on transcription elongation, we exposed a reconstituted RNAP elongation complex, TEC11, to both forms of MgHPO4 in the presence of 4 NTP substrates. Figure 5 shows that both dissolved and precipitated forms moderately inhibited RNA synthesis by retarding RNAP propagation (about 30 and 40%, respectively, at 20 mM MgHPO4). This activity, however, was much smaller than that observed in the previous assays, supporting the idea that precipitated MgHPO4 primarily inhibits an initiating complex rather than a TEC. TEC is much more stable than an open promoter complex, and therefore may be less susceptible to disruption.

Figure 5.

Figure 5.

Effect of dissolved and precipitated MgHPO4 on transcription elongation from assembled TEC. Reaction products were resolved by PAGE and visualized by phosphoimaging. Key reaction products are indicated.

Precipitated MgHPO4 does not affect intrinsic nuclease transcript degradation by RNAP in TEC

As seen in Figure 5, a shorter RNA product was generated along with elongated transcripts. This dinucleotide product (pCpA) originates from TEC11 as a result of the intrinsic nuclease activity of the enzyme. Precipitated MgHPO4 did not affect this reaction, again consistent with the notion that the agent selectively targets an RNAP initiation complex while having less effect on elongation and RNAP intrinsic transcript cleavage.

Precipitated MgHPO4 inhibits RNA synthesis from a plasmid template

We next tested the effect of precipitated MgHPO4 on RNA synthesis with a circular pTZ plasmid. This system permits multi-round RNA synthesis and monitors RNAP activity through a full transcription cycle. Figure 6 shows that as expected, MgHPO4, also inhibited this reaction. Notably, the response of total RNA synthesis to precipitated MgHPO4 was the same as that for abortive dinucleotide RNA synthesis, consistent with the primary effect of the agent on transcription initiation.

Figure 6.

Figure 6.

Inhibition of RNA synthesis from a plasmid template by precipitated MgHPO4. (a) Assay scheme. (b). Phosphoimage of the TCA-precipitated labeled RNA synthesized in the presence of MgHPO4. (c). Quantification of the results of B.

Discussion

Solubility, a fundamental property of compounds, is defined as the maximal concentration of the compound in solution. Two distinct kinds of solubility exist: i) equilibrium solubility, a type of dynamic chemical equilibrium between a compound in the solid state and a solution of that compound, and ii) kinetic solubility, when the concentration of the compound in solution exceeds its equilibrium (thermodynamic) solubility. The later represents a supersaturated solution. Even though these solutions are metastable, some compounds do not precipitate over prolonged time periods. Thus, we find that the ubiquitous metabolite, inorganic phosphate, Pi, in the cellular form of MgHPO4, can exist in vitro at physiologic concentrations in a supersaturated state, in which the MgHPO4 concentration in solution significantly exceeds its equilibrium solubility, or as a precipitate. We discovered that in vitro MgHPO4 in both these distinct physical states strongly modulates RNAP activity. In the metastable soluble form, MgHPO4 stimulates RNAP intrinsic exoribonuclease activity on a TEC10 substrate [21], although less with other substrates, e.g., TEC11 (Figure 5). As a precipitate, MgHPO4 inhibits initiation of RNA synthesis. Whereas stimulation of exonuclease can be rationalized by a structural model [21], how precipitated MgHPO4 inhibits initiation remains unclear. Importantly, the surface of MgHPO4 precipitates should contain densely arranged coordinated Mg2+ ions with free coordination valences. Inhibition of transcription initiation could, therefore, involve multiple interactions of RNAP open complexes with MgHPO4 particles through these coordinations. These interactions could weaken attachment of the enzyme to promoter DNA, disintegrating the open complex. The insensitivity of the more stable TEC to precipitated MgHPO4 is consistent with this notion.

Notably, inhibition of RNA synthesis as a function of the concentration of precipitated MgHPO4 abruptly rose at compound concentrations > 5 mM (see Figures 2–4, and 6), reflecting a complex inhibitory mechanism. This could be explained by the presence of multiple inhibition targets in the RNAP initiating complex, residing on different sides of the enzyme surface. In this scenario, a granule of precipitated MgHPO4 cannot interact simultaneously with more than one target. In such an arrangement, a small increase in granule concentrations will induce a disproportionally high inhibition, because the overall effect will be a composite of those caused by granules binding to each inhibitory site.

The properties of MgHPO4 described above suggest that Pi could play a major role in cell biology. How MgHPO4 effects transcription in vivo thus depends on its physical state in the cell, which, remarkably, has not yet been established. Life is a non-equilibrium process with respect to cellular energetics and concentrations of cellular metabolites [23]. Therefore, finding MgHPO4 in a metastable supersaturated state in the cell would contribute to understanding the life processes by extending the concept of non-equilibrium nature of life to the state of a particular cellular metabolite. Finding MgHPO4 as a precipitate would strongly suggest that the compound participates in transcription regulation by affecting RNA synthesis initiation.

Materials and methods

All chemicals were from Sigma-Aldrich. His6-tagged RNAP was purified from E. coli strain RL721. Ultra-pure ribonucleoside-5ʹ-triphosphates and dATP were from Pharmacia. [α-32P]CTP was from MP Biomed. Oligonucleotides were from Oligos. Radioactive products of polymerase reactions were resolved by electrophoresis in 15% polyacrylamide gel in the presence of 7 M urea, or by thin layer ion-exchange chromatography on PEI cellulose in 0.2 M KH2PO4 pH 4.0 developing system, and quantified by phosphoimagery using a Molecular Dynamics device (GE Healthcare).

Time course for precipitation of MgHPO4 from supersaturated solutions

Equimolar amounts of K2HPO4 and MgCl2 were mixed in 1 ml spectrophotometer cells to the desired concentration and kept at room temperature. Precipitation was monitored as increase in turbidity at 800 nm.

Preparation of supersaturated MgHPO4

This was generated directly in the reaction mixtures containing transcription cocktails by mixing equimolar amounts of K2HPO4 and MgCl2 to the desired concentration.

Effect of dissolved supersaturated MgHPO4 on transcription from the T7A2 promoter

Reaction mixtures (10 µl) containing 120 nM RNAP, 40 nM T7A2 promoter, and 500 nM ϭ subunit were incubated 5 min at 37ºC and supplemented with K2HPO4 and MgCl2 to the desired concentration, followed by addition of GTP, UTP, and ATP to final concentration of 0.2 mM and [32P] CTP (30 Ci/mmol) to a final concentration 1 µM. After incubation for 15 min at 37ºC, the reaction was quenched by addition of an equal volume of 10 M urea, 10 mM EDTA, 0.05% Bromophenol Blue and 0.05% Xylene Cyanol dyes. The reaction products were resolved by denaturing 20% PAAG. The samples were then analyzed by electrophoresis (20% (wt/vol) PAAG, 7 M urea).

Preparation of precipitated MgHPO4

0.5 ml of 0.4 M K2HPO4 was mixed with an equal volume of 0.4 M MgCl2 and left for 1 h at room temperature.

Effect of precipitated MgHPO4 on transcription from the T7A2 promoter

This was performed as in the case for dissolved supersaturated MgHPO4, but the precipitated compound was added instead to pre-formed open RNAP-promoter complex prior to NTP addition.

Effect of precipitated MgHPO4 on transcription from T7A1 and rnnB1 promoter

This was performed as described for T7A2 promoter by supplementing RNAP open promoter complexes with precipitated compound followed by NTP substrate addition.

Effect of precipitated MgHPO4 on abortive dinucleotide synthesis from the T7A2 promoter

Reaction mixtures (9 µl) containing 80 nM RNAP, 40 nM T7A2 promoter, and 200 nM σ subunit in transcription buffer, TB (20 mM Tris⋅HCl, pH 8.0, 0.1 M NaCl, 10 mM MgCl2) were incubated 5 min at 37ºC and supplemented with precipitated MgHPO4 to the desired concentration The reaction was initiated by addition of 1 μl of a mixture of 2 mM GTP, 20 μM [α-32P] CTP (specific activity 30 Ci/mmol). After 5 min of incubation at 37°C. the reaction was stopped by addition of 10 μl of 10 M urea with Bromphenol Blue and Xylene Cyanol dyes. Aliquots of the reaction mixture (1 μl) were applied to a PEI cellulose sheet (Sigma-Aldrich) and the reaction products were separated by thin-layer chromatography (TLC) using 0.5 M KH2PO4 as the developing solvent. The products were quantified by phosphoimagery.

RNAP elongation complex

TEC9A was assembled as previously described [21]. Briefly, RNA9 was mixed with equivalent amounts of DNA template strand to a final concentration of 1 µM in TB at 40°C and left to cool in a water bath to room temperature for ∼30 min. This mixture was added to an equivalent amount of His6-tagged RNAP immobilized on NTA agarose, and kept at room temperature in a shaker for 10 min followed by addition of the equivalent amount of DNA nontemplate strand. The mixture was agitated for another 10 min at room temperature and supplemented with TB containing 1 M NaCl. After 10 min the pellet was separated and washed with regular TB. Labeled TEC10C, was obtained by elongation of TEC9A by an equivalent amount of [α-32P] CTP (3000 Ci/mmol, 10 mCi/mL; MP Biomedicals) followed by washing with TB (4 × 1 mL). TEC11A was obtained from TEC10C by elongation with 10 µM ATP for 1 h at 0°C in TB containing 1 mM MgCl2.

Effect of precipitated and dissolved supersaturated MgHPO4 on elongation

A suspension of TEC11 on NTA beads in TB (8 µl) was supplemented with either precipitated MgHPO4 or K2HPO4 and MgCl2 to the desired concentration. This was followed by addition of 4 NTP substrates to a final concentration 40 μM and 10 min incubation at room temperature. The reaction was stopped by addition of 10 μl of 10 M urea with Bromphenol Blue and Xylene Cyanol dyes and the products analyzed by PAGE as described above.

Effect of precipitated MgHPO4 on multi-round transcription from plasmid template

The reaction mixture (8 μl) containing 2 pmol RNAP, 0.05 pmol pTZ plasmid with a cloned T7A1 promoter and 2 pmol purified σ subunit TB was incubated for 5 min at 37°C and supplemented with 1 μl of 2 mM ATP, UTP, GTP and 0.4 mM [α-32P]CTP (specific activity 30 Ci/mmol). After incubation for 30 min at 37°C the reaction was quenched by addition of 10 M urea and the aliquots (5 μl) were applied to Whatman 3 MM paper discs that were washed by 5% trichloroacetic acid (3 × 100 ml, 20 min each wash). The discs were rinsed with ethanol, dried and the remaining radioactive material quantified by phosphoimagery.

Funding Statement

This work was supported by Internal PHRI support grant to AM and by National Institutes of Health (grant number R01 GM037219) to MG.

Disclosure statement

No potential conflict of interest was reported by the authors.

References

  • [1].Losick R, Chamberlin M.. RNA polymerase: an overview. RNA Polymerase. NY: Cold Spring Harbor Laboratory Press; 1976. p. 17–67. [Google Scholar]
  • [2].Mustaev A, Goldfarb A.. RNA polymerase reaction in bacteria. Encyclopedia of biological chemistry. Academic Press, Elsevier Inc; 2004. p. 775–780. [Google Scholar]
  • [3].Nudler E, Mustaev A, Lukhtanov E, et al. The RNA-DNA hybrid maintains the register of transcription by preventing backtracking of RNA polymerase. Cell. 1997;89:33–41. [DOI] [PubMed] [Google Scholar]
  • [4].Komissarova N, Kashlev M. RNA polymerase switches between inactivated and activated states by translocating back and forth along the DNA and the RNA. J Biol Chem. 1997;272:15329–15338. [DOI] [PubMed] [Google Scholar]
  • [5].Borukhov S, Sagitov V, Goldfarb A. Transcript cleavage factors from E. coli. Cell. 1993;72:459–466. [DOI] [PubMed] [Google Scholar]
  • [6].Stebbins CE, Borukhov S, Orlova M, et al. Crystal structure of the GreA transcript cleavage factor from Escherichia coli. Nature. 1995;373:636–640. [DOI] [PubMed] [Google Scholar]
  • [7].Sosunova E, Sosunov V, Kozlov M, et al. Donation of catalytic residues to RNA polymerase active center by transcription factor Gre. Proc Natl Acad Sci U S A. 2003;100:15469–15474. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [8].Reines D, Ghanouni P, Li QQ, et al. The RNA polymerase II elongation complex. Factor-dependent transcription elongation nascent RNA cleavage. J Biol Chem. 1992;267:15516–15522. [PMC free article] [PubMed] [Google Scholar]
  • [9].Sosunov V, Sosunova E, Mustaev A, et al. Unified two-metal mechanism of RNA synthesis and degradation by RNA polymerase. Embo J. 2003;22:2234–2244. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [10].Browning DF, Busby SJW. Local and global regulation of transcription initiation in bacteria. Nat Rev Microbiol. 2016;14:638–650. [DOI] [PubMed] [Google Scholar]
  • [11].Balleza E, López-Bojorquez LN, Agustino Martínez-Antonio A, et al. Regulation by transcription factors in bacteria: beyond description. FEMS Microbiol Rev. 2009;33:133–151. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [12].Storz G, Vogel J, Wassarman KM. Regulation by small RNAs in bacteria: expanding frontiers. Mol Cell. 2011;43:880–891. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [13].Pasek MA, Kee TP. On the origin of phosphorylated biomolecules In: Egel R, Lankenau -D-D, Mulkidjanian AY, editors. Origins of life: the primal self-organization. Berlin: Springer; 2011. p. 57–84. [Google Scholar]
  • [14].Williams RJ. Phosphorus biochemistry. Ciba Found Symp. 1977. September 13–15;57:95–116. [DOI] [PubMed] [Google Scholar]
  • [15].Kamerlin SCL, Sharma PK, Prasad RB, et al. Why nature really chose phosphate. Q Rev Biophys. 2013;46:1–132. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [16].Westtheimer FH. Why nature chose phosphates. Science. 1987;235:1173–1178. [DOI] [PubMed] [Google Scholar]
  • [17].Mason PW, Carbone DP, Cushman RA, et al. The importance of inorganic phosphate in regulation of energy metabolism of Streptococcus lactis. J Biol Chem. 1981;2556:1861–1866. [PubMed] [Google Scholar]
  • [18].Bugg NC, Jones JA. Hypophosphataemia. Pathophysiology, effects and management on the intensive care unit. Anaesthesia. 1998;53:895–902. [DOI] [PubMed] [Google Scholar]
  • [19].Santos-Beneit F. The Pho regulon: a huge regulatory network in bacteria. Front Microbiol. 2015;6:402. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [20].Marzan LW, Shimizu K. Metabolic regulation of Escherichia coli and its phoB and phoR genes knockout mutants under phosphate and nitrogen limitations as well as at acidic condition. Microb Cell Fact. 2011;10:39. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [21].Gottesman ME, Mustaev A. Inorganic phosphate, arsenate, and vanadate enhance exonuclease transcript cleavage by RNA polymerase by 2000-fold. Proc Natl Acad Sci U S A. 2018;115:2746–2751. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • [22].Nudler E, Avetissova E, Markovtsov V, et al. Transcription processivity: protein-DNA interactions holding together the elongation complex. Science. 1996;273:211–217. [DOI] [PubMed] [Google Scholar]
  • [23].Ornes S. Core concept: how nonequilibrium thermodynamics speaks to the mystery of life. Proc Natl Acad Sci U S A. 2017;114:423–424. [DOI] [PMC free article] [PubMed] [Google Scholar]

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