Nanomolar Responsiveness of an Anaerobic Degradation Specialist to Alkylphenol Pollutants

Alkylphenols (like p-cresol and p-ethylphenol) represent bulk chemicals for industrial syntheses. Besides massive local damage events, large-scale micropollution is likewise of environmental and health concern. Next to understanding how such pollutants can be degraded by microorganisms, it is also relevant to determine the microorganisms’ lower threshold of responsiveness. Aromatoleum aromaticum EbN1 is a specialist in anaerobic degradation of aromatic compounds, employing a complex and substrate-specifically regulated catabolic network. The present study aims at verifying the predicted role of the PcrSR system in sensing p-cresol and at determining the threshold of responsiveness for alkylphenols. The findings have implications for the enigmatic persistence of dissolved organic matter (escape from biodegradation) and for the lower limits of aromatic compounds required for bacterial growth.

ABSTRACT

Anaerobic degradation of p-cresol (4-methylphenol) by the denitrifying betaproteobacterium Aromatoleum aromaticum EbN1 is regulated with high substrate specificity, presumed to be mediated by the predicted σ⁵⁴-dependent two-component system PcrSR. An unmarked, in-frame ΔpcrSR deletion mutant showed reduced expression of the genes cmh (21-fold) and hbd (8-fold) that encode the two enzymes for initial oxidation of p-cresol to p-hydroxybenzoate compared to their expression in the wild type. The expression of cmh and hbd was restored by in trans complementation with pcrSR in the ΔpcrSR background to even higher levels than in the wild type. This is likely due to ∼200-/∼30-fold more transcripts of pcrSR in the complemented mutant. The in vivo responsiveness of A. aromaticum EbN1 to p-cresol was studied in benzoate-limited anaerobic cultures by the addition of p-cresol at various concentrations (from 100 μM down to 0.1 nM). Time-resolved transcript profiling by quantitative reverse transcription-PCR (qRT-PCR) revealed that the lowest p-cresol concentrations just affording cmh and hbd expression (response threshold) ranged between 1 and 10 nM, which is even more sensitive than the respective odor receptors of insects. A similar response threshold was determined for another alkylphenol, p-ethylphenol, which strain EbN1 anaerobically degrades via a different route and senses by the σ⁵⁴-dependent one-component system EtpR. Based on these data and theoretical considerations, p-cresol or p-ethylphenol added as a single pulse (10 nM) requires less than a fraction of a second to reach equilibrium between intra- and extracellular space (∼20 molecules per cell), with an estimated K_d (dissociation constant) of <100 nM alkylphenol (p-cresol or p-ethylphenol) for its respective sensory protein (PcrS or EtpR).

IMPORTANCE Alkylphenols (like p-cresol and p-ethylphenol) represent bulk chemicals for industrial syntheses. Besides massive local damage events, large-scale micropollution is likewise of environmental and health concern. Next to understanding how such pollutants can be degraded by microorganisms, it is also relevant to determine the microorganisms’ lower threshold of responsiveness. Aromatoleum aromaticum EbN1 is a specialist in anaerobic degradation of aromatic compounds, employing a complex and substrate-specifically regulated catabolic network. The present study aims at verifying the predicted role of the PcrSR system in sensing p-cresol and at determining the threshold of responsiveness for alkylphenols. The findings have implications for the enigmatic persistence of dissolved organic matter (escape from biodegradation) and for the lower limits of aromatic compounds required for bacterial growth.

INTRODUCTION

Alkylphenols (including p-cresol and p-ethylphenol) are widespread environmental pollutants with continuous input from both anthropogenic and natural sources. Cresols represent high-production-volume chemicals, with worldwide annual production exceeding 470 kilotonnes (kt) (1), and are used for the industrial production of a wide variety of commodities (e.g., pesticides and plasticizers) (2). Moreover, because alkylphenols are constituents of crude oil and coal tars, they are released in large amounts through coal gasification and refineries (3–6). Alkylphenols have been detected in the micro- to nanomolar range in a variety of environmental settings, ranging from landfills to groundwater in and around industrial sites (7–10). Alkylphenols (including p-cresol) are chemicals of proven health concern due to their carcinogenic, reproductive, immunological, and neurological effects (11). Notably, alkylphenols have also a variety of natural sources, such as oils, and are produced as essences by various plants (11), as well as being metabolic products in animal excrements, e.g., approximately 180 kt of urinary p-cresol is produced per year by the human population (12, 13). Irrespective of the sources of alkylphenols, they are rapidly degraded in surface waters and soils but are comparatively persistent in anoxic groundwaters and sediments (11), motivating interest in studying the anaerobic degradation of these aromatic compounds of environmental concern.

Aromatoleum aromaticum EbN1 belongs to the Betaproteobacteria, and the genus includes a suite of specialist denitrifying degraders (14). A. aromaticum EbN1 is a well-studied model organism, anaerobically degrading a large variety of monoaromatic compounds via a complex catabolic network (15–17). The compound-specific regulation of individual peripheral degradation pathways suggests the presence of cognate sensory proteins to allow the bacterium to discriminate structurally highly similar aromatic molecules (15). A recent molecular genetic study demonstrated that the predicted σ⁵⁴-dependent one-component system EtpR controls the expression of the gene cluster for the anaerobic degradation of p-ethylphenol and p-hydroxyacetophenone (18). Furthermore, a subsequent physiological study revealed an in vivo response threshold of A. aromaticum EbN1 for p-hydroxyacetophenone in the range of 1 to 10 nM (19).

p-Cresol is assumed to enter cells of A. aromaticum EbN1 via passive diffusion. Differential proteomics indicated anaerobic degradation of p-cresol to be initiated by the formation of p-hydroxybenzaldehyde catalyzed by EbA5380, herein reannotated as flavin adenine dinucleotide (FAD)-dependent p-cresol methylhydroxylase (Cmh). Subsequent dehydrogenation by EbA5381 (herein reannotated p-hydroxybenzaldehyde dehydrogenase [Hbd]) forms p-hydroxybenzoate, which is then activated to the respective coenzyme A (CoA) ester by predicted CoA ligase HbcL-1 (herein reannotated Hcl2) (20) (Fig. 1). The cmh and hbd genes form an apparent operon and, together with hcl2, enframe the genes for the predicted two-component system EbA5371/-5 (herein reannotated PcrSR). The sensory His-kinase PcrS harbors various domains potentially serving effector (p-cresol) recognition. The presence of a σ⁵⁴ interaction domain in the response regulator (PcrR), as well as a σ⁵⁴ consensus sequence in the predicted promoter region of the cmh-hbd operon, provide circumstantial evidence that the PcrSR system controls the expression of this operon (Fig. 1).

FIG 1.

Scheme of the proposed transcriptional regulation of anaerobic degradation of p-cresol by the predicted σ⁵⁴-dependent two-component system PcrSR in the denitrifying bacterium Aromatoleum aromaticum EbN1. Compound names: 1, p-cresol; 2, p-hydroxybenzaldehyde; 3, p-hydroxybenzoate; 4, p-hydroxybenzoyl-CoA. Enzyme names: Cmh, FAD-dependent p-cresol methylhydroxylase; Hbd, p-hydroxybenzaldehyde dehydrogenase; Hcl2, 4-hydroxybenzoate CoA ligase. HTH, helix-turn-helix; 4VR, 4-vinyl-reductase; PAS, Per-Arnt-Sim; UBS, putative upstream binding sequence of PcrR; XylR, regulatory protein of the Pseudomonas TOL plasmid.

The involvement of one- or two-component systems in controlling gene expression for the degradation of aromatic compounds is well established in several bacteria. The one-component systems XylR and DmpR in Pseudomonas putida are among the best-studied representatives, controlling the operons for the aerobic catabolism of toluene/xylenes and phenol, respectively (21–27). The two-component system TodST in P. putida activates gene expression for the toluene degradation pathway from the todX promoter in response to toluene (28, 29). In most cases, the function of such sensors was analyzed using molecular genetics combined with promoter studies. A common theme of PcrS, EtpR, and many other known sensory proteins for monoaromatic compounds appears to be their cytoplasmic localization, as inferred from the absence of predicted signal peptides and transmembrane helices (Table 1). However, very little is known about the sensitivity of these sensors toward their aromatic effectors.

TABLE 1.

Examples of cytoplasmic sensor proteins for monoaromatic compounds^a

Substrate(s)	Sensor	Family	Sensory domain(s)	Bacterium	Reference
Alkylbenzenes
Tolueneb	TdiS	Two component	PAS (2×)	Aromatoleum aromaticum EbN1	15
Toluenec	TodS	Two component	PAS (2×)	Pseudomonas putida F1	28
Toluenec	TmoS	Two component	PAS (2×)	Pseudomonas mendocina	72
Toluenec , xylenec	XylR	XylR/DmpRd	4VR	Pseudomonas putida mt-2	22
Ethylbenzeneb	Tcs2	Two component	PAS (2×)	Aromatoleum aromaticum EbN1	15
Styrenec	StyS	Two component	PAS (2×)	Pseudomonas putida Y2	73
Alkylphenols
Phenolb	PdeR	XylR/DmpRd	XylR, 4VR	Aromatoleum aromaticum EbN1	15
Phenolc; o-, m-, and p-cresolc; 2,3-, 2,4-, 2,5-, and 3,4-dimethylphenolc	DmpR	XylR/DmpRd	4VR	Pseudomonas sp. strain CF600	25
p-Ethylphenolb ; p-hydroxyacetophenoneb	EtpR	XylR/DmpRd	XylR, 4VR	Aromatoleum aromaticum EbN1	18
p-Cresolb	PcrS	Two component	XylR, 4VR, PAS (2×)	Aromatoleum aromaticum EbN1	15
Aromatic ketones and carboxylates
Acetophenoneb	Tcs1	Two component	PAS	Aromatoleum aromaticum EbN1	15
Benzoatec; 2- and 3-methyl-, 2,3-, 2,5-, and 3,4-dimethylbenzoatec	XylS	AraC/XylSd	AraC	Pseudomonas putida	23
p-Hydroxybenzoate	PobR	AraC/XylSd	AraC	Azotobacter chroococcum	74
Salicylatec	NahR	LysRd	LysR	Pseudomonas putida	75
Protocatechuatec	PcaU	IclRd	GAF	Acinetobacter sp. strain ADP1	76

^aCytoplasmic localization was assessed using the programs SignalP (signal peptide prediction) and TMHMM (prediction of transmembrane helices). Transmembrane-spanning histidine kinases PhoQ of E. coli (77) and BpdS of Rhodococcus sp. strain M5 (78) served as controls.

^bEffector functionality predicted.

^cEffector functionality proven.

^dOne-component system.

In the present study, the predicted function of the two-component system PcrSR was verified by demonstrating that an in-frame ΔpcrSR mutant was impaired in expression of the cmh and hbd genes in the presence of p-cresol. Furthermore, the response threshold of A. aromaticum EbN1 cultures for p-cresol, along with that of the structurally related p-ethylphenol, was determined by targeted transcript analysis of genes involved in their respective catabolism.

RESULTS AND DISCUSSION

Generation of ΔpcrSR and pcrSR-complemented mutants.

To verify the predicted role of the two-component system PcrSR in controlling the p-cresol-dependent expression of cmh and hbd, a mutant with an unmarked in-frame ΔpcrSR mutation was generated. In this deletion mutant, only the start codon of pcrS and the stop codon of pcrR were preserved to maintain the reading frame (Fig. 2A). Accordingly, no PCR products could be observed using the primers specific for pcrS or pcrR. Moreover, using primers hybridizing immediately up- and downstream from the knockout region, only a small 310-bp amplicon was generated (the wild-type amplicon is 3,838 bp) (Fig. 2B). This newly generated ΔpcrSR mutant was then complemented in trans with pBBR1MCS-2 containing pcrSR. This complementation restored the expression of cmh and hbd (see below). The pcrSR-complemented mutant had the genotype ΔpcrSR/pBBR1MCS-2 ΩpcrSR, and PCR products of the expected size could be generated using gene-specific primers (Fig. 2B).

FIG 2.

Generation of in-frame ΔpcrSR deletion and pcrSR-complemented mutants. (A) Scale model of genes coding for the two-component system PcrSR and parts of the 3′- and 5′-neighboring regions on the chromosome of A. aromaticum EbN1, displaying the wild type (top) and the ΔpcrSR mutant (bottom). Chromosomal hybridization locations of primer pairs used for construction of the knockout vector pk19 Ωhcl2/3ʹ-IR-pcrR are in gray, while those for the complementation plasmid pBBR1MCS-2 ΩpcrSR are indicated in black. The hybridization positions of the gene-specific primer pairs for pcrS and pcrR, as well as the primer pair ΔpcrSR_F/_R for identifying the knockout genotype, are in brown (see Table S1 in the supplemental material). Expected lengths of the respective PCR products are shown below the model. (B) Electropherogram of PCR products obtained from the wild type, the ΔpcrSR mutant, and the pcrSR-complemented (pcrSR compl.) mutant using specifically designed primer pairs. Applying the primer pair ΔpcrSR_F/_R, a 3,838-bp amplicon was obtained from the chromosome of the wild type, whereas the ΔpcrSR mutant and the pcrSR-complemented mutant yielded shorter, 310-bp amplicons. Correspondingly, amplification of pcrS and pcrR was possible only from the wild type and the pcrSR-complemented mutant but not from the ΔpcrSR mutant.

PcrSR mediates substrate-specific expression of p-cresol genes.

To study the p-cresol-specific phenotype of the ΔpcrSR mutant, the same design of physiological experiments was used as for determination of the response thresholds (see below), corresponding to that previously reported for p-hydroxyacetophenone (19). Essentially, nonadapted cells were anaerobically grown with a limited supply of benzoate (1 mM); upon depletion of benzoate, a single pulse of p-cresol (final concentration, 100 μM) was applied (Fig. 3A). For transcript profiling, samples were retrieved 5 min prior to (reference sample) and 5, 15, 30, 60, and 120 min after the pulse (test states) (zoom-ins in Fig. 3A). The profiles of growth and benzoate depletion were rather similar for comparison of the ΔpcrSR mutant with the wild type and the pcrSR-complemented mutant, indicating that the in-frame deletion did not negatively affect the growth physiology of A. aromaticum EbN1. In contrast to the ΔpcrSR mutant, however, the pcrSR-complemented mutant displayed a slight increase in optical density approximately 10 h after p-cresol addition, similar to that observed for the wild type (indicating loss and regain of function).

FIG 3.

Characterization of the three different genotypes of A. aromaticum EbN1. (A) (Bottom) Wild type, ΔpcrSR mutant, and pcrSR-complemented mutant were initially cultivated with a growth-limiting supply of benzoate (1 mM). Following depletion of benzoate, p-cresol was added to each culture (red dashed lines), yielding a final concentration of 100 μM. (Top, enlargements from dashed-line boxes) Subsequently, samples for targeted transcript analysis were taken in a time-resolved manner (gray dashed lines). (B) Transcript analysis (qRT-PCR) of the denoted target genes. Data points were connected with LOESS (locally estimated scatterplot smoothing) regression curves, with shaded bands indicating 95% confidence intervals. (C) Increased transcript abundances of the signaling system components in the pcrSR-complemented mutant relative to their levels in the wild type. (D) MS-based protein identification, with numbers representing Mascot scores. n.d., not detected.

The effect of pcrSR deletion versus in trans complementation on the expression of the p-cresol catabolic genes (cmh, hbd, and hcl2) was studied by quantitative reverse transcription-PCR (qRT-PCR) (Fig. 3B). In the case of cmh and hbd (forming an operon-like structure), transcript abundances in the ΔpcrSR mutant were strongly reduced (21- and 8-fold, respectively) compared to their abundances in the wild type. The same effect was observed for the initial rates of transcript formation. Notably, the rate of transcript formation, as well as maximal transcript abundance, was markedly highest in the pcrSR-complemented mutant. This is probably due to the transcript levels of the pcrSR genes in the complementation mutant being well above those observed for the wild type (Fig. 3C). These findings support the idea that the PcrSR system is responsible for the p-cresol-dependent transcriptional control of cmh and hbd. Surprisingly, the hcl2 transcript profiles were rather similar across the three genotypes tested, suggesting that the PcrSR system being studied is not involved in transcriptional regulation of this gene (Fig. 3B). In accord with the transcript profiles of cmh and hbd, their protein products were specifically, and with high scores, identified exclusively in the wild type and the pcrSR-complemented mutant (Fig. 3D). The observation that Hcl2 remained undetectable in any of the three genotypes tested agrees with this protein also having not been identified in a previous study (20).

Response threshold for p-cresol.

To assess the response threshold for p-cresol, transcript profiles of the p-cresol catabolic genes cmh, hbd, and hcl2 were studied across a concentration range of this effector, extending from 100 μM down to 0.1 nM, using the same design of physiological experiments as described above. Highly reproducible growth curves with sampling time points for each of the eight p-cresol concentrations tested and a negative control (no addition of p-cresol) are provided in Fig. S1 in the supplemental material, and fold changes of transcript abundance are listed in Table S4.

Differential expression of the three catabolic genes was related to their individual expression levels directly prior to the effector pulse. The transcript level of each gene at this reference time point was constant across the tested concentration range of p-cresol (coefficient of variation [CV] of cycle threshold [C_T] values, <0.031), affording reliable cross-comparison. The transcript profiles determined for cmh and hbd (Fig. 4A) mirrored the tested concentration range of the effector p-cresol, as well as their presumptive organization in an operon-like structure. Agreeing with cmh representing the first gene, its increased transcript levels were observed earlier (6-fold after 15 min versus 6-fold after 30 min) and reached higher maximal values (150- versus 30-fold) than those of hbd, which may result from lower mRNA decay due to higher ribosomal occupancy rather than lower transcription termination (30). Reflecting these differences in expression profiles, the lowest p-cresol concentrations resulting in detectable increase in transcript abundance were 10 nM for cmh and 30 nM for hbd. In contrast, the transcript profiles of hcl2 indicated a markedly higher response threshold of between 1 and 0.1 μM p-cresol. This may be due to hcl2 not being under transcriptional control of the PcrSR system studied here, since hcl2 is neither part of the cmh-hbd operon nor anteceded by the same promoter region. Considering that the substrate of Hcl2, namely, p-hydroxybenzoate, is shared with the pathway for anaerobic degradation of phenol (17, 31), one may speculate that a different regulator, e.g., responsive to the intracellular level of p-hydroxybenzoate or its CoA ester, is involved.

FIG 4.

Time-resolved, quantitative transcript profiles of A. aromaticum EbN1 in response to different extracellular effector concentrations. (A) p-Cresol as the effector. The selected transcripts represent genes (Fig. 1) coding for enzymes involved in the anaerobic degradation of p-cresol (hcl2, cmh, and hbd). (B) p-Ethylphenol as the effector. The selected transcripts represent genes coding for enzymes involved in the anaerobic degradation of p-ethylphenol (acsA, hped, and emhF) (19). In both cases, relative transcript abundances were determined by means of qRT-PCR, with the time point of 5 min prior to effector addition serving as a reference. Each data point is based on 3 biological replicates with 3 technical replicates analyzed for each. Growth data of the cultures providing the RNA samples for all conditions tested are shown in detail in Fig. S1 (for p-cresol) and Fig. S2 (for p-ethylphenol).

Response threshold for p-ethylphenol.

We also investigated the response threshold for p-ethylphenol, because it shares high structural similarity with p-cresol. However, p-ethylphenol is degraded via a different peripheral route involving intermediary formation of p-hydroxyacetophenone (17). Furthermore, gene expression for this degradation pathway is mediated by the σ⁵⁴-dependent transcriptional activator EtpR (18). The response threshold for p-ethylphenol was determined with an experimental setup and effector concentration range analogous to those described above for p-cresol, targeting three selected p-ethylphenol catabolic genes, acsA (encoding acetoacetyl-CoA synthetase), hped [encoding 1-(4-hydroxyphenyl)ethanol dehydrogenase], and pchF (herein renamed emhF; encoding ethylphenol-methylhydroxylase) for transcript profiling as previously used for p-hydroxyacetophenone (19). Highly reproducible growth curves with sampling time points for each of the eight p-ethylphenol concentrations tested and a negative control (no addition of p-ethylphenol) are provided in Fig. S2, and fold changes of transcript abundance are listed in Table S5.

The genes selected for targeted transcript analysis (Fig. 4B) are located at the beginning (acsA), in the middle (hped), and at the end (emhF) of the large, 16.4-kb p-ethylphenol catabolic gene cluster (17, 19). The onset of detectable transcript level increase agreed very well with the earlier findings for p-hydroxyacetophenone (19), albeit with 2-fold-higher levels for the latter (acsA, 18- versus 40-fold after 5 min; hped, 10- versus 26-fold after 30 min; and emhF, 7.5- versus 14-fold after 60 min). Furthermore, the highest relative transcript levels were in 2 of 3 cases less pronounced with p-ethylphenol than with p-hydroxyacetophenone (acsA, 156- versus 250-fold after 120 min; hped, 64- versus 46-fold after 120 min; and emhF, 12-fold after 120 min versus 14-fold after 60 min) (19). Beyond that, the expression profiles for the colocalizing genes of a presumptive solvent-efflux system (ebA335 to ebA326) were congruent for these two aromatic effector molecules (Fig. S3). Thus, p-hydroxyacetophenone, which represents a growth substrate, as well as a catabolic intermediate, apparently possesses stronger effector properties than p-ethylphenol for the shared EtpR system.

Taken together, this and the previous study (19) revealed A. aromaticum EbN1 to have the same response threshold (between 10 and 1 nM) for three different aromatic compounds (p-cresol, p-ethylphenol, and p-hydroxyacetophenone), mediated by two different σ⁵⁴-dependent transcriptional activators (two-component PcrSR and one-component EtpR).

Theoretical considerations on availability of p-cresol.

The low-nanomolar threshold of responsiveness for p-cresol and p-ethylphenol prompts the questions of how many molecules of these alkylphenols are actually available to the respective cytoplasmic sensory proteins (PcrS and EtpR) and what factors determine the overall response time.

Bearing in mind that a concentration of 1 nM is equivalent to 0.6 molecule per 1 μm³ [10⁻⁹ × N_A l⁻¹/(10¹⁵ μm³ l⁻¹), where N_A is the Avogadro constant, 6.022 × 10²³ mol⁻¹], a single-cell volume of 3 μm³ thus contains an average intracellular amount of 20 (at 10 nM) or 2 (at 1 nM) molecules p-cresol per cell (Fig. 5A and B). Due to the higher membrane partitioning coefficient (K_m) of p-ethylphenol (85, versus 17 for p-cresol), the membrane accumulation is about 5-fold higher than calculated for p-cresol. Despite this, the intracellular number of molecules per cell at equilibrium (solely driven by passive diffusion) is the same for both alkylphenols. One may speculate that around 2 molecules per cell do not suffice to trigger sensory recognition of p-cresol and p-ethylphenol by the soluble signaling systems PcrSR and EtpR, respectively.

FIG 5.

Quantitative illustration of effector (p-cresol) availability at 10 nM. (A) Upon effector addition, the cell density is approximately 1 cell (ellipsoid, 3 μm³) in a cubic volume of 1,300 μm³. At 10 nM, such a cubic space element contains 8,000 solute particles (red dots), with the green-shaded zoom-in representing a 0.2-μm-wide slice. At equilibrium, the solute concentration in the cells equals that of the surrounding medium, while solute molecules are markedly enriched in the cell envelope. (B) Stages of the equilibration process. The initial concentration gradient of the effector across the cell envelope is enhanced by the lipophilic character of this aromatic solute and drives transmembrane diffusion until an equilibrium between intra- and extracellular spaces is reached ($\ll 1\text{s}$). In the final state of equilibrium, a gradient no longer exists and the elevated concentration of the solute in the cell envelope just reflects the lipophilic character of the latter. (C) Timeline from effector equilibration to full-scale gene expression.

The first response on the transcriptional level was not observed until 30 min after provision of 10 nM p-cresol but was determined already after 15 min in the case of 1,000 nM (2,400 molecules per cell). Considering that the equilibrium between the intra- and extracellular space is reached within a fraction of a second (Fig. 5B), response times are not limited by diffusion but rather by steady-state numbers of effector molecules per cell, the binding kinetics, and the transcription process (see further discussion below). Furthermore, the 17-fold-higher concentration of effector molecules in the cell envelope ensures constant numbers of effector molecules in the cell irrespective of binding to the sensory proteins, assuming that catabolic conversion of p-cresol (or p-ethylphenol) does not yet occur at a substantial rate. For reasons of simplicity, the following considerations focus on p-cresol.

Because sensory proteins responsive to aromatic compounds have proven recalcitrant to purification so far (21), data on in vitro binding affinities (1/K_d [dissociation constant]) are not available. However, the recombinant ligand-binding domain of chemotaxis-mediating PcaY_PP from Pseudomonas putida KT2440, recognizing 14 different aromatic ligands, showed K_d values ranging from 138 μM for 3-aminobenzoate down to 3.7 μM for quinate (32). Moreover, solute binding proteins of ABC-type uptake systems typically have K_d values ranging between 1 μM and 0.01 μM (33, 34). Given the clear response at a concentration of 10 nM p-cresol, we can place the K_d value of PcrS for p-cresol well within the submicromolar range. Generally, K_d equals [E][S]/[ES], where E, S, and ES refer to the concentration of the effector (p-cresol), the free sensor (PcrS), and the effector-sensor complex, respectively. Replacing [S]/[ES] with the absolute number of molecules per cell (N), i.e., K_d = [E]N_S/N_ES, we can then infer that N_ES must be ≥1 in order to produce a response. Furthermore, for the abundance of PcrS in A. aromaticum EbN1, we assume around 10 copies per cell (i.e., $N_S^{\text{total}}=N_S+N_{\text{ES}}\hspace{0.17em}\sim \hspace{0.17em}10$), as inferred from single-cell-based proteome profiling of Escherichia coli, establishing a copy number of at least 10 for essential proteins (35). With these assumptions, we obtain 0.1 μM as the upper limit for the K_d value.

At p-cresol concentrations of 0.01 μM, its binding to PcrS is diffusion limited. The maximum rate for diffusion-limited association of p-cresol with PcrS in the cytoplasm, k_on, is of the order of 1/(nM s) (Smoluchowski limit), but this can be reduced significantly when the binding site of the protein has a small cross-section for ligand capture (36). With k_off = k_onK_d and k_on of ∼10⁻² to ∼10⁻¹nM⁻¹ s⁻¹, the typical dwell times (1/k_off) of the solute on the sensor are 1 s to 0.1 s (for K_d ∼ 100 nM).

Against the background of the quickly attainable effector equilibrium and its binding to the sensory protein, it stands to reason to consider the time line of gene expression following effector recognition. The next step in signal transduction is phosphorelay from PcrS to PcrR, translating effector recognition by PcrS into activation of PcrR for transcriptional initiation. Again, this is a diffusion-limited association, but now with a markedly smaller k_on, in the order of 1/(μM s), viz., a lower rate (37), compared to that of the preceding effector-sensor interaction. The regulation and processivity of gene expression (here from the gene to its folded protein product) in bacteria constitute a multilayered and interwoven process. (i) The interplay of factors like promoter architecture (38), cognate sigma factors (39), and (two-component) sensory systems (40) conveys condition-specific initiation of transcription. (ii) Elongation of transcription can be influenced by the interaction of nascent RNA with RNA polymerase (41), and mRNA is also rapidly turned over depending on ribosomal occupancy (42). (iii) RNA polymerase is closely interlinked with ribosomes (43) such that the overall speed of gene expression is largely governed by ribosomal activity, viz., translational efficiency. The latter in turn depends on the interplay of several factors, including codon usage on mRNA (44), as well as cellular pools of resources like amino acyl-tRNAs and ribosomal factors (45). Moreover, mRNA and protein copy numbers are not correlated (35), and protein folding and complex assembly both occur cotranslationally (46). These multiple facets, taken together, create challenges for the determination of response time of gene expression. Early biochemical studies in conjunction with theoretical considerations on transcription-to-translation of the lac operon in IPTG (isopropyl-β-d-thiogalactopyranoside)-induced E. coli cells revealed an expression level of 20 copies of β-galactosidase cell⁻¹ s⁻¹ pg RNA⁻¹ versus 2.4 copies of galactoside acetyltransferase cell⁻¹ s⁻¹ pg RNA⁻¹, attributed to differing protection of the mRNA by ribosomes (47). More recently, single-cell analysis employing time-lapse microscopy has been applied to study the dynamics of gene expression. In noninduced cells of E. coli, the burst-like synthesis of β-galactosidase (5 to 10 copies per burst) yields ∼20 copies cell⁻¹ in 150 min and was attributed to stochastic and transient dissociation of the LacI repressor (48). At low intracellular inducer concentrations (50 μM methyl-β-d-thiogalactoside), a small burst of the lactose permease LacY (<10 copies cell⁻¹) after 10 to 20 min can be followed by a large burst (∼300 copies cell⁻¹) within less than 1 h (49). The LacI repressor controlling the expression of the lac operon requires less than 4.5 min of search time to find the operator site by facilitated diffusion (50). Therefore, even at low effector concentrations, the bottleneck for translating effector recognition into initiation of gene expression appears to be the singularity of the cmh-hbp operon in conjunction with the time required by active PcrR to find and bind the respective promoter. Taken together, recent findings suggest expression upon effector recognition to be well in the range of minutes, indicating that, overall, the response dynamics toward an effector are constrained by the velocity/processivity of gene expression rather than by the attainment of effector equilibrium across the cytoplasmic membrane and the interaction between effector and sensor (Fig. 5C).

Comparison to olfaction in insects.

Alkylphenols, in particular p-cresol and p-ethylphenol, are constituents of human sweat, recognized by the malaria-transmitting mosquito Anopheles gambiae and guiding its host-seeking behavior (51). An. gambiae possesses a large array of odor receptors (ORs) specialized for the recognition of different compound classes, e.g., aromatic compounds or fatty acids. Some ORs of An. gambiae are responsive to alkylphenols, with OR1 exhibiting a 50% effective concentration (EC₅₀) of ∼400 nM p-cresol and failing to respond at 10 nM p-cresol (52). Thus, PcrS of A. aromaticum EbN1 is obviously more sensitive than OR1 of An. gambiae. This can be rationalized by considering that insects need only to recognize complex odorant mixtures (by way of olfactory/odor coding) to guide their behavioral response; the individual odorant is not metabolized. In contrast, substrate sensing by bacteria aims at efficient regulation of the respective catabolic process and exploitation of available substrates even at very low concentrations.

Conclusions.

In this study, we were able to substantiate the predicted function of the two-component system PcrSR in mediating p-cresol recognition and its translation into specific expression of cmd and hbd. These genes encode the enzymes for initial anaerobic oxidation of p-cresol to p-hydroxybenzoate. To the best of our knowledge, PcrSR represents the first two-component system showing specific responsiveness to p-cresol. Considering the environmental relevance of p-cresol as a primary pollutant, as well as being a naturally occurring compound, these findings might have implications for, e.g., the development of novel biosensors to assess the occurrence of p-cresol under different environmental settings.

Time-resolved targeted transcript analysis of the cmd and hbd genes revealed an in vivo response threshold of A. aromaticum EbN1 for p-cresol within the range of 1 to 10 nM; similar values were determined for p-ethylphenol. Such a high in vivo sensitivity allows exploitation of low concentrations pertaining to most environmental conditions not affected by severe pollution. From the very low response threshold yielding substantial gene expression, we suggest the K_d value of PcrS for p-cresol to be below 0.1 μM, which in turn indicates a high binding affinity.

As calculated here, a single pulse of 10 nM p-cresol or p-ethylphenol to the extracellular space translates within <1 ms into a diffusion-driven equilibrium with 20 molecules alkylphenol residing in the cytoplasm of a single cell. This very low number of effector molecules apparently suffices to trigger PcrSR-/EtpR-mediated gene expression. Since most other known sensory proteins for aromatic compounds are localized in the cytoplasm, like PcrS and EtpR (Table 1), the present findings should have broader implications for sensing of aromatic compounds in bacteria. Considering the relatively high partitioning coefficients of aromatic compounds, their membrane accumulation accelerates the attainment of equilibrium (Fig. 5) and, thereby, the provision of aromatic effector molecules for their cytoplasmic sensory proteins. Hence, a cytoplasmic location of sensory proteins controlling gene expression for likewise cytoplasmic catabolism of these compounds seems plausible and contrasts with the predominant membrane anchoring and periplasmic orientation of sensory proteins involved in chemotaxis (53).

An enigmatic topic in biogeochemistry is the persistence of dissolved organic matter (DOM) in aquatic and marine systems. Fueled by phytoplankton production in surface ocean and riverine input of terrestrial material, refractory DOM is annually processed in the ocean in the range of <0.2 gigatonne (Gt) of carbon, is composed of at least 10⁴ to 10⁵ different organic molecules, and can reach an average age of several thousand years (54). Persistence of DOM is attributed to either the biochemical recalcitrance or vanishingly low concentrations of molecular DOM constituents, which may be well in the subnanomolar range (54). The current and a recent study (19), both with active batch cultures of A. aromaticum EbN1, revealed that extracellular concentrations of monoaromatic growth substrates somewhat below 10 nM are too low to be recognizable by their cognate sensory proteins. Thereby, these substrates may escape from biodegradation, which would favor the hypothesis of dilution as a driver of DOM persistence. Nonetheless, at unrecognizably low substrate concentrations, metabolic turnover affecting DOM could still occur, if low basal levels of the respective catabolic proteins are constitutively retained. Indeed, at low growth rates (μ_low in substrate-limited chemostats), A. aromaticum EbN1 forms a rather wide spectrum of uptake systems and catabolic enzymes despite the absence of the respective substrates, which was interpreted as a strategy to be prepared for future nutritional opportunities (55).

MATERIALS AND METHODS

Bacterial strains and cultivation conditions.

A. aromaticum EbN1 was cultivated under nitrate-reducing conditions in a defined, ascorbate-reduced and bicarbonate-buffered mineral medium at 28°C as previously described (56). Organic substrates (benzoate, p-cresol, and p-ethylphenol) were added from aqueous stock solutions sterilized by filtration. Every experiment was started from a glycerol stock of the respective genotype of A. aromaticum EbN1 anaerobically grown with benzoate (4 mM). The sequence of cultivation steps comprised the following. (i) A dilution series (10⁻¹ to 10⁻⁶), provided with benzoate (4 mM) as the sole source of organic carbon and energy, was inoculated from a glycerol stock and incubated for 4 days. (ii) The first preculture (80-ml culture volume in 100-ml flat-bottom glass bottles sealed with butyl rubber stoppers) was supplied with benzoate (2 mM), inoculated with 5% (vol/vol) of the 10⁻⁶ dilution, and incubated for 3 days. (iii) The second preculture was carried out under the same conditions by inoculation with 5% (vol/vol) from the first preculture and incubated for 17 h. (iv) The main cultures (400-ml culture volume in 500-ml flat-bottomed glass bottles sealed with butyl rubber stoppers), performed in triplicates, were supplied with 1 mM benzoate and inoculated with 2% (vol/vol) of the second preculture. All cultures of the pcrSR-complemented mutant contained kanamycin (50 μg ml⁻¹) as a selection marker, which was added from an aqueous stock solution sterilized by filtration. All chemicals were of analytical grade.

Generation of in-frame ΔpcrSR deletion mutation.

Genomic DNA and plasmids were isolated according to standard protocols as previously described (57). For unmarked knockout of pcrS and pcrR, a knockout vector was constructed in an E. coli strain S17-1 background on the basis of the suicide vector pK19mobsacB. The final knockout vector contained 1.5 kb of both the up- and downstream regions of pcrS and pcrR, respectively, resulting in the pk19 Ωhcl2/3′-IR-pcrR vector. Both inserts were cloned simultaneously into pk19mobsacB using the In-Fusion HD cloning plus kit (TaKaRa Bio, Inc., Kusatsu, Japan) according to the manufacturer’s instructions, using the PstI restriction site. For the cloning reaction, 125 ng of linearized pK19mobsacB and a molar ratio of 2:2:1 of the two inserts relative to the linearized vector were used. The respective primers were designed using the In-Fusion cloning primer design tool (TaKaRa Bio, Inc.), and the sequences are given in Table S1 in the supplemental material. Both homologous regions were amplified from genomic DNA of A. aromaticum EbN1 using the CloneAmp HiFi (high-fidelity) PCR premix (TaKaRa Bio, Inc.) according to the manufacturer’s instructions. The final knockout vector construct maintained the start and stop codon of pcrS and pcrR, respectively. The knockout vector pk19 Ωhcl2/3′-IR-pcrR was transferred from E. coli S17-1 to A. aromaticum EbN1 via conjugation as described previously (57). Kanamycin-resistant single-crossover clones were verified by PCR using the ΔpcrSR primer pair targeting the up- and downstream region of pcrS and pcrR, respectively. This yielded two amplicons of 310 bp and 3,838 bp, respectively (Fig. 2B). The single-crossover mutant was transferred into liquid medium (4 mM benzoate, 5 mM acetate, and 5 mM pyruvate) without kanamycin to induce the second crossover event, yielding either the ΔpcrSR or the wild-type genotype. Cells were plated on solid medium containing the same tripartite substrate mixture and 5% [wt/vol] sucrose. For identification of the ΔpcrSR genotype, colonies were screened as described above, yielding only one amplicon of 310 bp.

Complementation of pcrSR in trans into ΔpcrSR deletion mutant.

For in trans expression of pcrSR, a complementation vector based on the broad-host-range vector pBBR1 MCS-2 was generated in an E. coli S17-1 background. For this purpose, two nucleotide sequences (2,110 and 2,138 bp) were amplified by PCR using Phusion high-fidelity DNA polymerase (Thermo Fisher Scientific, Waltham, MA) and the compl-pcrS _F/_R and compl-pcrR_F/_R primer pairs (Fig. 2A). Both fragments were simultaneously cloned into the vector using the In-Fusion HD cloning plus kit (TaKaRa Bio, Inc.) according to the manufacturer’s instructions. The vector was linearized using its EcoRI restriction site. For the cloning reaction, a total vector amount of 150 ng and a molar ratio of 2:2:1 of the two inserts relative to the linearized vector were used. The final construct was verified by sequencing and contained both pcrS and pcrR, as well as 521 bp upstream from the pcrS start codon to include the ribosomal binding site. Via conjugation, the vector was transferred to the ΔpcrSR mutant, yielding the pcrSR-complemented mutant (genotype ΔpcrSR/pBBR1MCS-2 ΩpcrSR). The conjugational transfer via agar plate mating and the verification of positive clones were performed as previously described (57).

Sequence validation by Sanger sequencing.

For sequence validation of the ΔpcrSR mutant, a 3,151-bp region of genomic DNA spanning across the entire up- and downstream regions, including the deletion site, was analyzed via Sanger sequencing (58). Additionally, a 4,841-bp region of the complementation vector (pBBR1MCS-2 ΩpcrSR) spanning across the entire insert was sequenced to verify the pcrSR-complemented mutant. Genomic DNA was prepared according to standard methods (57). Plasmid DNA was prepared using the NucleoSpin plasmid easypure kit (Macherey-Nagel, Düren, Germany). The respective fragments were amplified from genomic DNA via PCR using a Phusion high-fidelity DNA polymerase (Thermo Fisher Scientific) according to the manufacturer’s instructions and the primer pairs compiled in Table S3. PCR products were purified using a NucleoSpin gel and PCR clean-up kit (Macherey-Nagel) according to the manufacturer’s instructions. For sequencing, samples were prepared using the BigDye buffer and BigDye terminator sequencing reagent and analyzed using a 3130xl genetic analyzer (Applied Biosystems, Foster City, CA) as described by the manufacturer. An amount of 10 ng of PCR product or 100 ng of plasmid DNA was used per reaction.

Growth experiments.

To assess the responsiveness of A. aromaticum EbN1 to various concentrations of p-cresol and p-ethylphenol, nonadapted cells were cultivated with growth-limiting provision of benzoate (1 mM) as the sole source of organic carbon and energy. Upon its complete depletion after 17.5 h (Fig. S1 and S2), a distinct pulse of either p-cresol or p-ethylphenol was added to the cultures, yielding 8 different final concentrations (100 μM, 1 μM, 100 nM, 50 nM, 30 nM, 10 nM, 1 nM, and 0.1 nM). A negative-control experiment without the addition of either p-cresol or p-ethylphenol was performed under the same conditions. Throughout the entire incubation period, 3-ml samples were frequently withdrawn by means of sterile, N₂-flushed syringes. Amounts of 1 ml were used for monitoring growth by measuring the optical density at 660 nm (OD₆₆₀). Amounts of 2 ml were immediately centrifuged (20,000 × g for 10 min at 4°C) and the supernatant was stored at −20°C for determining depletion of benzoate by means of micro-high-performance liquid chromatography (micro-HPLC). To assess the effect of the deletion mutation, the ΔpcrSR mutant and the pcrSR-complemented mutant were also cultivated as described above, with 100 μM p-cresol added after complete depletion of benzoate. Cultures of the pcrSR-complemented mutant contained kanamycin (50 μg ml⁻¹). For each test condition, three replicate cultures were conducted.

Cultivation and cell harvesting for transcript profiling and proteomic analysis.

Cultivation was performed as described above. For each experiment, samples for time-resolved transcript profiling were retrieved 5, 15, 30, 60, and 120 min after the addition of either p-cresol or p-ethylphenol. If p-cresol or p-ethylphenol was added at a final concentration of 100 μM, further samples were taken after 240 and 480 min. For every experiment, a sample taken 5 min prior to the addition of p-cresol or p-ethylphenol served as the reference state. At each sampling time point, 5 ml of culture broth was withdrawn using a sterile, N₂-flushed syringe and immediately added to 10 ml of RNAprotect bacterial reagent (Qiagen, Hilden, Germany), mixed thoroughly, incubated for 5 min at room temperature, and centrifuged (4,000 × g for 10 min at 4°C). Pellets were resuspended in 0.5 ml RNAprotect bacterial reagent (Qiagen), transferred into a 2-ml microcentrifuge tube, and centrifuged (20,000 × g for 10 min at room temperature). Pellets were shock frozen in liquid N₂ and stored at −80°C. For proteomic analysis, cultivation was performed as described above for all three genotypes and p-cresol was added (final concentration, 100 μM) after complete benzoate depletion. At 480 min after the addition of p-cresol, the entire 400-ml cultures were harvested for whole-cell shotgun proteomic analysis. The cells were centrifuged (14,334 × g for 30 min at 4°C), and the pellets were washed in 250 ml washing buffer (100 mM Tris-HCl, 5 mM MgCl₂·6H₂O, pH 7.5) and centrifuged again. The pellets were resuspended in 0.8 ml of the same washing buffer and transferred into 2-ml microcentrifuge tubes. After centrifugation (20,000 × g for 10 min at 4°C), pellets were shock frozen in liquid N₂ and stored at −80°C until further analysis.

Quantitation of benzoate by micro-HPLC.

Quantitative depletion profiling of benzoate was achieved using a micro-HPLC instrument (UltiMate 3000; Thermo Fisher Scientific, Germering, Bavaria, Germany) equipped with a Thermo Hypersil Gold column (C₁₈, 150 × 1 mm, 2.6-μm bead size; Thermo Fisher Scientific) and a rapid-separation (RS) diode array detector (Thermo Fisher Scientific) as described previously (19). The system was operated at 40°C with a flow rate of 100 μl min⁻¹. The 20-min gradient of eluent A (5% [vol/vol] acetonitrile in H₂O with 0.01% [vol/vol] H₃PO₄ [85%]) and eluent B (90% [vol/vol] acetonitrile in H₂O with 0.01% [vol/vol] H₃PO₄ [85%]) was constant for 2.5 min at 3% B, followed by a 4-min linear ramping to 65% B and a constant level of 3% B for 9 min. Benzoate was detected at 229 nm with a retention time of 9.32 min and a dynamic range from 5 nM to 50 μM.

Preparation of total RNA.

Total RNA was prepared as previously described (59, 60), comprising the following three major consecutive steps. (i) Stored cell pellets were resuspended in STE buffer (10 mM Tris-HCl, 1 mM EDTA, 100 mM NaCl, pH 8.3). Then, 20 μl SDS (10% [wt/vol]) and 900 μl Roti Aqua-Phenol (CarlRoth, Karlsruhe, Germany) were added, and the suspension was incubated at 60°C for 8 min (mixing by inversion every 30 s). Subsequent centrifugation (20,000 × g for 5 min at 4°C) yielded an aqueous phase, which was again treated with hot acidic phenol and centrifuged. The resultant aqueous phase was then transferred into a 2-ml 5Prime Phase Lock Gel tube (Quantabio, Beverly, MA). After adding one volume of phenol-chloroform-isoamyl alcohol (25:24:1), the tube was gently inverted for 5 min and centrifuged (20,000 × g for 5 min at room temperature). (ii) Subsequently, precipitation of nucleic acids was achieved by incubation with ice-cold ethanol (96%) at −80°C for 30 min followed by centrifugation (20,000 × g for 30 min at 4°C). The nucleic acid pellet was washed twice with ice-cold ethanol (75%) and centrifuged (20,000 × g for 15 min at 4°C). (iii) After drying, the pellet was resuspended in RNase-free water and subjected to digestion with DNase I (RNase free; Qiagen). DNA removal was validated by PCR using genomic DNA of A. aromaticum EbN1 as a positive control. To assess RNA quality, all 372 samples were analyzed using an Experion automated electrophoresis station (Bio-Rad). Quantification of RNA was performed using a TrayCell (Hellma Analytics, Müllheim, Germany) operated in a spectrophotometer (UV-1800; Shimadzu, Duisburg, Germany). RNA samples were stored at −80°C. All chemicals used for RNA preparation were of molecular-biology grade.

Transcript profiling by qRT-PCR.

Primers specific for the respective target genes (Table S2) were designed using the Primer3 software package (version 0.4.0; www.primer3.org). cDNA synthesis and real-time PCR were performed using 150 ng of total RNA. Samples were prepared using the Brilliant III ultrafast SYBR green quantitative reverse transcription-PCR (qRT-PCR) master mix (Agilent, Santa Clara, CA) and analyzed with a CFX96 real-time system (Bio-Rad). The settings comprised PCR initiation for 3 min at 95°C, 40 cycles of 10 s of denaturation at 95°C, 30 s of annealing at 60°C, and 30 s of extension at 60°C followed by real-time detection for 5 s. The specificity of accumulated products was verified by melting curve analysis, ranging from 60°C to 90°C in steps of 0.5°C. Samples taken 5 min prior to the addition of either p-cresol or p-ethylphenol were used as references, and all samples retrieved after that represented the test states. Per time point, 3 biological replicates were each analyzed with 3 technical replicates. Differences in relative transcript abundance were calculated as previously described (19) according to the following equation (61): ratio = E^{ΔCT (reference − test)}. Primer-specific PCR efficiencies (E) were determined as described previously (62).

Proteomic analysis.

Cell pellets were resuspended in 400 μl lysis buffer (30 mM Tris-HCl, 2 M thiourea, 7 M urea, pH 8.5). Cell disruption was achieved by bead beating (4 cycles of 6 m s⁻¹ for 10 s) using lysing matrix B (MP Biomedicals, Santa Ana, CA). The suspension was separated from the beads and centrifuged (100,000 × g for 1 h at 4°C). The pellets were discarded, and centrifugation was repeated as before. Subsequently, the supernatant was transferred into a clean microcentrifuge tube and protein quantification was performed according to the Bradford protein assay method (63). Whole-cell shotgun analysis was carried out as described previously (64). Tryptic peptides were separated using a nanoscale liquid chromatography (nano-LC) system (UltiMate3000 RSLCnano; Thermo Fisher Scientific) operated in a trap-column mode and equipped with a 25-cm separation column (C₁₈, 2-μm bead size, 75-μm inner diameter; Thermo Fisher Scientific), applying a 280-min linear acetonitrile gradient. An online-coupled ion trap mass spectrometer (amaZon speed ETD; Bruker Daltonik GmbH, Bremen, Germany) was used to analyze the nano-LC gradient continuously by means of a CaptiveSpray ion source (Bruker Daltonik GmbH). Ions were acquired via full-scan mass spectrometry (MS) (mass range, 400 to 1,400 m/z) and 20 tandem mass spectrometry (MS/MS) spectra of the most intense doubly (or more highly) charged ions, applying subsequent precursor exclusion for 0.2 min. Proteins were identified using the ProteinScape platform (version 3.1; Bruker Daltonik GmbH) on an in-house Mascot server (version 2.3; Matrix Science Ltd., London, UK) based on the genome sequence of A. aromaticum EbN1 (65) using a previously described target-decoy strategy (64). For each test state, the results of three biological replicates were compiled. Only proteins identified by at least two peptides were considered.

Calculation of diffusion time through cell envelope.

The time required to equilibrate the solute concentrations between extra- and intracellular space is determined by the permeability of the cell envelope to the solute, which in the absence of an active transport system for the solute is limited by (passive) diffusion. Diffusion-driven flux J (amount of substance, n [mol], per area S per time t) across the cell envelope into the cell volume is proportional to the concentration difference between intracellular (c_cell) and extracellular (c_ex) space,

$$J\equiv \frac{1}{S}\frac{\mathit{dn}}{\mathit{dt}}=P_{\text{env}}(c_{\text{cell}}-c_{\text{ex}})$$ (1)

where P_env is the compound permeability coefficient of the cell envelope. Since n = cV, equation 1 can be rewritten as coupled first-order differential equations for the two spaces,

$$\begin{array}{c}\frac{d{c}_{\text{cell}}}{\mathit{dt}}=\frac{S}{V_{\text{cell}}}{P}_{\text{env}}\left(c_{\text{cell}}-c_{\text{ex}}\right)\\ \frac{d{c}_{\text{ex}}}{\mathit{dt}}=-\nu \frac{S}{V_{\text{cell}}}{P}_{\text{env}}\left(c_{\text{cell}}-c_{\text{ex}}\right)\end{array}$$ (2)

where ν = V_cell/V_ex. Integration of equation 2 yields the time dependence of the concentrations,

$$\begin{array}{c}{c}_{\text{cell}}(t)=\frac{c_0}{1+\nu }\{1-\exp \hspace{0.17em}[-\frac{t\left(1+\nu \right)}{\tau }]\}\\ c_{\text{ex}}(t)=\frac{c_0}{1+\nu }\{1+\nu \hspace{0.17em}\exp \hspace{0.17em}[-\frac{t\left(1+\nu \right)}{\tau }]\}\end{array}$$ (3)

where c₀ = c_ex (t = 0) is the initial concentration of the solute and

$$\tau =\left(\frac{V_{\text{cell}}}{S}\right)\times \frac{1}{P_{\text{env}}}$$ (4)

is the characteristic (exponential) time constant of the process. Within t_eq = 5τ, the intracellular concentration has reached more than 99% of its saturation value and can be considered in equilibrium for practical purposes.

Equation 3 can be simplified when bearing in mind that the cell concentration in the cultures of A. aromaticum EbN1 after depletion of benzoate is 6.7 × 10⁵ ml⁻¹, which means a single cell in a “private” volume of (11 μm)³. In contrast, the volume of a single cell is ca. 3 μm³, as previously determined by means of transmission electron microscopy (55), so that V_ex ≈ 5 × 10² V_cell, and thus, $\nu =0.002\ll 1$. This implies that (i)

$$c_{\text{cell}}(t)\cong c_0\left[1-\exp \hspace{0.17em}\left(-\frac{t}{\tau }\right)\right]$$ (5)

and (ii) $c_{\text{ex}}\left(\tau \right)\cong c\left(0\right)$, i.e., depletion of the solute in the extracellular space is negligible.

Since the inverse permeability coefficient (as in equation 4) defines the diffusion resistance, the compound value for a layered structure can be found by series addition of resistances (66),

$$\frac{1}{P_{\text{env}}}=\frac{1}{P_{\text{om}}}+\frac{1}{P_{\text{ps}}}+\frac{1}{P_{\text{cm}}}$$ (6)

where the subscripts refer to the outer membrane (om), periplasmic space (ps), and cytoplasmic membrane (cm), respectively. For any homogenous layer, P can be related to more elementary properties,

$$P=\frac{K_{m}D}{d}$$ (7)

(67), where K_m is the membrane water partition coefficient for the solute, D is the diffusion coefficient of the solute in the membrane, and d is the thickness of the membrane. From equation 7, we obtain for the periplasmic space (K_m = 1), 1/P_ps = d_ps/D_ps, where d_ps is the thickness of the periplasmic layer (ca. 0.02 μm) and D_ps is the diffusion coefficient of the solute in the periplasmic space. The periplasm may well be 10 times more viscous than water due to macromolecular crowding, which reduces the diffusion coefficients accordingly (D_ps ∼ 10 D_H2O). For p-cresol at 25°C, D_H2O = 914 μm² s⁻¹ (68), so that we use D_pp = 10² μm² s⁻¹. With d ≈ 0.02 μm, the periplasmic permeability coefficient for p-cresol, P_pp = D_pp/d, can be estimated as 5 × 10³ μm s⁻¹.

The precise values for the membrane permeability coefficients of p-cresol are not known but can be constrained (order of magnitude) from experimentally determined P values of physicochemically similar solutes for model lipid bilayer membranes. We use benzoic acid as a proxy of p-cresol, because they have similar molecular weights (108 versus 122) and the same octanol-water coefficient, K_ow (K_ow = 80) (XLogP3 = 1.9, where XLogP3 is a predictor for the log P value, with P indicating the octanol-water partition coefficient; see https://pubchem.ncbi.nlm.nih.gov, compound numbers 243 and 2,879, respectively, computed after a previously described method [69]). The P value for diffusion of benzoic acid through egg phosphatidylcholine (pc)-decane bilayers was experimentally determined as P_pc = 5.5 × 10³ μm s⁻¹ (70). Setting P_om = P_cm = P_pc in equation 2, we obtain P_env ≈ P_pc/3 ≈ 1.7 × 10³ μm s⁻¹. With this estimate for P_env and the geometrically determined values of S ≈ 10 μm² and V ≈ 3 μm³ for A. aromaticum EbN1, we finally obtain τ of 0.2 ms (equation 4) as the characteristic time scale for passage of p-cresol through the cell envelope, implying complete equilibration of concentrations in a millisecond. Within t_eq = 5τ = 1 ms, the root mean square (rms) diffusion length for p-cresol in cytoplasm evaluates to

$$x_{\text{rms}}=\sqrt{2\hspace{0.17em}{D}_{\text{cp}}{t}_{\text{eq}}}\approx 0.5\hspace{0.17em}\mu \text{m}$$

(assuming D_cp = D_pp), i.e., which compares with the cell dimensions (half axes of 0.75 μm and 1.25 μm).

Membrane water partition coefficients.

The numerical value of the membrane-water-partition coefficient K_m for p-cresol can be determined from its XLogP3 value on the basis of the empirically determined correlation between log₁₀K_ow (XLogP3) and log₁₀K_m of biological membranes for a range of solutes compiled by Sikkema et al. (71). From the data in Fig. 3 in reference 71, we determined the following quantitative relation,

$${\log }_{10}\hspace{0.17em}{K}_m=-0.627+(0.984\pm 0.018){\text{log}}_{10}\hspace{0.17em}{K}_{\text{ow}}$$ (8a)

Since the slope is statistically indistinguishable from unity, we can simplify equation 8a to

$$K_m\cong {10}^{-0.627}{K}_{\text{ow}}=0.23K_{\text{ow}}$$ (8b)

Thus, K_m = 17 (p-cresol) and K_m = 85 (p-ethylphenol) (K_ow = 4 × 10², XLogP3 = 2.6; see https://pubchem.ncbi.nlm.nih.gov, compound number 31,242).

In general, lipophilic solutes (K_m > 1) have K_m-fold-higher concentrations in both membranes (outer membrane and cytoplasmic membrane) relative to their concentrations in the aqueous space. An obvious consequence of that enrichment is that the membranes serve as a solute concentration reservoir from which the solute can rapidly enter the intracellular space upon consumption by cytosolic enzymes. Also, as can be seen from equations 1 and 7, a high K_m value also increases the permeability coefficient and, thus, enhances the flux J accordingly.