Metabolic response to point mutations reveals principles of modulation of in vivo enzyme activity and phenotype (2021)
Figure 7

Figure 7: In vivo activity curves of representative E. coli enzymes show hyperbolic or cooperative behavior. Steady state levels of different metabolites obtained from metabolomics were used to derive activity curves for (A) Adenylate Kinase (AK) (B) Uridylate Kinase (PyrH) (C) Adenylosuccinate Lyase (PurB) and (D) GAR Transformylase (PurN). AK, PyrH and PurB appear to follow hyperbolic MM kinetics in vivo, while PurN shows Hill-like dependence with cooperativity. In panel (A), the red data points were acquired during growth in amino acid supplemented M9 medium in the absence of external AMP and are derived from WT and various stabilizing and destabilizing point mutations of AK (Adkar et al., 2019) as well as DHFR mutants used in the present study, while black points were derived exclusively from cultures of AK mutants supplemented with 1mM external AMP (Adkar et al., 2019). Data points for all other panels (B-D) are derived from mutant DHFR strains in the present study. Since SAICAR, AICAR, GAR and FGAR levels were undetectable in WT, all data points in (C-D) are relative to those observed in I91L+W133V mutant following 4 hours of growth at 40°C. Data points in all panels represent metabolite levels for individual biological replicates without averaging.

Methods

Strains and media. The mutant DHFR strains chosen for this study (W133V, I91L+W133V, V75H+I155A and V75H+I91L+I155A) were a subset of strains generated in and described in Bershtein et al (Bershtein et al., 2012). Briefly, using structural and sequence analyses, positions were chosen that were buried in the protein and located at least 4Å away from the active site, so that mutations introduced at these positions would have minimal effect on enzymatic activity. The identity of the mutations was selected such that they are appear with very low frequency in a multiple sequence alignment, and hence were intended to destabilize the protein, as was confirmed by stability measurements of the purified proteins (see Table below). The single mutants were in most cases mild to moderately destabilizing, and hence certain mutations were combined to increase the range of destabilization achieved. The following table summarizes the results of stability measurements on the single mutants (from (Bershtein et al., 2012)). However, the multiple site mutants could not be purified to quantities that were sufficient for in vitro biophysical and biochemical characterization.

Single as well as multiple site mutations were eventually introduced into the chromosomal copy of the folA at its endogenous locus keeping its regulatory region intact, and the effect of the mutations on its growth and morphology were measured at 30, 37 and 42°C. While WT, W133V and V75H+I155A could grow up to 42ºC, mutants I91L+W133V and V75H+I91L+I155A could only survive up to 40ºC, and hence these strains were grown at 40ºC instead of 42ºC. The reason for choosing a wide range of temperature instead of following a single conventional temperature of 37°C was that E. coli is a gut bacterium and inhabit hosts whose core body temperatures span a large range (37-38°C for mammals, 40-45°C for birds (Guenther et al, 2010; Torre-Bueno, 1976)). Moreover, since the chosen mutants were temperature sensitive, the phenotypic manifestation of the mutations was the largest at the extremes of temperatures, in case of E. coli at 42ºC.

Wherever mentioned, M9 minimal medium without amino acids was only supplemented with 0.2% glucose and 1mM MgSO4 while M9 media with amino acids was supplemented with 0.2% glucose, 1mM MgSO4, 0.1% casamino acids, and 0.5 μg/ml thiamine. Casamino acids is a commercially available mixture of all amino acids except tryptophan, and cysteine is present in a very small amount. Wherever mentioned, 1mM GMP was used as a source of purine, while dTMP (thymidine monophosphate) was used at a concentration of 0.25-1mM. Thymidine was used at two different concentrations of 0.5mM and 1mM.

Growth conditions. All strains were grown overnight from a single colony at 30°C, and subsequently the culture was diluted to a final OD600 of 0.01 in the specified medium and allowed to grow for 16-18 hours in Bioscreen C (Growth Curves, USA) at 30°C, 37°C or 42°C. Growth curves were fit to a 4‑parameter Gompertz equation as described in (Bhattacharyya et al, 2017) to derive growth parameters. Error bars were calculated as SEM of three biological replicates.

Light microscopy. Cells were grown overnight at 30°C from a single colony in the specified medium, diluted 1/100, and grown at various temperatures for 4 hours. For DIC images in Figures 1C, 1D, Figure EV1A, cells were pelleted, washed with PBS, and concentrated. DAPI staining (Molecular probes) was performed for 10 min at RT according to manufacturer instructions. 1 μl of a concentrated culture was then mounted on a slide and slightly pressed by a cover slip. DIC and DAPI images were obtained at room temperature by Nikon Ti Eclipse Microscope equipped with iXon EMCCD camera (Andor Technologies). For live phase contrast images and time-lapse experiments (Figure 4A), cells were mounted on supplemented M9 + 1.5% low melting agarose (Calbiochem) pads. Pads were then flipped on #1.5 glass dish (Willco Wells), and the images were acquired at room temperature with Zeiss Cell Observer microscope. For DIC images in Figure EV5A, cells were placed on agar pads and images were acquired with Zeiss Cell Discoverer microscope.

Analysis of cell lengths. MicrobeTracker Suite [http://microbetracker.org/](Sliusarenko et al, 2011) was used to obtain distributions of cell length for phase contrast images and Zeiss Intellesis Module was used to analyze DIC images. On average, 500 cells were analyzed for each presented distribution. The cell lengths are represented in all figures as box-plots, where the boundaries of the box represent the 25th and 75th percentile, the line inside the box represents the median of the distribution, whiskers represent the 10th and 90th percentile, while the dots represent the 5th and 95th percentile.

Statistical analysis. In our experiments, cell lengths of E. coli were not normally distributed (Shapiro-Wilk test). Hence non-parametric Mann-Whitney test was used to determine if the median cell lengths of two samples were significantly different. In Figure 6C, fits to two different models, Michaelis-Menten and 3-parameter Hill were compared using extra sum-of-squares F-test using GraphPad Prism software v9.0.0.

Metabolomics. Cells were grown overnight at 30°C from a single colony in the specified medium, diluted 1/100, and re-grown. WT, WT+0.5μg/ml Tmp and W133V mutant were grown at 42°C, while mutant I91L+W133V was grown at 40°C. For time course experiment, aliquots were removed after 2, 4, 6 and 8 hours, and metabolites were extracted as described in (Bhattacharyya et al., 2016). Briefly, the cells were washed 2 times with chilled 1×M9 salts, and metabolites were extracted using 300µl of 80:20 ratio of methanol:water that had been pre-chilled on dry ice. The cell suspension was immediately frozen in liquid nitrogen followed by a brief thawing (for 30 seconds) in a water bath maintained at 25°C and centrifugation at 4°C at maximum speed for 10 minutes. The supernatant was collected and stored on dry ice. This process of extraction of metabolite was repeated two more times. The final 900µl extract was spun down one more time and the supernatant was stored in -80°C till used for mass spectrometry. Metabolite levels were averaged over 2-3 biological replicates as increasing sample size beyond 3 did not significantly change the SEM. In Figures 6 and 7, data points represent metabolite levels for all biological replicates without averaging.

Expression of SOS response genes by qPCR. Cells were grown overnight at 30°C from a single colony in the specified medium, diluted 1/100, and grown at 37°C or 42°C for 4 hours. Based on OD600 of the cultures, a volume equivalent to 5×108 cells were spun down (assuming 1 OD600=8×108 cells) and Protect Bacteria RNA Mini Kit (Qiagen) was used to extract total RNA as described in (Bhattacharyya et al., 2018). Following reverse transcription (Bhattacharyya et al., 2018), expression of recA, recN and sulA genes were quantified using QuantiTect SYBR Green PCR kit (Qiagen) using the following primers:

recA_fwd ACAAACAGAAAGCGTTGGCG

recA_rev AGCGCGATATCCAGTGAAAG

recN_fwd TTGGCACAACTGACCATCAG

recN_rev GACCACCGAGACAAAGAC

sulA_fwd GTACACTTCAGGCTATGCAC

sulA_rev GCAACAGTAGAAGTTGCGTC

As it was difficult to find a reference gene that would be expressed to similar levels in WT vs mutant DHFR strains, we used total RNA to normalize the expression levels.

Expression levels reported are average of 3 biological replicates. Error bars in Figure 4 represent 12% of the mean value.

Tmk protein purification. The tmk gene was cloned in pET28a plasmid between NdeI and XhoI sites with an N-terminal histag. BL21(DE3) cells transformed with the plasmid were grown in Luria Broth at 37°C till an OD of 0.6, induced using 1mM IPTG and grown for an additional 5 hours at 37°C. The protein was purified using Ni-NTA affinity columns (Qiagen) and subsequently purified by gel filtration using a HiLoad Superdex 75 pg column (GE). The protein was concentrated and stored in 10 mM potassium phosphate buffer (pH 7.2). The concentration of the proteins was measured by BCA assay (ThermoScientific) with BSA as standard.

Tmk activity assay. Tmk catalyzes the following reaction , and the activity assay was carried out using the spectrophotometric assay as described in (Nelson & Carter, 1969). Briefly, the reaction mixture contained 5mM MgCl2, 65mM KCl, 350uM phosphoenolpyruvate (PEP), and 300uM NADH. To obtain KM for dTMP, ATP concentration was fixed at 1mM, while dTMP concentration was varied from 10μM to 500μM. The reaction mix without enzymes was incubated at 25ºC for 5 minutes, and the reaction was initiated by adding 100nM Tmk (final concentration) and 2 units of pyruvate/lactate dehydrogenase. The kinetic traces were recorded for every 5 seconds for a total time of 1 minute. The data corresponding to the first 20 seconds were fitted to a linear model to obtain initial rates. To obtain KI of dCTP for Tmk, ATP and dTMP concentrations were fixed at 100μM and 1mM respectively, while dCTP concentration was varied from 0.5mM to 7.5mM. Since conversion of dUMP to dTDP also produces ADP, the KI of dUMP could not be estimated by the spectrophotometric method. Instead, dTDP amounts produced in the reaction were determined by LC-MS. For the reaction, ATP and dTMP concentrations were fixed at 1mM and 100μM respectively, while dUMP concentration was varied from 0.25mM to 5mM. The reaction was quenched at 40 seconds using 80% MeOH. The resulting samples were subjected to LC-MS analysis to obtain dTDP levels. For Figure EV3(B and D), LC followed by mass spectrometry was used to directly measure dTDP levels.

Derivation of the relationship between steady state metabolite concentrations and kinetics of the enzyme in vivo.

Case I: Sequential enzymes in pathway with Michaelis-Menten kinetics

The following is an example of a pathway where several enzymes work sequentially:

For the pathway at steady state, the concentrations of the reactants, products and intermediates do not change with time. Therefore,

The enzyme concentrations can be written as:

are the steady state concentrations of two sequential substrates (or products) in the pathway. Based on equations , and , we deduce:

Again, at steady state,

Hence,

Similarly, one can show that:

Since the pathway is at steady state, concentrations of reactants and products of every reaction remain unchanged with time, hence

Using the expressions of ,,and from equations , , and into equation ,

Using , where is the Michaelis constant of for , is that of for ,is that of for and is that of for , equation can be written as:

Assuming that (in other words if and are very small) or the products have very low affinity back towards the enzyme, equation reduces to the following:

Equation can be re-arranged to get the following hyperbolic or Michaelis-Menten like dependence of on :

,

Case II: Sequential enzymes in pathway with Hill-like kinetics

For a single enzyme, initial rate , where '' is the Hill coefficient

Now again consider the following scheme of sequential enzymes:

For reactants and products to be at steady state, earlier we derive Equation, which essentially equates the rate of production and consumption of through the two enzymes (with the assumption that and are very small). In such a situation if either or both and have limited diffusion, equation can be written as the following based on equation :

Where m and n are the Hill coefficient analogs of the two consecutive enzymatic steps.

Equation can be rearranged as:

Therefore,

A numerical solution of equation shows that shows positive cooperativity as a function of only if (See Figure EV6).

Power law formalism for fractal kinetics

For a system where reactants and products diffuse freely, the rate constant of the reaction is time independent. However, under conditions of diffusion limitation (fractal kinetics), rate constant is no longer a constant, but varies with time in the following way:

Where is related to the fractal dimension of the medium.

In the following section, we adopt the power law formalism as shown in (Savageau, 1995) to convert the time dependent rate constant to a time independent one.

Considering the following simple reaction of two molecules of A forming a homodimer under conditions of diffusion limitation:

Integrating the above equation, we get [A] as a function of time

Rearranging this, we get

In the next step, we replace in equation with to get:

Where (Note that though this is a bimolecular reaction, the actual molecularity is >2 under fractal conditions)

Application for enzyme kinetics

Assume the following simple case:

Consider that the substrate S is diffusion limited, hence (a bimolecular rate constant) will be time dependent.

Where is the apparent time independent rate constant, and is related to the fractal dimension of the medium.

At steady state,

Rate of the reaction

Where is the apparent Michaelis constant, and is the Hill coefficient analog.

Data availability.

The datasets produced in this study are available in the following database:

Metabolomics data: Metabolights MTBLS2795 (www.ebi.ac.uk/metabolights/MTBLS2795). The processed data are included in source data for Figures 2 and 5.

Expanded View

The manuscript contains 6 Extended View figures (Figures EV 1-6).

Expanded View Figure Captions