Thermodynamic analysis of marine bacterial attachment to oligo(ethylene glycol)-terminated self-assembled monolayers
© Ista and López; licensee Springer. 2013
Received: 11 July 2013
Accepted: 23 August 2013
Published: 3 September 2013
Colloidal models are frequently used to model the thermodynamics of bacterial attachment to surfaces. The most commonly used of such models is that proposed by van Oss, Chaudhury and Good, which includes both non-polar and polar (including hydrogen bonding) interactions between the attaching bacterium, the attachment substratum and the aqueous environment. We use this model to calculate the free energy of adhesion, ∆Gadh, for attachment of the marine bacterium Cobetia marina to well defined attachment substrata that systematically vary in their chemistry and their ability to attach bacteria, namely a series of oligo(ethylene glycol) (OEG) terminated self-assembled monolayers that vary in the number of OEG moieties. For this system, the values of ∆Gadh calculated using VCG do not correlate with observed attachment profiles. We examine the validity of a number of assumptions inherent in VCG and other colloidal models of adhesion, with special attention paid to those regarding bacterial surfaces.
KeywordsFouling resistance Thermodynamics Oligo(ethylene glycol) Cobetia marina Surface tension Interfacial tension Bacterial attachment
Attachment of microorganisms to a submerged solid support is the first step in development of a biofilm [1–3]. Interactions of attaching bacteria with the substratum may strongly influence the final properties of the subsequent biofilm including structure , adhesion strength  and global developmental processes, such as quorum sensing  and exopolysaccharide production . As such, attachment is the most logical place to prevent, as in the case of biofouling, or engineer, as in the case of microbial biofuel cells, biofilm formation. Accurately modeling initial attachment events is, therefore, critical not only to understanding a fundamental biological process, but also to optimizing the formation of biofilms for a variety of applications.
Colloidal models remain a popular approach to predicting attachment for bacteria that do not have specific attachment peptide sor sugar binding proteins commonly found on pathogenic or commensal organisms [8–11], or for which such specific attachment mechanisms are unknown [12, 13]. Bacteria exhibit some colloid-like properties: their sizes fall within the upper limits of colloid particles as generally define (~1 μm) and they, like colloidal particles, tend to collect at interfaces. If and until selection pressure requires specific attachment mechanisms, bacteria may be best served by exploiting colloidal interactions at surfaces rather than expending metabolic energy to encode and express specific attachment molecules, thus allowing them a greater range of likely supports for biofilm formation.
A number of colloidal models have been proposed to explain biomolecular attachment in general, and bacterial attachment in particular [12, 14–17]. Of these the van der Waals-Lewis-Acid–base model proposed by van Oss, Chaudhury and Good (VCG) in the late 1980s  0020 seems to most accurately reflect the interfacial processes most likely to be important in biological attachment: nominally apolar Lifshitz-van der Waals interactions and polar Lewis acid–base interactions, including the special cases of hydrogen-bonding [13, 19, 20] and electrostatic interactions . In addition to the VCG model being used itself to study microbial interactions at the interface, it further informs the extended Derjauin-Landau-Verwey-Overbeek model, currently in widespread use [21–23] and also the recently developed Chen/Qi ratio .
We recently used VCG to examine the role of the substratum-water interfacial tension (γSL) in elucidating differences in fouling resistance between oligo(ethylene glycol) (OEG)-terminated self-assembled monolayers (SAMs), correlating γSL, and its components, with increased degrees of hydrogen bonding between the SAM and water . In that study, the increase in hydrogen bonding between OEG-SAMs and water correlated with increasing units of EG within the SAM and with decreased bacterial attachment. In this manuscript, we expand these studies to calculations of free energy of adhesion (∆Gadh), based on the VCG model, for attachment of the marine bacterium, C. marina, to OEG-SAMs.
SAMs of alkanethiolates on gold terminated with varying lengths of OEG  are a particularly attractive model system for studying the relationship between bacterial attachment and an estimated ∆Gadh. The number of ethylene glycol (EG) units (n = 1-6) in a SAM determines its resistance to protein adsorption , as well as attachment of mammalian cells , algal zoospores  and marine bacteria [30, 31]. The difference between OEG-SAMs that resist and permit cellular adsorption is one EG moiety ; for example, for the marine organism, Cobetia marina, an OEG-SAM with three OEG moieties (EG n = 3) permits bacterial attachment, whereas one in which EG n = 4 resists bacterial attachment . The OEG system is also unique in that the relatively low attachment observed on these surfaces means that over the course of our experiments (2 hr) it is extremely unlikely that an attachment maximum will be encountered, resulting in consistent attachment kinetics throughout the course of the study. Previous studies  suggest ∆Gadh for non-specific attachment to SAMs that attach bacteria will be negative.. Because the difference between OEG-SAMs that attach and those that do not attach microbes is one residue, the VCG model predicts that ∆Gadh be negative for those SAMs attaching C. marina and positive for those not attaching the organism, with the transition from negative to positive being associated with an increase of one EG residue. We observed no correlation between number of attaching bacteria and ∆Gadh of OEG-SAMs calculated using the VCG model of microbial attachment. In the process, we examined several parameters that might lead to this non-correlation and conclude that both errors endemic to the laboratory use of VCG and assumptions, common to all colloidal models of attachment, about the bacterial surface are the main source of the observed nonconcordance.
2.1 Preparation of self-assembled monolayers
SAMS were prepared as described previously . Briefly, glass coverslips (Fisher, Fairlawn, NJ) were treated with 70:30 H2SO4/H2O2 for at least 1 hour, rinsed in copious amounts of deionized water, and dried under dry nitrogen. The samples were then loaded into a thermal evaporator. After evacuating the chamber to 1 millitorr, 15 Å Cr was deposited followed by 300 Å Au. For Wilhelmy plate contact angle evaluation, metal was deposited on both sides of the sample.
2.2 Bacterial strains and culture conditions
All media and buffers were prepared with de-ionized water generated by a system using tap water processed sequentially through water softening, reverse osmosis and ion exchange (Barnstead-Thermolyne RoPure/Nanopure system). The final resistivity of the processed water was greater than 18MΩ cm-1. Marine Broth 2216 (MB, Difco, Franklin Lakes, NJ) was prepared according to manufacturer’s instructions. Marine Agar (MA) was prepared by the addition of 1.5% Bacto agar (Difco) to MB. Artificial sea water (ASW) contained 400 mM NaCl, 100 mM MgSO4, 20 mM KCl, 10 mM CaCl2. Modified basic marine medium plus glycerol (MBMMG) contained 0.5× ASW plus 19 mM NH4Cl, 0.33 mM K2HPO4, 0.1 mM FeSO4 · 7H2O, 5 mM Trishydroxyaminomethane hydrochloride pH 7, and 2 mM glycerol [34, 35]. Cobetia marina (basonym, Halomonas marina) ATCC 25374, is stored in frozen ( −70°C) stock aliquots, made from first generation cultures of the original ATCC lyophilate, in MB containing 20% glycerol. Experimental stock preparations were maintained on MA slants and were stored at 4°C for up to 2 weeks. Prior to inoculation into a chemostat, a single colony from a MA slant was inoculated into 50 mL of MB and grown overnight with shaking at 25°C. A chemostat culture was established by inoculating 3 mL of the overnight culture into MBMMG. The chemostat was maintained at a flow rate of 1 mL min-1 (dilution rate, 0.16 h-1) with constant stirring. The concentration of the subsequent culture was ~107 cells mL-1.
2.3 Bacterial attachment to surfaces
SAMs prepared on gold films coated on 60 × 24 mm coverslips were placed into a flow-cell apparatus  which was then mounted onto the stage of an optical microscope (Axioskop, Zeiss, Jena) and connected to the outflow of the chemostat. The C. marina culture was allowed to flow through the cell at a rate of 1 mL min-1 for two hours. Bacterial attachment was monitored through a CCD camera attached to the microscope. The images were fed to a computer using Axiovision software (Zeiss). At the end of the attachment time, images of 10 fields of view within 10 mm of the horizontal midline of the slide were captured, the number of attached bacteria counted and the average cell density for each slide determined.
2.4 Contact angle measurements
Contact angles of SAMs were measured using the Wilhelmy Plate method on a Krüss K100 tensiometer with Lab Desk 303 (Krüss, Jena) software. Contact angle liquids were water (18 MΩ cm-1; Millipore Academic System; Millipore, Billerica, MA), diiodomethane (99% ReagentPlus; Sigma-Aldrich, St. Louis,MO), formamide (Omipure; EMD; Gibbstown, NJ ), glycerol (anhydrous; J.T. Baker, Phillipsburg, NJ) and hexadecane (Sigma Aldrich). Samples were double-sided SAMs made on 22×40 mm, thickness 1 coverslips (Fisher). For measurement, SAMs were immersed to a depth of 1 cm, with contact angle measured on the sample six times per mm (a total of 60 data points per sample). For each SAM formulation, a minimum of three samples was measured per probe liquid (deionized water, diiodomethane, formamide, glycerol or hexadecane).
Contact angles of bacteria were taken on mats of bacteria supported on cellulose acetate filters (0.2 μm pores; Millipore, Billerica) [33, 36]. Approximately 120 mL of chemostat culture were filtered, followed by an equal volume of deionized water to remove residual salt. The filtered bacteria were then allowed to air dry before contact angle analysis. To ensure that the surface of the mat was dry without being totally dehydrated, water contact angles were initially taken every 10 minutes during the drying cycle until they became stable; contact angles for analysis were taken during the time period in which it was determined that the water contact angle did not change, in our case, 40–70 minutes after drying commenced . Contact angles were determined, using the angle analysis tool on ImageJ image processing software (NIH; ), from photographs taken with DROPImage software(Ramé-Hart, Succasunna, NJ) linked to a Ramé-Hart contact angle goniometer. Bacterial contact angles were measured with the same liquids as used for SAMs (deionized water, diiodomethane, formamide, glycerol and hexadecane).
2.5 Calculation of surface and interfacial tensions using VCG
where: ΥSV LW and ΥLV LW are the Lifshitz-van-der-Waals components of the surface tensions of the substratum and the probe liquid, respectively, ΥSV - and ΥLV - are the Lewis basic (electron donating, hydrogen bond accepting) components, and γSV + and ΥLV + are the Lewis acidic (electron accepting, hydrogen bond donating) components. ΥLV is the total surface tension of the probe liquid. Because there are 3 unknowns, contact angles were taken with three different probe liquids and the unknowns γSV LW, ΥSV - and γSV + calculated by simultaneously solving the three equations using MATLAB software (Mathworks, Natick). Values for the surface tension of bacteria (γBV) were obtained by substituting the contact angle of the probe liquids on bacterial mats into Equation (1).
and is quickly calculated using the values for γBS, γBL, and γSL obtained from Equation (2).
3 Results and discussion
3.1 Attachment of C. marina to SAMs
3.2 Contact angles
Contact angles of SAMs with different contact angle liquids
35 ± 1˚
24 ± 1˚
39 ± 2˚
5 ± 3˚
24 ± 2˚
29 ± 2˚
35 ± 2˚
7 ± 2˚
28 ± 2˚
29 ± 1˚
39 ± 1˚
15 ± 1˚
32 ± 1˚
27 ± 2˚
23 ± 2˚
38 ± 3˚
18 ± 1˚
33 ± 1˚
24 ± 3˚
27 ± 2˚
42 ± 1˚
1 ± 1˚
33 ± 1˚
26 ± 2˚
44 ± 3˚
11 ± 1˚
34 ± 1˚
27 ± 2˚
24 ± 3˚
47 ± 2˚
11 ± 1˚
33 ± 2˚
21 ± 1˚
60 ± 1˚
3 ± 2˚
37 ± 1˚
66 ± 1˚
90 ± 1˚
96 ± 0˚
36 ± 1˚
108 ± 2˚
NMe 3 +
26 ± 2˚
25 ± 1˚
39 ± 2˚
9 ± 3˚
18 ± 2˚
Contact angles (θ) of mats of logarithmic phase C. marina supported on cellulose acetate filters
34 ± 2˚
53 ± 2˚
64 ± 2˚
2 ± 1˚
34 ± 2˚
3.3 ∆G adh calculations
As demonstrated in Figure 2, ∆Gadh as calculated from contact angles of water, diiodomethane and glycerol on bacteria and OEG-SAMs did not reflect the resistance to attachment of bacteria to OEG-SAMs with OEG > 3, nor was attachment correlated in a systematic way to ∆Gadh. Based on previous applications of the VCG model, [35, 40] one would predict that ∆Gadh for SAMs with EG ≤ 3 would be negative; they are not. Clearly ∆Gadh as calculated from contact angles and the VCG model is either not physically meaningful or is not capturing all the relevant information in the system. We now consider how the inputs into the equations for ∆Gadh ((3) and (4)) influence this value and from where the discrepancy between attachment of C. marina and estimates of ∆Gadh may stem.
We have previously demonstrated [31, 39] that C. marina attaches in far greater numbers to SAMs terminated with a methyl group (CH3-SAM) when compared to OH-SAMs. When we calculated ∆Gadh for C. marina attaching to a CH3-SAM using liquid combination water, diiodomethane and glycerol (WDG), a value of −32.7 ± 5 mJ m-2 was obtained; the value is negative, as would be expected for a SAM attaching large numbers of bacteria (average coverage 1,121 ± 192 cells mm-2 under the same experimental conditions as for OEG-SAMs). When we calculated ΔGadh for attachment of C. marina to a trimethylamine-terminated SAM (NMe3 +-SAM; average coverage 662 ± 44 cells cm-2 under the same experimental conditions as for OEG-SAMs) using inputs from WDG, however, ∆Gadh = 24 ± 4 mJ m-2 is positive and statistically similar to OH-SAMs (∆Gadh = 21 ± 4 mJ m-2) that attached one fifth of the cells attached to NMe3 +-SAMs (Figure 1). Because the ∆Gadh calculated for CH3-SAMs is due only to Lifshitz-van-der-Waals interactions, with no polar components, and it had at least the expected negative sign for ∆Gadh, we explored the possibility that the VCG method of calculating ∆Gadh misses information about the polar components.
Most applications of the VCG model, and indeed the original model itself, assume that for water γLV + = γLV - =25.5 mJ m-2[13, 20, 33, 40], whereas others, most notably Lee , have shown that above 0°C, water is, in fact, much more likely to donate hydrogen bonds (be more Lewis acidic ) than accept them and that, at room temperature, γSV + = 1.8γSV -. Because the acid and base components for all other liquids were calculated based on the VCG assumption, surface tensions for other liquids, and the resulting surface tensions for measured solid surfaces, overestimated the Lewis-basic component [12, 42]. When we used WDF contact angle values to calculate ∆Gadh, the use of Lee values resulted in lower values for ∆Gadh, whereas there was no statistical difference (p ≥ 0.05) for ∆Gadh when calculated using contact angles from the WDG liquid set. Use of the Lee values in calculations did not, however, shift ∆Gadh such that it was negative for SAMs attaching cells, nor did it sufficiently raise the values of γSV + for NMe3 +-SAMs such that they now were predominantly Lewis acidic. We must, therefore, conclude, in agreement with others , that using the modified values of the components of γLV does not have a substantial effect on VCG calculations.
An assumption that, as far as we know, remains unchallenged with regard to the VCG model and, more accurately, its application to analysis of surface tension has to do with the way the apolar components of substratum and bacterial surface tension, γSV LW and γBV LW, are calculated. VCG includes in these values not only attractive London dispersion interactions resulting from fluctuating dipoles and resulting induced dipoles, but also possible repulsive interactions between fixed dipoles (Keesom interactions) and fixed dipole (Deybe) interactions . Although the latter are considered to be insignificant , we maintain that they are neglected, particularly given that the apolar liquid of choice for most VCG analysis [13, 19, 35, 40, 43], diiodomethane, although considered strictly apolar [13, 19, 33, 40, 42, 43], has a small, but possibly significant, acid monopole (0.72 mJ m-2) . To test the significance of this monopole, we examined the effect of including this monopole on calculations of surface tension components, ∆Gadh LW and ∆Gadh AB As an added test, we compared values obtained with diiodomethane, both including and ignoring the acid monopole, with those obtained with hexadecane, which is known to be completely apolar.
The differences in γSV LW of polar SAMs as measured with hexadecane and diiodomethane is substantial, whether or not the acidic monopole of the latter is considered; γSV LW calculated from diiodomethane is ~45 mJ m-2, if the acid monopole is included that value drops to ~35 mJ m-2, whereas that using hexadecane is ~27 mJ m-2, similar to that for the CH3-SAM. The inclusion of the acid monopole calculation of γSV LW, thus, has a profound effect on γSV LW. These results indicate that either the supposition that either Keesom or Debye interactions are insignificant may be false (as they seem to account for nearly 10 mJ m-2 when the acid monopole included in the calculation) or the assumption that acid or base components <1.0 mJ m-2 are insignificant [13, 18] is unwarranted; in either case, further re-examination of these assumptions is suggested by these results.
The value of γSV LW for organic polymers and biopolymers is noted by van Oss to be universally ~45 mJ m-2[13, 18], but we propose that this may be an artifact based on the use of diiodomethane as an apolar liquid that seems to always result in this value (see also the value of γBV LW in Figure 4). Examination of the γSV LW of SAMs as calculated with diiodomethane and hexadecane seems to indicate that this value may be an artifact. γSV LW of an OH-SAM, is, for example, about 20 mJ m-2 higher than γSV LW of an CH3-SAM using contact angles of diiodomethane and ignoring the acid component. If we compare γLV LW for n-decane (23.8 mJ m-2) and 1-decanol (22 mJ m-2) we see no such increase . More to the point, the total surface tension for dodecane (similar to CH3-SAM) is 25.6 mJ m-2, whereas that for dodecanol is 28.6 mJ m-2. Taking into account that γLV AB for most alcohols  is 3–6 mJ m-2, it seems very unlikely to us that a similar change on a SAM surface would nearly double the value of γSV LW. On the other hand, a SAM surface is well ordered, and the main surface exposed would be OH (or NMe3 +) so a slightly higher value for OEG-SAMs might be expected. If we take into account, however, the published values of γLV LW for (21.8 mJ m-2), glycerol (34 mJ m-2) and ethylene glycol (29 mJ m-2) , are still much lower than those proposed for most polymer surfaces calculated using diiodomethane. We propose, therefore, that hexadecane or some other completely apolar liquid is the most relevant when analyzing SAMs. We should note, however, that using hexadecane alone is insufficient to bring about a correlation between ∆Gadh and attachment.
The role of the organization of water around the OEG-SAMs as it relates to thermodynamics has been extensively discussed both in our previous work on the relationship between γSL and attachment of C. marina and its included references, with the conclusion that γSL calculated using VCG supports current mathematical theories that suggest hydrogen bonding between OEG moieties and water renders bacterial attachment to these surfaces entropically disfavored. The observation that bacterial attachment to a CH3-SAM is increased in this system is energetically favored might lead one to make similar arguments that attachment of bacteria is entropically favored near a hydrophobic surface; in other bacterial systems [31, 39, 43], however, attachment to CH3-SAMs is lower than to other SAMs, suggesting that the influence of the increased entropy upon bacterial attachment is not significant.
We suspect, however, that calculations of γBV and the resultant interfacial tensions γBS and γBL do not capture information most relevant to attachment. An assumption common to even the most carefully considered models of non-specific bacterial attachment is that surface tension is uniform across the bacterial cell (and, indeed, across a monoculture population). This assumption is simply invalid. The role of extracellular appendages such as flagella and pili in attachment are well known [45, 46], and even though we deliberately chose C. marina as a model organism partly due to the lack of observable extracellular structures , years of observation have led us to conclude that the surface is very likely not uniform as we have observed the cells orient themselves differently on different SAMs during attachment. We and others have also proposed that bacteria have different attachment mechanisms on different surfaces [4, 35, 48]. Furthermore an emerging field of study, based on observations of attachment of Caulobacter crescentus, has made a strong case that during cell division the biochemistry of the cell envelope of the two daughter cells may be very different, and that genetically programmed biochemical heterogeneity on individual cells is present . The relevant γBV and components to include in a free-energy calculation are, therefore, less likely to be those of the whole bacterium, but rather that of the part of the cell which is interacting with the SAM. We are currently developing a method by which the areas of individual cells involved in attachment to each SAM may be accurately assayed; preliminary results indicate that different regions of the C. marina cell surface do, indeed, interact differently with when SAM surface chemistry is altered.
We also initially assumed that attachment of C. marina to SAMs is nonspecific, i.e., unmediated by receptor-ligand interactions. The lack of correlation ∆Gadh and attachment called this assumption into question. It has been demonstrated previously that ∆Gadh calculated using VCG does not correlate with attachment when the interaction between the bacteria and the surface is ligand mediated, i.e., specific [33, 40]. It is possible that C. marina possesses receptors that interact specifically with components of SAMs. We also considered the possibility that exopolymeric substances (EPS) secreted by planktonic C. marina might form conditioning films that would present specific ligands for attachment. Marine bacteria are known to produce exopolymeric substances while growing planktonically  and to attach to conditioning films of EPS formed on surfaces . It was not hard, therefore to envision a scenario in which C. marina could produce EPS, even while in carbon-limited chemostat conditions, that could form conditioning films on SAMs, to which C. marina could bind specifically.
We tested for the presence of EPS deposited onto SAMs from filtered (0.45 μm nylon) chemostat and also tested the filtered effluent directly for carbohydrate, DNA and protein. The lectin concavalin A (ConA) binds specifically to α-D-mannosyl and α-D-glucosyl groups in carbohydrates and glycoproteins. These residues are frequently found in the EPS of Pseudomonas aeruginosa and that of marine pseudomonads . Alexa-dye-conjugated ConA staining of CH3-SAMs exposed for two hours under flow to filtered chemostat effluent showed no discernable deposits, whereas the same SAMs exposed to 1 μg mL-1 dextran stained easily. The amount of dissolved carbohydrate in filtered chemostat effluent was estimated using the phenol-sulfuric acid method as modified by Jain for use in salt water  and no detectable (i.e. < 1 μg/mL) carbohydrate was found when compared with a glucose standard. Bradford assays for protein of the filtered effluent were similarly negative and no absorption peak was detected at 260 nm indicating the absence of nucleic acid. We thus conclude that, at least under our experimental conditions, EPS-derived conditioning films do not play a role in attachment of C. marina to SAMs.
A final criticism of VCG may lie in the ability of calculations based on so many contact angles and their attendant errors may make error propagation an issue, particularly for low contact angles (as in OH-SAMs in this study) where accuracy and precision during contact angle measurement is difficult. A model developed for much simpler systems may not be applicable to more complex systems involving heterogeneous cells and populations. We believe that the measurements required to accurately model this system are becoming increasing possible, however, and that more comprehensive explanations will be rapidly forthcoming.
We have undertaken a systematic study of VCG model as it pertains to bacterial attachment and ∆Gadh. The key to this investigation is a series of SAMs differing only in the length of ethylene glycol chains presented at the surface, resulting in profoundly different attachment profiles. ∆Gadh as calculated using the VCG model, however, did not reveal even a qualitative correlation between this value and attachment. We conclude that the VCG model as currently utilized is insufficient to describe the relevant interaction occurring between the bacteria, attachment substratum and water. These results call into question the generalized use of contact angles and colloidal models based on them, such as VCG, as a substitute for surface energy in thermodynamic analyses of bacterial attachment. Because VCG is used not only in its own right, but also informs other models of attachment, most notably, the highly popular extended DLVO model, caution should be taken when drawing conclusions regarding the effect of substratum surface energy on attachment of microbes, at least until such time as contact angle probe liquids are identified which can accurately account for all components of surface tension.
In addition to the limitations VCG as applied to calculating γSV, we suggest a second important factor preventing accurate modeling of microbial attachment is inherent assumptions made about the surface energy of bacteria themselves. To date, all surface energy analyses of microbial cells assume that the population is uniform and that the surfaces of cells themselves are homogenous ; the average surface energy of both the population and individual cells is, thus the relevant information needed for input into VCG or any colloidal model. We and others, however, have demonstrated that different part of the cell are relevant for attachment to different substrata [34, 48, 54]. We are currently developing a method to probe which parts of the bacterial surface are relevant to attachment to different substrata is currently underway that might eventually lead to a more nuanced view of the bacterial cell surface and its relevance in attachment.
This work was supported by grants N00014-08-1-0741 and N00014-10-1-09007 from the Office of Naval Research and HDTRA-1-11-1-0004 from the Defense Threat Reduction Agency. We thank M. Grunze and A. Rosenhahn (University of Heidelberg and Karlsruhe Institute of Technology) for thoughtful discussion and for providing some of the OEG thiols used in this study. We also thank M. Werner-Washburne, D. Northup, and C. Takacs-Vesbach for helpful discussions. Technical assistance from Ms. Maria Pilar Arpa-Sancet (KIT/UH), Mr. Phanindhar Shivapooja (UNM/Duke) and Mr. José Cornejo (UNM) is greatly appreciated. We also thank Mr. Shivapooja and Dr. Kristin Wilde for careful reading of this manuscript.
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