Modelling of growth kinetics of Vibrio cholerae in presence of gold nanoparticles: effect of size and morphology

Emergence of multiple drug resistant strains of pathogenic bacteria calls for new initiatives to combat infectious diseases. Gold nanoparticles (AuNPs), because of their non-toxic nature and size/shape dependent optical properties, offer interesting possibility. Here we report the antibacterial efficacy of AuNPs of different size and shape (AuNS10, AuNS100 and AuNR10; the number indicating the diameter in nm; S stands for sphere and R for rod) against the classical (O395) and El Tor (N16961) biotypes of Vibrio cholerae, the etiological agent responsible for cholera. Growth kinetics was monitored by measuring optical density at different time intervals and fitted by non-linear regression of modified Buchanan model. Sigmoidal growth curve for VcO395 indicated the existence of single phenotype population and was affected by AuNR10 only, implying the importance of morphology of AuNP. Growth of VcN16961 was affected by all three AuNPs indicating the vulnerability of El Tor biotype. Interestingly, VcN16961 exhibited the occurrence of two phenotypic subpopulations – one with shorter (vulnerable Type 1) and the other with extended (tolerant Type 2) lag phase. Various assays were conducted to probe the impact of AuNPs on bacterial cells. Apart from AuNR10, antimicrobial efficacy of AuNS10 was better compared to AuNS100.

variation of lag phase for the biotypes. As both the biotypes were found to be vulnerable with nanorod, cell viability assay using FACS at different time intervals was carried out after treatment with AuNR. As the attachment of bacteria to the nanoparticle surface may cause damage of cell membrane, we conducted membrane fluidity assay by fluorescence anisotropy using the fluorescent probe DPH. As the membrane fluidization may lead to the protein leakage and damage of DNA, we carried out Bardford's protein quantitation assay and fluorescence based assay using DAPI for DNA damage.
The unique feature of the existence of two phenotypic subpopulations for VcN16961 compared to the classical one has been revealed by modelling and fitting the data of growth kinetics. Though two distinct phenotypes of VcN16961 have been observed before 19 , to the best of our knowledge this unique feature of V. cholerae biotypes and their individual responses towards AuNP, based on the modelling of growth kinetics have not been reported in literature.

Theory
Growth kinetics of V. cholerae O395 and N16961 using AuNS and AuNR. The study of bacterial growth kinetics is an indispensable tool covering different areas of microbiology and has eventually gained immense importance for the understanding of the behaviour of microorganism in a given experimental condition 20 . Various mathematical models have been used to fit the kinetic data, which allows describing the behaviour of a particular bacterium under a specific condition. To date, various mathematical models have been reported in literature, such as the Gompertz, Monod, Barayani, etc 21 . Microbial growth curves were typically characterized by four-phases (i.e. lag, growth, stationary and decay). Initially bacterial growth starts from a zero (or near zero) till it reaches a maximum (growth phase), giving a sigmoidal nature of the growth curve 22 , after which it declines (death phase).
Buchanan presented a sigmoidal model 23 of bacterial growth (eqn. 1) as F I F m which is derivable from the Logistic model (assuming a linear relation between the OD and the number density of bacteria; (for details see Supporting Information) and can be rewritten as where the parameters OD F and OD I are the estimates of the final and initial optical densities, t m is the delay time where the OD is midway between OD F and OD I , and k is a parameter which controls the maximum growth rate.
The new lumped parameters, = + a OD OF , and = d t k 2 m are used here to simplify the equations. This was found to be suitable for the growth kinetics of VcO395. Lag or delay times are envisaged from other growth models, however, this model allows for the delay time t m to vary independent of k, which governs the maximum growth rate.
When modelling a bacterial population comprising of two phenotypes, the Buchanan model (eqn. 2) can be modified as where the parameters e, f and g have similar functions as of b, c and d for the second phenotype (here the first and second subpopulations are arbitrarily referred to as the two phenotyes). Such a co-existing two variant model has been found suitable in the growing bacterial colony of VcN16961. It may be added that the derivation of eqn. 3 for the growth of two populations implicitly ignores the interaction and/or switching between the two phenotypes as an approximation. The Buchanan model used here is based on the Logistic model. This in general, is applicable to most species of bacteria, which do not depend on co-operativity (Allee effect).

Results
Growth kinetics of VcO395 strains in the presence of AuNR10. The growth kinetics of both biotypes of V. cholerae was monitored by measuring OD at 595 nm at different time intervals. For VcO395 strain, growth curve was found to be predominantly sigmoidal both in the absence and presence of AuNR10 (Fig. 1a). The data fitted well to the Buchanan model, as given in eqn. (2), indicating that VcO395 was dominated by a single phenotype of bacteria. Also, the growth of VcO395 was found to be affected only by AuNR10 and not by AuNS10 or AuNS100 (Fig. S1), implying the importance of morphology on bacterial growth 24 .
The maximum growth rate (or the maximum slope s of OD 595 with time) of VcO395 in the presence of AuNR10, obtained from data fitting is given by the following equation (eqn. 4) and is shown in Fig. 1b The maximum or saturation value of the OD can be fitted by the following equation (eqn. 5) which implies the antibacterial efficacy of AuNR10 for VcO395. The kinetic parameters obtained for VcO395 is given in Table 1. The efficiency of AuNR10 against VcO395 is also reflected from the IC 50 value of 3.04 μM obtained from the growth rate (Fig. 1b).
The "lag phase", originally described by Monod, is an important phase of bacterial growth cycle in which cells adopt to the new environment 25,26 . This lag phase continues till the "delay time" (t), the time where the population of the bacteria reaches half that of maximum value. The delay time (in min) was found to increase with the increasing concentration of AuNR as seen in Fig. 1c.
This observed trend indicated that the extended time taken by VcO395 was to overcome the stress created by AuNR10 before reaching the log phase. Here OD 595 is half way between minimum and maximum values, and the slope is also a maximum.
Growth kinetics of VcN16961 strain in the presence of AuNS10 and AuNS100. The growth kinetics of VcN16961 was found to be affected by AuNP of different size (AuNS10 and AuNS100) and shape (AuNR10), indicating the vulnerability of the El Tor biotype towards AuNP over the classical one. The striking feature of the growth kinetics of VcN16961 is in the existence of two phenotypic subpopulations (Type 1-with a shorter lag phase; Type 2 -with a longer lag phase) both in the absence and presence of AuNP. The growth curve of VcN16961 in the absence of nanoparticles is shown in Fig. 2. Data obtained for the growth curves after treatment with AuNS10 were analyzed and fitted using eqn. (3) (Fig. 3a, Table 2).
The maximum growth rate (or the maximum slopes of OD 595 of the two subpopulations with time) s 1 and s 2 for two subpopulations of VcN16961 in presence of AuNS10 as obtained from modified Buchanan model can be represented by eqns 6 and 7 as = .
− .  It is evident from Fig. 3b that the growth rate constants for both the subpopulations decreased with the increase in concentration of AuNS10. The delay times for two subpopulations vary very little with concentration AuNS10 (Fig. 3c) and are given by eqns 8 and 9 as = .
. The IC 50 (obtained from the growth rate, Fig. 3b) value for Type 1 subpopulation was found to be 21.9 μM, while that for Type 2 was 25.6 μM.
The growth kinetics of VcN16961 was also studied using AuNS100 to understand the effect size of NP on the two subpopulations (Fig. 3d). The maximum growth rates (eqns 10 and 11) for two subpopulations of VcN16961 in presence of AuNS100 as obtained from modified Buchanan model shows that For AuNS100 the subpopulation of Type 1 phenotype declines faster than Type 2 phenotype with the increase in concentration of AuNS100 as evident from Fig. 3e. The delay times obtained for the Type 1 and Type 2 phenotypes (eqns. 12 and 13) with the change in concentration of AuNS100 ( Fig. 3f) can be shown as follows The IC 50 values obtained for VcN16961 using AuNS100 were 21 μM and 34.8 μM respectively, for Type 1 and Type 2 ( Fig. 3e). This indicates that the Type 2 subpopulation is much more tolerant to AuNS100, while the Type 1 shows the same vulnerability as that observed with AuNS10.
Growth kinetics of VcN16961 strain in the presence of AuNR10. Growth kinetics of VcN16961 in presence of AuNR10 showed varied effects on the two subpopulations (Fig. 3g). Type 1 phenotype, which is marked by a shorter lag-phase, showed extreme susceptibility to AuNR10 causing it to vanish even at a low concentration of about 4 μM. Beyond 4 μM of AuNR10, modelling was done using single population model due to the survival of Type 2 phenotype (the one with the longer lag-phase) only. The maximum growth rate (eqn. 14) obtained for Type 1 phenotype of VcN16961 using AuNR10 was = .
AuNR 1 0 3233 [ 10] and for Type 2 was found to be constant at about 0.0016 ± 0.0002 OD/min up to a concentration of 12 μM, after which it declined. The lag-phase of Type 1 phenotype increased rapidly with concentration of AuNR10, while that for Type 2 phenotype varied little up to about 10 μM after which it increased rapidly with the increasing concentration of AuNR10. This difference in behaviour of two subpopulations to the stress created by AuNR10 is perplexing. The present observation may imply that even a low concentration of AuNR10 led to selective growth of tolerant Type 2 phenotype by enabling them to multiply over the vulnerable Type 1 phenotype. The IC 50 values for Type 1 phenotype was found to be as low as 2.1 μM (Fig. 3h) indicating extreme vulnerability of this phenotype of El Tor towards nanorod.  Effect of AuNS10 and AuNR10 on membrane fluidity of V. cholerae strains. For monitoring fluidity of cell membrane the rod shaped fluorescent probe DPH is widely used reflecting their rotational motion in membrane 27 . DPH is almost non-fluorescent in aqueous environment; the fluorescent intensity, however, largely increased when DPH binds to the hydrophobic region of cell membrane, essentially composed of lipid bilayer 28 . This lipid bilayer acts as a mechanical barrier on the rotational mobility of DPH molecules. Hence "fluidization" of membrane leads to increase in mobility of the dye, as reflected from a low pI value, whereas "rigidity" or "integrity" corresponds to a high value of pI. In the present study, the membrane integrity of VcO395 was examined after treatment with AuNR10 whereas that of VcN16961 was studied with both AuNS10 and AuNR10. In all the cases the membrane integrity was affected, though to different extent (Fig. 4a). On treatment with AuNR10 the membrane of VcN16961 was found to be affected more as compared to VcO395, as reflected from the lower value of pI for the former as compared to the respective control cells.
Protein leakage from V. cholerae strains after treatment with AuNPs. Protein leakage caused due to damage of cell membrane for AuNP treated strains of V. cholerae were quantified spectroscopically by Bradford assay. Increase of protein leakage was observed with the increase in incubation time for both classical and El Tor strains after treatment with AuNR10, compared to the control cells (Fig. 4b). VcN16961 was more susceptible towards AuNP -protein leakage was also observed after treatment with AuNS10. This observation may be attributed due to the greater disordered structure of cell membrane for El tor biotype, coupled with the variation in gene expression 29 . ZnO nanoparticles were also found to be more disruptive towards VcN16961 cell membrane, leading to more protein leaching 30 . DNA was monitored by DAPI staining. The fluorescence dye DAPI is known to specifically bind to the minor groove of DNA with a preference for AT rich nucleic bases 31,32 . Confocal microscope images showed fragmentation of DNA for both VcO395 and VcN16961 after treatment with AuNR10 (Fig. 5). This may be attributed due to the loss of integrity of cell membrane upon treatment with AuNR10.

Discussion
The emergence of MDR strains has added a new dimension in the fight against pathogenic organisms, bolstering our search for developing alternatives to antibiotics 33 . Literature reports the potential threat of Gram negative bacteria as compared to the Gram positive one, because of the MDR exhibited by the former 3 . To date there are only a few reports of antimicrobial potency of NPs against V. cholerae 33,34 In the present paper, we have studied the efficacy of AuNPs of different size and shape against two biotypes of V. cholerae, VcO395 and VcN16961. Out of seven cholera pandemics that the world has faced since 1817, the first six were caused by the classical one, while the El Tor biotype replaced the classical one since 1961 35 . The growth kinetics of both the biotypes revealed efficacy of AuNR10 over AuNS10. In fact, the classical one is susceptible only to AuNR10 and not to AuNS10 or AuNS100. The efficacy of AuNR10 towards VcO395 is also evident from the IC 50 value of 3.04 μM. There are several reports in literature stating the unique capability of nanorod in destroying pathogenic bacteria 36,37 . AuNR10 used in our study has an aspect ratio of 3.8; an aspect ratio value of <5 is reported to have Au(100) facets on the tip of the rod and Au(110) facets on the side walls of the cylindrical rod 38 . On the other hand, AuNS10 is only composed of Au(111) facets. The higher antibacterial activity of AuNR10 compared to AuNS10 may be due to the presence of larger number of surface atoms at the corners and edges of the nanorod 39 . This may allow facile

Materials and Methods
Materials. Gold nanospheres of different sizes (AuNS10, product code #752584 and AuNS100, product code #753688) and gold nanorod (AuNR10, product code #716812) were purchased from Sigma-Aldrich, USA and were used as supplied. LB powder was purchased from Himedia. DAPI, DPH and PI were purchased from Sigma Aldrich. All other chemicals, of analytical grade, were purchased from Merck, India.

Growth kinetics of VcO395 and VcN16961 using AuNPs. To determine the growth curve of VcO395
and VcN16961 in presence of AuNPs, cells were cultured in 5 mL LB media at 37 °C overnight. Growth kinetics were performed in 96 well plates (Nunc TM ) after adding 2% inoculum from overnight cultures in LB supplemented with different AuNPs. A control group for each strain without any AuNP was also maintained. The OD at 595 nm was monitored every 15 min in Tecan Genios microplate reader (Austria) at 37 °C with shaking for 24 h. For each strain, ten independent growth curves were monitored and the data were fitted. Effect of AuNS and AuNR on protein leakage from bacterial cell membranes. Leakage of protein from bacterial cells was detected spectroscopically using Bradford's reagent for protein assay. Both strains of V. cholerae were grown in LB at 37 °C overnight. From the overnight culture, 2% inoculums were added to LB and shaked. Cell pellet was washed and resuspended in 1X PBS, after which the cell suspension was incubated with and without AuNPs at 37 °C. Samples were withdrawn after specific time interval and were centrifuged (5000 rpm at 4 °C) for 10 min. For each sample, 100 μl of supernatant containing protein was mixed with 900 μl of Bradford reagent and incubated in dark for 10 min, after which the OD 595 nm was measured on a Shimadzu UV Spectrophotometer UV-1800.

Effect of AuNS and AuNR on fragmentation of DNA.
To monitor DNA damage of AuNP treated strains of V. cholerae, cells were treated with a cell permeable stain DAPI and visualized in CLSM (Carl Zeiss, Germany). Typically, 5 ml LB was inoculated with overnight cultures of VcO395 and VcN16961 strains and were shaken at 37 °C for 3 h followed by 1 h treatment with AuNS and AuNR. Cell pellet was then washed with 1 X PBS buffer and incubated with 0.3 μg/ml DAPI in dark for 1 h. Excess stain was removed by washing with PBS and cell pellet was finally suspended in 1X PBS. Samples were placed on glass slide with a glass cover slip and viewed with confocal microscope using an excitation wavelength of 543 nm.