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Assessment of Renal Function by the Stable Oxygen and Hydrogen Isotopes in Human Blood Plasma

Assessment of Renal Function by the Stable Oxygen and Hydrogen Isotopes in Human Blood Plasma

  • Tai-Chih Kuo, 
  • Chung-Ho Wang, 
  • Hsiu-Chen Lin, 
  • Yuan-Hau Lin, 
  • Matthew Lin, 
  • Chun-Mao Lin, 
  • Hsien-Shou Kuo
PLOS
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Abstract

Water (H2O) is the most abundant and important molecule of life. Natural water contains small amount of heavy isotopes. Previously, few animal model studies have shown that the isotopic composition of body water could play important roles in physiology and pathophysiology. Here we study the stable isotopic ratios of hydrogen (δ2H) and oxygen (δ18O) in human blood plasma. The stable isotopic ratio is defined and determined by δsample = [(Rsample/RSTD)−1] * 1000, where R is the molar ratio of rare to abundant, for example, 18O/16O. We observe that the δ2H and the δ18O in human blood plasma are associated with the human renal functions. The water isotope ratios of the δ2H and δ18O in human blood plasma of the control subjects are comparable to those of the diabetes subjects (with healthy kidney), but are statistically higher than those of the end stage renal disease subjects (p<0.001 for both ANOVA and Student's t-test). In addition, our data indicate the existence of the biological homeostasis of water isotopes in all subjects, except the end stage renal disease subjects under the haemodialysis treatment. Furthermore, the unexpected water contents (δ2H and δ18O) in blood plasma of body water may shed light on a novel assessment of renal functions.

Introduction

Water (H2O) molecule is the base of life, yet the most important molecule, making up about seventy percent of body mass. Despite the notice of importance of water, an often overlooked facet is the uniqueness of water isotopes. Natural water contains trace amount of heavy isotope hydrogen and oxygen atoms, and among which the 2H and 18O are the major ones. The ratio of 1H to 2H is about 6240 to 1, or about 155 ppm [1], [2], [3] in the V-SMOW (Vienna Standard Mean Ocean Water) water standard, and the ratio of 16O to 18O is about 499 to 1, or about 2005 ppm [4]. In terms of the molar unit, the concentrations of 2H and 18O are in the range of millimolar, which is comparable to the concentrations of many biochemical metabolites. This naturally raises an intriguing question, “Is there any biological/biomedical role played by these isotopic waters?”. However, due to a high-level complexity of human physiology, the significance of the presence of isotopic water in vivo remains unclear.

In general, water molecules that contain the 2H and 18O atoms (isotopic waters) are considered as behave identically as the abundant water (1H216O). Accordingly, the isotopic water has been used as a marker to estimate body water content [5], [6] or the tracer of energy metabolism [7]. However, in terms of the physical and chemical properties, the isotopic waters possess subtle yet unique differences to the abundant waters [8]. This causes the isotopic variations in meteoric waters, varied by geographic locations [9], [10]. Moreover, with the unique properties of isotopic waters, the stable isotopic ratios of hydrogen (δ2H) and oxygen (δ18O) in various biological materials have been used as “atomic fossils or tracers” in paleodietary, meteorology, anthropology, ecology, and modern food-chained network [9], [11], [12], [13], [14], [15], [16].

Furthermore, several studies do indicate that the isotopic water may have profound biochemical and physiological effects. For example, the 2H2O can promote the formation of microtubules by stimulating the polymerization of tubulin subunits [17], [18], and result in cell death [19]. Vasdev and coworkers showed the increase of 2H2O content can prevent hypertension in the spontaneous hypertension rat [20]. On the other hand, the depletion of deuterium (2H) in the water of culture medium reduces the growth rates of different animal cell lines [21]. O'Grady and coworkers showed that the signatures of hydrogen (δ2H) and oxygen (δ18O) isotope ratios in the body water of an untreated streptozotocin-induced diabetes mellitus are distinct from those of the normal mice [22]. Thus, it is clear that the concentration of the rare isotopes (2H and 18O) in water do have biological meanings, although the cause-effect relationships and mechanism remain unknown.

Here we study and explore the possible role played by the isotopic waters in biology. We investigate relationship between the human health conditions and the stable isotope ratios of hydrogen (δ2H) and oxygen (δ18O) in human blood plasma. We observe that the δ2H and δ18O values in human blood plasma are associated with the human renal conditions. The δ18O in the blood plasma of the control subjects and diabetes subjects (without renal dysfunction) are 87% and 160% higher than the end stage renal disease subjects (renal dysfunction cases), respectively. The δ2H in blood plasma of the healthy kidney groups (the control subjects and the diabetes subjects) are 72% and 92% higher than the renal dysfunction group. However the blood plasma water contents (δ2H and δ18O) in the control subjects and the diabetes patients have no difference.

Results

The stable isotope ratios of hydrogen (δ2H) and oxygen (δ18O) from 48 human blood plasma's water samples were measured. The samples were randomly obtained from five groups of participants, the non-fasting control subjects (CSR, n = 6, Table 1), the fasting control subjects (CSF, n = 5, Table 1), the fasting end stage renal disease subjects without haemodialysis treatment (ESRDnHD, n = 5, Table 2), the fasting end stage renal disease subjects with the haemodialysis treatment (ESRDHD, n = 27, Table 2), and the fasting diabetes subjects (DB, n = 5, Table 3). It is worth a note that this is a pilot study conducted in a small scale to explore the isotopes level in human, which allows one to carry out a large scale study later. Furthermore, to avoid any biased and carefully interpret our data, we analyzed the entire datasets (n = 48) by using the k-means clustering algorithm with a total number of 10,000 repeated runs. By applying the k-means clustering algorithm [23] with a preset of 4 clusters to the entire datasets, the four clusters are to be found as a CSF plus DB cluster, a CSR cluster, a ESRDHD, and a ESRDnHD cluster (Figure 1 and Table S1). Twenty two percent of the ESRDHD data locate in the CSR cluster and forty four percent are within the ESRDnHD cluster, indicates that the ESRDHD data are dispersed between the CSR and the ESRDnHD clusters. In addition, the level of blood urea nitrogen (BUN), creatinine, and estimated glomerular filtration rate (eGFR) from the ESRDHD patients are lower than that of the ESRDnHD. However, the level of δ2H and δ18O from the ESRDnHD are lower than that of the ESRDHD but more clustered (Table 2 and Figure 1). It should be noted that a more negative value of δ2H (or δ18O) means a lower concentration of water 2H (or 18O) than that of the international V-SMOW water standard.

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Figure 1. The stable isotopic ratios of hydrogen (δ2H) and oxygen (δ18O) in human blood plasma.

Squares represent the distributions of the δ2H and δ18O of human blood plasma, colored by group: CSR in cyan, CSF in blue, ESRDnHD in red, ESRDHD in yellow, and DB in green. The colored circles are the clusters obtained by applying the k-means analysis with a preset of 4 clusters to the all datasets. The blue circle comprises all CSF (100%) and all DB (100%). The cyan circle is constituted of most CSR (83%) and several ESRDHD (22%). The yellow circle encloses about half of the ESRDHD data (44%). The ESRDnHD (100%) is clustered in the red circle along with 9 ESRDHD data points (33%). The triangle denotes the centroid of each cluster.

https://doi.org/10.1371/journal.pone.0032137.g001

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Table 2. Isotopic values of end stage renal disease (ESRD) patient's blood plasma.

https://doi.org/10.1371/journal.pone.0032137.t002

The water δ18O and δ2H values of the ESRD are distinctively lower than those of the CS

The values of water δ18O and δ2H in the blood plasma of the ESRDnHD show distinct characteristics from those of the CSF (Figure 1). By applying the Student's t-test and the ANOVA statistical analysis to the ESRDnHD and the CSF datasets, the water contents (δ18O and δ2H) of the blood plasma in the ESRDnHD and the CSF show significant difference [t0.05; 8 = 13.78 and F0.05; 1,8 = 189.83 for δ18O; t0.05; 8 = 15.08 and F0.05; 1,8 = 227.47 for δ2H]. The distributions of the δ18O and δ2H in blood plasma of the ESRDHD are scattered between the CS and the ESRDnHD (Figure 1). The δ18O and δ2H in the blood plasma water of the ESRDHD are also significantly lower than those of the CSF and the CSR.

The homeostasis of 18O and 2H of blood plasma resists the fluctuation of 18O and 2H levels of water sources

The δ2H and δ18O values of the rain precipitation fluctuate seasonally. Since the majority of water 2H and 18O in the blood plasma would eventually come from the rain precipitation-the source of the drinking and dietary water, it would be interesting to examine the relationships between the δ2H and δ18O values in the rain water and the plasma water.

Here, we compared the δ2H and δ18O values of our data with those of Taipei monthly precipitation from 2000 to 2010 [24] (Figures 2A and B). From January to May, the δ2H and δ18O values of the rain water show little variation. These values start to drop in the June, reaching the minimum in the July and August and climbing back from the September to December. On the other hand, the plasma water isotope ratios in the CS group are always lower than those of the rain precipitation from January to May. However, the isotope ratios of plasma water are in the standard error of rain precipitation from July to December (Figures 2A and B). Therefore, a homeostasis of isotope δ2H and δ18O in the blood plasma of CS group is observed to against the fluctuation of daily intake water.

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Figure 2. A comparison of stable isotopic water in human blood plasma and monthly mean precipitation in 2000–2010 at Taipei, Taiwan.

(A) The mean values of Taipei precipitation in March, July and September from the past 11 years are idiosyncrasies to the δ18O in blood plasma of the ESRDnHD (100%) and the ESRDHD (100%). This occurrence is observed in the DB and the CSF. 50% of the CSR are corresponding to the precipitation. (B) Both δ2H and δ18O in blood plasma of the ESRDnHD, ESRDHD, and CSR are observed in a comparable manner of the monthly precipitation. None of the CSF is corresponding to the precipitation. The δ18O and δ2H in blood plasma are indicated by squares, colored as in figure 1. The mean δ18O and δ2H in precipitation are indicated by circles, connected by gray lines. Error bars (black vertical lines connected by breaks) represent the standard deviation of the mean.

https://doi.org/10.1371/journal.pone.0032137.g002

Due to frequent typhoons in July of Taiwan, the isotope content of rain precipitation is least but varies most among all other months. The isotope ratios of plasma water of ESRDHD in July and March are significant lower than that of precipitation, again indicates a strong independency of rain water (Figures 2A and B). Although the isotope ratio of precipitation in September is close to that of CS, the same manner remains observed in ESRDnHD, about 35% lower than that of the precipitation. For the DB group, the δ18O of plasma water is comparable to that of rain precipitation in December [t0.05; 14 = 0.27 and F0.05; 1,14 = 0.07], but the δ2H of plasma water shows the independency of rain precipitation [t0.05; 14 = 3.03 and F0.05; 1,14 = 9.21].

The water δ18O and δ2H values in the DB and the CSF groups are similar

The values of the δ18O and δ2H from the DB are similar to those of the CSF. The ANOVA analysis suggests that the plasma water content (δ18O and δ2H) of the DB and the CSF are comparable [F0.05; 1,8 = 4.63 for δ18O; F0.05; 1,8 = 0.20 for δ2H]. The k-means clustering analysis shows that the CSF and the DB are similar and within the same cluster (Figure 1).

The control subject groups (CS)

The overall mean values of the δ2H and δ18O for the CStotal are −5.63‰ and −38.0‰ (Table 1). The mean values of the δ2H and δ18O for the CSR are −6.67‰ and −40.3‰. The means of the δ2H and δ18O for the CSF are −4.76‰ and −35.2‰. From the δ2H and δ18O values of the CSR and CSF groups, the differences between these two groups are significant [t0.05; 9 = 2.88 and F0.05; 1,9 = 8.31 for δ18O; t0.05; 9 = 2.62 and F0.05; 1,9 = 6.87 for δ2H].

The end stage renal disease group (ESRD)

The mean values of δ2H and δ18O for the ESRDnHD are −11.89‰ and −72.44‰, and are −10.37‰ and −59.10‰ for the ESRDHD (Table 2). The ESRDHD (std. 2.9 for δ18O and 11.54 for δ2H) is more scattered than the ESRDnHD (std. 0.9 for δ18O and 4.9 for δ2H) (Figure 1). In terms of δ2H, the difference between the ESRDHD and ESRDnHD are significant [t0.05; 30 = 2.5 and F0.05; 1,30 = 6.33]. However for the δ18O, the difference is insignificant [t0.05; 30 = 1.17 and F0.05; 1,30 = 1.37].

The diabetes group (DB)

In the DB group, the mean of δ2H in blood plasma is −4.04‰, and is −34.08‰ for the δ18O. The mean fasting plasma glucose level of DB subject is 160.8±36.7 mg/dL. The creatinine level and the eGFR indicate normal kidney function of DB subjects (Table 3).

Discussion

The water δ18O and δ2H values in the ESRD blood plasma are distinctively lower than those in the CS and the DB

In terms of the δ18O and δ2H values, the water 18O and 2H in the blood plasma of the CS and DB groups are significantly higher than those of the ESRD (p<0.001). The δ18O and δ2H in blood plasma of ESRD (including ESRDnHD and ESRDHD) are 87% and 72% lower than the CS (CSF and CSR) and are 160% and 92% lower than the DB. Thus, the values of δ18O and δ2H in blood plasma correlate with renal function in the present study.

The lowered level of water 18O and 2H in the blood plasma of the ESRD patients are intriguing, since both the normal control subjects and renal patients share the same source of drinking and dietary water. It seems that the 2H and 18O isotopes are being selectively “removed” from the water of blood plasma in patients with renal dysfunction. One of the many functions of kidney is the reabsorption of water, which is now known, at least in part, mediated by different types of renal aquaporins (AQPs), a plasma membrane protein that forms water channel [25], [26], [27]. For example, aquaporin 1 (AQP1) is localized at the proximal tubules, and descending thin limb that increases the water permeability [28]. The AQP2, AQP3, and AQP4 are localized at the collecting duct, where AQP2 is a vasopressin regulation target for the water permeability at the collecting duct [29]. Questions naturally arise whether or not these aquaporin proteins involve in the lower level of 18O and 2H in blood plasma in renal dysfunction patients. In a previous study, the molecular dynamics (MD) simulation and solution experiment of the prototypical AQP1 show that the permeability of 2H2O is similar to that of water [30], while another study shows that point mutation in the aromatic/arginine region of AQP1 allows protons pass through it [31]. Moreover, in the ESRD patients, a higher concentration of vasopressin is found [32]. Vasopressin and water deprivation accompany upregulation of AQP2 in renal collecting duct [33], [34], and downregulation of AQP2 in aging is posttranscriptional [34]. Further investigation on the level of monovalent ions such as Na+, K+, and Cl in blood plasma of ESRDHD reveals that the normal functioning of active transport of ascending limb of the loop of Henle (Table 2), whereas this part of the nephron contains no aquaporins [25], [26]. Therefore, it would be interesting to find the differences of aquaporins, in terms of their biophysical, biochemical, and physiological functions in the 2H and 18O enriched water, among healthy individuals and persons with various degree of renal dysfunction. Such studies will provide clues to the observed hypo 2H and 18O in the blood plasma of people with renal dysfunctions.

The biological isotope homeostasis of human blood plasma

It was previously shown, at the tissue level (i.e. liver, blood, nail, etc.), the nonexchangeable hydrogen isotope of quails is influenced by the deuterium-enriched dietary and drinking water [11]. Similarly, the hydrogen (δ2H) in human body water and hair are also affected by the intake of water and food [13]. Although it is clear that “you are what you eat”, those studies show no sign of the biological homeostasis of water isotopes. If there is no biological homeostasis of water isotopes, the isotope ratios of the water hydrogen and oxygen in the blood plasma would seasonally fluctuate with those of the rain precipitation. However, that is not what we find. In this study, the drinking and dietary water of all the participants is not artificially augmented or depleted with heavy water isotopes. Although the δ2H and δ18O values of the precipitation of Taipei city are severely associated with the asymmetric heating of island and sea during the seasonal changes [24], [35], the levels of water 18O and 2H in the blood plasma of all subjects, except the ESRDHD, show distinct homeostasis (Figures 2A and 2B).

Our concept of biological homeostasis of water isotopes is coherent with the studies of Berdea et al [36]. The stable isotope δ2H in the blood plasma of healthy people lived in Cluj-Napoca, the fourth most populous city in Romania in Europe, is in the range of −32.3 to −38.7‰ [36], which is comparable with our CS data (Table 1). When we compare the isotope contents of monthly precipitation in Cluj-Napoca and in Taipei using the algorithm, developed by Bowen et. al. [12], [37], the isotope precipitation patterns between the two cities are distinct (Figure 3). Apparently, in the two cities, people intake very different sources of drinking and dietary water, in terms of the water isotope contents. However, the biological isotope homeostasis in human blood plasma of healthy people in Taipei in Asia is consensus of that in Cluj-Napoca in Europe. We believe that the human homeostasis is a fundamental mechanism to maintain the high level complex physiological functions.

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Figure 3. The stable isotopes of monthly precipitation in Taipei, Taiwan and in Cluj-Napoca, Romania.

Shown is the estimated stable isotope of monthly precipitation, generated by using algorithm, developed by Bowen et. al. [12], [37]. The square denotes the estimated isotope of monthly precipitation in Taipei with settings of latitude 25°, longitude 121.5°, and altitude 10 m. The circle denotes the estimated isotope of monthly precipitation in Cluj-Napoca with settings of latitude 46.7°, longitude 23.6°, and altitude 335 m.

https://doi.org/10.1371/journal.pone.0032137.g003

It appears that there is a fine tune of the biological homeostasis of water isotopes reflecting differential renal conditions. For example, the ESRDnHD and the normal renal groups (the CS and the DB) have different homeostasis levels. Note that the three groups with normal renal function (Tables 1 and 3), the δ18O and δ2H levels of the CSF and DB are similar, yet higher than those of the CSR group (Figure 1). The difference between these groups are that the CSF and DB are under an 8-hr fasting while the CSR group is not. In addition, we notice that the age of the CS subject (range from 27 to 67 yr.) is independence of the DB and ESRD subjects (p<0.001). However, the age of the DB is highly correlated to that of the ESRD (p = 0.93). The stable isotopic values of δ18O and δ2H in blood plasma of the ESRDHD are scattered between CS and ESRDnHD (Figure 1). The lack of the 18O and 2H homeostasis in the ESRDHD group could be due to the times and durations of each haemodialysis, and the hydration status of different ESRDHD subjects [38]. Therefore, we suggest that the levels of δ2H and δ18O in blood plasma of renal dysfunction patients may need to be monitored during the haemodialysis treatment.

Is the hypo stable isotope of blood plasma a cause or a consequence of renal dysfunction?

In rat, when about 30% of the body water is replaced by 2H2O, histologic examination shows demolition of renal tubules but the morphology of glomerular remains unchanged [39]. Another study with the 2H2O replacement in rats has shown changes in renal function that both the glomerular filtration rate and renal plasma flow decrease. Recovery of renal function is achieved by the restoration of 1H2O [40]. Despite the above studies were carried out in rats, evidently, heavy water is toxic to the kidney as it could damage the renal tubules and change the renal function. On the other hand, since the renal patients share the same drinking and dietary water with the healthy people, we cannot attribute the renal dysfunction to the presence of the heavy water isotopes.

In fact, the causes of renal dysfunction are usually very complicated, including medications, diabetes mellitus, hypertension, sepsis, personal life style, and so on. Nonetheless, an impaired kidney causes the accumulation of metabolites, which may result in the replacement of 2H for 1H and 18O for 16O. Such replacement forms stronger chemical bonds (more stable) between the heavy atoms (from water) and light atoms (from metabolites) and thus, the isotopes level in water becomes lower. Moreover, the fluid retention caused by renal dysfunction would affect the total water flux (TWF), an important factor to monitor the isotope level of water that is highly correlated to levels of water intake and urine output [22], of human compartments. All these could eventually lead to the hypo isotope of blood plasma. In the present study, we show that the renal dysfunction is associated with the much reduced δ18O and δ2H in human blood plasma. We observe a signature of hypo isotope of blood plasma, exhibits in renal dysfunction patients but not in healthy persons or diabetes patients, although the age of diabetes subjects are correlated to that of renal dysfunction subjects. We urge further biochemical and biophysical assessments to figure out the hypo isotope of blood plasma in the ESRD patients.

As of today, the serum creatinine has become the most widely used marker in estimating the glomerular filtration rate (GFR) of kidney function. Despite the GFR estimation is based on the chronic renal disease model, this model underestimates the GFR in healthy population but overestimate in patients with impaired kidney [41], [42]. In addition, the serum creatinine used to evaluate renal function is encumbered by association with sex, age, muscle mass, race, and diet [43]. Our data and results suggest that the δ18O and δ2H of blood plasma is sensitive to the renal function but seems insensitive to age, race and diet, probably due to the biological isotope homeostasis. In sum, this pilot study along with biological data forms the base for further investigations on the hypo isotope of blood plasma in renal dysfunction patients, and opens up the possibility of using level of δ18O and δ2H in blood plasma as a potential marker for renal dysfunction. Therefore, a large scale quantitative study on the hypo isotope of renal dysfunction patients are currently planned to conduct.

Summary

The stable isotopic ratios of hydrogen (δ2H) and oxygen (δ18O) in human blood plasma are biological isotopic homeostasis in the CS, the ESRDnPD, and the DB. The water status (δ18O and δ2H) of blood plasma of the CS and the DB are comparable, but is significantly distinct from the ESRD. The unexpected water in blood plasma of the human body could provide an insightful index to assess the condition of the human kidney.

Materials and Methods

Ethics Statement

The Taipei Medical University Institutional Review Board approved this study (approval ID: TMUH-02-09-01). The informed consent from all subjects involved in this study was not obtained as the data were analyzed anonymously. The ethics committee approved this procedure.

Participants

According to the biochemical parameters and doctor descriptions on the participants' records, the participants were classified into three categories, the control subject (CS), the patients diagnosed with the end stage renal disease (ESRD), and the individuals with diabetes yet without detectable renal dysfunction (DB). All the DB subjects are under diabetes control. All forty eight subjects (11 CSs, 32 ESRDs, and 5 DBs) are native Taiwanese, live in the Taipei city. They had not traveled abroad for at least three months prior to the sampling date. Thus we can eliminate the isotope ratio variations caused by the geographical isotopic compositions of food and water [10], [11], [15], [16].

Water samples

3 ml of human blood plasma sample is stored in a 15 ml falcon tube. The tube is then placed into a pre-dried vacuumed round bottle flask with 15 g of CaCl2 granule (Sigma-Aldrich). The round bottle flask is then capped and sealed carefully to make sure no water in air gets into the flask. The flask is incubated at room temperature for CaCl2 to absorb water from the human blood plasma sample for seven days. The water sample (about 2 ml) is obtained from the hydrated CaCl2 by vacuum distillation (Buchi Glass Oven B-585, Kugelrohr).

Determination of hydrogen (δ2H) and oxygen (δ18O) in human blood plasma

The assessment of hydrogen (δ2H) and oxygen (δ18O) in the water samples was conducted as the following. The stable oxygen isotopic compositions were analyzed by the well-known CO2–H2O equilibration method [44], [45]. The equilibrated CO2 gas was measured by a VG SIRA 10 isotope ratio mass spectrometer. The hydrogen isotopic compositions were determined on a VG MM602D isotope ratio mass spectrometer after reduction of water to H2 using Zinc shots made by Biogeochemical Laboratory of Indiana University [46]. All isotopic ratio results are reported as the δ-notation (‰) relative to the international V-SMOW (Vienna Standard Mean Ocean Water) standard and normalized on the scale that the δ 18O and δ2H of SLAP (Standard Light Antarctic Precipitation) are −55.5‰ and −428‰, respectively [47]. The analytical precisions expressed as 1σ for the laboratory standards are better than 1.3‰ for δ2H and 0.08‰ for δ18O, respectively. The average differences of duplicate analyses of water samples are ± 1.5‰ for δ2H and ± 0.11‰ for δ18O, respectively.

Date Analysis

To very carefully interpret our data and avoid any biased, we first analyzed the entire datasets (n = 48) by using the k-means clustering algorithm with a total number of 10,000 repeated runs. The ANOVA and the Student's t-test were performed by using the STASTISTICA 8.0 (StartSoft. Inc., Tulsa, OK). The k-means clustering was performed in the MATLAB R2011a (MathWorks. Inc., Natick, MA) that data are partitioned into a preset of four clusters. Euclidean distance is measured to compute the centroid of cluster, a mean of the data points within that cluster. A total number of 10,000 repeated clustering processes were performed, as a new set of initial cluster centroid position was given in each round. This procedure returns the best solution of a four clusters that each cluster is with the lowest value of sum of point-to-centroid distances.

Supporting Information

Table S1.

The partition table of the whole dataset (n = 48) into the 4 preset groups (clusters) and the centroid of each cluster are obtained via the k-means clustering algorithm with a total number of 10,000 repeated runs.

https://doi.org/10.1371/journal.pone.0032137.s001

(DOCX)

Acknowledgments

The authors thank Drs. I-Chun Chou and Chiaolong Hsiao from Georgia Tech for helpful discussions.

Author Contributions

Conceived and designed the experiments: HSK TCK CHW. Performed the experiments: HSK CHW TCK. Analyzed the data: HSK TCK. Contributed reagents/materials/analysis tools: CHW HCL YHL ML CML. Wrote the paper: HSK TCK.

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