The extremophile microorganism Thermus scotoductus primarily exhibits aerobic metabolism, though some strains are capable of anaerobic growth, utilizing diverse electron acceptors. We focused on the T. scotoductus K1 strain, exploring its aerobic growth and metabolism, responses to various carbon sources, and characterization of its bioenergetic and physiological properties. The strain grew on different carbon sources, depending on their concentration and the medium's pH, demonstrating adaptability to acidic environments (pH 6.0). It was shown that 4 g L−1 glucose inhibited the specific growth rate by approximately 4.8-fold and 5.6-fold compared to 1 g L−1 glucose at pH 8.5 and pH 6.0, respectively. However, this inhibition was not observed in the presence of fructose, galactose, lactose, and starch. Extracellular and intracellular pH variations were mainly alkalifying during growth. At pH 6.0, the membrane potential (ΔΨ) was lower for all carbon sources compared to pH 8.5. The proton motive force (Δp) was lower only during growth on lactose due to the difference in the transmembrane proton gradient (ΔpH). Moreover, at pH 6.0 during growth on lactose, a positive Δp was detected, indicating the cells' ability to employ a unique energy-conserving strategy. Taken together, these findings concluded that Thermus scotoductus K1 exhibits different growth and bioenergetic properties depending on the carbon source, which can be useful for biotechnological applications. These findings offer valuable insights into how bacterial cells function under high-temperature conditions, which is essential for applying bioenergetics knowledge in future biotechnological advancements.
Citation: Hripsime Petrosyan, Karen Trchounian. Growth characteristics, redox potential changes and proton motive force generation in Thermus scotoductus K1 during growth on various carbon sources[J]. AIMS Microbiology, 2024, 10(4): 1052-1067. doi: 10.3934/microbiol.2024045
[1] | Guojun Gan, Qiujun Lan, Shiyang Sima . Scalable Clustering by Truncated Fuzzy c-means. Big Data and Information Analytics, 2016, 1(2): 247-259. doi: 10.3934/bdia.2016007 |
[2] | Marco Tosato, Jianhong Wu . An application of PART to the Football Manager data for players clusters analyses to inform club team formation. Big Data and Information Analytics, 2018, 3(1): 43-54. doi: 10.3934/bdia.2018002 |
[3] | Jinyuan Zhang, Aimin Zhou, Guixu Zhang, Hu Zhang . A clustering based mate selection for evolutionary optimization. Big Data and Information Analytics, 2017, 2(1): 77-85. doi: 10.3934/bdia.2017010 |
[4] | Zhouchen Lin . A Review on Low-Rank Models in Data Analysis. Big Data and Information Analytics, 2016, 1(2): 139-161. doi: 10.3934/bdia.2016001 |
[5] | Pawan Lingras, Farhana Haider, Matt Triff . Fuzzy temporal meta-clustering of financial trading volatility patterns. Big Data and Information Analytics, 2017, 2(3): 219-238. doi: 10.3934/bdia.2017018 |
[6] | Yaguang Huangfu, Guanqing Liang, Jiannong Cao . MatrixMap: Programming abstraction and implementation of matrix computation for big data analytics. Big Data and Information Analytics, 2016, 1(4): 349-376. doi: 10.3934/bdia.2016015 |
[7] | Ming Yang, Dunren Che, Wen Liu, Zhao Kang, Chong Peng, Mingqing Xiao, Qiang Cheng . On identifiability of 3-tensors of multilinear rank (1; Lr; Lr). Big Data and Information Analytics, 2016, 1(4): 391-401. doi: 10.3934/bdia.2016017 |
[8] | Subrata Dasgupta . Disentangling data, information and knowledge. Big Data and Information Analytics, 2016, 1(4): 377-390. doi: 10.3934/bdia.2016016 |
[9] | Robin Cohen, Alan Tsang, Krishna Vaidyanathan, Haotian Zhang . Analyzing opinion dynamics in online social networks. Big Data and Information Analytics, 2016, 1(4): 279-298. doi: 10.3934/bdia.2016011 |
[10] | Ugo Avila-Ponce de León, Ángel G. C. Pérez, Eric Avila-Vales . A data driven analysis and forecast of an SEIARD epidemic model for COVID-19 in Mexico. Big Data and Information Analytics, 2020, 5(1): 14-28. doi: 10.3934/bdia.2020002 |
The extremophile microorganism Thermus scotoductus primarily exhibits aerobic metabolism, though some strains are capable of anaerobic growth, utilizing diverse electron acceptors. We focused on the T. scotoductus K1 strain, exploring its aerobic growth and metabolism, responses to various carbon sources, and characterization of its bioenergetic and physiological properties. The strain grew on different carbon sources, depending on their concentration and the medium's pH, demonstrating adaptability to acidic environments (pH 6.0). It was shown that 4 g L−1 glucose inhibited the specific growth rate by approximately 4.8-fold and 5.6-fold compared to 1 g L−1 glucose at pH 8.5 and pH 6.0, respectively. However, this inhibition was not observed in the presence of fructose, galactose, lactose, and starch. Extracellular and intracellular pH variations were mainly alkalifying during growth. At pH 6.0, the membrane potential (ΔΨ) was lower for all carbon sources compared to pH 8.5. The proton motive force (Δp) was lower only during growth on lactose due to the difference in the transmembrane proton gradient (ΔpH). Moreover, at pH 6.0 during growth on lactose, a positive Δp was detected, indicating the cells' ability to employ a unique energy-conserving strategy. Taken together, these findings concluded that Thermus scotoductus K1 exhibits different growth and bioenergetic properties depending on the carbon source, which can be useful for biotechnological applications. These findings offer valuable insights into how bacterial cells function under high-temperature conditions, which is essential for applying bioenergetics knowledge in future biotechnological advancements.
In data clustering or cluster analysis, the goal is to divide a set of objects into homogeneous groups called clusters [10,18,20,26,12,1]. For high-dimensional data, clusters are usually formed in subspaces of the original data space and different clusters may relate to different subspaces. To recover clusters embedded in subspaces, subspace clustering algorithms have been developed, see for example [2,15,19,17,9,21,16,22,3,25,7,11,13]. Subspace clustering algorithms can be classified into two categories: hard subspace clustering algorithms and soft subspace clustering algorithms.
In hard subspace clustering algorithms, the subspaces in which clusters embed are determined exactly. In other words, each attribute of the data is either associated with a cluster or not associated with the cluster. For example, the subspace clustering algorithms developed in [2] and [15] are hard subspace clustering algorithms. In soft subspace clustering algorithms, the subspaces of clusters are not determined exactly. Each attribute is associated to a cluster with some probability. If an attribute is important to the formation of a cluster, then the attribute is associated to the cluster with high probability. Examples of soft subspace clustering algorithms include [19], [9], [21], [16], and [13].
In soft subspace clustering algorithms, the attribute weights associated with clusters are automatically determined. In general, the weight of an attribute for a cluster is inversely proportional to the dispersion of the attribute in the cluster. If the values of an attribute in a cluster is relatively compact, then the attribute will be assigned a relatively high value. In the FSC algorithm [16], for example, the attribute weights are calculated as
wlj=1∑dh=1(Vlj+ϵVlh+ϵ)1α−1, l=1,2,…,k,j=1,2,…,d, | (1) |
where
Vlj=∑x∈Cl(xj−zlj)2. | (2) |
Here
wlj=exp(−Vljγ)∑ds=1exp(−Vlsγ), k=1,2,…,n,l=1,2,…,d, | (3) |
where
One drawback of the FSC algorithm is that a positive value of
w1=e−10e−10+e−30=11+e−20=1, w2=e−30e−10+e−30=11+e20=0. |
If we use
w1=e−1e−1+e−3=11+e−2=0.88, w2=e−3e−1+e−3=11+e2=0.12. |
From the above example we see that choosing an appropriate value for the parameter
In this paper, we address the issue from a different perspective. Unlike the group feature weighting approach, the approach we employ in this paper involves using the log transformation to transform the distances so that the attribute weights are not dominated by a single attribute with the smallest dispersion. In particular, we present a soft subspace clustering algorithm called the LEKM algorithm (log-transformed entropy weighting
The remaining part of this paper is structured as follows. In Section 2, we give a brief review of the LAC algorithm [9] and the EWKM algorithm [21]. In Section 3, we present the LEKM algorithm in detail. In Section 4, we present numerical experiments to demonstrate the performance of the LEKM algorithm. Section 5 concludes the paper with some remarks.
In this section, we introduce the EWKM algorithm [21] and the LAC algorithm [9], which are soft subspace clustering algorithms using the entropy weighting.
Let
F(U,W,Z)=k∑l=1[n∑i=1d∑j=1uilwlj(xij−zlj)2+γd∑j=1wljlnwlj], | (4) |
where
k∑l=1uil=1, i=1,2,…,n, | (5a) |
uil∈{0,1}, i=1,2,…,n,l=1,2,…,k, | (5b) |
d∑j=1wlj=1, l=1,2,…,k, | (5c) |
and
wlj>0, l=1,2,…,k,j=1,2,…,d. | (5d) |
Like the
uil={1, if ∑dj=1wlj(xij−zlj)2≤∑dj=1uiswsj(xij−zsj)2 for 1≤s≤k,0, if otherwise, |
for
wlj=exp(−Vljγ)∑ds=1exp(−Vlsγ) |
for
Vlj=n∑i=1uil(xij−zlj)2. |
Given
zlj=∑ni=1uilxij∑ni=1uil |
for
The parameter
The LAC algorithm (Locally Adaptive Clustering) [9] and the EWKM algorithm are similar soft subspace clustering algorithms in that both algorithms discover subspace clusters via exponential weighting of attributes. However, the LAC algorithm differs from the EWKM algorithm in the definition of objective function. Clusters found by the LAC algorithm are referred to as weighted clusters. The objective function of the LAC algorithm is defined as
E(C,Z,W)=k∑l=1d∑j=1(wlj1|Cl|∑x∈Cl(xj−zlj)2+hwljlogwlj), | (6) |
where
Like the
Sl={x:d∑j=1wlj(xj−zlj)2<d∑j=1wsj(xj−zsj)2,∀s≠l} | (7) |
for
wlj=exp(−Vlj)/h∑ds=1exp(−Vls/h) | (8) |
for
Vlj=1|Sl|∑x∈Sl(xj−zlj)2. |
Given the set of clusters
zlj=1|Sl|∑x∈Slxj | (9) |
for
Comparing Equation (6) with Equation (4), we see that the distances in the objective function of the LAC algorithm are normalized by the sizes of the corresponding clusters. As a result, the dispersions (i.e.,
In this section, we present the LEKM algorithm. The LEKM algorithm is similar to the EWKM algorithm [21] and the LAC algorithm [9] in that the entropy weighting is used to determine the attribute weights.
Let
P(U,W,Z)=k∑l=1n∑i=1uild∑j=1wljln[1+(xij−zlj)2]+λk∑l=1n∑i=1uild∑j=1wljlnwlj=k∑l=1n∑i=1uil[d∑j=1wljln[1+(xij−zlj)2]+λd∑j=1wljlnwlj], | (10) |
where
Similar to the EWKM algorithm, the LEKM algorithm tries to minimize the objective function given in Equation (10) iteratively by finding the optimal value of
Theorem 3.1. Let
uil={1, if D(xi,zl)≤D(xi,zs) for all s=1,2,…,k;0, if otherwise, | (11) |
for
D(xi,zs)=d∑j=1wljln[1+(xij−zsj)2]+λd∑j=1wljlnwlj. |
Proof. Since
f(ui1,ui2,…,uik)=k∑l=1uilD(xi,zl) | (12) |
is minimized. Note that
k∑l=1uil=1. |
The function defined in Equation (12) is minimized if Equation (11) holds. This completes the proof.
Theorem 3.2. Let
wlj=exp(−Vljλ)∑ds=1exp(−Vlsλ) | (13) |
for
Vlj=∑ni=1uilln[1+(xij−zlj)2]∑ni=1uil. |
Proof. The weight matrix
d∑j=1wlj=1, l=1,2,…,k, |
is the matrix
f(W)=P(U,W,Z)+k∑l=1βl(d∑j=1wlj−1) =k∑l=1n∑i=1uil[d∑j=1wljln[1+(xij−zlj)2]+λd∑j=1wljlnwlj] +k∑l=1βl(d∑j=1wlj−1). | (14) |
The weight matrix
∂f(W)∂wlj=n∑i=1uil(ln[1+(xij−zlj)2]+λlnwlj+λ)+βl=0 |
for
∂f(W)∂βl=d∑j=1wlj−1=0 |
for
From Equation (13) we see that the attribute weights of the
Theorem 3.3. Let
zlj=∑ni=1uil[1+(xij−zlj)2]−1xij∑ni=1uil[1+(xij−zlj)2]−1 | (15) |
for
Proof. If the set of cluster centers
∂P∂zlj=wljn∑i=1uil[1+(xij−zlj)2]−1[−2(xij−zlj)]=0. |
Since
n∑i=1uil[1+(xij−zlj)2]−1[−2(xij−zlj)]=0, |
from which Equation (15) follows.
In the standard
zlj=∑ni=1uil[1+(xij−z∗lj)2]−1xij∑ni=1uil[1+(xij−z∗lj)2]−1 | (16) |
for
To find the optimal values of
![]() |
The LEKM algorithm requires four parameters:
Parameter | Default Value |
1 | |
100 |
In this section, we present numerical experiments based on both synthetic data and real data to demonstrate the performance of the LEKM algorithm. We also compare the LEKM algorithm with the EWKM algorithm and the LAC algorithm in terms of accuracy and runtime. We implemented all three algorithms in Java and used the same convergence criterion as shown in Algorithm 1.
In our experiments, we use the corrected Rand index [8,13] to measure the accuracy of clustering results. The corrected Rand index is calculated from two partitions of the same dataset and its value ranges from -1 to 1, with 1 indicating perfect agreement between the two partitions and 0 indicating agreement by chance. In general, the higher the corrected Rand index, the better the clustering result.
Since the all the three algorithms are
To test the performance of the LEKM algorithm, we generated two synthetic datasets. The first synthetic dataset is a 2-dimensional dataset with two clusters and is shown in Figure 1. From the figure we see that the cluster in the top is compact but the cluster in the bottom contains several points that are far away from the cluster center. We can consider this dataset as a dataset containing noises.
Table 2 shows the average corrected Rand index of 100 runs of the three algorithms on the first synthetic dataset. From the table we see that the LEKM algorithm produced more accurate results than the LAC algorithm and the EWKM algorithm. The EWKM produced the least accurate results. Since the dispersion of an attribute in a cluster is normalized by the size of the cluster in the LAC and LEKM algorithms, the LAC and LEKM algorithms are less sensitive to the parameter.
Parameter | EWKM | LAC | LEKM |
1 | 0.0351 (0.0582) | 0.0024 (0.0158) | 0.9154 (0.2704) |
2 | 0.0378 (0.0556) | 0.9054 (0.2322) | 0.9063 (0.2827) |
4 | 0.012 (0.031) | 0.8019 (0.2422) | 0.9067 (0.2815) |
8 | -0.0135 (0.0125) | 0.7604 (0.2406) | 0.9072 (0.2799) |
16 | -0.013 (0.0134) | 0.7527 (0.2501) | 0.9072 (0.2799) |
Table 3 shows the confusion matrices produced by the best run of the three algorithms on the first synthetic dataset. We run the EWKM algorithm, the LAC algorithm, and the LEKM algorithm 100 times on the first synthetic dataset with parameter 2 (i.e.,
1 | 2 | 1 | 2 | 1 | 2 | |||||
C2 | 35 | 25 | C2 | 59 | 0 | C2 | 60 | 0 | ||
C1 | 25 | 15 | C1 | 1 | 40 | C1 | 0 | 40 | ||
(a) | (b) | (c) |
Table 4 shows the attribute weights of the two clusters produced by the best runs of the three algorithms. As we can see from the table that the attribute weights produced by the EWKM algorithm are dominated by one attribute. The attribute weights of one cluster produced by the LAC algorithm is also affected by the noises in the cluster. The attribute weights of the clusters produced by the LEKM algorithm seem reasonable as the two clusters are formed in the full space and approximate the same attribute weights are expected.
Weight | Weight | Weight | ||||||||
C1 | 1 | 3.01E-36 | C1 | 0.8931 | 0.1069 | C1 | 0.5448 | 0.4552 | ||
C2 | 1 | 2.85E-51 | C2 | 0.5057 | 0.4943 | C2 | 0.5055 | 0.4945 | ||
(a) | (b) | (c) |
Table 5 shows the average runtime of the 100 runs of the three algorithms on the first synthetic dataset. From the table we see that the EWKM algorithm converged the fastest. The LAC algorithm and the LEKM algorithm converged in about the same time.
Parameter | EWKM | LAC | LEKM |
1 | 0.0005 (0.0005) | 0.0021 (0.0032) | 0.0016 (0.0009) |
2 | 0.0002 (0.0004) | 0.0018 (0.0026) | 0.0013 (0.0006) |
4 | 0.0002 (0.0004) | 0.0017 (0.0025) | 0.0014 (0.0011) |
8 | 0.0003 (0.0004) | 0.0018 (0.0026) | 0.0016 (0.0017) |
16 | 0.0002 (0.0004) | 0.0018 (0.0025) | 0.0016 (0.002) |
The second synthetic dataset is a 100-dimensional dataset with four clusters. Table 6 shows the sizes and dimensions of the four clusters. This dataset was also used to test the SAP algorithm developed in [13]. Table 7 summarizes the clustering results of the three algorithms. From the table we see that the LEKM algorithm produced the most accurate results when the parameter is small. When the parameter is large, the attribute weights calculated by the LEKM algorithm become approximately the same. Since the clusters are embedded in subspaces, assigning approximately the same weight to attributes prevents the LEKM algorithm from recovering these clusters.
Cluster | Cluster Size | Subspace Dimensions |
A | 500 | 10, 15, 70 |
B | 300 | 20, 30, 80, 85 |
C | 500 | 30, 40, 70, 90, 95 |
D | 700 | 40, 45, 50, 55, 60, 80 |
Parameter | EWKM | LAC | LEKM |
1 | 0.557 (0.1851) | 0.5534 (0.1857) | 0.9123 (0.147) |
2 | 0.557 (0.1851) | 0.5572 (0.1883) | 0.928 (0.1361) |
4 | 0.557 (0.1851) | 0.5658 (0.1902) | 0.6128 (0.1626) |
8 | 0.557 (0.1851) | 0.574 (0.2028) | 0.3197 (0.1247) |
16 | 0.5573 (0.1854) | 0.6631 (0.2532) | 0.2293 (0.0914) |
Table 8 shows the confusion matrices produced by the runs of the three algorithms with the lowest objective function value. From the table we see that only three points were clustered incorrectly by the LEKM algorithm. Many points were clustered incorrectly by the EWKM algorithm and the LAC algorithm. Figures 2, 3, and Figure 4 plot the attribute weights of the four clusters corresponding to the confusion matrices given in Table 8. From Figures 2 and 3 we can see that the attribute weights were dominated by a single attribute. Figure 4 shows that the LEKM algorithm was able to recover all the subspace dimensions correctly.
Table 9 shows the average runtime of 100 runs of the three algorithms on the second synthetic dataset. From the table we see that the LEKM algorithm is slower than the other two algorithms. Since the center calculation of the LEKM algorithm is more complicate than that of the EWKM algorithm and the LAC algorithm, it is expected that the LEKM algorithm is slower than the other two algorithms.
Parameter | EWKM | LAC | LEKM |
1 | 0.7849 (0.4221) | 1.1788 (0.763) | 10.4702 (0.1906) |
2 | 0.7687 (0.4141) | 0.8862 (0.4952) | 10.3953 (0.1704) |
4 | 0.7619 (0.4101) | 0.8412 (0.4721) | 10.5236 (0.2023) |
8 | 0.7567 (0.4074) | 0.8767 (0.4816) | 10.5059 (0.2014) |
16 | 0.7578 (0.4112) | 0.8136 (0.5069) | 10.4122 (0.189) |
In summary, the test results on synthetic datasets have shown that the LEKM algorithm is able to recover clusters from noise data and recover clusters embedded in subspaces. The test results also show that the LEKM algorithm is less sensitive to noises and parameter values that the EWKM algorithm and the LEKM algorithm. However, the LEKM algorithm is in general slower than the other two algorithm due to its complex center calculation.
To test the algorithms on real data, we obtained two cancer gene expression datasets from [8]1. The first dataset contains gene expression data of human liver cancers and the second dataset contains gene expression data of breast tumors and colon tumors. Table 10 shows the information of the two real datasets. The two datasets have known labels, which tell the type of sample of each data point. The two datasets were also used to test the SAP algorithm in [13].
Dataset | Samples | Dimensions | Cluster sizes |
Chen-2002 | 179 | 85 | 104, 76 |
Chowdary-2006 | 104 | 182 | 62, 42 |
The datasets are available at http://bioinformatics.rutgers.edu/Static/Supplements/CompCancer/datasets.htm
Table 11 and Table 12 summarize the average accuracy and the average runtime of 100 runs of the three algorithms on the Chen-2002 dataset, respectively. From the average corrected Rand index shown in Table 11 we see that the LEKM algorithm produced more accurate results than the EWKM algorithm and the LAC algorithm did. However, the LEKM algorithm was slower than the other two algorithm.
Parameter | EWKM | LAC | LEKM |
1 | 0.025 (0.0395) | 0.0042 (0.0617) | 0.2599 (0.2973) |
2 | 0.0203 (0.0343) | 0.0888 (0.1903) | 0.2563 (0.2868) |
4 | 0.0135 (0.0279) | 0.041 (0.1454) | 0.2743 (0.2972) |
8 | 0.0141 (0.0449) | 0.0484 (0.1761) | 0.2856 (0.2993) |
16 | 0.0002 (0.0416) | 0.0445 (0.1726) | 0.2789 (0.2984) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0111 (0.0031) | 0.0162 (0.0083) | 0.102 (0.0297) |
2 | 0.0123 (0.0033) | 0.0124 (0.006) | 0.1035 (0.0286) |
4 | 0.0143 (0.006) | 0.0151 (0.0105) | 0.1046 (0.0316) |
8 | 0.0122 (0.0043) | 0.0137 (0.0089) | 0.1068 (0.0337) |
16 | 0.0144 (0.007) | 0.014 (0.0091) | 0.105 (0.0323) |
The average accuracy and runtime of 100 runs of the three algorithms on the Chowdary-2006 dataset are shown in Table 13 and Table 14, respectively. From Table 13 we see than the LEKM algorithm again produced more accurate clustering results than the other two algorithm did. When the parameter was set to be 1, the LAC produced better results than the EWKM algorithm did. For other cases, however, the EWKM algorithm produced better results than the LAC algorithm did. The LAC algorithm and the EWKM algorithm are much faster than the LEKM algorithm as shown in Table 14.
Parameter | EWKM | LAC | LEKM |
1 | 0.3952 (0.3943) | 0.5197 (0.2883) | 0.5826 (0.3199) |
2 | 0.3819 (0.3825) | 0.19 (0.2568) | 0.5757 (0.3261) |
4 | 0.3839 (0.3677) | 0.0772 (0.1016) | 0.5823 (0.3221) |
8 | 0.4188 (0.3584) | 0.0595 (0.0224) | 0.5756 (0.3383) |
16 | 0.4994 (0.3927) | 0.0625 (0.0184) | 0.582 (0.3363) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0115 (0.0048) | 0.0109 (0.0042) | 0.1369 (0.0756) |
2 | 0.011 (0.0046) | 0.0156 (0.0093) | 0.1446 (0.0723) |
4 | 0.0103 (0.0042) | 0.0147 (0.0076) | 0.1514 (0.0805) |
8 | 0.0107 (0.005) | 0.0141 (0.0063) | 0.1524 (0.0769) |
16 | 0.0113 (0.0047) | 0.0138 (0.0068) | 0.1542 (0.0854) |
In summary, the test results on real datasets show that the LEKM algorithm produced more accurate clustering results on average than the EWKM algorithm and the LAC algorithm did. However, the LEKM algorithm was slower than the other two algorithms.
The EWKM algorithm [21] and the LAC algorithm [9] are two soft subspace clustering algorithms that are similar to each other. In both algorithms, the attribute weights of a cluster are calculated as exponential normalizations of the negative attribute dispersions in the cluster scaled by a parameter. Setting the parameter is a challenge when the attribute dispersions in a cluster have a large range. In this paper, we proposed the LEKM (log-transformed entropy weighting
We tested the performance of the LEKM algorithm and compared it with the EWKM algorithm and the LAC algorithm. The test results on both synthetic datasets and real datasets have shown that the LEKM algorithm is able to outperform the EWKM algorithm and the LAC algorithm in terms of accuracy. However, one limitation of the LEKM algorithm is that it is slower than the other two algorithm because updating the cluster centers in each iteration in the LEKM algorithm is more complicate than that in the other two algorithms.
Another limitation of the LEKM algorithm is that it is sensitive to initial cluster centers. This limitation is common to most of the
The authors would like to thank referees for their insightful comments that greatly improve the quality of the paper.
[1] |
Sharp R, Williams R (1995) Thermus Species. New York: Springer. https://doi.org/10.1007/978-1-4615-1831-0 ![]() |
[2] |
Saghatelyan A, Panosyan H, Trchounian A, et al. (2021) Characteristics of DNA polymerase I from an extreme thermophile, Thermus scotoductus strain K1. MicrobiologyOpen 10: e1149. https://doi.org/10.1002/mbo3.1149 ![]() |
[3] |
Kristjánsson JK, Hjörleifsdóttir S, Marteinsson VT, et al. (1994) Thermus scotoductus, sp. nov., a pigment-producing thermophilic bacterium from hot tap water in iceland and including Thermus sp. X-1. Syst Appl Microbiol 17: 44-50. https://doi.org/10.1016/S0723-2020(11)80030-5 ![]() |
[4] |
Babák L, Šupinová P, Burdychová R (2013) Growth models of Thermus aquaticus and Thermus scotoductus. Acta Univ Agric Silvic Mendel Brun 60: 19-26. https://doi.org/10.11118/actaun201260050019 ![]() |
[5] |
Aulitto M, Fusco S, Fiorentino G, et al. (2017) Thermus thermophilus as source of thermozymes for biotechnological applications: Homologous expression and biochemical characterization of an α-galactosidase. Microb Cell Fact 16: 28. https://doi.org/10.1186/s12934-017-0638-4 ![]() |
[6] |
Wheaton S, Hauer M (2011) Recent applications of THERMUS. Phys Part Nuclei Lett 8: 869-873. https://doi.org/10.1134/S1547477111080152 ![]() |
[7] |
Da Costa MS, Rainey FA, Nobre MF (2006) The Genus Thermus and relatives. The Prokaryotes . New York: Springer 797-812. https://doi.org/10.1007/0-387-30747-8_32 ![]() |
[8] |
Elleuche S, Schröder C, Sahm K, et al. (2014) Extremozymes—biocatalysts with unique properties from extremophilic microorganisms. Curr Opin Biotechnol 29: 116-123. https://doi.org/10.1016/j.copbio.2014.04.003 ![]() |
[9] | Chen L, Biosketch S, Sharmili A, et al. (2019) Advances and Trends in Biotechnology and Genetics, Vol. 3. London: Book Publisher International, SCIENCEDOMAIN International Ltd. http://dx.doi.org/10.9734/bpi/atbg/v3 |
[10] |
Albers SV, Vossenberg JL, Driessen AJ, et al. (2001) Bioenergetics and solute uptake under extreme conditions. Extremophiles 5: 285-294. https://doi.org/10.1007/s007920100214 ![]() |
[11] |
Somayaji A, Dhanjal CR, Lingamsetty R, et al. (2022) An insight into the mechanisms of homeostasis in extremophiles. Microbiol Res 263: 127115. https://doi.org/10.1016/j.micres.2022.127115 ![]() |
[12] |
Vieille C, Zeikus GJ (2001) Hyperthermophilic Enzymes: Sources, uses, and molecular mechanisms for thermostability. Microbiol Mol Biol Rev 65: 1-43. https://doi.org/10.1128/MMBR.65.1.1-43.2001 ![]() |
[13] |
Rekadwad BN, Li WJ, Gonzalez JM, et al. (2023) Extremophiles: the species that evolve and survive under hostile conditions. 3 Biotech 13: 316. https://doi.org/10.1007/s13205-023-03733-6 ![]() |
[14] |
Siliakus MF, van der Oost J, Kengen SWM (2017) Adaptations of archaeal and bacterial membranes to variations in temperature, pH and pressure. Extremophiles 21: 651-670. https://doi.org/10.1007/s00792-017-0939-x ![]() |
[15] |
Dick JM, Boyer GM, Canovas PA, et al. (2023) Using thermodynamics to obtain geochemical information from genomes. Geobiology 21: 262-273. https://doi.org/10.1111/gbi.12532 ![]() |
[16] |
Cava F, Hidalgo A, Berenguer J (2009) Thermus thermophilus as biological model. Extremophiles 13: 213-231. https://doi.org/10.1007/s00792-009-0226-6 ![]() |
[17] |
Mefferd CC, Zhou E, Seymour CO, et al. (2022) Incomplete denitrification phenotypes in diverse Thermus species from diverse geothermal spring sediments and adjacent soils in southwest China. Extremophiles 26: 23. https://doi.org/10.1007/s00792-022-01272-1 ![]() |
[18] |
Saghatelyan A, Poghosyan L, Panosyan H, et al. (2015) Draft genome sequence of Thermus scotoductus strain K1, Isolated from a Geothermal Spring in Karvachar, Nagorno Karabakh. Genome Announc 3: 10. https://doi.org/10.1128/genomeA.01346-15 ![]() |
[19] |
Kieft TL, Fredrickson JK, Onstott TC, et al. (1999) Dissimilatory reduction of Fe(III) and other electron acceptors by a Thermus Isolate. Appl Environ Microbiol 65: 1214-1221. https://doi.org/10.1128/AEM.65.3.1214-1221.1999 ![]() |
[20] |
Skirnisdottir S, Hreggvidsson GO, Holst O, et al. (2001) Isolation and characterization of a mixotrophic sulfur-oxidizing Thermus scotoductus. Extremophiles 5: 45-51. https://doi.org/10.1007/s007920000172 ![]() |
[21] |
Cordova LT, Lu J, Cipolla RM, et al. (2016) Co-utilization of glucose and xylose by evolved Thermus thermophilus LC113 strain elucidated by 13 C metabolic flux analysis and whole genome sequencing. Metab Eng 37: 63-71. https://doi.org/10.1016/j.ymben.2016.05.001 ![]() |
[22] |
Boyer GM, Schubotz F, Summons RE, et al. (2020) Carbon oxidation state in microbial polar lipids suggests adaptation to hot spring temperature and redox gradients. Front Microbiol 11: 229. https://doi.org/10.3389/fmicb.2020.00229 ![]() |
[23] |
Straub CT, Zeldes BM, Schut GJ, et al. (2017) Extremely thermophilic energy metabolisms: Biotechnological prospects. Curr Opin Biotechnol 45: 104-112. https://doi.org/10.1016/j.copbio.2017.02.016 ![]() |
[24] |
Gounder K, Brzuszkiewicz E, Liesegang H, et al. (2011) Sequence of the hyperplastic genome of the naturally competent Thermus scotoductus SA-01. BMC Genomics 12: 577. https://doi.org/10.1186/1471-2164-12-577 ![]() |
[25] |
Radax C, Sigurdsson O, Hreggvidsson GO, et al. (1998) F- and V-ATPases in the genus Thermus and related species. Syst Appl Microbiol 21: 12-22. https://doi.org/10.1016/S0723-2020(98)80003-9 ![]() |
[26] |
Ranawat P, Rawat S (2017) Stress response physiology of thermophiles. Arch Microbiol 199: 391-414. https://doi.org/10.1007/s00203-016-1331-4 ![]() |
[27] |
Bruins ME, Janssen AEM, Boom RM (2001) Thermozymes and their applications: A review of recent literature and patents. Appl Biochem Biotechnol 90: 155-186. https://doi.org/10.1385/abab:90:2:155 ![]() |
[28] |
Tadevosyan M, Yeghiazaryan S, Ghevondyan D, et al. (2022) Extremozymes and Their Industrial Applications. Elsevier 177-204. https://doi.org/10.1016/B978-0-323-90274-8.00007-1 ![]() |
[29] |
Pantazaki A, Pritsa A, Kyriakidis D (2002) Biotechnologically relevant enzymes from Thermus thermophilus. Appl Microbiol Biotechnol 58: 1-12. https://doi.org/10.1007/s00253-001-0843-1 ![]() |
[30] |
Mandelli F, Miranda VS, Rodrigues E, et al. (2012) Identification of carotenoids with high antioxidant capacity produced by extremophile microorganisms. World J Microbiol Biotechnol 28: 1781-1790. https://doi.org/10.1007/s11274-011-0993-y ![]() |
[31] |
Krulwich TA, Sachs G, Padan E (2011) Molecular aspects of bacterial pH sensing and homeostasis. Nat Rev Microbiol 9: 330-343. https://doi.org/10.1038/nrmicro2549 ![]() |
[32] |
Kim YJ, Lee HS, Kim ES, et al. (2010) Formate-driven growth coupled with H2 production. Nature 467: 352-355. https://doi.org/10.1038/nature09375 ![]() |
[33] |
Petrosyan H, Vanyan L, Mirzoyan S, et al. (2020) Roasted coffee wastes as a substrate for Escherichia coli to grow and produce hydrogen. FEMS Microbiol Lett 367: fnaa088. https://doi.org/10.1093/femsle/fnaa088 ![]() |
[34] |
Puchkov EO, Bulatov IS, Zinchenko VP (1983) Investigation of intracellular pH in Escherichia coli by 9-aminoacridine fluorescence measurements. FEMS Microbiol Lett 20: 41-45. https://doi.org/10.1111/j.1574-6968.1983.tb00086.x ![]() |
[35] |
Gevorgyan H, Khalatyan S, Vassilian A, et al. (2021) The role of Escherichia coli FhlA transcriptional activator in generation of proton motive force and FoF1-ATPase activity at pH 7.5. IUBMB Life 73: 883-892. https://doi.org/10.1002/iub.2470 ![]() |
[36] |
Gevorgyan H, Khalatyan S, Vassilian A, et al. (2022) Metabolic pathways and ΔpH regulation in Escherichia coli during the fermentation of glucose and glycerol in the presence of formate at pH 6.5: The role of FhlA transcriptional activator. FEMS Microbiol Lett 369: fnac109. https://doi.org/10.1093/femsle/fnac109 ![]() |
[37] |
Katsu T, Nakagawa H, Yasuda K (2002) Interaction between polyamines and bacterial outer membranes as investigated with ion-selective electrodes. Antimicrob Agents Chemother 46: 1073-1079. https://doi.org/10.1128/AAC.46.4.1073-1079.2002 ![]() |
[38] |
Zakharyan E, Trchounian A (2001) K+ influx by Kup in Escherichia coli is accompanied by a decrease in H+ efflux. FEMS Microbiol Lett 204: 61-64. https://doi.org/10.1111/j.1574-6968.2001.tb10863.x ![]() |
[39] | Nicholls DG, Ferguson SJ (2013) Bioenergetics. Elsevier 419. https://doi.org/10.1016/C2010-0-64902-9 |
[40] |
Shirvanyan A, Mirzoyan S, Trchounian K (2023) Relationship between proton/potassium fluxes and central carbon catabolic pathways in different Saccharomyces cerevisiae strains under osmotic stress conditions. Process Biochem 133: 309-318. https://doi.org/10.1016/j.procbio.2023.09.015 ![]() |
[41] |
Swarup A, Lu J, DeWoody KC, et al. (2014) Metabolic network reconstruction, growth characterization and 13C-metabolic flux analysis of the extremophile Thermus thermophilus HB8. Metab Eng 24: 173-180. https://doi.org/10.1016/j.ymben.2014.05.013 ![]() |
[42] | Saghatelyan A, Panosyan H, Birkeland NK (2021) The genus Thermus: A brief history of cosmopolitan extreme thermophiles: Diversity, distribution, biotechnological potential and applications. Microbial Communities and their Interactions in the Extreme Environment. Microorganisms for Sustainability 32: 141-175. https://doi.org/10.1007/978-981-16-3731-5_8 |
[43] |
Slonczewski JL, Fujisawa M, Dopson M, et al. (2009) Cytoplasmic pH measurement and homeostasis in bacteria and archaea. Adv Microb Physiol 55: 1-317. https://doi.org/10.1016/S0065-2911(09)05501-5 ![]() |
[44] |
Cook GM (2000) The intracellular pH of the thermophilic bacterium Thermoanaerobacter wiegelii during growth and production of fermentation acids. Extremophiles 4: 279-284. https://doi.org/10.1007/s007920070014 ![]() |
[45] |
Cook GM, Russell JB, Reichert A, et al. (1996) The intracellular pH of Clostridium paradoxum, an anaerobic, alkaliphilic, and thermophilic bacterium. Appl Environ Microbiol 62: 4576-4579. https://doi.org/10.1128/aem.62.12.4576-4579.1996 ![]() |
[46] |
Gezgin Y, Tanyolac B, Eltem R (2013) Some characteristics and isolation of novel thermostable β-galactosidase from Thermus oshimai DSM 12092. Food Sci Biotechnol 22: 63-70. https://doi.org/10.1007/s10068-013-0009-9 ![]() |
[47] |
Pantazaki AA, Papaneophytou CP, Pritsa AG, et al. (2009) Production of polyhydroxyalkanoates from whey by Thermus thermophilus HB8. Process Biochem 44: 847-853. https://doi.org/10.1016/j.procbio.2009.04.002 ![]() |
[48] |
Kang SK, Cho KK, Ahn JK, et al. (2005) Three forms of thermostable lactose-hydrolase from Thermus sp. IB-21: Cloning, expression, and enzyme characterization. J Biotechnol 116: 337-346. https://doi.org/10.1016/j.jbiotec.2004.07.019 ![]() |
1. | Tongfeng Sun, 2018, Chapter 15, 978-3-030-00827-7, 140, 10.1007/978-3-030-00828-4_15 | |
2. | Qi He, Zhenxiang Chen, Ke Ji, Lin Wang, Kun Ma, Chuan Zhao, Yuliang Shi, 2020, Chapter 49, 978-3-030-16656-4, 530, 10.1007/978-3-030-16657-1_49 | |
3. | Guojun Gan, Yuping Zhang, Dipak K. Dey, Clustering by propagating probabilities between data points, 2016, 41, 15684946, 390, 10.1016/j.asoc.2016.01.034 |
Parameter | Default Value |
1 | |
100 |
Parameter | EWKM | LAC | LEKM |
1 | 0.0351 (0.0582) | 0.0024 (0.0158) | 0.9154 (0.2704) |
2 | 0.0378 (0.0556) | 0.9054 (0.2322) | 0.9063 (0.2827) |
4 | 0.012 (0.031) | 0.8019 (0.2422) | 0.9067 (0.2815) |
8 | -0.0135 (0.0125) | 0.7604 (0.2406) | 0.9072 (0.2799) |
16 | -0.013 (0.0134) | 0.7527 (0.2501) | 0.9072 (0.2799) |
1 | 2 | 1 | 2 | 1 | 2 | |||||
C2 | 35 | 25 | C2 | 59 | 0 | C2 | 60 | 0 | ||
C1 | 25 | 15 | C1 | 1 | 40 | C1 | 0 | 40 | ||
(a) | (b) | (c) |
Weight | Weight | Weight | ||||||||
C1 | 1 | 3.01E-36 | C1 | 0.8931 | 0.1069 | C1 | 0.5448 | 0.4552 | ||
C2 | 1 | 2.85E-51 | C2 | 0.5057 | 0.4943 | C2 | 0.5055 | 0.4945 | ||
(a) | (b) | (c) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0005 (0.0005) | 0.0021 (0.0032) | 0.0016 (0.0009) |
2 | 0.0002 (0.0004) | 0.0018 (0.0026) | 0.0013 (0.0006) |
4 | 0.0002 (0.0004) | 0.0017 (0.0025) | 0.0014 (0.0011) |
8 | 0.0003 (0.0004) | 0.0018 (0.0026) | 0.0016 (0.0017) |
16 | 0.0002 (0.0004) | 0.0018 (0.0025) | 0.0016 (0.002) |
Cluster | Cluster Size | Subspace Dimensions |
A | 500 | 10, 15, 70 |
B | 300 | 20, 30, 80, 85 |
C | 500 | 30, 40, 70, 90, 95 |
D | 700 | 40, 45, 50, 55, 60, 80 |
Parameter | EWKM | LAC | LEKM |
1 | 0.557 (0.1851) | 0.5534 (0.1857) | 0.9123 (0.147) |
2 | 0.557 (0.1851) | 0.5572 (0.1883) | 0.928 (0.1361) |
4 | 0.557 (0.1851) | 0.5658 (0.1902) | 0.6128 (0.1626) |
8 | 0.557 (0.1851) | 0.574 (0.2028) | 0.3197 (0.1247) |
16 | 0.5573 (0.1854) | 0.6631 (0.2532) | 0.2293 (0.0914) |
Parameter | EWKM | LAC | LEKM |
1 | 0.7849 (0.4221) | 1.1788 (0.763) | 10.4702 (0.1906) |
2 | 0.7687 (0.4141) | 0.8862 (0.4952) | 10.3953 (0.1704) |
4 | 0.7619 (0.4101) | 0.8412 (0.4721) | 10.5236 (0.2023) |
8 | 0.7567 (0.4074) | 0.8767 (0.4816) | 10.5059 (0.2014) |
16 | 0.7578 (0.4112) | 0.8136 (0.5069) | 10.4122 (0.189) |
Dataset | Samples | Dimensions | Cluster sizes |
Chen-2002 | 179 | 85 | 104, 76 |
Chowdary-2006 | 104 | 182 | 62, 42 |
Parameter | EWKM | LAC | LEKM |
1 | 0.025 (0.0395) | 0.0042 (0.0617) | 0.2599 (0.2973) |
2 | 0.0203 (0.0343) | 0.0888 (0.1903) | 0.2563 (0.2868) |
4 | 0.0135 (0.0279) | 0.041 (0.1454) | 0.2743 (0.2972) |
8 | 0.0141 (0.0449) | 0.0484 (0.1761) | 0.2856 (0.2993) |
16 | 0.0002 (0.0416) | 0.0445 (0.1726) | 0.2789 (0.2984) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0111 (0.0031) | 0.0162 (0.0083) | 0.102 (0.0297) |
2 | 0.0123 (0.0033) | 0.0124 (0.006) | 0.1035 (0.0286) |
4 | 0.0143 (0.006) | 0.0151 (0.0105) | 0.1046 (0.0316) |
8 | 0.0122 (0.0043) | 0.0137 (0.0089) | 0.1068 (0.0337) |
16 | 0.0144 (0.007) | 0.014 (0.0091) | 0.105 (0.0323) |
Parameter | EWKM | LAC | LEKM |
1 | 0.3952 (0.3943) | 0.5197 (0.2883) | 0.5826 (0.3199) |
2 | 0.3819 (0.3825) | 0.19 (0.2568) | 0.5757 (0.3261) |
4 | 0.3839 (0.3677) | 0.0772 (0.1016) | 0.5823 (0.3221) |
8 | 0.4188 (0.3584) | 0.0595 (0.0224) | 0.5756 (0.3383) |
16 | 0.4994 (0.3927) | 0.0625 (0.0184) | 0.582 (0.3363) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0115 (0.0048) | 0.0109 (0.0042) | 0.1369 (0.0756) |
2 | 0.011 (0.0046) | 0.0156 (0.0093) | 0.1446 (0.0723) |
4 | 0.0103 (0.0042) | 0.0147 (0.0076) | 0.1514 (0.0805) |
8 | 0.0107 (0.005) | 0.0141 (0.0063) | 0.1524 (0.0769) |
16 | 0.0113 (0.0047) | 0.0138 (0.0068) | 0.1542 (0.0854) |
Parameter | Default Value |
1 | |
100 |
Parameter | EWKM | LAC | LEKM |
1 | 0.0351 (0.0582) | 0.0024 (0.0158) | 0.9154 (0.2704) |
2 | 0.0378 (0.0556) | 0.9054 (0.2322) | 0.9063 (0.2827) |
4 | 0.012 (0.031) | 0.8019 (0.2422) | 0.9067 (0.2815) |
8 | -0.0135 (0.0125) | 0.7604 (0.2406) | 0.9072 (0.2799) |
16 | -0.013 (0.0134) | 0.7527 (0.2501) | 0.9072 (0.2799) |
1 | 2 | 1 | 2 | 1 | 2 | |||||
C2 | 35 | 25 | C2 | 59 | 0 | C2 | 60 | 0 | ||
C1 | 25 | 15 | C1 | 1 | 40 | C1 | 0 | 40 | ||
(a) | (b) | (c) |
Weight | Weight | Weight | ||||||||
C1 | 1 | 3.01E-36 | C1 | 0.8931 | 0.1069 | C1 | 0.5448 | 0.4552 | ||
C2 | 1 | 2.85E-51 | C2 | 0.5057 | 0.4943 | C2 | 0.5055 | 0.4945 | ||
(a) | (b) | (c) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0005 (0.0005) | 0.0021 (0.0032) | 0.0016 (0.0009) |
2 | 0.0002 (0.0004) | 0.0018 (0.0026) | 0.0013 (0.0006) |
4 | 0.0002 (0.0004) | 0.0017 (0.0025) | 0.0014 (0.0011) |
8 | 0.0003 (0.0004) | 0.0018 (0.0026) | 0.0016 (0.0017) |
16 | 0.0002 (0.0004) | 0.0018 (0.0025) | 0.0016 (0.002) |
Cluster | Cluster Size | Subspace Dimensions |
A | 500 | 10, 15, 70 |
B | 300 | 20, 30, 80, 85 |
C | 500 | 30, 40, 70, 90, 95 |
D | 700 | 40, 45, 50, 55, 60, 80 |
Parameter | EWKM | LAC | LEKM |
1 | 0.557 (0.1851) | 0.5534 (0.1857) | 0.9123 (0.147) |
2 | 0.557 (0.1851) | 0.5572 (0.1883) | 0.928 (0.1361) |
4 | 0.557 (0.1851) | 0.5658 (0.1902) | 0.6128 (0.1626) |
8 | 0.557 (0.1851) | 0.574 (0.2028) | 0.3197 (0.1247) |
16 | 0.5573 (0.1854) | 0.6631 (0.2532) | 0.2293 (0.0914) |
Parameter | EWKM | LAC | LEKM |
1 | 0.7849 (0.4221) | 1.1788 (0.763) | 10.4702 (0.1906) |
2 | 0.7687 (0.4141) | 0.8862 (0.4952) | 10.3953 (0.1704) |
4 | 0.7619 (0.4101) | 0.8412 (0.4721) | 10.5236 (0.2023) |
8 | 0.7567 (0.4074) | 0.8767 (0.4816) | 10.5059 (0.2014) |
16 | 0.7578 (0.4112) | 0.8136 (0.5069) | 10.4122 (0.189) |
Dataset | Samples | Dimensions | Cluster sizes |
Chen-2002 | 179 | 85 | 104, 76 |
Chowdary-2006 | 104 | 182 | 62, 42 |
Parameter | EWKM | LAC | LEKM |
1 | 0.025 (0.0395) | 0.0042 (0.0617) | 0.2599 (0.2973) |
2 | 0.0203 (0.0343) | 0.0888 (0.1903) | 0.2563 (0.2868) |
4 | 0.0135 (0.0279) | 0.041 (0.1454) | 0.2743 (0.2972) |
8 | 0.0141 (0.0449) | 0.0484 (0.1761) | 0.2856 (0.2993) |
16 | 0.0002 (0.0416) | 0.0445 (0.1726) | 0.2789 (0.2984) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0111 (0.0031) | 0.0162 (0.0083) | 0.102 (0.0297) |
2 | 0.0123 (0.0033) | 0.0124 (0.006) | 0.1035 (0.0286) |
4 | 0.0143 (0.006) | 0.0151 (0.0105) | 0.1046 (0.0316) |
8 | 0.0122 (0.0043) | 0.0137 (0.0089) | 0.1068 (0.0337) |
16 | 0.0144 (0.007) | 0.014 (0.0091) | 0.105 (0.0323) |
Parameter | EWKM | LAC | LEKM |
1 | 0.3952 (0.3943) | 0.5197 (0.2883) | 0.5826 (0.3199) |
2 | 0.3819 (0.3825) | 0.19 (0.2568) | 0.5757 (0.3261) |
4 | 0.3839 (0.3677) | 0.0772 (0.1016) | 0.5823 (0.3221) |
8 | 0.4188 (0.3584) | 0.0595 (0.0224) | 0.5756 (0.3383) |
16 | 0.4994 (0.3927) | 0.0625 (0.0184) | 0.582 (0.3363) |
Parameter | EWKM | LAC | LEKM |
1 | 0.0115 (0.0048) | 0.0109 (0.0042) | 0.1369 (0.0756) |
2 | 0.011 (0.0046) | 0.0156 (0.0093) | 0.1446 (0.0723) |
4 | 0.0103 (0.0042) | 0.0147 (0.0076) | 0.1514 (0.0805) |
8 | 0.0107 (0.005) | 0.0141 (0.0063) | 0.1524 (0.0769) |
16 | 0.0113 (0.0047) | 0.0138 (0.0068) | 0.1542 (0.0854) |