Identifying Similarities and Disparities Between DNA Copy Number Changes in Cancer and Matched Blood Samples

Abstract

Background: Non-small cell lung cancer (NSCLC) is the first cause of cancer-related mortality for men and women in the United States. In spite of curative resection in early-stage, patient survival is not optimal and recurrence rate is high. Consequently, early detection and staging is essential to increase the patient’s survival.

Methods: Copy number (CN) changes in cancer populations have been broadly investigated to identify CN gains and deletions associated with cancer. In contrast, in this research, we quantify the similarities and disparities between cancer and paired peripheral blood samples using maximal information coefficient (MIC). We then detect the spatial locations with substantially high and the spatial locations with very low MICs in each chromosome. These locations can potentially help with early diagnosis, treatment, and prevention of cancer by identifying the similarities and disparities between cancer and healthy tissues.

Results: Lung cancer data used in this project contains CN pairs for cancer and blood (non-involved) samples for 63 subjects. MIC was obtained to quantify the relation (linear or nonlinear) between cancer-blood pair samples for 63 subjects at each location for each chromosome. MIC values above a high threshold and MIC values below a low threshold were located. Among them top five (with lowest MIC’s and with highest MIC’s) were identified for each chromosome. For these identified locations, a high MIC score indicates high similarity between blood (non-involved) and cancer samples, while a low MIC score shows lack of similarity between the two samples.

Conclusions: The results showed that a few chromosomes have a large number of MICs exceeding a high threshold. These locations can potentially be used to identify early indicators of NSCLC. In contrast, second group of chromosomes have several locations with small MICs which are potential candidates to develop biomarkers for discriminating cancer from the matched blood sample. Moreover, there is a third group of chromosomes with a large number of MICs exceeding a high threshold and a large set of MICs below a low threshold. These locations can help with both finding early indicators of cancer and developing biomarkers for discriminating cancer from non-involved tissue.

Keywords:

• Maximal information coefficient
• nonlinear correlation
• lung cancer
• DNA copy number

1. Background

Gene-cancer mapping helps to discover genes that are associated with disease, such as cancer. With improvements in high-throughput genotyping in the past two decades, it is possible to screen for disease loci on a genome-wide scale. The recent improvement in high throughput genotyping has been a result of the development of computational methods for human gene-related diseases (1–7). To this end, human gene-cancer mapping has been investigated intensively to address cancer association with single-nucleotide polymorphism (SNP) and copy number (CN) changes (8–11). CN changes that can lead to cancer have been under investigation (12–14) and discovery of correlation between cancer and healthy tissue is a subject of ongoing research.

In our previous works (14–16), to discover population patterns, i.e., CN changes that are common among populations, we integrated the population summaries and located genes that have significant differences in the mean CNs between cancer and non-involved tissue (15). We also identified regions with significantly amplified or deleted CNs (14). In contrast, in this work, correlations between cancer and blood (non-involved) samples are measured at each individual location of each chromosome to identify the spatial locations with high and low correlations with regard to CN. Mapping these correlations is very useful, since identifying locations with high similarities in cancer and blood (non-involved) samples can potentially be used as early indicators of cancer in the non-involved cells. On the other hand, identifying locations with low similarities (disparities) in cancer and blood (non-involved) samples, can be used to discriminate cancer from healthy cells.

2. Data description

A set of 63 early stage (1–2) non-small cell lung cancer (NSCLC) patients were prospectively enrolled at the Massachusetts General Hospital (MGH), Boston, MA (10, 11). A snap-frozen tumor sample was gathered for each patient during biopsy or surgery in addition to a blood sample. Table 1 shows the structure of the data. The scores are related to CN changes which range from 1 to 3; values below two indicates deleted CNs while values above two indicates gained CNs.

Table 1. Structure of the data for chromosome 2 (as an example).

Patient	Location 1		Location 2		……		Location 22,215
	Cancer sample	Blood sample	Cancer sample	Blood sample			Cancer sample	Blood sample
Patient 1	1.06	1.92	1.06	1.92			1.39	2
Patient 2	1.9	2.07	1.99	2.07			1.92	2.12
Patient 3	2.45	2.09	2.45	2.2			2.26	2.01
Patient 4	….	….	….	….			….	….
Patient 5	….	….	….	….			….	….
.	.	.	.	.			.	.
.	.	.	.	.			.	.
Patient 62	2.14	2.06	2.14	2.03			2.05	2.33
Patient 63	1.91	1.64	1.91	1.64			1.67	1.77

2.1. DNA quality, histopathology and genechip

DNA samples were extracted from tumor after manual microdissection of 5 µ histopathologic sections. A pathologist who had no knowledge of the clinical and genetic information reviewed section of each patient. Each specimen was evaluated for amount and quality of tumor cells and histologically classified using the WHO criteria. Specimens with lower than 70% cancer cellularity, inadequate DNA concentration (50 ng/µL), or a smearing pattern in gel electrophoresis were not included for genotyping. A total of 126 DNA samples (63 from tumors and 63 from paired blood) were hybridized onto Affymetrix 250 K Nsp GeneChipH, which contains 262,264 probes (256,554 probes on somatic chromosomes and 5710 probes on sex chromosome).

2.2. Data preprocessing

CNs were obtained with dChip software. The probe intensities were calculated by model-based expression after invariant set normalization. For each SNP in each sample, the raw CN was computed (mean signal of reference samples at this SNP) using blood samples as the referent. Inferred CNs were computed from the raw CNs by median smoothing with the window of 11 SNPs for each locus of 262,264 SNPs. Only 256,554 probes on somatic chromosomes were analyzed. The SNP probes were mapped to the RefSeq genes with 2 kb extension both upstream and downstream using the UCSC Genome Browser. Among the 256,554 probes on somatic chromosomes, 104,256 probes were mapped to 11,700 genes.

3. Methods

In order to discover locations with high similarities between cancer and blood samples as well as recognizing locations to discriminate cancer from blood (non-involved) samples, we compute maximal information coefficient (MIC) at each SNP location of each chromosome between cancer and blood samples for 63 patients. For example for chromosome 2, we will have 22,215 MIC values corresponding to each SNP location in this chromosome.

MIC takes a value between zero and one (17) and can identify linear and nonlinear associations. MIC values above 0.5 demonstrate substantial correlation (similarities) while MIC values below 0.2 indicate low or no correlation (disparities) between the samples. MIC for the ${j\mathrm{th}}^{}$ location for a typical chromosome is calculated by (18): (1) $$\begin{array}{cc}\mathrm{M}\mathrm{I}{\mathrm{C}}_j=\max \left\{\frac{I({\mathrm{blood}}_j,\mathrm{cance}{\mathrm{r}}_j)}{{\log }_2\min \left\{n\_{\mathrm{blood}}_j,n_{{\mathrm{cancer}}_j}\right\}}\right\},& j=1,2,\dots ,\end{array}m$$(1) where (2) $$I\left({\mathrm{blood}}_j,\mathrm{cance}{\mathrm{r}}_j\right)=H\left({\mathrm{blood}}_j\right)+H\left(\mathrm{cance}{\mathrm{r}}_j\right)-H\left({\mathrm{blood}}_j,\mathrm{cance}{\mathrm{r}}_j\right)$$(2) $$=\sum _{w=1}^{n_{{\mathrm{blood}}_j}}p\left({{\mathrm{blood}}_j}_w\right){\log }_2\frac{1}{p\left({{\mathrm{blood}}_j}_w\right)}$$ $$+\sum _{s=1}^{n_{\mathrm{cance}{\mathrm{r}}_j}}p\left({\mathrm{cance}{\mathrm{r}}_j}_s\right){\log }_2\frac{1}{p\left({\mathrm{cance}{\mathrm{r}}_j}_s\right)}$$ $$-\sum _{w=1}^{n_{{\mathrm{blood}}_j}}\sum _{s=1}^{n_{\mathrm{cance}{\mathrm{r}}_j}}p\left({{\mathrm{blood}}_j}_w,{\mathrm{cance}{\mathrm{r}}_j}_s\right){\log }_2\frac{1}{p\left({{{\mathrm{blood}}_j}_w,\mathrm{cance}{\mathrm{r}}_j}_s\right)}$$ where $p\left({\mathrm{blood}}_j,\mathrm{ }\mathrm{cance}{\mathrm{r}}_j\right)$ is the joint probability distribution of $j\mathrm{th}$ blood and $j\mathrm{th}$ cancer samples, respectively, $p\left({\mathrm{blood}}_j\right)$ and $p\left(\mathrm{cance}{\mathrm{r}}_j\right)$ are the marginal distributions of $j\mathrm{th}$ blood sample and $j\mathrm{th}$ cancer sample, respectively, $n_{{\mathrm{blood}}_j}$ and $n_{\mathrm{cance}{\mathrm{r}}_j}$are the number of bins for the partition of the blood-axis and cancer-axis, respectively, $n_{{\mathrm{blood}}_j}{n}_{\mathrm{cance}{\mathrm{r}}_{\mathrm{j}}}<B\left(n\right)$ where $B\left(n\right)=n^{0.6},$ and $n$ is the sample size $(n=63).$

After calculating MIC values for all SNP locations in all chromosomes, we identify spatial locations with considerably high or notably low correlation scores between cancer and blood samples. To do this, we locate MIC values that are at least two standard deviations away from the mean MIC of the chromosome, i.e., [MIC_i < $\mu -2\sigma$ or $\mu +2\sigma <$ MIC_i] where $\mu$ and $\sigma$ are the sample mean and standard deviation of MIC values of the chromosome, respectively. Estimated $\mu \prime s$ for different chromosomes are about 0.3 and hence the lower threshold of $\mu -2\sigma$ is below 0.2 for all chromosomes. MICs falling below this threshold indicate no or weak correlation between cancer and blood samples. In contrast, the upper threshold of $\mu +2\sigma$ is about 0.4 which indicates moderate correlation and there are several MIC values that are above this threshold. In order to identify substantial correlations (MIC >0.5), we set the threshold value to 0.5, 0.55, and 0.6 and calculate the number of standard deviations that the set threshold is above the mean: (3) $$z=\frac{a-\mu }{\sigma }$$(3) where $a$ is the set threshold. MIC scores higher than these thresholds indicate high correlations (similarities).

4. Results

As previously mentioned, lung cancer data contains CN pairs for cancer and blood (non-involved) samples for 63 patients. The correlation measure, i.e., MIC, was obtained at each location for each chromosome, and MIC values above upper threshold and below lower threshold were located. Among them top five (lowest as well as highest) were identified for each chromosome. A high MIC score at an identified location indicates high similarity between blood (non-involved) and cancer samples, while a low MIC score shows lack of similarity between the two samples.

The results obtained for chromosomes 1–6 are depicted in Figure 1, chromosomes 7–12 in Figure 2, chromosomes 13–18 in Figure 3, and chromosomes 19–22 in Figure 4. A gray dot represents the calculated MIC value at a spatial location, the solid black line is the mean MIC value for the chromosome, the dashed black line is the lower threshold, and the dashed blue, green, and red lines show upper threshold of 0.5, 0.55, and 0.6, respectively.

Figure 1. MIC scores for chromosomes 1–6 (gray dots), mean MIC value (solid black line), lower threshold (dashed black line), and upper thresholds of 0.5, 0.55, and 0.6 (dashed blue, dashed green, and dashed red lines, respectively).

Figure 2. MIC scores for chromosomes 7–12 (gray dots), mean MIC value (solid black line), lower threshold (dashed black line), and upper thresholds of 0.5, 0.55, and 0.6 (dashed blue, dashed green, and dashed red lines, respectively).

Figure 3. MIC scores for chromosomes 13–18 (gray dots), mean MIC value (solid black line), lower threshold (dashed black line), and upper thresholds of 0.5, 0.55, and 0.6 (dashed blue, dashed green, and dashed red lines, respectively).

Figure 4. MIC scores for chromosomes 19–22 (gray dots), mean MIC value (solid black line), lower threshold (dashed black line), and upper thresholds of 0.5, 0.55, and 0.6 (dashed blue, dashed green, and dashed red lines, respectively).

4.1. Chromosomes with high similarities between cancer and blood

Table 2 summarizes the number of locations with corresponding MIC values greater than specified threshold of 0.5, 0.55, or 0.6 for each chromosome. MIC values above 0.5 indicate substantial correlations (similarities) between the cancer and the blood sample which is potentially related to the early stage of cancer. We should point out that the numbers of locations with MIC values exceeding the thresholds are cumulative. That is the numbers of locations with MIC values higher than 0.55 contains numbers of locations with MIC values higher than 0.6, and similarly the numbers of locations with MIC values higher than 0.5 contains numbers of locations with MIC values higher than 0.55 and higher than 0.6. As shown in Table 2, chromosome 2 has the highest number of locations with MIC values exceeding all three thresholds. There are 594 locations with MICs above 0.5, among them 199 locations with MICs above 0.55 from which 58 locations with MICs above 0.6 in this chromosome. Chromosome 4 is in the second place with regard to the number of locations with MIC values exceeding 0.5. However, it is in the third place with regard to the locations with MIC values exceeding 0.55 and 0.6. Chromosome 3 is in the third place with 348 locations with MIC values exceeding 0.5. However, it has the second highest number of locations with MIC values exceeding 0.55. Chromosome 12 has the second highest number of locations with MIC values exceeding 0.6. In contrast with chromosomes 2, 3, 4, and 12, chromosome 19 has only 4 locations with corresponding MIC values greater than 0.5, none of them greater than 0.55.

Table 2. Number of locations with corresponding MIC values greater than thresholds for a = (0.5, 0.55, 0.6).

Chromosome no.	Numbers of locations whose MIC exceed the threshold a
	a = 0.5	a = 0.55	a = 0.6
1	210	64	15
2	594	199	58
3	348	120	26
4	355	114	34
5	102	20	4
6	108	23	7
7	256	61	13
8	39	8	1
9	161	39	6
10	89	22	5
11	282	87	24
12	341	113	38
13	142	40	9
14	133	45	14
15	72	17	7
16	37	7	2
17	85	34	14
18	22	1	0
19	4	0	0
20	55	9	3
21	36	13	3
22	23	2	2

4.2. Top five locations with high similarities in each chromosome

The spatial locations and associated MIC values of top five MICs in descending order are listed in Table 3 for each chromosome. For example, the locations in the chromosome 2 (with the highest number of locations with MIC values exceeding all three thresholds) associated with top five MIC values are 193.11, 98.29, 193.13, 193.13, and 98.36.

Table 3. Spatial locations in each chromosome associated with top five highest MIC values.

Chromosome no.	Location	MIC	Location	MIC	Location	MIC	Location	MIC	Location	MIC
1	60.81	0.725	76.20	0.704	78.34	0.692	60.85	0.666	57.09	0.647
2	193.11	0.720	98.29	0.693	193.13	0.691	193.13	0.684	98.36	0.683
3	87.63	0.725	74.61	0.717	31.28	0.674	5.45	0.653	21.59	0.651
4	46.182	0.750	16.94	0.749	46.18	0.699	23.35	0.686	32.72	0.679
5	102.14	0.722	105.60	0.618	84.15	0.615	128.32	0.611	77.13	0.599
6	47.80	0.680	8.45	0.661	46.70	0.643	8.45	0.609	6.49	0.609
7	103.11	0.665	69.23	0.655	83.85	0.639	69.26	0.627	88.23	0.613
8	105.77	0.699	130.29	0.582	105.78	0.575	107.49	0.572	1.27	0.562
9	28.28	0.642	70.77	0.631	9.38	0.609	84.31	0.606	9.77	0.606
10	113.48	0.631	113.47	0.620	53.87	0.619	127.65	0.606	113.44	0.604
11	26.26	0.724	26.26	0.717	26.26	0.701	42.15	0.642	5.05	0.642
12	90.34	0.673	97.05	0.667	99.74	0.663	91.34	0.659	96.24	0.656
13	48.10	0.661	42.64	0.652	55.55	0.637	42.64	0.631	58.66	0.630
14	84.29	0.685	87.47	0.648	74.38	0.647	78.07	0.638	75.69	0.619
15	96.44	0.702	76.64	0.627	96.43	0.626	19.31	0.621	96.40	0.617
16	20.88	0.679	49.99	0.602	55.67	0.587	46.94	0.579	20.94	0.572
17	31.48	0.743	29.52	0.678	47.44	0.668	51.53	0.642	31.49	0.635
18	71.72	0.560	55.11	0.546	68.81	0.538	3.21	0.538	47.28	0.526
19	62.98	0.548	24.01	0.524	22.09	0.507	24.03	0.502	53.17	0.493
20	12.22	0.663	16.32	0.627	53.77	0.626	53.77	0.567	13.53	0.563
21	45.50	0.621	18.82	0.603	34.33	0.601	35.02	0.589	23.97	0.589
22	33.05	0.692	18.45	0.607	31.64	0.538	32.66	0.535	33.22	0.535

Number of standard deviations a set threshold (0.5, 0.55, and 0.6) is above the mean MIC is reported in Table 4 for each chromosome. For instance, the upper threshold of 0.5 is 3.56 standard deviation (σ) away from the mean for chromosome 19 which is the highest number of standard deviations for threshold 0.5 among all chromosomes. That is, MIC values above 0.5 are at least 3.56σ higher than the mean MIC in chromosome 19 (Figure 4(a)). Figure 4 shows that only a few MIC values exceed the threshold of 0.5 in chromosome 19. In contrast, the threshold of 0. 6 has the smallest number of standard deviations above the mean (3.57σ) for chromosome 12 (Table 4). This is consistent with observing a high number of locations (38) with MIC values exceeding 0.6 in chromosome 12 (Table 2).

Table 4. Number of standard deviations that a set threshold is above the mean for a = (0.5, 0.55, and 0.6).

Chromosome no.	Number of standard deviation
	a = 0.5	a = 0.55	a = 0.6
1	2.88	3.64	4.39
2	2.28	2.94	3.60
3	2.48	3.18	3.88
4	2.50	3.21	3.92
5	3.11	3.90	4.69
6	3.11	3.89	4.68
7	2.48	3.19	3.89
8	3.69	4.57	5.45
9	2.67	3.41	4.16
10	3.18	3.97	4.76
11	2.44	3.13	3.83
12	2.27	2.92	3.57
13	2.68	3.41	4.14
14	2.63	3.35	4.07
15	2.91	3.66	4.41
16	3.14	3.94	4.73
17	2.61	3.30	4.00
18	3.50	4.35	5.20
19	3.56	4.41	5.27
20	2.99	3.74	4.50
21	2.86	3.61	4.37
22	2.89	3.65	4.41

4.3. Chromosomes with low similarities between cancer and blood

Table 5 shows the number of locations in each chromosome with corresponding MIC values below the specified threshold of$\mathrm{ }\mu -2\sigma .$ MIC values below this threshold indicate weak or no similarities between the two samples (cancer and blood), and hence these locations can potentially help for discriminating cancer from non-involved that can be used for diagnosis. Chromosome 8 has the highest number of locations (62) with MIC values below the lower threshold. Chromosome 4 with 57 locations is the second, and chromosome 6 is the third with 54 locations with MIC values below the threshold. Figures 1(d,f), and 2(b) demonstrate the MIC values for these locations in chromosomes 4, 6, and 8. In contrast as shown in Figures 3(c,e) and 4(a,d), there are only a few locations with MIC values below threshold in chromosomes 15, 17, 19, and 22. It means there are fewer locations in these chromosomes that can be used to differentiate cancer from blood (non-involved) sample. Top five locations with regard to dissimilarities between cancer and blood, i.e., the locations in each chromosome with the smallest MIC values (below 0.17) are listed in ascending order in Table 6. These locations indicate low or very weak similarity between cancer and non-involved (blood) and can potentially be used for lung cancer diagnosis. Top five locations in chromosome 8 (with the highest number of such locations) are at 123.84, 41.17, 96.86, 83.97, and 78.06.

Table 5. Number of locations with corresponding MIC values less than the threshold of μ – 2σ (μ and σ are the MIC mean and standard deviation, respectively).

Chromosome no.	Number of locations
1	44
2	39
3	49
4	57
5	45
6	54
7	37
8	62
9	36
10	29
11	24
12	22
13	23
14	21
15	9
16	28
17	5
18	29
19	3
20	10
21	16
22	7

Table 6. Spatial locations in each chromosome associated with top five smallest MIC values.

Chromosome no.	Location	MIC	Location	MIC	Location	MIC	Location	MIC	Location	MIC
1	213.38	0.145	205.25	0.148	225.52	0.151	94.32	0.154	32.77	0.155
2	34.25	0.154	142.02	0.156	11.45	0.157	15.89	0.158	64.42	0.159
3	83.52	0.151	102.62	0.156	113.84	0.157	100.21	0.160	115.38	0.160
4	123.29	0.145	182.87	0.152	170.98	0.156	61.95	0.164	162.37	0.167
5	121.80	0.127	163.29	0.145	155.18	0.149	121.80	0.151	51.79	0.151
6	166.17	0.129	155.04	0.151	123.98	0.157	142.34	0.159	10.61	0.159
7	52.54	0.137	155.06	0.157	30.63	0.157	133.47	0.160	48.83	0.163
8	123.84	0.150	41.17	0.156	96.86	0.157	83.97	0.157	78.06	0.158
9	0.84	0.146	35.98	0.157	126.29	0.161	120.89	0.168	116.27	0.169
10	54.34	0.140	16.34	0.150	58.61	0.154	1.67	0.157	37.29	0.160
11	32.42	0.149	21.73	0.152	36.23	0.157	2.69	0.163	118.42	0.167
12	33.41	0.146	77.16	0.148	50.89	0.151	50.88	0.159	33.47	0.165
13	36.24	0.146	111.79	0.162	109.76	0.162	34.77	0.163	34.79	0.165
14	35.02	0.142	53.38	0.160	99.45	0.161	24.45	0.166	89.32	0.167
15	66.43	0.159	94.19	0.161	89.59	0.161	23.10	0.161	30.06	0.164
16	85.31	0.163	53.16	0.164	59.99	0.165	80.25	0.165	85.02	0.165
17	8.72	0.149	66.77	0.156	36.79	0.159	68.35	0.161	24.62	0.166
18	9.83	0.154	59.87	0.161	28.57	0.163	10.70	0.163	46.19	0.163
19	37.17	0.165	4.86	0.169	48.43	0.174	6.64	0.176	59.89	0.177
20	24.93	0.161	24.35	0.165	24.04	0.166	43.61	0.166	10.12	0.166
21	26.38	0.157	14.69	0.161	40.83	0.166	23.18	0.166	45.83	0.168
22	31.09	0.172	19.30	0.172	27.78	0.173	28.28	0.176	24.81	0.176

4.4. Top 10 locations with high similarities among all chromosomes

Next, we identify top 10 locations with highest MIC values among all chromosomes (Table 7). We can see that top two highest MIC values of 0.750 and 0.749 are located in chromosome 4 at locations 46.18 and 16.94, respectively. As we saw earlier, chromosome 4 has the second highest number of locations with MIC values exceeding the upper threshold. It has also the second highest number of the locations with MIC values below the lower threshold. Therefore, chromosome 4 is a potential candidate for discrimination of cancer from blood (non-involved), and it could potentially contain lung cancer-related genes.

Table 7. Spatial locations among all chromosomes associated with top 10 highest MIC values.

Chromosome no.	Location	MIC
4	46.18	0.750
4	16.94	0.749
17	31.48	0.743
1	60.81	0.7252
3	87.63	0.7249
11	26.26	0.724
5	102.14	0.722
2	193.11	0.720
11	26.263	0.7172
3	74.61	0.7168

Chromosome 11 has also several locations with MIC values above the threshold (Figure 2(e)). The top five MIC values in chromosome 11 are 0.724, 0.717, 0.701, 0.642, and 0.642 associated with spatial locations at 26.26, 26.26, 26.26, 42.15, and 5.05, respectively (Table 3). As shown in Table 7, two of them (0.724 and 0.717) are among the top 10 chromosome-wide MIC values (the sixth and the ninth highest MIC values). These MIC values locate positions with high similarities between the CN changes in cancer and blood samples. As a result, chromosome 11 can be a good candidate for early indicator of cancer in healthy tissues.

Chromosome 3 has 348 locations with MIC values exceeding 0.5 (Table 2) including fifth and tenth highest MIC values (Table 7). As listed in Table 7, remaining top 10 locations with regard to MIC values are in chromosomes 17, 1, 5, and 2. Among them, chromosome 2 has the highest number of locations exceeding thresholds 0.5, 0.55, and 0.6. Hence, these chromosomes are potential candidates for early indication of cancer (Table 2).

4.5. Top 10 locations with low similarities among all chromosomes

Table 8 summarizes the locations associated with top 10 locations among all chromosomes with lowest MIC values. Chromosome 5 has 45 locations with MIC values below threshold (Tables 5 and 6), two of them among top 10 smallest MIC values (0.127 and 0.145) at 121.80 and 163.29, respectively. The remaining locations among top 10 smallest values are in chromosomes 1, 4, and 6 (Table 8). Therefore, these locations are the possible candidates to discriminate cancer from peripheral blood samples and potentially can help with lung cancer diagnosis.

Table 8. Spatial locations among all chromosomes associated with top 10 lowest MIC values.

Chromosome no.	Location	MIC
5	121.80	0.127
6	166.17	0.129
7	52.54	0.137
10	54.34	0.140
14	35.02	0.142
1	213.38	0.145
4	123.29	0.145
5	163.29	0.145
9	0.84	0.146
12	33.41	0.146
13	36.24	0.146

5. Discussion

We used MIC to identify the underlying relationships between CN’s of cancer-blood pairs regardless of whether the relation is linear or nonlinear. The results showed that Chromosome 12 has a large number of MICs exceeding the upper threshold. These locations can potentially be used to identify early indicators of NSCLC. In contrast, several locations in chromosomes 1, 5, 6, and 8 with small MICs are potential candidates to develop biomarkers for discriminating cancer from matched blood samples. Moreover, chromosome 2, 3, and 4 have a large number of MICs exceeding the upper threshold and a large set of MICs below the lower threshold. These locations can help with both finding early indicators of cancer and developing biomarkers for discriminating cancer from non-involved tissue. As a result, these chromosomes may contain lung cancer-associated genes. The results agree with previous research (9, 10, 15). Our future work is focused on identifying the associated genes with the located peaks in each chromosome.

6. Conclusions

In our previous work, we investigated common CN changes among cancer population. In this work, we studied correlations between cancer and matched blood samples by measuring MIC at each spatial location of each chromosome. In this way, we generated MIC values for all chromosomes for a sample of 63 patients. In the next step, we set up thresholds to locate MIC values that exceed upper threshold or fall below the lower threshold. Finally, we identified top five highest and top five smallest MIC values in each chromosome as well as top 10 largest and top 10 smallest MIC values among all chromosomes. High MIC values demonstrate locations with potential similarities between CN changes in cancer and blood samples, while low MIC values point to locations with potential disparity between the two samples. Similarity between the samples can be used as early indicator of cancer in healthy tissues. In contrast, disparity between the samples can help with lung cancer diagnosis.

We should point out that in this study, the spatial locations with high similarities were observed in cancer and blood samples collected from early stage lung cancer patients where blood samples were considered as primary control. Further investigation will be conducted with a secondary control from matched healthy samples to narrow down the list of spatial locations with high similarities between cancer and blood samples. Moreover, future investigation can reveal the potential interactions between the spatial locations with high MIC values of cancer-blood pairs in a chromosome.

Acknowledgments

This work was partially supported by NIH grant: U01 CA209414 to Dr. David C. Christiani.

Disclosure statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the article.