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Towards a Universal Law Controlling All Human Cancer Chromosome LOH Deletions, Perspectives in Prostate and Breast Cancers Screening

Jean-Claude Perez*

Retired Interdisciplinary Researcher (IBM emeritus), 7 Avenue de Terre-rouge, F33127 Martignas, Bordeaux Metropole, France

*Corresponding Author:
Jean-Claude Perez
PhD Maths and Computer Science
Retired Interdisciplinary Researcher (IBM emeritus)
7 Avenue de Terre-rouge F33127 Martignas
Bordeaux Metropole, France
Tel: 330781181112
E-mail: [email protected]

Received Date: September 27, 2017; Accepted Date: October 06, 2017; Published Date: October 13, 2017

Citation: Perez JC (2017) Towards a Universal Law Controlling All Human Cancer Chromosome LOH Deletions, Perspectives in Prostate and Breast Cancers Screening. Res J Oncol. Vol.1 No.1: 3

 
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Abstract

Background: Global analysis of 3 human genomes of increasing levels of evolution (Neanderthal/Sapiens Build34/Sapiens hg38) reveals 2 levels of numerical constraints controlling, structuring and optimizing these genome's DNA sequences. A global constraint - called "HGO" for "Human Genome Optimum" - optimizes the genome at its global scale. The same operator applied to each of the 24 individual chromosomes reveals a hierarchical structure of these 24 chromosomes. Methods: We analyze how this HGO genomic optimum is perturbed by hundred single or multiple LOH (Loss of Heterozygosity) deletions relating to different chromosomes and cancers. Results: The generic law highlighted is stated as follows "When an LOH deletion affects a chromosome upstream of the HGO point (chromosomes 4 13). In the chromosomal spectrum, this deletion degrades the genomic optimum of the cancer genome. When an LOH deletion affects a chromosome downstream of the HGO point (chromosomes 19 22) in the chromosomal spectrum, this deletion improves the genomic optimum of the cancer genome. The exhaustive analysis of the 240 LOHs for the following 6 cases: Chromosome 13 (breast cancer), chromosome 5 (breast cancer), chromosome 10 (glioblastoma cancer), chromosome 1 (colorectal cancer), chromosome 1 (neuroblastoma cancer) and chromosome 16 (prostate cancer) obey this law in 227 cases and do not obey this law for 13 cases (success rate of our law=94.58%). In this article we will detail this type of analysis on 153 LOH relating to breast and prostate tumors affecting respectively chromosome 13, chromosome 5 (breast) and chromosome 16 (prostate). In this detailed study, the HGO law described here is verified in 143 cases out of 153 or 93.46% of favorable cases. Conclusion: The main application of this fundamental discovery will be the genomic characterization and classification of tumors, making it possible to predict the dangerousness and even the pathogenicity.

Keywords

Human genome; Cancer; Loss of Heterozygosity; Biomathematics; Evolution

Introduction

Thanks to the CRISPR (Clustered regularly interspaced short palindromic repeats) technology, it is now possible to locally modify the genomes, and particularly the human genome [1]. Almost simultaneously, the fractal and global structures of the human genome were demonstrated [2]. In such a context, apart from ethical questions, can a local technology as powerful as CRISPR be applied, ignoring its possible effect on the possible global and long-range equilibria and balancing at the chromosome scale or even the entire genome scale? For more than 25 years, we have been looking for possible global, even numerical, structures that would organize DNA, genes, chromosomes and even whole genomes [3-6]. Curiously, the method of numerical analysis of whole genomes as well as the discovery of a global law of impact of the LOH deletions associated with tumors that will be the subject of this article may seem to the reader too simple or even "naive". In effect, these laws are based on a wellknown type of analysis that could be thought to have explored all aspects: the analysis of GC/TA ratios. It has long been known that such ratios [7] characterize the diversity of chromosomes. Under the name of "isochores," Giorgio Bernardi has extensively explored its richness and diversity [8,9]. We have already demonstrated a numerical structure at the scale of each human chromosome as well as on the whole genome [10-13]. In [10] we have already highlighted this numerical value of 0.6909830056, the HGO in this article: it controls the population of triplet codons analyzing single stranded DNA sequence from the whole human genome. However, it is only by deepening the notion of "fractal periodicity", outlined in [14], and we will highlight in various articles in preparation [15] that we have re-discovered the major role that this GC/TA ratio at the whole chromosome and whole genome scales. Particularly, in 2015, we have demonstrated [14] how a global structure organizes any DNA sequence. This numerical organization is based on the atomic masses of the "G" bases of the double stranded DNA sequence, therefore on the bases C and G of the single stranded DNA sequence. Here is another reason sufficient to consider the relations and proportions between bases C+G on the one hand, and T+A on the other hand. Comparing the three genomes of reference of Neanderthal [15], Sapiens Build 34 of 2003 [16] and Sapiens hg38 of 2013 [17], we will demonstrate in [15] the evidence of "Fractals periods" and "resonance periods" characterizing each of the 24 human chromosomes. It is for these simple reasons that we have decided to focus on these C+G/T+A ratios at the scale of each of the 24 human chromosomes as well as on the whole genome analyzing the 46 chromosomes single stranded DNA sequences.

Materials and Methods

Analyzed whole human genomes

We analyzed completely and systematically each of the 24 chromosomes of each of the following three reference genomes:

Neanderthal genome: Neanderthal genome (2014) [15] http://www.nature.com/nature/journal/v505/n7481/full/nature12886.html Sapiens Build 34 (2003) human genome [16]: Sapiens Build34 (2003) genome http://www.nature.com/nature/journal/v431/n7011/full/nature03001.html Sapiens HG38 (2013) human genome [17]: Sapiens HG38 (2013) genome https://www.ncbi.nlm.nih.gov/grc/human

Computing the HGOs

Let us now distinguish the three types of HGO that will be discussed

Theoretical HGO (tHGO): tHGO=(3-PHI) ÷ 2=0.6909830056, where PHI is the Golden Ratio PHI=1.618033989.

Reference woman HGO (rwHGO): rwHGO=0.6913477936, error (tHGO-rwHGO)=0.6909830056-0.6913477936=0.0003647879784 and Reference man HGO (rmHGO): rmHGO=0.6922864236, error (tHGO-rmHGO)=0.6909830056-0.6922864236=0.001303417973.

HGO (LOH) is considered as a function: With LOH the deletion disturbing the computed CG/TA whole human genomic ratio and « n » the LOH partially deleted chromosome and « chrs » all chromosomes from 1 to 22 which are different with « n ». HGO is computed by compiling C+G and T+A nucleotides populations from each 46 chromosomes DNA single strand.

Example: HGOwoman (LOH chr n)=[(C+G population from 46 chromosomes strand1)+(C+G population from 46 chromosomes strand1)]/[(T+A population from 46 chromosomes strand1)+(T+A population from 46 chromosomes strand1)]. Then: HGOwoman (LOH chr n)=[(sum C+G single strand 1 to 22 chromosomes except chrn)+(sum C+G chrn)+(sum C+G chrX)+(sum C+G single strand 1 to 22 chromosomes except chrn)+(sum C+G chr LOH n)+(sum C+G chrX)]/[(sum T+A single strand 1 to 22 chromosomes except chrn)+(sum T+A chrn)+(sum T+A chrX)+(sum T+A single strand 1 to 22 chromosomes except chrn)+(sum T+A chr LOH n)+(sum T+A chrX)]. HGOman (LOH chr n)=[(sum C+G single strand 1 to 22 chromosomes except chrn)+(sum C+G chrn)+(sum C+G chrX)+(sum C+G single strand 1 to 22 chromosomes except chrn) +(sum C+G chr LOH n)+(sum C+G chrY)]/[(sum T+A single strand 1 to 22 chromosomes except chrn)+(sum T+A chrn)+(sum T+A chrX) +(sum T+A single strand 1 to 22 chromosomes except chrn)+(sum T+A chr LOH n)+(sum T+A chrY)] [18,19].

Results

In all that follows, the general methodology will be as follows: we calculate, for the 46 chromosomes constituting each genome studied, only the single-stranded DNA sequences. In these sequences, we count the relative populations of bases T+A on the one hand, and C+G on the other hand.

HGo of the 3 whole genomes: Neanderthal, Sapiens Build34 and Sapiens hg38

The three genomes we compare here are differentiated on the one hand by their respective evolution levels, on the other hand by the sample of individual genomes of which they form the syntheses, and finally by the precision of the sequencing of DNA.

For example, this work by the Craig Venter team demonstrates this level of dispersion between more than 10,000 individual genomes and reference genomes such as HG28 [20].

The 3 analysed genomes are:

• Neanderthal genome (2014) [15]

• Sapiens Build34 (2003) genome [16]

• Sapiens hg38 (2013) genome [17]

The methods of computing the different HGOs are given in "supporting information part 1".

The detailed data related to the 3 whole genomes shows the various distances and errors between real computed HGOs for each genome and theoretical HGO optimum value= 0.6909830055.

Particularly, it is found that the 3 HGOs calculated for the respective 3 genomes of Neanderthal, Sapiens (2003 Build34 and 2013 hg38 Sapiens) are very close to the ideal theoretical optimal HGO=0.6909830056 (99.67% for the least optimal genome).

It is also observed that female genomes (XX) are more optimal than male genomes (XY).

On the other hand, the genomes of Neanderthal and Sapiens (Build34 of 2003) have very close optimization levels. We believe these results from the fact that the precisions of their respective DNA sequencing are similar. On the contrary, the hg38 genomes of 2013 show the most optimal levels, this is most certainly due to the deeper quality of their DNA sequencing. Figure 1 summarizes HGO results for these 3 human genomes of varying levels of evolution.

research-journal-oncology-respective

Figure 1: The respective HGOs of 3 human genomes of varying levels of evolution are shown here.

Finally, we note that it is the downstream region (Figure 2) that contributes the most to the superiority of optimality of sapiens hg38 compared to sapiens Build34. However, a more detailed analysis of the upstream and downstream regions shows that when passing from sapiens Build34 2003 to hg38 2013, the notorious optimization obeys the global strategy law of the LOH. Also of note is that 20 out of 24 chromosomes are OK, with the exception of chromosomes 13, X, Y, and 1. The law presented here states that there is reduction of optimality for upstream chromosomes and improvement of optimality for downstream regions.

It is therefore remarkable that this is the same and only law which seems to simultaneously control two domains as different as: 1) the global strategy of LOH deletions of tumors on the one hand and 2) the difference of evolution of the same genome following two increasing precision levels of DNA sequencing (Build34 2003 and hg38 2013) on the other.

Recall the single stranded C+G, T+A and individual chromosome HGO values:

In Table 1, we have sorted the 24 chromosomes by increasing values of CG/TA ratios in the 3 cases of compared genomes.

Table 1 CG values, TA values and CG/TA ratio for each sapiens HG38 individual chromosome.

Chromosome C+G T+A (C+G)/(T+A)
Chromosomes upstream HGO point=(3-Phi)÷2=0.6909830056
4 72568001 117184666 0.6192619178
13 37772797 60210328 0.627347
5 37772797 60210328 0.627347471
X 71611274 109654104 0.6530651511
6 61221521 93671508 0.6535767632
3 67360020 102718502 0.6557729979
18 78577742 119522393 0.6574311309
Y 31856106 48233499 0.6604560453
8 10572683 15842360 0.66736793
2 58133960 86634176 0.6710280248
7 96769083 143779145 0.6730397722
12 64696843 94273288 0.686269084
14 54275482 78862334 0.6882307338
Chromosomes downstream HGO point=(3-Phi)÷2=0.6909830056
21 16411625 23676994 0.693146478
9 50270473 71520077 0.70288617
11 55885058 78648684 0.7105657102
10 55359481 77903481 0.7106162689
1 96166571 134314441 0.7159808751
15 35578844 49062481 0.7251741713
20 28010605 35933652 0.7795089962
16 36472718 45333225 0.8045471726
17 37575444 45344760 0.8286612169
22 18406838 20752939 0.8869509037
19 28015712 30425046 0.9208108346

HGO spectral hierarchy of the 24 human chromosomes

The following Figures 2 and 3 illustrate the hierarchical spectrum of the individual HGOs of each of the 24 chromosomes for each of the three genomes analyzed. It should be noted that the upstream/downstream tipping point lies between chromosomes 14 and 21, which is closely related to the probable mechanisms explaining trisomy21 (whose disorders involve precisely these two chromosomes).

research-journal-oncology-chromosomes

Figure 2: Diversity of HGOs of human chromosomes downstream of the numerical attractor HGO=0.6909830056.

research-journal-oncology-upstream

Figure 3: HGO diversity of human chromosomes upstream of the numerical attractor HGO=0.6909830056.

It then reveals a hierarchical classification scale of 24 chromosomes ranging from 1/Phi (chromosome4) to 3/2 Phi (chromosome 19).

HGO disturbed by 240 LOH deletions related to 5 different chromosomes and 5 different tumors.

After demonstrating how 3 human genomes with increasing levels of sequencing quality and evolution accuracy seem to "fit" this theoretical value of HGO, we will now analyze how small mutations on one of the chromosomes can "disrupt" this HGO. For this purpose there are a very large number of publications associating such nucleotide regions with deletions of the chromosomal DNA of different tumor cells.

We analyzed the Loss of Heterozygosity associated with 240 cases published in [21-26]. These 240 cases relate successively to the Breast [21,22], Glioblastoma [23], Colorectal [24], Neuroblastoma [21], and Prostate [23] cancers. They successively affect the chromosomes 13, 5, 10, 1 and 16.

This exhaustive analysis will then reveal the following generic law: "When an LOH deletion affects a chromosome upstream of the HGO point, in the chromosomal spectrum, this deletion degrades the genomic optimum of the cancer genome.

When an LOH deletion affects a chromosome downstream of the HGO point, in the chromosomal spectrum, this deletion improves the genomic optimum of the cancer genome.

The full details of these analyses are available in Table 2, below summarizing these results.

Table 2 Table of synthesis of 240 LOH relating to 5 types of cancer and 5 different chromosomes, the shaded areas represent those that comply with the HGO law, i.e., 227 cases out of 240.

Cancer type Chromosome
LOH deletions
LOH deletions decreasing HGO (Human Genome Optimum) LOH deletions increasing HGO (Human Genome Optimum) Total number of LOH % law is OK
  Upstream HGO      
Breast Chromosome 13 36 4 40  
Breast Chromosome 5 37 5 42  
   Downstream HGO    
Glioblastoma Chromosome 10 1 14 15  
Colorectal Chromosome 1 0 33 33  
Neuroblastoma Chromosome 1 2 36 38  
Prostate Chromosome 16 1 71 72  
Total   77 163 240  
    LOH deletions respecting the HGO Law LOH deletions unrespecting the HGO Law Total number of LOH % law is OK
Total   227 13 240 94.58%

In Table 2 the shaded areas represent cases of LOH complying with the generic rule, while the unshaded areas represent cases of LOH that do not comply with this rule. In total, 227 cases respect the rule and only 13 cases of LOH do not respect it, a success rate of this law equal to 94.58%. In Bold we represented the 153 Breast and prostate LOH deletions cases detailed in this article.

Global graphical analysis of the 240 LOH tumor cases: In Figures 4-7 the 4 images below present an overall analysis of the HGOs resulting from the 240 cases of LOH deletions associated with 5 types of cancers and 5 distinct chromosomes.

research-journal-oncology-woman-genome

Figure 4: Case of a woman genome, the 82 on the left are for decreased HGO chromosomes: 1/ at the bottom axis level, the theoretical HGO, 2/ in blue, the reference woman HGO value, then, 3/ the 240 LOH cases curve: on the left part of the figure LOH HGO values are principally higher than reference woman HGO, on the right part of the figure LOH HGO values are principally lower than reference woman HGO.

research-journal-oncology-principally

Figure 5: Case of a woman genome, the 82 on the left are for decreased HGO chromosomes: 1/ at the zero axis level, the theoretical HGO, 2/ in blue, the reference woman HGO error, then, 3/ the 240 LOH cases curve: on the left part of the figure LOH HGO errors are principally higher than reference woman HGO error, on the right part of the figure LOH HGO errors are principally lower than reference woman HGO error.

research-journal-oncology-higher

Figure 6: Case of a man genome, the 82 on the left are for decreased HGO chromosomes: 1/ at the bottom axis level, the theoretical HGO, 2/ in blue, the reference man HGO value, then, 3/ the 240 LOH cases curve: on the left part of the figure LOH HGO values are principally higher than reference man HGO, on the right part of the figure LOH HGO values are principally lower than reference man HGO.

research-journal-oncology-axis

Figure 7: Case of a man genome, the 82 on the left are for decreased HGO chromosomes: 1/ at the zero axis level, the theoretical HGO, 2/ in blue, the reference man HGO error, then, 3/ the 240 LOH cases curve: on the left part of the figure LOH HGO errors are principally higher than reference man HGO error, on the right part of the figure LOH HGO errors are principally lower than reference man HGO error.

For this purpose we recall how to distinguish 3 types of HGO: the theoretical HGO:(3-Phi)÷2=0.6909830055, where Phi is the golden ratio Phi=1.618033.

The 2 reference HGOs relating to the respective hg38 reference genomes of the female (0.691347793) and man (0.692286423).

The 240 HGOs relating to each of the 240 chromosomes having ubi LOH deletions, On the other hand, the chromosomes are presented in these 4 figures according to the order sequence of the hierarchical spectrum shown in Figures 2 and 3 above.

Consequently, these 240 cases are presented in the order of upstream towards downstream with respect to the theoretical HGO.

In particular, this is the case for the first 82 LOHs for breast tumors affecting chromosomes13 and 5, both of which are upstream (Figure 3) on the contrary, all remaining LOHs will be downstream (Figure 2) of the theoretical HGO point, thus downstream.

Thus, Figures 4 and 6 will synthesize the relative positions of all these HGOs. Similarly, the errors or distances (Figures 5 and 7) will also be calculated relative to the respective distances between HGO of the 240 cases of LOH deletions, or of the reference HGOs, with respect to the HGO theoretical.

These 4 graphs of Figures 4 to 7 summarize the relevance of the generic law in visual form. Indeed, the fact of having ordered the chromosomes and their associated LOHs according to the classification of the 24 chromosomes of Figures 2 and 3 has helped to highlight the statistical reality of this law.

Results

We have successively demonstrated that, in the Human Genome Evolution and in the precision of sequencing of the genomes, these genomes seemed to "seek" a sort of numerical optimum: HGO (Figure 1).

Then, we demonstrated how the LOH deletions affecting the tumor cell chromosomes obeyed a generic law based on the chromosome hierarchization illustrated in Figures 2 and 3.

However, an important open-ended question: do these LOH deletions affecting the HGO optimum have any potential significance for the pathogenicity and aggressiveness of these tumors?

This is what we are going to demonstrate now in 3 analyses of 153 Breast and Prostate LOH deletions tumors.

First analysis: 40 breast tumors LOH in chromosome 13

Basic data: The article supporting our analysis.

We analyze here 40 LOH associated with Breast cancer of chromosome 13 from the publication (19), of the 46 LOH cases published, only 40 cases of exploitable LOH were identified. Indeed some LOH are reduced to a single marker that is to say approximately 200000bp, which is too insignificant. For example, the first of the markers in this study is D13S1695: chr13: 32,849,425-33,049,658 200,234 bp. However, such a length of 200234 bp is too insignificant.

Example of LOH effect on the HGO, the case of a single LOH deletion in chromosome 13 breast tumor.

We therefore retain only the LOHs corresponding to regions delimited by 2 markers (for example the first LOH referenced in Table 3), as well as regions comprising at least 2 markers alone (for example the LOH referenced D13S1694 D13S267 in Table 3).

Table 3 Computing HGO ratio disturbed by a sample LOH on chr13 breast tumor.

LOH references :
number/ref number in published figure/ Markers Id.
 Deleted LOH regions Woman genome XX     Man genome XY
Reference Human Genome (HG38 2013)    Reference HGO
0.69134779
Error 
ideal HGO – reference HGO
-0.00036
  Reference HGO
0.69228642
Error
ideal HGO – reference HGO
-0.00130341
 
Region A              
2    4  
D13S1694   D13S267
 33097286  33790250 0.69135215 -0.00036915  0 0.69229100  0.00130799 0

The chromosome support of our analysis: chr13:1- 114,364,328 114,364,328 bp [26]

The supporting (Figure 8) of our analysis:

research-journal-oncology-tumours

Figure 8: Deletion mapping of chromosome 13q in 46 breast tumours. Schematic representation of loss of heterozygosity (LOH): solid boxes show LOH, open boxes show retention of heterozygosity and cross-hatched boxes are homozygous for the given marker. nd=not determined. Case numbers are shown at the top. The data were obtained by polymerase chain reaction (PCR) with the markers listed on the left. Tumours in group A are indicative of LOH at 13q12-q13, in group B at 13q12-q13 as well as 13q31-q34, and in group C the retinoblastoma gene is involved in the tumours, as well as the two regions depicted in groups A and B.

Figure 8 the case analysed from Figure 1 in publication [19].

To Conclude: Recall that (Table 4) chromosome 13 is upstream with respect to the tipping point HGO (Figure 2). Thus, according to our "global strategy law of LOH by chromosomes", the majority of LOH "should" degrade the value of the HGO: in effect, we observe that 36 out of 40 cases degrade the HGO.

Table 4 Detail of 40 breast tumors LOH deletions of chromosome 13.

LOH references :
number /
ref number in published figure / Markers Id.
Deleted LOH regions Woman genome XX Man genome XY  
Reference Human Genome (HG38 2013)   Reference HGO
0.69134779
Error
ideal HGO – reference HGO
-0.00036478
OK Reference HGO
0.69228642
Error
ideal HGO – reference HGO
-0.00130341
OK
Region A              
1    3  
D13S1695  D13S1694
32849425  33297510   0.69134714  -0.00036413  1  0.69228583  -0.00130282 1
2    4  
D13S1694   D13S267
33097286  33790250   0.69135215  -0.00036915  0  0.69229100 -0.00130799 0
3     6  
D13S171   D13S1694
32579775   33297510   0.69135118  -0.00036817  0  0.69229001 -0.00130700 0
4   7 
D13S171   D13S267
32579775  33790250   0.69135563  -0.00037262  0  0.69229464 -0.00131163 0
5   8 
D13S217   D13S1246
D13S171  
D13S267
28697654  30631622
32579775 32780083
33589982 33790250
  0.69134338 -0.00036038  1   0.69228229 -0.00129929 1
6   9   D13S260   D13S1694 31762621  33297510   0.69135713 -0.00037412  0  0.69229623 -0.00131323 0
7   10 
D13S1246 
D13S1694   D13S219
30431300 30631622
33097286   36684592
  0.69138996 -0.00040695  0  0.69233021 -0.00134721 0
8   11 
D13S217   D13S260
D13S1694   D13S267
28697654  31962968
33097286  33790250
  0.69133825 -0.00035524  1  0.69227730 -0.00129430 1
9    12 
D13S1246   D13S1694
D13S263
30431300  33297510
41406784 41607094
  0.69134803 -0.00036503  0 0.69228718 -0.00130417 0
Region B              
10  13 
D13S1246   D13S260
D13S1695
D13S219
D13S276
30431300  31962968
32849425 33049658
36484263 36684592
68335674 68536043
  0.69135049 -0.00036748  0 0.69228953 -0.00130653 0
11   14  
D13S260
D13S1694  D13S267
D13S160
31762621 31962968
33097286  33790250
78504466 78704740
  0.69135525 -0.00037225 0 0.69229424 -0.00131123 0
12   15 
D13S1246   D13S267
D13S263
D13S276  D13S160
30431300  33790250
41406784 41607094
68335674  78704740
  0.69157604 -0.00059304  0  0.69252240  -0.00153939 0
13    18 
D13S154
D13S173   D13S285
95510028 95710383
107054541 112241249
  0.69131884 -0.00033583  1   0.69225765  -0.00127465 1
14   19 
D13S154   D13S158
95510028  103424175   0.69136848 -0.00038548  0  0.69230891  -0.00132590 0
15    20 
D13S217   D13S171
D13S1694   D13S267
D13S155
D13S158
D13S285
28697654   32780083
33097286  33790250
53494781 53695047
10322447 103424175
112041068 112241249
  0.69242518 -0.00144217  0   0.69339874 -0.00241573 0
16   21  
D13S217   D13S260
D13S1694    D13S263
D13S158   D13S285
28697654  31962968
33097286   41607094
103224047 112241249
  0.69146697 -0.00048396  0   0.69241186   -0.00142885 0
17     22 
D13S217
D13S1695
D13S267   D13S155
D13S158    D13S285
28697654 28898018
32849425 33049658
33589982   53695047
103224047  12241249
  0.69151941  -0.00053641  0   0.69246701  -0.00148400 0
18   23 
D13S1246
D13S171
D13S1694   D13S267
D13S263   D13S155
D13S158   D13S285
30431300 30631622
32579775 32780083
33097286  33790250
41406784   53695047
103224047 112241249
  0.69143522 -0.00045222  0  0.69237962  -0.00139662 0
19   24  
D13S1246   D13S260
D13S1695
D13S267  D13S155
D13S158
D13S285
30431300   31962968
32849425 33049658
33589982   53695047
103224047 103424175
112041068 112241249
  0.69147014 -0.00048713  0  0.69241536 -0.00143235 0
20   25 
D13S1246   D13S171
D13S1694   D13S267
D13S154   D13S285
30431300  32780083
33097286  33790250
95510028  112241249
  0.69141228 -0.00042928  0  0.69235570 -0.00137270 0
21    26 
D13S260   D13S1695
D13S154   D13S158
31762621  33049658
95510028  103424175
  0.69137794  -0.00039494  0  0.69231881 -0.00133580 0
22   27 
D13S260   D13S267
D13S154
D13S173
31762621  33790250
95510028 95710383
107054541 107254838
  0.69136439 -0.00038139  0  0.69230382 -0.00132081 0
23   28 
D13S217   D13S1246
D13S171   D13S1694
D13S160
D13S158   D13S285
28697654   30631622
32579775   33297510
78504466 78704740
103224047 112241249
  0.69138262 -0.00039962  0 0.69232403 -0.00134102 0
24   29  
D13S1246   D13S171
D13S219
D13S154
D13S158   D13S285
30431300    32780083
36484263 36684592
95510028 95710383
103224047 112241249
  0.69139238 -0.00040937  0   0.69233399 -0.00135099 0
25  30 
D13S217   D13S1246
D13S171   D13S263
D13S160   D13S154
D13S173   D13S285
28697654   30631622
32579775   41607094
78504466    95710383
107054541 112241249
  0.69182195 -0.00083895  0 0.69277740 -0.00179439 0
26   31  
D13S1246
D13S171   D13S1694
D13S219   D13S263
D13S176   D13S154
D13S173   D13S285
30431300 30631622
32579775   33297510
36484263   41607094
59839530   95710383
107054541 112241249
  0.69226137 -0.00127836  0  0.69322965 -0.00224664 0
27   32  
D13S260
D13S1694  D13S263
D13S160   D13S154
31762621 31962968
33097286   41607094
78504466    95710383
  0.69185808 -0.00087507  0   0.69281315 -0.00183014 0
Region C              
28    33  
D13S1695   D13S153
D13S276
D13S158
32849425    48416872
68335674 68536043
103224047 103424175
  0.69148233 -0.00049932  0  0.69242680 -0.00144379 0
29   34 
D13S217   D13S260
D13S1695   D13S1694
D13S219   D13S155
D13S276
D13S285
28697654  31962968
32849425   33297510
36484263  53695047
68335674 68536043
112041068 112241249
  0.69142726 -0.00044425  0   0.69237131 -0.00138830 0
30   35  
D13S260   D13S171
D13S267
D13S263   D13S154
31762621   32780083
33589982 33790250
41406784   95710383
  0.69246020 -0.00147720  0  0.69343471 -0.00245171 0
31   36 
D13S1246   D13S1695
D13S267   D13S219
D13S155
D13S176   D13S160
D13S285
30431300   33049658
33589982  36684592
53494781 53695047
59839530  78704740
112041068 112241249
  0.69185880 -0.00087579  0 0.69281373 -0.00183073 0
32   37  
D13S217
D13S171   D13S1695
D13S267   D13S219
D13S155   D13S153
D13S154
28697654 28898018
32579775   33049658
33589982  36684592
53494781   48416872
95510028 95710383
  0.69138483 -0.00040183  0   0.69232416 -0.00134115 0
33   38 
D13S260   D13S1695
D13S267
D13S155
D13S176
D13S160
D13S158
31762621    33049658
33589982 33790250
53494781 53695047
59839530 60039900
78504466 78704740
103224047 103424175
  0.69137359 -0.00039058  0  0.69231321 -0.00133020 0
34    39  
D13S171   D13S1695
D13S267   D13S263
D13S153
D13S276
32579775   33049658
33589982    41607094
48216598 48416872
68335674 68536043
  0.69145145 -0.00046845  0 0.69239401 -0.00141101 0
35   40 
D13S1694   D13S267
D13S263
D13S153
33097286   33790250
41406784 41607094
48216598 48416872
  0.69135325 -0.00037024  0  0.69229219 -0.00130918 0
36   41  
D13S1246
D13S1695
D13S267
D13S153
30431300 30631622
32849425 33049658
33589982 33790250
48216598 48416872
  0.69135043 -0.00036743  0  0.69228926 -0.00130625 0
37   42  
D13S217   D13S171
D13S267
D13S276
28697654  32780083
33589982 33790250
68335674 68536043
  0.69135015 -0.00036714  0  0.69228957 -0.00130657 0
38   43   
D13S1246   D13S260
D13S1695
D13S267   D13S219
D13S153
30431300   31962968
32849425 33049658
33589982   36684592
48216598 48416872
  0.69138489  -0.00040188  0  0.69232523 -0.00134222 0
39   44  
D13S219
D13S154   D13S173
36484263 36684592
95510028  107254838
  0.69143858 -0.00045558  0  0.69238134 -0.00139834 0
40   45  
D13S219
D13S153   D13S176
36484263 36684592
48216598    60039900
  0.69153928  -0.00055628  0   0.69248445 -0.00150144 0
Total LOH which are OK with the HGO Law (then 0)       36 by 40     36 by 40

Second analysis: 42 breast tumors LOH in Chromosome 5

Basic data: The article supporting our analysis, in the analysis from [20].

The chromosome support of our analysis: chr5:1- 181,538,259 181,538,259 bp [27].

The supporting Figure 9 of our analysis:

research-journal-oncology-heterozygosity

Figure 9: LOH pattern in breast tumors showing partial and interstitial LOH at chromosome 5 in BRCA1 mutated tumors (a), BRCA2 mutated tumors (b) and sporadic tumors (c), LOH (loss of heterozygosity); ROH (retention of heterozygosity); homozygosity or not informative. Tumors showing LOH or retention of heterozygosity at all informative markers are not shown. The chromosome regions showing highest frequencies of deletion in BRCA1 tumors according to the array CGH analysis are marked on the left side. The homozygous deletions (HZ1 and 2) detected by the array CGH analysis are indicated with arrows. Indicate an LOH target between markers D5S392 and D5S406 (4.7 Mb) in BRCA1 tumors, as well as in BRCA2 and sporadic tumors.

Figure 9 the case analysed from Figure 2 in publication [20].

To conclude: Recall that (Table 5) chromosome 5 is upstream with respect to the tipping point HGO (Figure 2) Therefore, by virtue of our "global strategy law for LOH by chromosomes", most LOHs "should" degrade the HGO value: in effect, 37 out of 42 cases degrade HGO.

Table 5 Detail of 42 breast tumors LOH deletions of chromosome 5.

LOH references :
number /
ref number in published figure/Markers Id.
Deleted LOH regions Woman genome XX Man genome XY  
Reference Human Genome (HG38 2013)   Reference HGO
0.69134779
Error
ideal HGO – reference HGO
-0.00036478
OK Reference HGO
0.69228642
Error
ideal HGO – reference HGO
-0.00130341
OK
BRCA1 Breast tumors (a)       0     0
3
D5S432
D5S618
D5S669 D5S404
D5S636
D5S412
10593074 10793430
90370500 90570824
104539362 117611769
150416827 150617121
158675514 158875859
0.69155669 -0.00057368 0 0.69250257 -0.00151957 0
5
D1S455 D1S398
D1S618 D1S404
D1S636
D1S412
35894219 58373409
90370500 117611769
150416827 150617121
158675514 158875859
0.69211454 -0.00113153 0 0.69307982 -0.00209682 0
6
D5S664 D5S404
D5S2011 D5S2006
55577693 150617121
141742521 181021853
0.69210365 -0.00112064 0 0.69308176 -0.00209875 0
9
D5S1977
D5S618
D5S669 D5S404
D5S636 D5S410
D5S671 D5S211
76918678 77119014
90370500 90570824
104539362 117611769
158675514 153495801
168195357 173921549
0.69147538 -0.00049238 0 0.69241936 -0.00143636 0
10
D5S664
D5S618 D5S644
D5S412 D5S671
55577693 55778017
90370500 96577305
158675514 168395689
0.69158353 -0.00060053 0 0.69253043 -0.00154743 0
13
D5S2858 D5S1977
D5S618 D5S410
D5S671
D5S2030 D5S2006
64525211 77119014
90370500 153495801
168195357 168395689
178280172 181021853
0.69189479 -0.00091179 0 0.69285973 -0.00187672 0
14
D5S664
D5S2858 D5S647
D5S620 D5S412
D5S211
D5S2006
55577693 55778017
64525211 67051713
82277212 158875859
141742521 141942802
180821594 181021853
0.69214664 -0.00116364 0 0.69311486 -0.00213186 0
17
D5S1977 D5S620
D5S2078
D5S2011
D5S2030
76918678 82477566
128727878 128928206
173721274 173921549
178280172 178480512
0.69136039 -0.00037738 0 0.69230034 -0.00131733 0
18
D5S455 D5S1977
D5S644 D5S636
D5S412
D5S211
D5S2006
35894219 77119014
96376990 150617121
158675514 158875859
173721274 173921549
180821594 181021853
0.69221927 -0.00123627 0 0.69319501 -0.00221201 0
24
D5S644 D5S669
D5S2078
96376990 104739650
128727878 128928206
0.69153474 -0.00055174 0 0.69247922 -0.00149622 0
25
D5S432
D5S455 D5S664
10593074 10793430
35894219 55778017
0.69159059 -0.00060759 0 0.69253830 -0.00155529 0
26
D5S406
D5S455 D5S398
D5S644
D5S393 D5S636
D5S671 D5S211
4893930 5094254
35894219 58373409
96376990 96577305
136265641 150617121
168195357 173921549
0.69142146 -0.00043846 0 0.69236897 -0.00138596 0
BRCA2 breast tumors (b)              
2
D5S398
D5S636 D5S211
58173160 58373409
158675514 173921549
0.69137007 -0.00038707 0 0.69231178 -0.00132878 0
4
D5S392 D5S406
D5S618 D5S644
D5S404
D5S211
202025 5094254
90370500 96577305
117411476 117611769
173721274 173921549
0.69132495 -0.00034195 1 0.69226494 -0.00128194 1
11
D5S398
D5S647
D5S404 D5S393
D5S412 D5S671
D5S2006
58173160 58373409
66851322 67051713
173721274 136465819
158675514 168395689
180821594 181021853
0.69154086 -0.00055785 0 0.69247962 -0.00149661 0
12
D5S620 D5S618
D5S2078
82277212 90570824
128727878 128928206
0.69154344 -0.00056043 0 0.69248811 -0.00150511 0
13
D5S664 D5S647
D5S620 D5S618
55577693 67051713
82277212 90570824
0.69166055 -0.00067754 0 0.69260989 -0.00162689 0
14
D5S648
D5S644 D5S669
D5S2011 D5S636
D5S671 D5S211
25695625 25895922
96376990 104739650
141742521 158875859
168195357 173921549
0.69140625 -0.00042325 0 0.69235149 -0.00136848 0
15
D5S1997
D5S2858
D5S1977 D5S6218
D5S2078
D5S412 D5S2006
16882261 17082552
64525211 64725504
76918678 90570824
128727878 128928206
158675514 181021853
0.69137649 -0.00039348 0 0.69232188 -0.00133887 0
28
D5S392 D5S406
D5S647 D5S1977
D5S618
D5S393
D5S412 D5S671
202025 5094254
66851322 77119014
90370500 90570824
136265641 136465819
158675514 168395689
0.69137200 -0.00038899 0 0.69231539 -0.0013323 0
29
D5S392 D5S406
D5S1997
D5S664 D5S620
D5S644 D5S669
D5S2011
202025 5094254
16882261 17082552
55577693 82477566
96376990 104739650
141742521 141942802
0.69156230 -0.00057929 0 0.69251279 -0.00152978 0
31
D5S1977 D5S620
D5S644
D5S636
D5S2006
76918678 82477566
96376990 96577305
150416827 150617121
180821594 181021853
0.69136130 -0.00037830 0 0.69230127 -0.00131826 0
32
D5S2858
D5S1977 D5S620
D5S404
D5S412 D5S211
D5S2006
64525211 64725504
76918678 82477566
117411476 117611769
158675514 173921549
180821594 181021853
0.69139558 -0.00041257 0 0.69233889 -0.00135588 0
36
D5S392 D5S406
D5S636
D5S412 D5S2030
202025 5094254
150416827 150617121
158675514 178480512
0.69160321 -0.00062020 0 0.69255168 -0.00156867 0
40
D5S432
D5S455 D5S398
D5S647
10593074 10793430
35894219 58373409
66851322 67051713
0.69135641 -0.00037340 0 0.69230022 -0.00131721 0
42
D5S620
D5S644
D5S404
D5S2011 D5S671
D5S2030 D5S2006
82277212 82477566
96376990 96577305
117411476 117611769
141742521 168395689
178280172 181021853
0.69102838 -0.00004537 1 0.69196161 -0.00097860 1
Sporadic (c)              
5
D5S406
D5S398 D5S1977
D5S2011 D5S410
4893930 5094254
58173160 77119014
141742521 153495801
0.69148573 -0.00050272 0 0.69243277 -0.00144976 0
6
D5S648
D5S664 D5S398
D5S1977
D5S2011
25695625 25895922
55577693 58373409
76918678 77119014
141742521 141942802
0.69135535 -0.00037235 0 0.69229472 -0.00131172 0
9
D5S644 D5S404
D5S636
D5S412
96376990 117611769
150416827 150617121
158675514 158875859
0.69173687 -0.00075387 0 0.69268834 -0.00170534 0
10
D5S620
D5S644
D5S2078 D5S412
D5S211
D5S2006
82277212 82477566
96376990 96577305
128727878 158875859
173721274 173921549
180821594 181021853
0.69121921 -0.00023620 1 0.69215990 -0.00117690 1
11
D5S406 D5S432
D5S455
4893930 10793430
35894219 36094418
0.69132699 -0.00034399 1 0.69226614 -0.00128313 1
12
D5S432
D5S648 D5S647
D5S620 D5S2078
D5S2011 D5S410
10593074 10793430
25695625 67051713
82277212 128928206
173721274 153495801
0.69275045 -0.00176744 0 0.69373407 -0.00275107 0
13
D5S398
D5S647
D5S644
D5S393 D5S412
D5S211
58173160 58373409
66851322 67051713
96376990 96577305
136265641 158875859
173721274 173921549
0.69125826 -0.00027525 1 0.69219863 -0.00121563 1
15
D5S455 D5S2858
D5S2006
35894219 64725504
180821594 181021853
0.69168749 -0.00070448 0 0.69263900 -0.00165600 0
19
D5S392 D5S455
D5S398 D5S2858
D5S644 D5S669
D5S410
D5S2030
202025 36094418
58173160 64725504
96376990 104739650
153295415 153495801
178280172 178480512
0.69186327 -0.00088027 0 0.69282275 -0.00183974 0
21
D5S392
D5S398
D5S647
D5S404 D5S2078
D5S636 D5S410
202025 402151
58173160 58373409
66851322 67051713
117411476 128928206
150416827 153495801
0.69151381 -0.00053081 0 0.6924589 -0.00147589 0
24
D5S664 D5S620
D5S644
D5S404
55577693 82477566
96376990 96577305
117411476 117611769
0.69154041 -0.00055740 0 0.69248815 -0.00150515 0
26
D5S664 D5S398
D5S2078
D5S636
55577693 58373409
128727878 128928206
150416827 150617121
0.69135403 -0.00037102 0 0.69229333 -0.00131033 0
31
D5S636
D5S412 D5S671
150416827 150617121
158675514 168395689
0.69145662 -0.00047361 0 0.69239947 -0.00141646 0
33
D5S648
D5S2858
D5S618 D5S644
D5S2078
D5S211
25695625 25895922
64525211 64725504
90370500 96577305
128727878 128928206
173721274 173921549
0.69147158 -0.00048858 0 0.69241431 -0.00143130 0
34
D5S2858 D5S647
D5S620 D5S618
D5S404
D5S2011 D5S410
D5S671
64525211 67051713
82277212 90570824
117411476 117611769
141742521 153495801
168195357 168395689
0.69155438 -0.00057137 0 0.69250173 -0.00151872 0
36
D5S455 D5S398
D5S2078
D5S2011
35894219 58373409
128727878 128928206
141742521 141942802
0.69160183 -0.00061883 0 0.69255027 -0.00156727 0
Total LOH which are OK with the HGO Law (then 0)       37 by 42     37 by 42

Third analysis: 72 prostate tumors LOH in chromosome 16

Basic data: The article supporting our analysis [24].

The chromosome support of our analysis: chr16:1- 90,338,345 90,338,345 bp [28].

The supporting Figure 10 of our analysis:

research-journal-oncology-chromosome

Figure 10: LOH analysis at various chromosome arm 16q loci in prostate cancer. Only tumors showing partial 16q LOH are illustrated. Left, the probes used; O, •, informative loci; homozygous (uninformative) loci: ∎. maximum extent of the LOH. As defined by one or more probes; right SCDR.

Figure 10 the case analysed from Figure 1 in publication [24].

To conclude: Recall that (Table 6) chromosome 16 is downstream with respect to the tipping point HGO (Figure 3). Therefore, by virtue of our "global LOH strategy law by chromosomes", most LOHs "should" improve the HGO value: in fact, 66 cases out of 72 increase the HGO in the case of a Genome (XX) but 71 out of 72 cases increase HGO in the case of a male genome (XY).

Table 6 Detail of 72 prostate tumors LOH deletions of chromosome 16.

LOH references :
number /
ref number in published figure/Markers Id.
Deleted LOH regions Woman genome XX Man genome XY  
Reference Human Genome (HG38 2013)   Reference HGO
0.69134779
Error
ideal HGO – reference HGO
-0.00036478
OK Reference HGO
0.69228642
Error
ideal HGO – reference HGO
-0.00130341
OK
Regions
1/3 Minimal
             
1 T56
D16S413 D16S3023
87760230 88555205  0.69129368 -0.00031068 1 0.69223116 -0.00124815 1
2 T63
D16S304 D16S520
86382506 86582729  0.69133837 -0.00035536 1 0.69227681 -0.00129380 1
3 T12
D16S507 D16S303
79942534 90182695  0.69094866 0.00003434 1 0.69187951 -0.00089651 1
4 T18
D16S518 D16S3023
78004124 88555205  0.69104347 -0.00006046 1 0.69197662 -0.00099361 1
5 T27
D16S515 D16S520
76383131 86582729  0.69115928 -0.00017628 1 0.69209512 -0.00111212 1
6 T30
D16S515 D16S520
76383131 86582729  0.69115928 -0.00017628 1 0.69209512 -0.00111212 1
7 T32
D16S515 D16S303
76383131 90182695  0.69094149 0.00004152 1 0.69187275 -0.00088975 1
8 T68
D16S507 D16S303
79942534 90182695  0.69094866 0.00003434 1 0.69187951 -0.00089651 1
9 T78
D16S507 D16S303
79942534 90182695  0.69094866 0.00003434 1 0.69187951 -0.00089651 1
10 T24
D16S518 D16S520
78004124 86582729  0.69114909 -0.00016609 1 0.69208443 -0.00110142 1
11 T45
D16S507 D16S520
79942534 86582729  0.69116632 -0.00018332 1 0.69210174 -0.00111874 1
12 T42
D16S515 D16S413
76383131 87960566  0.69109574 -0.00011274 1 0.69203030 -0.00104730 1
13 T65
D16S301 D16S413
66802038 87960566  0.69092211 0.00006089 1 0.69185412 -0.00087111 1
14 T13
D16S347 D16S303
7161888 90182695  0.69019295 0.00079006 0 0.69111633 -0.00013333 1
15 T23
D16S496 D16S303
68814802 90182695  0.69085034 0.00013267 1 0.69178068 -0.00079767 1
16 T60
D16S496 D16S402
68814802 83360293  0.69120855 -0.00022555 1 0.69214628 -0.00116328 1
17 T28
D16S347 D16S413
7161888 87960566  0.69034898 0.00063402 0 0.69127574 -0.00029274 1
18 T66
D16S304 D16S413
7161888 87960566  0.69034898 0.00063402 0 0.69127574 -0.00029274 1
19 T1
D16S421 D16S303
67161726 90182695  0.69078070 0.00020231 1 0.69170965 -0.00072664 1
20 T10
D16S304 D16S413
7161888 87960566  0.69034898 0.00063402 0 0.69127574 -0.00029274 1
21 T31
D16S304 D16S413
7161888 87960566  0.69034898 0.00063402 0 0.69127574 -0.00029274 1
22 T39
D16S421 D16S520
67161726 86582729  0.69099890 -0.00001589 1 0.69193244 -0.00094944 1
23 T48
D16S421 D16S413
67161726 87960566  0.69093523 0.00004778 1 0.69186749 -0.00088448 1
24 T55
D16S402 D16S3023
67161726 88555205  0.69089304 0.00008997 1 0.69182440 -0.00084139 1
25 T72
D16S402 D16S3023
67161726 88555205  0.69089304 0.00008997 1 0.69182440 -0.00084139 1
26 T73
D16S421 D16S518
67161726 78204435  0.69119627 -0.00021327 1 0.69213313 -0.00115013 1
27 T71
D16S301 D16S518
66802038 78204435  0.69118319 -0.00020019 1 0.69211980 -0.00113679 1
28 T51
D16S507 D16S402
79942534 83360293  0.69130612 -0.00032311 1 0.69224433 -0.00126132 1
29 T62
D16S496 D16S507
68814802 80142885  0.69125013 -0.00026713 1 0.69218832 -0.00120531 1
30 T2
D16S318
67161888 67362019  0.69133725 -0.00035425 1 0.69227567 -0.00129266 1
2/3 Regions              
31 T12
D16S507
D16S520 D16S303
79942534 80142885
86382506 90182695
 0.69112078 -0.00013778 1 0.69205469 -0.00107169 1
32 T18
D16S518
D16S402 D16S3023
78004124 78204435
83159809 88555205
 0.69110000 -0.00011699 1 0.69203368 -0.00105067 1
33 T27
D16S515
D16S507 D16S520
76383131 76583505
79942534 86582729
 0.69117068 -0.00018767 1 0.69210623 -0.00112323 1
34 T32
D16S515 D16S507
D16S413 D16S303
76383131 80142885
87760230 90182695
 0.69117454 -0.00019154 1 0.69211008 -0.00112708 1
35 T68
D16S507
D16S520
D16S3023 D16S303
79942534 80142885
86382506 86582729
88354919 90182695
 0.69120697 -0.00022396 1 0.69214262 -0.00115962 1
36 T45
D16S507
D16S520
 79942534 80142885
86382506 86582729
 0.69133815 -0.00035514 1 0.69227661 -0.00129361 1
 37 T42
D16S515 D16S518
D16S520 D16S413
76383131 78204435
86382506 87960566
 0.69128331 -0.00030030 1 0.69222097 -0.00123796 1
38 T65
D16S301 D16S518
D16S413
66802038 78204435
87760230 87960566
 0.69117107 -0.00018806 1 0.69210742 -0.00112442 1
39 T13
D16S421
D16S301
D16S515 D16S402
D16S413
D16S303
67161726 67362083
66802038 67002181
76383131 83360293
87760230 87960566
89982590 90182695
 0.69128322 -0.00030022 1 0.69222151 -0.00123851 1
40 T23
D16S 496
D16S507
D16S3023 D16S303
68814802 69015161
79942534 80142885
88354919 90182695
 0.69121462 -0.00023162 1 0.69215046 -0.00116746 1
41 T60
D16S496 D16S515
D16S402
68814802 76583505
83159809 83360293
0.69126101 -0.00027800 1 0.69219890 -0.00121589 1
42 T28
D16S347
D16S515 D16S413
67161726 67362083
76383131 87960566
0.69108516 -0.00010216 1 0.69201950 -0.00103650 1
43 T66
D16S304 D16S507
D16S520 D16S413
67161726 80142885
86382506 87960566
0.69110767 -0.00012467 1 0.69204301 -0.00106000 1
44 T1
D16S421 D16S518
D16S402
D16S413 D16S303
67161726 78204435
83159809 83360293
87760230 90182695
0.69102923 -0.00004622 1 0.69196255 -0.00097954 1
45 T10
D16S304
D16S496 D16S515
D16S507
D16S520 D16S413
67161726 67362083
68814802 76583505
79942534 80142885
86382506 87960566
0.69117796 -0.00019496 1 0.69211417 -0.00113117 1
46 T31
D16S347
D16S515 D16S413
67161726 67362083
76383131 87960566
0.69108516 -0.00010216 1 0.69201950 -0.00103650 1
47 T39
D16S421 D16S301
D16S507 D16S520
67161726 67002181
79942534 86582729
0.69117039 -0.00018738 1 0.69210588 -0.00112287 1
48 T48
D16S421
D16S402 D16S413
67161726 67362083
83159809 87960566
0.69113337 -0.00015037 1 0.69206774 -0.00108474 1
49 T55
D16S304 D16S318
D16S515
D16S402 D16S3023
67161726 67362019
76383131 76583505
83159809 88555205
0.69109567 -0.00011266 1 0.69202927 -0.00104627 1
50 T72
D16S347 D16S421
D16S301 D16S496
D16S518
D16S402
D16S413 D16S3023
67161726 67362083
66802038 69015161
78004124 78204435
83159809 83360293
87760230 88555205
0.69122003 -0.00023703 1 0.69215614 -0.00117313 1
51 T73
D16S421
D16S301 D16S518
67161726 67362083
66802038 78204435
0.69119627 -0.00021327 1 0.69213313 -0.00115013 1
52 T71
D16S301
D16S515 D16S518
66802038 67002181
76383131 78204435
0.69134716 -0.00036415 1 0.69228611 -0.00130310 1
53 T62
D16S496
D16S518 D16S507
68814802 69015161
78004124 80142885
0.69132865 -0.00034564 1 0.69226721 -0.00128421 1
Regions
3/3 Maximal
      1     1
54 T18
D16S515 D16S303
76383131 90182695 0.69094149 0.00004152 1 0.69187275 -0.00088975 1
55 T27
D16S301 D16S303
66802038 90182695 0.69076757 0.00021544 1 0.69169627 -0.00071326 1
56 T78
D16S518 D16S303
78004124 90182695 0.69093136 0.00005165 1 0.69186211 -0.00087911 1
57 T23
D16S347 D16S303
67161726 90182695 0.69078070 0.00020231 1 0.69170965 -0.00072664 1
58 T28
D16S421 D16S3023
67161726 88555205 0.69089304 0.00008997 1 0.69182440 -0.00084139 1
59 T66
D16S421 D16S413
67161726 87960566 0.69093523 0.00004778 1 0.69186749 -0.00088448 1
60 T71
D16S421 D16S518
67161726 78204435 0.69119627 -0.00021327 1 0.69213313 -0.00115013 1
Autres multiples maximums       1     1
61 T42
D16S515 D16S518
D16S402 D16S413
76383131 78204435
83159809 87960566
0.69115224 -0.00016924 1 0.69208733 -0.00110432 1
62 T10
D16S421
D16S301 D16S413
67161726 67362083
66802038 87960566
0.69093523 0.00004778 1 0.69186749 -0.00088448 1
63 T31
D16S421 D16S301
D16S515 D16S303
67161726 67002181
76383131 90182695
0.69094556 0.00003744 1 0.69187690 -0.00089389 1
64 T39
D16S421 D16S301
D16S518 D16S303
67161726 67002181
78004124 90182695
0.69093543 0.00004757 1 0.69186626 -0.00088325 1
65 T48
D16S421
D16S518 D16S413
67161726 67362083
78004124 87960566
0.69107499 -0.00009199 1 0.69200883 -0.00102582 1
66 T1
D16S421 D16S518
D16S402 D16S303
67161726 78204435
83159809 90182695
0.69083756 0.00014545 1 0.69176705 -0.00078404 1
67 T10
D16S421
D16S301 D16S413
67161726 67362083
66802038 87960566
0.69093523 0.00004778 1 0.69186749 -0.00088448 1
68 T72
D16S421 D16S402
D16S413 D16S303
67161726 83360293
87760230 90182695
0.69097256 0.00001045 1 0.69190535 -0.00092234 1
69 T73
D16S421
D16S301 D16S3023
67161726 67362083
66802038 88555205
0.69089304 0.00008997 1 0.69182440 -0.00084139 1
70 T71
D16S421 D16S301
D16S515 D16S518
67002181 67161726
76383131 78204435
0.69135616 -0.00037315 0 0.69229529 -0.00131228 0
71 T51
D16S518 D16S402
78004124 83360293 0.69128895 -0.00030594 1 0.69222706 -0.00124406 1
72 T2
D16S421 D16S496
67161726 69015161 0.69127674 -0.00029373 1 0.69221399 -0.00123098 1
Total LOH which are OK with the HGO Law (then 1)       66 by 72     71 by 72

Discussion

First analysis: 40 breast tumors LOH in chromosome 13

In the analysis from publication [19], we show that HGO conforms to the above law in 36 of 40 cases (chromosome 13 is in the region upstream of the HGO point) (Figure 2).

In Figure 11, it is interesting to note that the effect on a female genome (XX) is greater than the effect on this same male genome (XY), which is in agreement with the fact that this cancer is almost exclusively feminine. A rapid analysis of the degradations of HGO - for the same LOH - depending on whether the genome is XY (masculine) or XX (feminine) will show that these expected degradations are 1.27 times higher in the case of a female genome (XX). This would reinforce the fact that the female genome is more sensitive to these LOH deletions than the male genome.

research-journal-oncology-cancers

Figure 11: Effect of LOH of chromosome 13 on HGO ratio in breast cancers on the same genome according to whether it is female (XX) or male (XY), ratio decreasing HGO female/male=1.27.

Second analysis: 42 breast tumors LOH in chromosome 5

In the analysis from publication [20], we show (Figure 12) that the HGO conforms to the above-mentioned law in 37 cases out of 42 (chromosome 5 is located in the region upstream of the HGO point) (Figure 2). The analysis below concerns cases of LOH affecting BRCA1 mutations. It is interesting to observe - even if only visually - that the effect on a female genome (XX) is greater than the effect on the same male genome (XY), which is in agreement with the fact that this cancer is almost exclusively feminine.

research-journal-oncology-ratio

Figure 12: Effect of LOH of chromosome 5 on the HGO ratio in breast cancers affecting the BRCA1 gene on the same genome according to whether it is female (XX) or male (XY).

Third analysis: 72 prostate tumors LOH in chromosome 16

Of 72 cases analyzed from article [24], 71 cases improved HGO while only one did not (Chromosome 16 is located in the region downstream of the HGO point (Figure 3). The evaluation below analyzes the evolution of the HGO according to the 3 grades of pathogenicity of the tumors studied.

Grade A: patients with disease limited to the prostate.

Grade B: patients with local extracapsular extension.

Grade C: patients with regional lymph node involvement or distant metastases.

Between Grade A and Grade B, an average HGO improvement of 4.88% was observed.

The graph below (Figure 13) illustrates this optimization. The HGO of grade C is of the same order as that of grade A, which may be explained by the fact that the LOHs of grades A and B are generally monochromosomes whereas the LOHs of grade C are multichromosomes. There are therefore more complexes to be demonstrated in monochromosome studies.

research-journal-oncology-optimality

Figure 13: Increased impact of the HGO optimality between grade A and grade B in prostate cancer involving LOH on chromosome 16.

It is interesting to note that the effect on a female genome (XX) is 4.86 times lower than the effect on the same male genome (XY), which is in agreement with the fact that this cancer is exclusively male (Figure 14).

research-journal-oncology-prostate

Figure 14: Incidence of chromosome 16 LOH on HGO ratio in prostate cancers on the same genome according to whether it is female (XX) or male (XY).

Conclusion

It is remarkable to discover this strong correlation between the pathogenicity and the aggressiveness of tumors on the one hand, and the categorization and hierarchization of mutations LOH of the mutant genomes at the origin of tumors. The law discovered here is universal, common to all types of cancers and to all chromosomes. Its nature is mathematical, proceeding only from the DNA information of the genomes. The method is exhaustive, systematic, and predictive, making it possible to anticipate the knowledge of the pathogenicity of an existing tumor or even of a mutation before the tumor disappears.

The mutant genome thus constitutes a kind of signature, virtual and numerical image of the tumor. Thus it is remarkable to discover that the LOH genome of a breast tumor, a cancer that is exclusively feminine by its nature, will lead to an overall HGO genomic degradation much greater than the same mutation affecting a male genome.

Conversely, it will be the same, but in the opposite way for a cancer of the prostate which, it is, exclusively masculine.

Finally, in this same prostate cancer, the impact on HGO between grade A and grade B is significant: recall.

Grade A: patients with disease limited to the prostate.

Grade B: patients with local extracapsular extension.

Grade C: patients with regional lymph node involvement or distant metastases.

Between Grade A and Grade B, an average HGO improvement of 4.88% was observed.

To conclude, the most important fact is the universal character of this HGO law, presented here for both breast and prostate cancers, the universal character of this law has been widely generalized experimentally on a large number of cancers differences affecting most chromosomes, this generalization will be described in [28,29].

Acknowledgement

We especially thank Dr. Robert Friedman M.D. practiced nutritional and preventive medicine in Santa Fe, New Mexico, woldwide expert on Golden ratio Life applications. We also thank the mathematician Pr. Diego Lucio Rapoport (Buenos aires), the french biologist Pr. François Gros (Pasteur institute, co-discoverer of RNA messenger with James Watson and Walter Gilbert) and Pr. Luc Montagnier, medicine Nobel prizewinner for their interest in my research of biomathematical laws of genomes.

References

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