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Live Notes, Real Time Conference Coverage 2020 AACR Virtual Meeting April 27, 2020 Minisymposium on AACR Project Genie & Bioinformatics 4:00 PM – 6:00 PM

SESSION VMS.MD01.01 – Advancing Cancer Research through an International Cancer Registry: AACR Project GENIE Use Cases
 
Reporter: Stephen J. Williams, PhD

April 27, 2020, 4:00 PM – 6:00 PM
Virtual Meeting: All Session Times Are U.S. EDT

Session Type
Virtual Minisymposium
Track(s)
Bioinformatics and Systems Biology
17 Presentations
4:00 PM – 6:00 PM
– Chairperson Gregory J. Riely. Memorial Sloan Kettering Cancer Center, New York, NY

4:00 PM – 4:01 PM
– Introduction Gregory J. Riely. Memorial Sloan Kettering Cancer Center, New York, NY

Precision medicine requires an end-to-end learning healthcare system, wherein the treatment decisions for patients are informed by the prior experiences of similar patients. Oncology is currently leading the way in precision medicine because the genomic and other molecular characteristics of patients and their tumors are routinely collected at scale. A major challenge to realizing the promise of precision medicine is that no single institution is able to sequence and treat sufficient numbers of patients to improve clinical-decision making independently. To overcome this challenge, the AACR launched Project GENIE (Genomics Evidence Neoplasia Information Exchange).

AACR Project GENIE is a publicly accessible international cancer registry of real-world data assembled through data sharing between 19 of the leading cancer centers in the world. Through the efforts of strategic partners Sage Bionetworks (https://sagebionetworks.org) and cBioPortal (www.cbioportal.org), the registry aggregates, harmonizes, and links clinical-grade, next-generation cancer genomic sequencing data with clinical outcomes obtained during routine medical practice from cancer patients treated at these institutions. The consortium and its activities are driven by openness, transparency, and inclusion, ensuring that the project output remains accessible to the global cancer research community for the benefit of all patients.AACR Project GENIE fulfills an unmet need in oncology by providing the statistical power necessary to improve clinical decision-making, particularly in the case of rare cancers and rare variants in common cancers. Additionally, the registry can power novel clinical and translational research.

Because we collect data from nearly every patient sequenced at participating institutions and have committed to sharing only clinical-grade data, the GENIE registry contains enough high-quality data to power decision making on rare cancers or rare variants in common cancers. We see the GENIE data providing another knowledge turn in the virtuous cycle of research, accelerating the pace of drug discovery, improving the clinical trial design, and ultimately benefiting cancer patients globally.

 

The first set of cancer genomic data aggregated through AACR Project Genomics Evidence Neoplasia Information Exchange (GENIE) was available to the global community in January 2017.  The seventh data set, GENIE 7.0-public, was released in January 2020 adding more than 9,000 records to the database. The combined data set now includes nearly 80,000 de-identified genomic records collected from patients who were treated at each of the consortium’s participating institutions, making it among the largest fully public cancer genomic data sets released to date.  These data will be released to the public every six months. The public release of the eighth data set, GENIE 8.0-public, will take place in July 2020.

The combined data set now includes data for over 80 major cancer types, including data from greater than 12,500 patients with lung cancer, nearly 11,000 patients with breast cancer, and nearly 8,000 patients with colorectal cancer.

For more details about the data, analyses, and summaries of the data attributes from this release, GENIE 7.0-public, consult the data guide.

Users can access the data directly via cbioportal, or download the data directly from Sage Bionetworks. Users will need to create an account for either site and agree to the terms of access.

For frequently asked questions, visit our FAQ page.

  • In fall of 2019 AACR announced the Bio Collaborative which collected pan cancer data in conjuction and collaboration and support by a host of big pharma and biotech companies
  • they have a goal to expand to more than 6 cancer types and more than 50,000 records including smoking habits, lifestyle data etc
  • They have started with NSCLC have have done mutational analysis on these
  • included is tumor mutational burden and using cbioportal able to explore genomic data even further
  • treatment data is included as well
  • need to collect highly CURATED data with PRISM backbone to get more than outcome data, like progression data
  • they might look to incorporate digital pathology but they are not there yet; will need good artificial intelligence systems

 

4:01 PM – 4:15 PM
– Invited Speaker Gregory J. Riely. Memorial Sloan Kettering Cancer Center, New York, NY

4:15 PM – 4:20 PM
– Discussion

4:20 PM – 4:30 PM
1092 – A systematic analysis of BRAF mutations and their sensitivity to different BRAF inhibitors: Zohar Barbash, Dikla Haham, Liat Hafzadi, Ron Zipor, Shaul Barth, Arie Aizenman, Lior Zimmerman, Gabi Tarcic. Novellusdx, Jerusalem, Israel

Abstract: The MAPK-ERK signaling cascade is among the most frequently mutated pathways in human cancer, with the BRAF V600 mutation being the most common alteration. FDA-approved BRAF inhibitors as well as combination therapies of BRAF and MEK inhibitors are available and provide survival benefits to patients with a BRAF V600 mutation in several indications. Yet non-V600 BRAF mutations are found in many cancers and are even more prevalent than V600 mutations in certain tumor types. As the use of NGS profiling in precision oncology is becoming more common, novel alterations in BRAF are being uncovered. This has led to the classification of BRAF mutations, which is dependent on its biochemical properties and affects it sensitivity to inhibitors. Therefore, annotation of these novel variants is crucial for assigning correct treatment. Using a high throughput method for functional annotation of MAPK activity, we profiled 151 different BRAF mutations identified in the AACR Project GENIE dataset, and their response to 4 different BRAF inhibitors- vemurafenib and 3 different exploratory 2nd generation inhibitors. The system is based on rapid synthesis of the mutations and expression of the mutated protein together with fluorescently labeled reporters in a cell-based assay. Our results show that from the 151 different BRAF mutations, ~25% were found to activate the MAPK pathway. All of the class 1 and 2 mutations tested were found to be active, providing positive validation for the method. Additionally, many novel activating mutations were identified, some outside of the known domains. When testing the response of the active mutations to different classes of BRAF inhibitors, we show that while vemurafenib efficiently inhibited V600 mutations, other types of mutations and specifically BRAF fusions were not inhibited by this drug. Alternatively, the second-generation experimental inhibitors were effective against both V600 as well as non-V600 mutations. Using this large-scale approach to characterize BRAF mutations, we were able to functionally annotate the largest number of BRAF mutations to date. Our results show that the number of activating variants is large and that they possess differential sensitivity to different types of direct inhibitors. This data can serve as a basis for rational drug design as well as more accurate treatment options for patients.

  • Molecular profiling is becoming imperative for successful  targeted therapies
  • 500 unique mutations in BRAF so need to use bioinformatic pipeline; start with NGS panels then cluster according to different subtypes or class specific patterns
  • certain mutation like V600E mutations have distinct clustering in tumor types
  • 25% of mutations occur with other mutations; mutations may not be functional; they used highthruput system to analyze other V600 braf mutations to determine if functional
  • active yet uncharacterized BRAF mutations seen in a major proportion of human tumors
  • using genomic drug data found that many inhibitors like verafanib are specific to a specific mutation but other inhibitors that are not specific to a cleft can inhibit other BRAF mutants
  • 40% of 135 mutants were functionally active
  • USE of Functional Profiling instead of just genomic profiling
  • Q?: They have already used this platform and analysis for RTKs and other genes as well successfully
  • Q? how do you deal with co reccuring mutations: platform is able to do RTK plus signaling protiens

4:30 PM – 4:35 PM
– Discussion

4:35 PM – 4:45 PM
1093 – Calibration Tool for Genomic Aggregates (CTGA): A deep learning framework for calibrating somatic mutation profiling data from conventional gene panel data. Jordan Anaya, Craig Cummings, Jocelyn Lee, Alexander Baras. Johns Hopkins Sidney Kimmel Comprehensive Cancer Center, MD, Genentech, Inc., CA, AACR, Philadelphia, PA

Abstract: It has been suggested that aggregate genomic measures such as mutational burden can be associated with response to immunotherapy. Arguably, the gold standard for deriving such aggregate genomic measures (AGMs) would be from exome level sequencing. While many clinical trials run exome level sequencing, the vast majority of routine genomic testing performed today, as seen in AACR Project GENIE, is targeted / gene-panel based sequencing.
Despite the smaller size of these gene panels focused on clinically targetable alterations, it has been shown they can estimate, to some degree, exomic mutational burden; usually by normalizing mutation count by the relevant size of the panels. These smaller gene panels exhibit significant variability both in terms of accuracy relative to exomic measures and in comparison to other gene panels. While many genes are common to the panels in AACR Project GENIE, hundreds are not. These differences in extent of coverage and genomic loci examined can result in biases that may negatively impact panel to panel comparability.
To address these issues we developed a deep learning framework to model exomic AGMs, such as mutational burden, from gene panel data as seen in AACR Project GENIE. This framework can leverage any available sample and variant level information, in which variants are featurized to effectively re-weight their importance when estimating a given AGM, such as mutational burden, through the use of multiple instance learning techniques in this form of weakly supervised data.
Using TCGA data in conjunction with AACR Project GENIE gene panel definitions, as a proof of concept, we first applied this framework to learn expected variant features such as codons and genomic position from mutational data (greater than 99.9% accuracy observed). Having established the validity of the approach, we then applied this framework to somatic mutation profiling data in which we show that data from gene panels can be calibrated to exomic TMB and thereby improve panel to panel compatibility. We observed approximately 25% improvements in mean squared error and R-squared metrics when using our framework over conventional approaches to estimate TMB from gene panel data across the 9 tumors types examined (spanning melanoma, lung cancer, colon cancer, and others). This work highlights the application of sophisticated machine learning approaches towards the development of needed calibration techniques across seemingly disparate gene panel assays used clinically today.

 

4:45 PM – 4:50 PM
– Discussion

4:50 PM – 5:00 PM
1094 – Genetic determinants of EGFR-driven lung cancer growth and therapeutic response in vivoGiorgia Foggetti, Chuan Li, Hongchen Cai, Wen-Yang Lin, Deborah Ayeni, Katherine Hastings, Laura Andrejka, Dylan Maghini, Robert Homer, Dmitri A. Petrov, Monte M. Winslow, Katerina Politi. Yale School of Medicine, New Haven, CT, Stanford University School of Medicine, Stanford, CA, Stanford University School of Medicine, Stanford, CA, Yale School of Medicine, New Haven, CT, Stanford University School of Medicine, Stanford, CA, Yale School of Medicine, New Haven, CT

5:00 PM – 5:05 PM
– Discussion

5:05 PM – 5:15 PM
1095 – Comprehensive pan-cancer analyses of RAS genomic diversityRobert Scharpf, Gregory Riely, Mark Awad, Michele Lenoue-Newton, Biagio Ricciuti, Julia Rudolph, Leon Raskin, Andrew Park, Jocelyn Lee, Christine Lovly, Valsamo Anagnostou. Johns Hopkins Sidney Kimmel Comprehensive Cancer Center, Baltimore, MD, Memorial Sloan Kettering Cancer Center, New York, NY, Dana-Farber Cancer Institute, Boston, MA, Vanderbilt-Ingram Cancer Center, Nashville, TN, Amgen, Inc., Thousand Oaks, CA, AACR, Philadelphia, PA

5:15 PM – 5:20 PM
– Discussion

5:20 PM – 5:30 PM
1096 – Harmonization standards from the Variant Interpretation for Cancer Consortium. Alex H. Wagner, Reece K. Hart, Larry Babb, Robert R. Freimuth, Adam Coffman, Yonghao Liang, Beth Pitel, Angshumoy Roy, Matthew Brush, Jennifer Lee, Anna Lu, Thomas Coard, Shruti Rao, Deborah Ritter, Brian Walsh, Susan Mockus, Peter Horak, Ian King, Dmitriy Sonkin, Subha Madhavan, Gordana Raca, Debyani Chakravarty, Malachi Griffith, Obi L. Griffith. Washington University School of Medicine, Saint Louis, MO, Reece Hart Consulting, CA, Broad Institute, Boston, MA, Mayo Clinic, Rochester, MN, Washington University School of Medicine, Saint Louis, MO, Washington University School of Medicine, Saint Louis, MO, Baylor College of Medicine, Houston, TX, Oregon Health and Science University, Portland, OR, National Cancer Institute, Bethesda, MD, Georgetown University, Washington, DC, The Jackson Laboratory for Genomic Medicine, Farmington, CT, National Center for Tumor Diseases, Heidelberg, Germany, University of Toronto, Toronto, ON, Canada, University of Southern California, Los Angeles, CA, Memorial Sloan Kettering Cancer Center, New York, NY

Abstract: The use of clinical gene sequencing is now commonplace, and genome analysts and molecular pathologists are often tasked with the labor-intensive process of interpreting the clinical significance of large numbers of tumor variants. Numerous independent knowledge bases have been constructed to alleviate this manual burden, however these knowledgebases are non-interoperable. As a result, the analyst is left with a difficult tradeoff: for each knowledgebase used the analyst must understand the nuances particular to that resource and integrate its evidence accordingly when generating the clinical report, but for each knowledgebase omitted there is increased potential for missed findings of clinical significance.The Variant Interpretation for Cancer Consortium (VICC; cancervariants.org) was formed as a driver project of the Global Alliance for Genomics and Health (GA4GH; ga4gh.org) to address this concern. VICC members include representatives from several major somatic interpretation knowledgebases including CIViC, OncoKB, Jax-CKB, the Weill Cornell PMKB, the IRB-Barcelona Cancer Biomarkers Database, and others. Previously, the VICC built and reported on a harmonized meta-knowledgebase of 19,551 biomarker associations of harmonized variants, diseases, drugs, and evidence across the constituent resources.In that study, we analyzed the frequency with which the tumor samples from the AACR Project GENIE cohort would match to harmonized associations. Variant matches increased dramatically from 57% to 86% when broader matching to regions describing categorical variants were allowed. Unlike precise sequence variants with specified alternate alleles, categorical variants describe a collection of potential variants with a common feature, such as “V600” (non-valine alleles at the 600 residue), “Exon 20 mutations” (all non-silent mutations in exon 20), or “Gain-of-function” (hypermorphic alterations that activate or amplify gene activity). However, matching observed sequence variants to categorical variants is challenging, as the latter are typically only described as unstructured text. Here we describe the expressive and computational GA4GH Variation Representation specification (vr-spec.readthedocs.io), which we co-developed as members of the GA4GH Genomic Knowledge Standards work stream. This specification provides a schema for common, precise forms of variation (e.g. SNVs and Indels) and the method for computing identifiers from these objects. We highlight key aspects of the specification and our work to apply it to the characterization of categorical variation, showcasing the variant terminology and classification tools developed by the VICC to support this effort. These standards and tools are free, open-source, and extensible, overcoming barriers to standardized variant knowledge sharing and search.

https://cancervariants.org/

  • store information from different databases by curating them and classifying them then harmonizing them into values
  • harmonize each variant across their knowledgebase; at any level of evidence
  • had 29% of patients variants that matched when compare across many knowledgebase databases versus only 13% when using individual databases
  • they are also trying to curate the database so a variant will have one code instead of various refseq codes or protein codes
  • VIC is an open consortium

 

 

5:30 PM – 5:35 PM
– Discussion

5:35 PM – 5:45 PM
1097 – FGFR2 in-frame indels: A novel targetable alteration in intrahepatic cholangiocarcinoma. Yvonne Y. Li, James M. Cleary, Srivatsan Raghavan, Liam F. Spurr, Qibiao Wu, Lei Shi, Lauren K. Brais, Maureen Loftus, Lipika Goyal, Anuj K. Patel, Atul B. Shinagare, Thomas E. Clancy, Geoffrey Shapiro, Ethan Cerami, William R. Sellers, William C. Hahn, Matthew Meyerson, Nabeel Bardeesy, Andrew D. Cherniack, Brian M. Wolpin. Dana-Farber Cancer Institute, Boston, MA, Dana-Farber Cancer Institute, Boston, MA, Massachusetts General Hospital, Boston, MA, Brigham and Women’s Hospital, Boston, MA, Dana-Farber Cancer Institute, Boston, MA, Dana-Farber Cancer Institute, Boston, MA, Broad Institute of MIT and Harvard, Cambridge, MA, Massachusetts General Hospital, Boston, MA

5:45 PM – 5:50 PM
– Discussion

5:50 PM – 6:00 PM
– Closing RemarksGregory J. Riely. Memorial Sloan Kettering Cancer Center, New York, NY

 

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A Nonlinear Methodology to Explain Complexity of the Genome and Bioinformatic Information

Reporter: Stephen J. Williams, Ph.D.

Multifractal bioinformatics: A proposal to the nonlinear interpretation of genome

The following is an open access article by Pedro Moreno on a methodology to analyze genetic information across species and in particular, the evolutionary trends of complex genomes, by a nonlinear analytic approach utilizing fractal geometry, coined “Nonlinear Bioinformatics”.  This fractal approach stems from the complex nature of higher eukaryotic genomes including mosaicism, multiple interdispersed  genomic elements such as intronic regions, noncoding regions, and also mobile elements such as transposable elements.  Although seemingly random, there exists a repetitive nature of these elements. Such complexity of DNA regulation, structure and genomic variation is felt best understood by developing algorithms based on fractal analysis, which can best model the regionalized and repetitive variability and structure within complex genomes by elucidating the individual components which contributes to an overall complex structure rather than using a “linear” or “reductionist” approach looking at individual coding regions, which does not take into consideration the aforementioned factors leading to genetic complexity and diversity.

Indeed, many other attempts to describe the complexities of DNA as a fractal geometric pattern have been described.  In a paper by Carlo Cattani “Fractals and Hidden Symmetries in DNA“, Carlo uses fractal analysis to construct a simple geometric pattern of the influenza A virus by modeling the primary sequence of this viral DNA, namely the bases A,G,C, and T. The main conclusions that

fractal shapes and symmetries in DNA sequences and DNA walks have been shown and compared with random and deterministic complex series. DNA sequences are structured in such a way that there exists some fractal behavior which can be observed both on the correlation matrix and on the DNA walks. Wavelet analysis confirms by a symmetrical clustering of wavelet coefficients the existence of scale symmetries.

suggested that, at least, the viral influenza genome structure could be analyzed into its basic components by fractal geometry.
This approach has been used to model the complex nature of cancer as discussed in a 2011 Seminars in Oncology paper
Abstract: Cancer is a highly complex disease due to the disruption of tissue architecture. Thus, tissues, and not individual cells, are the proper level of observation for the study of carcinogenesis. This paradigm shift from a reductionist approach to a systems biology approach is long overdue. Indeed, cell phenotypes are emergent modes arising through collective non-linear interactions among different cellular and microenvironmental components, generally described by “phase space diagrams”, where stable states (attractors) are embedded into a landscape model. Within this framework, cell states and cell transitions are generally conceived as mainly specified by gene-regulatory networks. However, the system s dynamics is not reducible to the integrated functioning of the genome-proteome network alone; the epithelia-stroma interacting system must be taken into consideration in order to give a more comprehensive picture. Given that cell shape represents the spatial geometric configuration acquired as a result of the integrated set of cellular and environmental cues, we posit that fractal-shape parameters represent “omics descriptors of the epithelium-stroma system. Within this framework, function appears to follow form, and not the other way around.

As authors conclude

” Transitions from one phenotype to another are reminiscent of phase transitions observed in physical systems. The description of such transitions could be obtained by a set of morphological, quantitative parameters, like fractal measures. These parameters provide reliable information about system complexity. “

Gene expression also displays a fractal nature. In a Frontiers in Physiology paper by Mahboobeh Ghorbani, Edmond A. Jonckheere and Paul Bogdan* “Gene Expression Is Not Random: Scaling, Long-Range Cross-Dependence, and Fractal Characteristics of Gene Regulatory Networks“,

the authors describe that gene expression networks display time series display fractal and long-range dependence characteristics.

Abstract: Gene expression is a vital process through which cells react to the environment and express functional behavior. Understanding the dynamics of gene expression could prove crucial in unraveling the physical complexities involved in this process. Specifically, understanding the coherent complex structure of transcriptional dynamics is the goal of numerous computational studies aiming to study and finally control cellular processes. Here, we report the scaling properties of gene expression time series in Escherichia coliand Saccharomyces cerevisiae. Unlike previous studies, which report the fractal and long-range dependency of DNA structure, we investigate the individual gene expression dynamics as well as the cross-dependency between them in the context of gene regulatory network. Our results demonstrate that the gene expression time series display fractal and long-range dependence characteristics. In addition, the dynamics between genes and linked transcription factors in gene regulatory networks are also fractal and long-range cross-correlated. The cross-correlation exponents in gene regulatory networks are not unique. The distribution of the cross-correlation exponents of gene regulatory networks for several types of cells can be interpreted as a measure of the complexity of their functional behavior.

 

Given that multitude of complex biomolecular networks and biomolecules can be described by fractal patterns, the development of bioinformatic algorithms  would enhance our understanding of the interdependence and cross funcitonality of these mutiple biological networks, particularly in disease and drug resistance.  The article below by Pedro Moreno describes the development of such bioinformatic algorithms.

Pedro A. Moreno
Escuela de Ingeniería de Sistemas y Computación, Facultad de Ingeniería, Universidad del Valle, Cali, Colombia
E-mail: pedro.moreno@correounivalle.edu.co

Eje temático: Ingeniería de sistemas / System engineering
Recibido: 19 de septiembre de 2012
Aceptado: 16 de diciembre de 2013


 

 


Abstract

The first draft of the human genome (HG) sequence was published in 2001 by two competing consortia. Since then, several structural and functional characteristics for the HG organization have been revealed. Today, more than 2.000 HG have been sequenced and these findings are impacting strongly on the academy and public health. Despite all this, a major bottleneck, called the genome interpretation persists. That is, the lack of a theory that explains the complex puzzles of coding and non-coding features that compose the HG as a whole. Ten years after the HG sequenced, two recent studies, discussed in the multifractal formalism allow proposing a nonlinear theory that helps interpret the structural and functional variation of the genetic information of the genomes. The present review article discusses this new approach, called: “Multifractal bioinformatics”.

Keywords: Omics sciences, bioinformatics, human genome, multifractal analysis.


1. Introduction

Omic Sciences and Bioinformatics

In order to study the genomes, their life properties and the pathological consequences of impairment, the Human Genome Project (HGP) was created in 1990. Since then, about 500 Gpb (EMBL) represented in thousands of prokaryotic genomes and tens of different eukaryotic genomes have been sequenced (NCBI, 1000 Genomes, ENCODE). Today, Genomics is defined as the set of sciences and technologies dedicated to the comprehensive study of the structure, function and origin of genomes. Several types of genomic have arisen as a result of the expansion and implementation of genomics to the study of the Central Dogma of Molecular Biology (CDMB), Figure 1 (above). The catalog of different types of genomics uses the Latin suffix “-omic” meaning “set of” to mean the new massive approaches of the new omics sciences (Moreno et al, 2009). Given the large amount of genomic information available in the databases and the urgency of its actual interpretation, the balance has begun to lean heavily toward the requirements of bioinformatics infrastructure research laboratories Figure 1 (below).

The bioinformatics or Computational Biology is defined as the application of computer and information technology to the analysis of biological data (Mount, 2004). An interdisciplinary science that requires the use of computing, applied mathematics, statistics, computer science, artificial intelligence, biophysical information, biochemistry, genetics, and molecular biology. Bioinformatics was born from the need to understand the sequences of nucleotide or amino acid symbols that make up DNA and proteins, respectively. These analyzes are made possible by the development of powerful algorithms that predict and reveal an infinity of structural and functional features in genomic sequences, as gene location, discovery of homologies between macromolecules databases (Blast), algorithms for phylogenetic analysis, for the regulatory analysis or the prediction of protein folding, among others. This great development has created a multiplicity of approaches giving rise to new types of Bioinformatics, such as Multifractal Bioinformatics (MFB) that is proposed here.

1.1 Multifractal Bioinformatics and Theoretical Background

MFB is a proposal to analyze information content in genomes and their life properties in a non-linear way. This is part of a specialized sub-discipline called “nonlinear Bioinformatics”, which uses a number of related techniques for the study of nonlinearity (fractal geometry, Hurts exponents, power laws, wavelets, among others.) and applied to the study of biological problems (https://pharmaceuticalintelligence.com/tag/fractal-geometry/). For its application, we must take into account a detailed knowledge of the structure of the genome to be analyzed and an appropriate knowledge of the multifractal analysis.

1.2 From the Worm Genome toward Human Genome

To explore a complex genome such as the HG it is relevant to implement multifractal analysis (MFA) in a simpler genome in order to show its practical utility. For example, the genome of the small nematode Caenorhabditis elegans is an excellent model to learn many extrapolated lessons of complex organisms. Thus, if the MFA explains some of the structural properties in that genome it is expected that this same analysis reveals some similar properties in the HG.

The C. elegans nuclear genome is composed of about 100 Mbp, with six chromosomes distributed into five autosomes and one sex chromosome. The molecular structure of the genome is particularly homogeneous along with the chromosome sequences, due to the presence of several regular features, including large contents of genes and introns of similar sizes. The C. elegans genome has also a regional organization of the chromosomes, mainly because the majority of the repeated sequences are located in the chromosome arms, Figure 2 (left) (C. elegans Sequencing Consortium, 1998). Given these regular and irregular features, the MFA could be an appropriate approach to analyze such distributions.

Meanwhile, the HG sequencing revealed a surprising mosaicism in coding (genes) and noncoding (repetitive DNA) sequences, Figure 2 (right) (Venter et al., 2001). This structure of 6 Gbp is divided into 23 pairs of chromosomes (diploid cells) and these highly regionalized sequences introduce complex patterns of regularity and irregularity to understand the gene structure, the composition of sequences of repetitive DNA and its role in the study and application of life sciences. The coding regions of the genome are estimated at ~25,000 genes which constitute 1.4% of GH. These genes are involved in a giant sea of various types of non-coding sequences which compose 98.6% of HG (misnamed popularly as “junk DNA”). The non-coding regions are characterized by many types of repeated DNA sequences, where 10.6% consists of Alu sequences, a type of SINE (short and dispersed repeated elements) sequence and preferentially located towards the genes. LINES, MIR, MER, LTR, DNA transposons and introns are another type of non-coding sequences which form about 86% of the genome. Some of these sequences overlap with each other; as with CpG islands, which complicates the analysis of genomic landscape. This standard genomic landscape was recently clarified, the last studies show that 80.4% of HG is functional due to the discovery of more than five million “switches” that operate and regulate gene activity, re-evaluating the concept of “junk DNA”. (The ENCODE Project Consortium, 2012).

Given that all these genomic variations both in worm and human produce regionalized genomic landscapes it is proposed that Fractal Geometry (FG) would allow measuring how the genetic information content is fragmented. In this paper the methodology and the nonlinear descriptive models for each of these genomes will be reviewed.

1.3 The MFA and its Application to Genome Studies

Most problems in physics are implicitly non-linear in nature, generating phenomena such as chaos theory, a science that deals with certain types of (non-linear) but very sensitive dynamic systems to initial conditions, nonetheless of deterministic rigor, that is that their behavior can be completely determined by knowing initial conditions (Peitgen et al, 1992). In turn, the FG is an appropriate tool to study the chaotic dynamic systems (CDS). In other words, the FG and chaos are closely related because the space region toward which a chaotic orbit tends asymptotically has a fractal structure (strange attractors). Therefore, the FG allows studying the framework on which CDS are defined (Moon, 1992). And this is how it is expected for the genome structure and function to be organized.

The MFA is an extension of the FG and it is related to (Shannon) information theory, disciplines that have been very useful to study the information content over a sequence of symbols. Initially, Mandelbrot established the FG in the 80’s, as a geometry capable of measuring the irregularity of nature by calculating the fractal dimension (D), an exponent derived from a power law (Mandelbrot, 1982). The value of the D gives us a measure of the level of fragmentation or the information content for a complex phenomenon. That is because the D measures the scaling degree that the fragmented self-similarity of the system has. Thus, the FG looks for self-similar properties in structures and processes at different scales of resolution and these self-similarities are organized following scaling or power laws.

Sometimes, an exponent is not sufficient to characterize a complex phenomenon; so more exponents are required. The multifractal formalism allows this, and applies when many subgroups of fractals with different scalar properties with a large number of exponents or fractal dimensions coexist simultaneously. As a result, when a spectrum of multifractal singularity measurement is generated, the scaling behavior of the frequency of symbols of a sequence can be quantified (Vélez et al, 2010).

The MFA has been implemented to study the spatial heterogeneity of theoretical and experimental fractal patterns in different disciplines. In post-genomics times, the MFA was used to study multiple biological problems (Vélez et al, 2010). Nonetheless, very little attention has been given to the use of MFA to characterize the content of the structural genetic information of the genomes obtained from the images of the Chaos Representation Game (CRG). First studies at this level were made recently to the analysis of the C. elegans genome (Vélez et al, 2010) and human genomes (Moreno et al, 2011). The MFA methodology applied for the study of these genomes will be developed below.

2. Methodology

The Multifractal Formalism from the CGR

2.1 Data Acquisition and Molecular Parameters

Databases for the C. elegans and the 36.2 Hs_ refseq HG version were downloaded from the NCBI FTP server. Then, several strategies were designed to fragment the genomic DNA sequences of different length ranges. For example, the C. elegans genome was divided into 18 fragments, Figure 2 (left) and the human genome in 9,379 fragments. According to their annotation systems, the contents of molecular parameters of coding sequences (genes, exons and introns), noncoding sequences (repetitive DNA, Alu, LINES, MIR, MER, LTR, promoters, etc.) and coding/ non-coding DNA (TTAGGC, AAAAT, AAATT, TTTTC, TTTTT, CpG islands, etc.) are counted for each sequence.

2.2 Construction of the CGR 2.3 Fractal Measurement by the Box Counting Method

Subsequently, the CGR, a recursive algorithm (Jeffrey, 1990; Restrepo et al, 2009) is applied to each selected DNA sequence, Figure 3 (above, left) and from which an image is obtained, which is quantified by the box-counting algorithm. For example, in Figure 3 (above, left) a CGR image for a human DNA sequence of 80,000 bp in length is shown. Here, dark regions represent sub-quadrants with a high number of points (or nucleotides). Clear regions, sections with a low number of points. The calculation for the D for the Koch curve by the box-counting method is illustrated by a progression of changes in the grid size, and its Cartesian graph, Table 1

The CGR image for a given DNA sequence is quantified by a standard fractal analysis. A fractal is a fragmented geometric figure whose parts are an approximated copy at full scale, that is, the figure has self-similarity. The D is basically a scaling rule that the figure obeys. Generally, a power law is given by the following expression:

Where N(E) is the number of parts required for covering the figure when a scaling factor E is applied. The power law permits to calculate the fractal dimension as:

The D obtained by the box-counting algorithm covers the figure with disjoint boxes ɛ = 1/E and counts the number of boxes required. Figure 4 (above, left) shows the multifractal measure at momentum q=1.

2.4 Multifractal Measurement

When generalizing the box-counting algorithm for the multifractal case and according to the method of moments q, we obtain the equation (3) (Gutiérrez et al, 1998; Yu et al, 2001):

Where the Mi number of points falling in the i-th grid is determined and related to the total number Mand ɛ to box size. Thus, the MFA is used when multiple scaling rules are applied. Figure 4 (above, right) shows the calculation of the multifractal measures at different momentum q (partition function). Here, linear regressions must have a coefficient of determination equal or close to 1. From each linear regression D are obtained, which generate an spectrum of generalized fractal dimensions Dfor all q integers, Figure 4 (below, left). So, the multifractal spectrum is obtained as the limit:

The variation of the q integer allows emphasizing different regions and discriminating their fractal a high Dq is synonymous of the structure’s richness and the properties of these regions. Negative values emphasize the scarce regions; a high Dindicates a lot of structure and properties in these regions. In real world applications, the limit Dqreadily approximated from the data using a linear fitting: the transformation of the equation (3) yields:

Which shows that ln In(Mi )= for set q is a linear function in the ln(ɛ), Dq can therefore be evaluated as q the slope of a fixed relationship between In(Mi )= and (q-1) ln(ɛ). The methodologies and approaches for the method of box-counting and MFA are detailed in Moreno et al, 2000, Yu et al, 2001; Moreno, 2005. For a rigorous mathematical development of MFA from images consult Multifractal system, wikipedia.

2.5 Measurement of Information Content

Subsequently, from the spectrum of generalized dimensions Dq, the degree of multifractality ΔDq(MD) is calculated as the difference between the maximum and minimum values of : ΔD qq Dqmax – Dqmin (Ivanov et al, 1999). When qmaxqmin ΔDis high, the multifractal spectrum is rich in information and highly aperiodic, when ΔDq is small, the resulting dimension spectrum is poor in information and highly periodic. It is expected then, that the aperiodicity in the genome would be related to highly polymorphic genomic aperiodic structures and those periodic regions with highly repetitive and not very polymorphic genomic structures. The correlation exponent t(q) = (– 1)DqFigure 4 (below, right ) can also be obtained from the multifractal dimension Dq. The generalized dimension also provides significant specific information. D(q = 0) is equal to the Capacity dimension, which in this analysis is the size of the “box count”. D(q = 1) is equal to the Information dimension and D(q = 2) to the Correlation dimension. Based on these multifractal parameters, many of the structural genomic properties can be quantified, related, and interpreted.

2.6 Multifractal Parameters and Statistical and Discrimination Analyses

Once the multifractal parameters are calculated (D= (-20, 20), ΔDq, πq, etc.), correlations with the molecular parameters are sought. These relations are established by plotting the number of genome molecular parameters versus MD by discriminant analysis with Cartesian graphs in 2-D, Figure 5 (below, left) and 3-D and combining multifractal and molecular parameters. Finally, simple linear regression analysis, multivariate analysis, and analyses by ranges and clusterings are made to establish statistical significance.

3 Results and Discussion

3.1 Non-linear Descriptive Model for the C. elegans Genome

When analyzing the C. elegans genome with the multifractal formalism it revealed what symmetry and asymmetry on the genome nucleotide composition suggested. Thus, the multifractal scaling of the C. elegans genome is of interest because it indicates that the molecular structure of the chromosome may be organized as a system operating far from equilibrium following nonlinear laws (Ivanov et al, 1999; Burgos and Moreno-Tovar, 1996). This can be discussed from two points of view:

1) When comparing C. elegans chromosomes with each other, the X chromosome showed the lowest multifractality, Figure 5 (above). This means that the X chromosome is operating close to equilibrium, which results in an increased genetic instability. Thus, the instability of the X could selectively contribute to the molecular mechanism that determines sex (XX or X0) during meiosis. Thus, the X chromosome would be operating closer to equilibrium in order to maintain their particular sexual dimorphism.

2) When comparing different chromosome regions of the C. elegans genome, changes in multifractality were found in relation to the regional organization (at the center and arms) exhibited by the chromosomes, Figure 5 (below, left). These behaviors are associated with changes in the content of repetitive DNA, Figure 5 (below, right). The results indicated that the chromosome arms are even more complex than previously anticipated. Thus, TTAGGC telomere sequences would be operating far from equilibrium to protect the genetic information encoded by the entire chromosome.

All these biological arguments may explain why C. elegans genome is organized in a nonlinear way. These findings provide insight to quantify and understand the organization of the non-linear structure of the C. elegans genome, which may be extended to other genomes, including the HG (Vélez et al, 2010).

3.2 Nonlinear Descriptive Model for the Human Genome

Once the multifractal approach was validated in C. elegans genome, HG was analyzed exhaustively. This allowed us to propose a nonlinear model for the HG structure which will be discussed under three points of view.

1) It was found that the HG high multifractality depends strongly on the contents of Alu sequences and to a lesser extent on the content of CpG islands. These contents would be located primarily in highly aperiodic regions, thus taking the chromosome far from equilibrium and giving to it greater genetic stability, protection and attraction of mutations, Figure 6 (A-C). Thus, hundreds of regions in the HG may have high genetic stability and the most important genetic information of the HG, the genes, would be safeguarded from environmental fluctuations. Other repeated elements (LINES, MIR, MER, LTRs) showed no significant relationship,

Figure 6 (D). Consequently, the human multifractal map developed in Moreno et al, 2011 constitutes a good tool to identify those regions rich in genetic information and genomic stability. 2) The multifractal context seems to be a significant requirement for the structural and functional organization of thousands of genes and gene families. Thus, a high multifractal context (aperiodic) appears to be a “genomic attractor” for many genes (KOGs, KEEGs), Figure 6 (E) and some gene families, Figure 6 (F) are involved in genetic and deterministic processes, in order to maintain a deterministic regulation control in the genome, although most of HG sequences may be subject to a complex epigenetic control.

3) The classification of human chromosomes and chromosome regions analysis may have some medical implications (Moreno et al, 2002; Moreno et al, 2009). This means that the structure of low nonlinearity exhibited by some chromosomes (or chromosome regions) involve an environmental predisposition, as potential targets to undergo structural or numerical chromosomal alterations in Figure 6 (G). Additionally, sex chromosomes should have low multifractality to maintain sexual dimorphism and probably the X chromosome inactivation.

All these fractals and biological arguments could explain why Alu elements are shaping the HG in a nonlinearly manner (Moreno et al, 2011). Finally, the multifractal modeling of the HG serves as theoretical framework to examine new discoveries made by the ENCODE project and new approaches about human epigenomes. That is, the non-linear organization of HG might help to explain why it is expected that most of the GH is functional.

4. Conclusions

All these results show that the multifractal formalism is appropriate to quantify and evaluate genetic information contents in genomes and to relate it with the known molecular anatomy of the genome and some of the expected properties. Thus, the MFB allows interpreting in a logic manner the structural nature and variation of the genome.

The MFB allows understanding why a number of chromosomal diseases are likely to occur in the genome, thus opening a new perspective toward personalized medicine to study and interpret the GH and its diseases.

The entire genome contains nonlinear information organizing it and supposedly making it function, concluding that virtually 100% of HG is functional. Bioinformatics in general, is enriched with a novel approach (MFB) making it possible to quantify the genetic information content of any DNA sequence and their practical applications to different disciplines in biology, medicine and agriculture. This novel breakthrough in computational genomic analysis and diseases contributes to define Biology as a “hard” science.

MFB opens a door to develop a research program towards the establishment of an integrative discipline that contributes to “break” the code of human life. (http://pharmaceuticalintelligence. com/page/3/).

5. Acknowledgements

Thanks to the directives of the EISC, the Universidad del Valle and the School of Engineering for offering an academic, scientific and administrative space for conducting this research. Likewise, thanks to co authors (professors and students) who participated in the implementation of excerpts from some of the works cited here. Finally, thanks to Colciencias by the biotechnology project grant # 1103-12-16765.


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