Algebraic Morphology of DNA--RNA Transcription and Regulation

Algebraic Morphology of DNA--RNA Transcription and Regulation, updated 3/21/23, 9:48 PM


Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. In this paper, we describe the algebraic geometry of both TFs and miRNAs thanks to group theory. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group π, we compute the SL(2,C) character variety, where SL(2,C) is simultaneously a \lq space-time’ (a Lorentz group) and a \lq quantum’ (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when π looks like a free group Fr (r=1 to 3) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis G of the variety. A surface with simple singularities (like the well known Cayley cubic) within G is a signature of a potential disease even when G looks like a free group Fr in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA/RNA bases in {A,T/U,G,C}. Several human TFs and miRNAs are investigated in detail thanks to our approach.

About Klee Irwin

Klee Irwin is an author, researcher and entrepreneur who now dedicates the majority of his time to Quantum Gravity Research (QGR), a non-profit research institute that he founded in 2009. The mission of the organization is to discover the geometric first-principles unification of space, time, matter, energy, information, and consciousness.


As the Director of QGR, Klee manages a dedicated team of mathematicians and physicists in developing emergence theory to replace the current disparate and conflicting physics theories. Since 2009, the team has published numerous papers and journal articles analyzing the fundamentals of physics.

Klee is also the founder and owner of Irwin Naturals, an award-winning global natural supplement company providing alternative health and healing products sold in thousands of retailers across the globe including Whole Foods, Vitamin Shoppe, Costco, RiteAid, WalMart, CVS, GNC and many others. Irwin Naturals is a long time supporter of Vitamin Angels, which aims to provide lifesaving vitamins to mothers and children at risk of malnutrition thereby reducing preventable illness, blindness, and death and creating healthier communities.

Outside of his work in physics, Klee is active in supporting students, scientists, educators, and founders in their aim toward discovering solutions to activate positive change in the world.  He has supported and invested in a wide range of people, causes and companies including, Upworthy, Donors Choose, Moon Express, Mayasil, the X PRIZE Foundation, and Singularity University where he is an Associate Founder.

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