QUANTUM INTERACTOMICS AND CANCER MECHANISMS I.C. Baianu University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

Email address: ibaianu@uiuc.edu

*Abstract Single cell interactomics in simpler organisms, as well as somatic cell interactomics in multicellular organisms, involve biomolecular interactions in complex signalling pathways that were recently represented in modular terms by quantum automata with ‘reversible behavior’ representing normal cell cycling and division. Other implications of such quantum automata, modular modeling of signaling pathways and cell differentiation during development are in the fields of neural plasticity and brain development leading to quantum-weave dynamic patterns and specific molecular processes underlying extensive memory, learning, anticipation mechanisms and the emergence of human consciousness during the early brain development in children. Cell interactomics is here represented for the first time as a mixture of ‘classical’ states that determine molecular dynamics subject to Boltzmann statistics and ‘steady-state’, metabolic (multi-stable) manifolds, together with ‘configuration’ spaces of metastable quantum states emerging from complex quantum dynamics of interacting networks of biomolecules, such as proteins and nucleic acids that are now collectively defined as quantum interactomics. On the other hand, the time dependent evolution over several generations of cancer cells --that are generally known to undergo frequent and extensive genetic mutations and, indeed, suffer genomic transformations at the chromosome level (such as extensive chromosomal aberrations found in many colon cancers)-- cannot be correctly represented in the ‘standard’ terms of quantum automaton modules, as the normal somatic cells can. This significant difference at the cancer cell genomic level is therefore reflected in major changes in cancer cell interactomics often from one cancer cell ‘cycle’ to the next, and thus it requires substantial changes in the modeling strategies, mathematical tools and experimental

designs aimed at understanding cancer mechanisms. Novel solutions to this important problem in carcinogenesis are proposed and experimental validation procedures are suggested: http://www.ag.uiuc.edu/fs401/ComplexSystemsBiology.htm . From a medical research and clinical standpoint, this approach has important consequences for addressing and preventing the development of cancer resistance to medical therapy in ongoing clinical trials involving stage III cancer patients, as well as improving the designs of future clinical trials for cancer treatments. *Communicated to: The Institute of Genomic Biology (currently under construction at UIUC, at 905 S. Goodwin Avenue, Urbana,IL.61801,USA). KEYWORDS: Cancer cell interactomics; Somatic cell genomics and Proteomics; current limitations of modular models of carcinogenesis; Complex quantum dynamics; Quantum Automata models and Quantum Interactomics; quantum-weave dynamic patterns underlying human consciousness; specific molecular processes underlying extensive memory, learning, anticipation mechanisms and human consciousness; emergence of human consciousness during the early brain development in children; Cancer cell ‘cycling’; interacting networks of proteins and nucleic acids; genetic mutations and chromosomal aberrations in cancers, such as colon cancer; development of cancer resistance to therapy; ongoing clinical trials involving stage III cancer patients’ possible improvements of the designs for future clinical trials and cancer treatments.

1. Introduction

1.1. The Concepts of Quantum Automata and Quantum Dynamics in terms of The Theory of Categories, Functors and Natural Transformations Quantum Computation and Quantum Automata were introduced in 1971 in a paper published in the Bulletin of Mathematical Biophysics, 33:339-354 (Baianu, 1971a). Categorical computations, both algebraic and topological, were also introduced the same year based on adjoint functor pairs in the theory of categories, functors and natural transformations (Baianu, 1971b). The notions of topological semigroup, quantum automaton, or computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983, 2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens (Baianu,1987). 1.1. Cell Cycle regulation

Fig. 1: Gene database of Cyclin-D1, from the PBD website:

http://www.dsi.univ-paris5.fr/genatlas/fiche.php?symbol=CCND1

Fig. 2. Cdk2/Cyclin A In Complex With An 11-Residue Recruitment Peptide From Retinoblastoma-Associated Protein X-ray Diffraction.

Fig. 3. The dual role of D-type cyclins and p27 in proliferation and differentiation. Cells employ CDK4/6– cyclin D complexes to flexibly titrate p27 from the complexes containing CDK2, and thereby they control their proliferation. However, mutual dependency between cyclin D and p27 serves also some yet unidentified function in differentiation-related processes.

Fig. 5. Regulation of p27 Phosphorylation during Cell Cycling

http://cgap.nci.nih.gov/Pathways/BioCarta/h_p27Pathway

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email: ibaianu@uiuc.edu