Complex Systems Analysis of Cell Cycling Models in Carcinogenesis

Carcinogenesis is a complex process that involves dynamically inter-connected modular subnetworks that evolve under the influence of micro-environmental, as well as, in many cases, cancer therapy-induced perturbations, in non-random, pseudo-Markov chain processes. An appropriate n-stage model of carcinogenesis involves therefore n-valued Logic treatments of such processes, nonlinear dynamic transformations of complex functional genomes and cell interactomes. Lukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous, Boolean or "fuzzy", logic models of genetic activities in vivo. Such models are then applied to cell transformations during carcinogenesis based on very extensive genomic transcription and translation data from the CGAP databases supported by NCI. Inter-related signaling pathways include very large numbers of different biomolecules, such as proteins, in the intercellular, membrane, cytosolic, nuclear and nucleolar compartments. One such family of pathways contains the cell cyclins. Cyclins are proteins that link several critical pro-apoptotic and other cell cycling/division components, including the tumor suppressor gene TP53 and its product, the ThomsenFriedenreich antigen (T antigen), Rb, mdm2, c-Myc, p21, p27, Bax, Bad and Bcl-2, which all play major roles in carcinogenesis of many cancers. A categorical and Lukasiewicz-Topos (LT) framework for Lukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional genomes and cell interactomes. An algebraic formulation of varying 'next-state functions' is extended to a Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logics subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogeness. Specific models for different types of cancer are then derived from representations of the dynamic state-space of LT non-random, pseudo-Markov chain process, network models in terms of cDNA and proteomic, high throughput analyses by ultra-sensitive techniques. This novel theoretical analysis is based on extensive CGAP genomic data for human tumors , as well as recently published studies of cyclin signaling, with special emphasis placed on the roles of cyclins D1 and E. Several such specific models suggest novel clinical trials and rational therapies of cancer through re-establishment of cell cycling inhibition in stage III cancers.