Organismic Supercategories and Qualitative Dynamics of Systems

The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete results concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived

Nonlinear Models of Neural and Genetic Network Dynamics:\ud \ud Natural Transformations of Łukasiewicz Logic LM-Algebras in a Łukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations \ud

A categorical and Łukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Łukasiewicz Algebraic Logic models of both neural and 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 logical models of both genetic activities and neural networks. An algebraic formulation of variable next-state/transfer functions is extended to a Łukasiewicz Topos with an N-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.\u

Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

A categorical and Łukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Łukasiewicz Algebraic Logic models of both neural and 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 logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis

COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

The ability to simulate a biological organism by employing a computer is related to the ability of the computer to calculate the behavior of such a dynamical system, or the "computability" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, "quantum" computer (Baianu, 1971b) for analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001)

Complex Systems Analysis of Arrested Neural Cell Differentiation during Development and Analogous Cell Cycling Models in Carcinogenesis

A new approach to the modular, complex systems analysis of nonlinear dynamics of arrested neural cell Differentiation--induced cell proliferation during organismic development and the analogous cell cycling network transformations involved in carcinogenesis is proposed. Neural tissue arrested differentiation that induces cell proliferation during perturbed development and Carcinogenesis are complex processes that involve dynamically inter-connected biomolecules in the intercellular, membrane, cytosolic, nuclear and nucleolar compartments. Such 'dynamically inter-connected' biomolecules form numerous inter-related pathways referred to as 'molecular networks'. One such family of signaling 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 Thomsen-Friedenreich antigen (T antigen), Rb, mdm2, c-Myc, p21, p27, Bax, Bad and Bcl-2, which play major roles in various neoplastic transformations of many tissues. The novel theoretical analysis presented here is based on recently published studies of arrested cell differentiation that normally leads to neural system formation during early developmental stages; the perturbed development may involve cyclin signaling and cell cycling responsible for rapidly induced cell proliferation without differentiation into neural cells in such experimental studies; special emphasis in this modular model is placed upon the roles of cyclins D1 and E, and does suggest novel clinical trials as well as rational therapies of cancer through re-establishment of cell cycling inhibition in metastatic cancer cells. Cyclins are proteins that are often over-expressed in cancerous cells (Dobashi et al., 2004). They may also be over-expressed in cells whose differentiation is arrested during the early stages of organismic development, leading to increased cell proliferation instead of differentiation into specialized tissues such as those forming the neural system. Cyclin-dependent kinases (CDK), their respective cyclins, and inhibitors of CDKs (CKIs) were identified as instrumental components of the cell cycle-regulating machinery. In mammalian cells the complexes of cyclins D1, D2, D3, A and E with CDKs are considered motors that drive cells to enter and pass through the “S” phase. Cell cycle regulation is a critical mechanism governing cell division and proliferation, and it is finely regulated by the interaction of cyclins with CDKs and CKIs, among other molecules (Morgan et al., 1995). A categorical and Topos framework for Łukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional genomes and cell interactomes is also proposed. Łukasiewicz 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 logical models of both genetic activities and neural networks. An algebraic formulation of varying 'next-state' functions is extended in a Łukasiewicz-Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. Important aspects of Cell Cycling, the Control of Cell Division,and the Neoplastic Transformation in Carcinogenesis are being considered and subjected to algebraic-logico- relational, and computer-aided investigations. The essential roles of various levels of c-Myc, p27 quasi-complete inhibition/blocking, TP53 and/or p53 inactivation, as well as the perpetual hTERT activation of Telomerase biosynthesis are pointed out as key conditions for Malignant Cell transformations and partial re-differentiation leading to various types of cancer such as lung, breast,skin, prostate and colon. Rational Clinical trials, Individualized Medicine and the potential for optimized Radio-, Chemo-, Gene-, and Immuno- therapies of Cancers are suggested on the basis of integrated complex systems biology modeling of oncogenesis, coupled with extensive genomic/proteomic and interactomic High-throughput/high-sensitivity measurements of identified, sorted cell lines that are being isolated from malignant tumors of patients undergoing clinical trials with adjuvant signaling drug therapies. The implications of the cyclin model for abnormal neural development during early development are being considered in this model that may lead to explanations of subsequent cognitive changes associated with abnormal neural cell differentiation in environmentally-affected embryos. This new model may also be relevant to detecting the onset of senescing neuron transformations in Alzheimer's and related diseases of the human brain in ageing populations at risk

Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems

A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or Łukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms