On the holistic approach in cellular and cancer biology: Nonlinearity, complexity, and quasi-determinism of the dynamic cellular network

Abstract

A keystone of the molecular reductionist approach to cellular biology is a specific deductive strategy relating genotype to phenotype—two distinct categories. This relationship is based on the assumption that the intermediary cellular network of actively transcribed genes and their regulatory elements is deterministic (i.e., a link between expression of a gene and a phenotypic trait can always be identified, and evolution of the network in time is predetermined). However, experimental data suggest that the relationship between genotype and phenotype is nonbijective (i.e., a gene can contribute to the emergence of more than just one phenotypic trait or a phenotypic trait can be determined by expression of several genes). This implies nonlinearity (i.e., lack of the proportional relationship between input and the outcome), complexity (i.e. emergence of the hierarchical network of multiple cross‐interacting elements that is sensitive to initial conditions, possesses multiple equilibria, organizes spontaneously into different morphological patterns, and is controled in dispersed rather than centralized manner), and quasi‐determinism (i.e., coexistence of deterministic and nondeterministic events) of the network. Nonlinearity within the space of the cellular molecular events underlies the existence of a fractal structure within a number of metabolic processes, and patterns of tissue growth, which is measured experimentally as a fractal dimension. Because of its complexity, the same phenotype can be associated with a number of alternative sequences of cellular events. Moreover, the primary cause initiating phenotypic evolution of cells such as malignant transformation can be favored probabilistically, but not identified unequivocally. Thermodynamic fluctuations of energy rather than gene mutations, the material traits of the fluctuations alter both the molecular and informational structure of the network. Then, the interplay between deterministic chaos, complexity, self‐organization, and natural selection drives formation of malignant phenotype. This concept offers a novel perspective for investigation of tumorigenesis without invalidating current molecular findings. The essay integrates the ideas of the sciences of complexity in a biological context. J. Surg. Oncol. 1998;68:70–78. © 1998 Wiley‐Liss, Inc.

On the Gompertzian growth in the fractal space–time

“…The possibility of mapping the experimental Gompertz curve, characterizing the Brown-Pearce tumor growth, onto the fractal power-law scaling function confirms that Gompertzian growth is a self-similar and allometric process (Bajzer, 1999) of a holistic nature (Waliszewski et al, 1998;Molski and Konarski, 2003). It means that all spatially separated sublements (cells) of the whole system (tumor) are interrelated via long-range (slowly decaying) interactions, which seem to be an essential ingredient of the self-organized Gompertzian growth (Mombach et al, 2002).…”

Spectral Markers in Preneoplastic Intestinal Mucosa: An Accurate Predictor of Tumor Risk in the MIN Mouse

“…This variable is well established in the fields of pathology and cancer biology (36). Indeed, it has been suggested that altered fractal dimension is one of the earliest events in colon carcinogenesis (37). Whereas fractal dimension assesses tissue organization at the cellular to the large organelle level, spectral slope is affected by much smaller structures (small organelles to macromolecular complexes).…”

The Effect of Spatially Inhomogeneous Electromagnetic Field and Local Inductive Hyperthermia on Nonlinear Dynamics of the Growth for Transplanted Animal Tumors

“…They tend to be quasi (almost but not quite)-periodic, the periodicities are a complex of many periods, and they can swing between different quasi-periodic states. But they are not at all random (Waliszewski et al, 1998;Marino et al, 2000Marino et al, ,2009. Living systems are organized such that they manifest operational features ascribed to hierarchical and heterarchical structures from quantum to organism levels (Dirks, 2008).…”