BIPOLAR LINEAR ALGEBRA AND YINYANG-N-ELEMENT CELLULAR NETWORKS FOR EQUILIBRIUM-BASED BIOSYSTEM SIMULATION AND REGULATION

Bipolar linear algebra (BLA) and YinYang-N-Element bipolar cellular networks (BCNs) are presented for equilibrium-based biological simulation and regulation at the system, molecular, and genetic levels. Bipolar fusion, interaction, oscillation, and quantum entanglement with growing, aging, degenerating, equilibrium, and non-equilibrium properties are mathematically characterized; bipolar dynamic equations with metabolic nourishing and regulating relations are formulated; global and local equilibrium conditions are established and proved. Two families of YinYang-N-Element BCNs are compared and analyzed: one family has predefined nourishing and regulation cycles following the classical YinYang-5-Element protocol in Traditional Chinese Medicine (TCM); another family has random connectivity and link weights. Applicability of the theory is illustrated in equilibrium and non-equilibrium simulation of bio-agent interaction and regulation. The significance of this work is two-fold: (1) BLA provides a unique and unifying mathematical foundation for bipolar fusion, interaction, and oscillation in biophysics and bioeconomics; (2) YinYang-N-Element BCNs provide a unique and unifying architecture for modeling equilibrium and non-equilibrium processes at the system, molecular, and genetic levels.

Experimental testing of a mathematical model relevant to the extrinsic pathway of apoptosis

Apoptosis is a programmed cell death process, whose complexity led researchers to build mathematical models that could help to identify its crucial steps. In previous works, we theoretically analyzed and numerically simulated a model that describes a pathway from an external stimulus to caspase-3 activation. Here, the results of experiments performed on populations of synchronized cells treated with the inducer Apo2L/TRAIL are reported and are compared with model predictions. In particular, we have compared in vitro and in silico results relevant to the time evolutions of caspase-3 and caspase-8 activities, as well as of the dead cells fractions. In addition, the effect of the BAR gene silencing was evaluated. Caspase-3 activation and cell death is faster in silenced than in nonsilenced cells, thus confirming previous simulation results. Interestingly, Apo2L/TRAIL treatment in itself reduces the BAR gene expression. The qualitative agreement between model predictions and cell cultures behavior suggests that the model captures the essential features of the biological process and could be a tool in further studies of caspases activation. In this manuscript, we report the results of in vitro experiments aimed at revealing the dynamics of caspase activation in a cell population. A qualitative agreement between these results and a mathematical model describing a pathway from an external stimulus to caspase-3 activation was obtained, thus showing that the model captures the essential features of the biological process and may be a reliable tool in further studies of caspase activation.