Robustness Of Calcium Homeostasis In Human Umbilical Vein Endothelial Cells

Biological robustness is a property that allows a biological system to maintain its structural and functional stability despite internal or(and)external perturbations.It is indicated by research that biological robustness is a universal phenomenon existing in biological systems.From molecular level to system level,biological robustness could be seen everywhere,which mediates energy supply system,circadian rhythm and bacterial chemotaxis,etc.Robustness in biological systems is attained by several principles including system control,fail-safe mechanism,modularity and decoupling.Biological robustness is also closely related to the generation and development of disease.The breakdown of robustness systems may lead to the generation of disease.Furthermore,some disease could also use robustness principles to maintain and develop their states.Insights into inherent properties of robust systems will provide us with a better understanding of complex disease and a guiding principle for therapy design. As a second messenger,intracellular Ca²⁺is of vital importance in maintaining the normal function of endothelial cells.Ca²⁺metabolism in a cell has the function of mass exchange,energy conversion and signal transduction.Three major elements of life activities including mass,energy and information can be integrated in calcium regulating systems in endothelial cells.Ca²⁺is also an important index to reflect the physiological state of an endothelial cell.Abnormal increases of intracellular calcium concentration are closely related to the injury and death of a cell.So it is helpful for us to understand the dynamic property of calcium regulating systems by exploring its way to maintain its structural and functional stability despite internal or(and)external perturbations in endothelial cells.We detected the calcium concentration in endothelial cells by using a laser-scanning confocal microscope,selected K⁺ and H₂O₂ as external perturbations and recorded the dynamic behavior of calcium systems with perturbations of five different concentrations of K⁺ and H₂O₂.Before further analysis,original data was normalized to assure the comparability of each cell.Then we used the Lyapunov stability theory,phase graphs and a method for judging stability robustness of a system based on Lyapunov stability theory to analyse stability robustness of calcium regulating systems disturbed by K⁺ or H₂O₂.Finally, we discussed the impact of normalization method on data analysis.We got four conclusions as follows:1.Calcium regulating systems in endothelial cells are typical non-linear systems.They have the basic character and typical traits of non-linear systems.2.When disturbed by different intensities of K⁺ or H₂O₂,changing forms of calcium concentration in calcium regulating systems were different.Low intensities of perturbations (5mmol/L K⁺,1μamol/L H₂O₂)had little effect on calcium regulating systems whose stability robustness was strong.Middle intensities of perturbations(7.5mmol/L or 10mmol/LK⁺, 10μmol/L or 30μmol/LH₂O₂)would break calcium equilibrium states of some cells,but calcium states of some cells were still maintained stable.High intensities of perturbations (20mmol/L or 50mmol/LK⁺,50μtmol/L or 100μmol/LH₂O₂)would break calcium equilibrium states of nearly all cells.It indicates that intracellular calcium concentration could only be maintained when disturbed by a certain range of perturbations.So the stability robustness of calcium regulating systems against perturbations in endothelial cells is regional.3.On the one hand,stability robustness of calcium regulating systems in endothelial cells was influenced by the intensity of perturbations.Systems' stability robustness was gradually damaged by increases of intensities.On the other hand,stability robustness of calcium regulating systems in endothelial cells was influenced by states of cells.Stability robustness of different cells may be different when they were disturbed by the same intensity of perturbations.Accordingly,stability robustness of endothelial cells is determined by intensities of perturbations and their own states.4.Normalization method could only be applied to compare cells whose calcium intensities are within a certain range.If calcium intensities were very high or very low and exceed a certain range,the result might be inaccurate when original data was normalized before analysis.