Robustness Of Calcium System In Neuron

Biological robustness is a system property to keep a stability of live-body structure and function as uncertainty factor from external and internal variety disturbs it. Up to now, it is known robustness always arises in whole, organ, cell and molecule, for example, bacterial chemotaxis, cell cycle, intercellular communication, gene mutation, development, gene network, and so on. In the organism, using feedback control, redundancy, modularity and structure stability attains robustness. Stability robustness and character robustness are two important issues in the research, and mathematics model is a method for biological robustness. The knowledge of biological robustness signifies to illness's generation, development and therapy, such as cancer, AIDS and diabetes.Calcium system is the main system that guarantees the survival, growth, development and cell function of neuron. Calcium metabolism has the function of substance exchange, calcium pump is able to converse energy and calcium ion channel plays a key role in information transduction. Three major elements of life activities as mass, energy and information can be integrated in the calcium system in neuron. So it is attracting to find out how is the neuron to maintain its stability of the structure and function with the perturbation of external and internal uncertainty factors. It is important to make knowledge ofthe dynamical property of the calcium system. We detected the calcium concentration in neuron using the laser-scanning confocal microscope, selected glutamate as the external perturbation, recorded the dynamic of the calcium system with the perturbation of five different concentrations of glutamate and using Lyapunov stability theory and phase graph to analysis the stability robustness of calcium system in neuron. We obtained the following two points:1. The calcium concentration with the perturbation of glutamate of various concentrations and its stability robustness are also different. When the glutamate concentration is 5 μmol/l, the calcium concentration can be maintained at a stable equilibrium state, the stability robustness is higher lever. When glutamate concentration increases to 10 μmol/l, calcium concentration in neuron changes in slow calcium oscillation. This oscillation is Lyapunov stability. When glutamate concentration increases to 50 μmol/l, it appeared to spike-like calcium oscillation in neuron, the amplitude of calcium oscillation arises and the frequency of calcium oscillation increased, calcium concentration changes from the stable equilibrium state to limit cycle state and then back to the stable equilibrium state. Although, calcium concentration deviated from normal value at a large range, but it still can return to the initial equilibrium state. Calcium system in neuron keeps robust, and is Lyapunov asymptotic stability. When glutamate concentration increases to 500 μmol/l, calcium oscillations do not appear, and cell apoptosis or necrosis happened, the stability robustness of calcium system in neuron was damaged.2. The stability robustness of calcium system in neuron is not only associated with the concentration of glutamate, but also associated with the initial concentration of calcium. If the initial calcium concentration is higher, the stability robustness of calcium system in neuron will be lower. And if the initial calcium concentration is lower, the stability robustness of calcium system in neuron will be higher. Therefore, to control the glutamate concentration in extracellular environment and keep calcium concentration in neuron at a low level can be used to maintain the stability robustness of neuronal calcium system.