Effects Of Time Delays And Noise On The Biological Signaling Pathways

The research of diverse biological networks is very important in biology and is a central issue in biological information and biological science.Thus it is very important to study the different signaling pathways that make up the biological network.More and more experimental evidences show that the signal transmission process has the characteristics of nonlinear interaction,time delays and noise.These characteristics are ubiquitous in biological systems and play important roles in various processes.Therefore,the information transmission and the effects of random fluctuations in the biological signaling pathways is one of the research topics in the present research of life science.In this paper,by using nonlinear tine delays theory,stochastic theory and numerical simulation techniques,the time delay effects in bone remodeling system with multiple myeloma,and the noise and information transmission in signal module in biological network are investigated deeply respectively.The main results are as follows:For the mathematical model of bone remodeling with multiple myeloma,the kinetic behaviors of osteoblasts,osteoclasts and myeloma cells were studied in the system.By virtue of the numerical simulation technique,for two representative systemic parameters:osteoclast-derived paracrine signaling of tumor and tumor-derived paracrine signaling of osteoclast,the processes of normal bone remodeling,bone remodeling with multiple myeloma and therapeutic scenarios,the evolution of cell populations over time are simulated and analyzed respectively.It is found that for the osteoclast-derived paracrine signaling,with the change of time delays,the system exhibits diversified properties.In such a case,the growth of tumor cells slows down and the severity of bone destruction is reduced due to the variation of time delays.Moreover,there is a vicious cycle between osteoclasts activity and tumor activity in such a way that the tumor development enhances bone resorption of osteoclasts,which in turn promotes the growth of tumor,leading to further bone destruction and severe bone disease.For tumor-derived paracrine signaling,the kinetic properties of the system are different from those of the former case.In this case,there is an optimal coupling between the tumor-derived paracrine signaling of osteoclasts and time delays during the progression of bone diseases,which suppresses the tumor growth and the regression of bone disease.Our model can not only be used to analyze many qualitative properties of time delays and systemic parameters,but also might provide guidelines for probing the mechanism of bone destruction and exploring more effective therapeutic approaches for multiple myeloma induced bone disease.Based on the information transmission models of signal module,the effects of noise and information transmission in the signaling cascade are studied by introducing the four feedback mechanisms:positive feedback,negative feedback,self-activation and self-inhibition.The mathematical expressions of the Fano factor,mutual information and signal-to-noise ratio of the signal module around the steady states are derived theoretically by virtue of the linear noise approximation.The characteristics of noise and information transmission in this system under different feedback mechanisms are deeply analyzed by numerical simulation technique.It is found that the signaling cascade exhibits different responses to the four feedback mechanisms,which depend on the relationships between degradation rates of components.When the degradation rate of the input component is slower than that of the intermediate component,compared with negative feedback and self-inhibition,there is more mutual information between input and output components in the case of positive feedback and self-activation.In such a case,high signal-noise ratio of the system is obtained in the processes of information transmission.Moreover,when the degradation rate of the input component is faster than that of the intermediate component,the significant relative fluctuations in output component are obtained in the case of positive feedback and self-activation.However,the small fluctuations are achieved in the case of negative feedback and self-inhibition.These results not only help to understand how organisms adapt to the changing environments by using the signaling pathways of different feedback mechanisms,but also play guiding roles in the design of artificial networks and artificial devices in biology.