关键词：生物模块；模拟计算；射流；信息网络
摘 要：Central to this investigation are a pair of models for the phosphorelay, one of which is an Ordinary Differential Equations based model, and the other of which is a Chemical Master Equation based model. The ODE based model is used to rigorously demonstrate that a phosphorelay is monotone, and thus converges to some steady state. In turn, the steady state output is elucidated in terms of the parameters that determine the net influx and net efflux at each stage as well as the growth rate. This steady state output function provides an elaboration on a prior hypothesis which suggests that a long phosphorelay provides additional phosphoregulation targets. Specifically, we find that the output of a phosphorelay is proportional to the net influx rate divided by the sum of various products of efflux signals. In the large efflux signal limit, effluxes are effectively multiplied to generate the final output. In this way, the activity of phosphatases which act on multiple stages in the relay are multiplied, allowing the phosphorelay to act as an analog computation device for this specific function. Growth is shown to have an unexpectedly powerful effect on relay output. In the most extreme cases, the phosphorelay output is shown to obey a power law with respect to growth, with an exponent which can be as large as the length of the relay, and which is also mediated by other key architectural variations. Thus, the phosphorelay can be utilized as a device which allows an organism to select behavior by comparing its growth rate to a threshold, where the level and sharpness of this threshold can be controlled by architectural and parametric changes. These results also provide design laws for building phosphorelays which are robust to growth rate variation.