転写現象の方程式

Abstract

The ratio of some gene-transcripts in the thymus of mouse had a maximum with aging. A second order differential equation, x + 2 ak+ bx = bD , could be used to analyze such measurements. This equation resembled one used in a damped harmonic oscillator, then, it was supposed that the quantities of transcripts increased and decreased repeatedly in time-course under the influence of some factors. The general solution of abovementioned differential equation took the form x = Ce^-a1 cos( √<b-a^2>t + β)+ D in the case of b —a ＾2＞0 or x - Ae^-(a+√<a^e-b>)t + B e^-(a-√<a^2-b>)t + D in b — a^ 2 ＜ 0. The ratios of interleukin2(IL2),4(IL4), T cell receptor fl-chain(TCRβ), immunoglobulin E(IgE) and M(IgM)-transcripts were measured in the thymus of mice by realtime PCR. LogIL4/TCRβ and logIgE/IgM increased rapidly from birth to about 50 days and then decreased, namely had maximums. Otherwise, logIL2/ TCRβ increased slightly after birth and remained constantly. The calculated values by the equation using adequate parameters were in fair agreement with those measured