DSolve: Gene production concentration

*To*: mathgroup at smc.vnet.net*Subject*: [mg131708] DSolve: Gene production concentration*From*: jes <jespervng at gmail.com>*Date*: Sun, 22 Sep 2013 02:46:41 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hi i have never used Mathematica, i was wondering if it would be an nice tool to use for a course i am taking. Could someone shown me this would be solved and plotted using Mathematica ? A gene Y with simple regulation is produced at a constant rate Beta1. The production rate suddenly shifts to a different rate Beta2. Calculate and plot the gene product concentration Y(t) Solution: Let us mark the time when the shift occurs as t = 0. Before the shift Y reaches steady state at a level Y(t=0) = Tst = Beta1/a after the shift. dY/dt = Beta2 - a*Y The solution of such an equation is generally Y = C1 + C2 * e^(-at) Where the constants C1 and C2 need to be determined so that Y(t=0) = Beta1/a and Y after a long time reaches its new steady state Beta2/a. This yields the following sum of an exponential and a constant: Y(t) = Beta2/a + (Beta1/a - Beta2/a) e^(-at) Take the derivative with respect to time, dY/dt, and verify that the equation is fulfilled. And plot the gene product concentration Y(t)