grandR (version 0.2.6)

f.old.equi: Functions to compute the abundance of new or old RNA at time t.

Description

The standard mass action kinetics model of gene expression arises from the differential equation \(df/dt = s - d f(t)\), with s being the constant synthesis rate, d the constant degradation rate and \(f0=f(0)\) (the abundance at time 0).

Usage

f.old.equi(t, s, d)
f.old.nonequi(t, f0, s, d)
f.new(t, s, d)

Value

the RNA abundance at time t

Arguments

t

time in h

s

synthesis date in U/h (arbitrary unit U)

d

degradation rate in 1/h

f0

the abundance at time t=0

Functions

• f.old.equi(): abundance of old RNA assuming steady state (i.e. f0=s/d)

• f.old.nonequi(): abundance of old RNA without assuming steady state

• f.new(): abundance of new RNA (steady state does not matter)

Examples

 d=log(2)/2
 s=10

 f.new(2,s,d)  # Half-life 2, so after 2h the abundance should be half the steady state
 f.old.equi(2,s,d)
 s/d

 t<-seq(0,10,length.out=100)
 plot(t,f.new(t,s,d),type='l',col='blue',ylim=c(0,s/d))
 lines(t,f.old.equi(t,s,d),col='red')
 abline(h=s/d,lty=2)
 abline(v=2,lty=2)
 # so old and new RNA are equal at t=HL (if it is at steady state at t=0)

 plot(t,f.new(t,s,d),type='l',col='blue')
 lines(t,f.old.nonequi(t,f0=15,s,d),col='red')
 abline(h=s/d,lty=2)
 abline(v=2,lty=2)
 # so old and new RNA are not equal at t=HL (if it is not at steady state at t=0)