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

In grandR: Comprehensive Analysis of Nucleotide Conversion Sequencing Data

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)

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

Value

the RNA abundance at time t

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)

grandR documentation built on April 4, 2025, 2:27 a.m.