fix ID dna/toggle N speciesDNA-ID Kon Koff reactRNA-ID Ktranscription Kconstitutive reactDNA-ID bind-ID Vratio
fix mine dna/toggle 1 DNA 2.0e5 0.02 RNA-reac 100.0 0.1 DNA-reac NFkB-nuc 10.0
Adjust two reaction rates based on a DNA species which toggles on and off. This is a method for modeling the state of a DNA site as occupied (on) by a transcription factor or unoccupied (off). When occupied, mRNA transcripts are produced at a transcription rate; when unoccupied they are produced at a 2nd constitutive rate.
Here is how the fix operates. Assume a speciesDNA-ID is defined. Also assume 2 reactions are defined. The first is reactRNA-ID which produces mRNA transcripts. The second is reactDNA-ID which toggles the DNA on and off. They should be specified in the following form where NULL means there are no reactants. As discussed below, their specified rates are ignored since the rates are set by this fix, so they can be specified as 0.0.
NULL -> mRNA NULL -> speciesDNA-ID
reaction reactRNA-ID 0.0 mRNA-ID reaction reactDNA-ID 0.0 speciesDNA-ID
Every N timesteps, two operations are performed. First the concentration or count of speciesDNA-ID is reset. For continuum ODE simulations it will be a continuous value between 0 and 1. For stochastic models, it will be a discrete count, either 0 or 1. A value of 0 represents an "off" or unbound state for the DNA, while 1 represents an "on" or bound state. As discussed below, in stochastic models, the 2nd reaction will potentially set the DNA count to 1 or 2; the latter value will be changed to 0 by the fix. I.e. the DNA toggles on or off.
Second, the rates of the 2 reactions are reset in the following way. The rate of the 1st reaction is set to be
Knew = Ktranscription * Koff/Kon * DNA + Kconstitutive * (1 - DNA)
Ktranscription and Kconstitutive are the parameters specified in the fix command, as are Koff and Kon. Ktranscription is the rate at which mRNA is produced when the transcription factor is bound to the DNA site. Kconstitutive is the native rate mRNA is produced when the DNA site is unbound. Koff/Kon has units of molarity and represents an average concentration. DNA is a unitless number between 0 and 1. The units of both terms and thus the overall rate Knew is molarity/sec which is the rate at which the mRNA species in the 1st reaction will be produced.
The rate of the 2nd reaction is set to be
Knew = sign * Koff * DNA + Kon * [bind-ID] * (1 - DNA)
Koff, Kon, and DNA are as above. [bind-ID] is the concentration of the transcription factor species which binds to the DNA site. This concentration will be boosted by Vratio if you need to account for the fact that the transcription factor species is in a smaller-volume compartment, e.g. the nucleus. This is only relevant for stochastic models since the concentration should already be scaled appopriately in an ODE model. The units of Knew are thus per second which is the rate at which the DNA toggles its state.
Sign is set to a value of -1 for continuum ODE models. This is what keeps the value of DNA between 0 and 1. Sign is set to +1 for stochastic models. If this reaction is performed when DNA is on (value of 1), then the DNA count will increase from 1 to 2, and be reset to 0 on the subsequent timestep as described above. Thus the DNA will effectively be turned off.
This fix can only be used with non-spatial simulations.
Related commands: none