By calculating conditional probabilities (see Methods), the channel transition probability diagram for this pathological channel model can be constructed.
It corresponds to the pathological channel model where all the molecules are equally probable to be dysfunctional.
So, in our pathological channel model the dysfunctionality likelihoods of the dominant and the other sixteen molecules are k/ k + 16) and 1/ k + 16), respectively.
According to our calculations (see Methods), in 3 out of 34 cases, caspase3 will be inactive, 0, when (EGF, insulin, TNF) = (0, 0, 1) in our pathological channel model.
For the pathological channel model introduced earlier, we have calculated P(1|EGF, insulin, TNF) for different input combinations using (10) and Additional file 1: Table S2.
To calculate the capacity of the molecular channel, one needs the transition probability channel matrix M. Depending on which molecule is dominant in the pathological channel, one can use the matrices given in (12 - 16 12 - 16
This approach takes advantage of the concepts of communication engineering and signal transmission, to model and analyze networks with dysfunctional molecules as pathological communication channels.
Using the total probability theorem and by considering all the error events, we have calculated the transmission error probability for the pathological caspase3 channel, which is P e, abnormal channel = 11/136 ≈ 0.08 (see Methods).
In order to model a pathological molecular channel, one needs to specify the equations that determine the channel output, in terms of the channel inputs.
Now we introduce a simple pathological communication channel model for the caspase3 network.
