Disease evolution in reaction networks: Implications for a diagnostic problem.

We study the time evolution of symptoms (signs) with some defects in the dynamics of a reaction network as a (microscopic) model for the progress of disease phenotypes. To this end, we take a large population of reaction networks and follow the stochastic dynamics of the system to see how the development of defects affects the macroscopic states of the signs probability distribution. We start from some plausible definitions for the healthy and disease states along with a dynamical model for the emergence of diseases by a reverse simulated annealing algorithm. The healthy state is defined as a state of maximum objective function, which here is the sum of mutual information between a subset of signal variables and the subset of assigned response variables. A disease phenotype is defined with two parameters controlling the rate of mutations in reactions and the rate of accepting mutations that reduce the objective function. The model can provide the time dependence of the sign probabilities given a disease phenotype. This allows us to obtain the accuracy of diagnosis as a function of time by using a probabilistic model of signs and diseases. The trade-off between the diagnosis accuracy (increasing in time) and the objective function (decreasing in time) can be used to suggest an optimal time for medical intervention. Our model would be useful in particular for a dynamical (history-based) diagnostic problem, to estimate the likelihood of a disease hypothesis given the temporal evolution of the signs.