A Mechanistic, Stochastic Model Helps Understand Multiple Sclerosis Course and Pathogenesis
Table 1
Disease characteristics and parameters of the mechanistic stochastic model. The table summarizes analogies and links between MS characteristics (left column) and model parameters in (4), in the right column.
Disease characteristics during the relapsing-remitting phase
Mechanistic, stochastic model
Two states are observed that we referred to as health and no health.
: double-well potential (two minima associated with the two states).
The disease develops in patients with a certain degree of heritable and nonheritable risk.
: control parameter that sets the barrier to overcome for going from one state to the other.
It is found that the time spent in the state of health is much longer than in the no health state.
: asymmetry parameter of the potential.
Random variability of biological processes (i.e. randomness in transcription and translation leading to cell-to-cell variations) [8].
: stochastic perturbation with zero mean and variance .
Genetic background and environmental factors alone are not enough to trigger the transitions between the two states.
The noise provides the required energy for the random transitions.
