  We develop a modeling framework for cancer progression that distinguishes the
order of two possible mutations. Recent observations and information on
myeloproliferative neoplasms are analyzed within our framework. In some
patients with myeloproliferative neoplasms, two genetic mutations can be found,
JAK2 V617F and TET2. Whether or not one mutation is present will influence how
the other subsequent mutation affects the regulation of gene expression. When
both mutations are present, the order of their occurrence has been shown to
influence disease progression and prognosis. In this paper, we propose a
nonlinear ordinary differential equation (ODE) and Markov chain models to
explain the non-additive and non-commutative clinical observations with respect
to different orders of mutations: gene expression patterns, proportions of
cells with different mutations, and ages at diagnosis. We also propose
potential experiments measurements that can be used to verify our models.
