Presented by Michael Nicholson, Dana Farber Cancer Institute, Harvard University

Abstract: Investigating  the  emergence  of  a  particular  cell  type  is  a  recurring  theme  in  models  of  growing  cellular populations.  The evolution of resistance to therapy is a classic example.  Common questions are:  when does the cell type first occur, and via which sequence of steps is it most likely to emerge?  For growing populations, these questions can be formulated in a general framework of branching processes spreading through a graph from a root to a target vertex.  Cells have a particular fitness value on each vertex and can transition along edges  at  specific  rates.   Vertices  represents  cell  states,  say  genotypes  or  physical  locations,  while  possible transitions are acquiring a mutation or cell migration.  We focus on the setting where cells at the root vertex have the highest fitness and transition rates are small.  Simple formulas are derived for the time to reach the target vertex and for the probability that it is reached along a given path in the graph.  We demonstrate our  results  on  several  scenarios  relevant  to  the  emergence  of  drug  resistance,  including:  the  orderings  of resistance-conferring mutations in bacteria and the impact of imperfect drug penetration in cancer