. Cancer progression is a process of somatic evolution within the body. Cancer results from a sequence of genetic and epigenetic changes which lead to a variety of abnormal cell phenotypes including increased proliferation and survival of somatic cells, and therefore, to a selective advantage of (pre-)cancerous cells. (Pre-)cancerous tissues often evolve in cell populations with
distinct spatial structure (epithelia). In spatial domains, clones expand through the tissue via (adaptive) selective waves which can be described by stochastic Fisher waves (sFKPP model). Once a mutation occurs somewhere in the habitat (stars), its fate is not yet decided: mutations are subject to stochastic number fluctuations (genetic drift) and may go extinct. When mutations survive number fluctuations and get established, they may spread throughout the entire population (fixation), giving rise to the adaptive wave. Each time a mutation is fixated, the fitness of the entire population is increased by the selective fitness effect of the mutation, as indicated by changing colors in the figure below (A,B). - Two dynamic scenarios are feasible: periodic selection (panel A) where mutations spread strictly consequently, i.e., the time to fixation is always shorter than the waiting time until the next mutations occurs (tfix < tmut). In the converse case, called clonal interference, multiple clones may compete to reach fixation. Research indicates that this complex nonlinear scenario is much more abundant in nature than previously thought and that it also occurs in (pre-)cancerous epithelial cells.Project description.
The diagnostics of cancer patients histological analysis today is increasingly using genetic sequencing. An important goal is to interpret the genetic cell diversity (mosaic) in tissues to accurately estimate the stage of the cancer so that the treatment can be optimized, and ideally, to capture and monitor pre-cancerous states before the disease becomes rampant. - Prostate cancer is one of the most abundant cancers, costing a lot of lives. However, researchers today are still working on finding a detailed understanding of the progression of these cancers. Recent research efforts reconstructing the 3D structure of such
tumors reveals a complicated spatial structure composed of glands and channels connecting channels, thus forming a complex network. The goal of this project is to take the results for the spread of selective Fisher waves of mutant cells valid for simple topologies and extend to network structures observed in tumors and to estimate the time to accumulate the necessary mutations that trigger malignancy of the cells, and to estimate genetic diversity. Network data from 3D reconstructed tumors are available through a collaboration with medical researchers at the University of Bonn, Germany.Goals.
i) Develop network model based on statistical network properties extracted from imaging data.
ii) Numerical stochastic model of evolutionary dynamics on a spatial network.
iii) Analytic estimation of different tumor progression models using scaling arguments, characterization of genetic diversity.
iv)* Dynamics of clonal interference in heterogeneous fitness landscape.
v)* Modeling and analysis of growth of channel network (dynamics of evolving network, analytic and/or numerical).
The project may include the tasks: numerical simulation, network theory, stochastic processes, biophysical modeling/math biology.
In collaboration withYuri Tolkach, University of Bonn, Germany