Theoretical understanding of evolutionary dynamics on inhomogeneous networks.

Evolution is the main feature of all biological systems that allows populations to change their characteristics over successive generations. A powerful approach to understand evolutionary dynamics is to investigate fixation probabilities and fixation times of novel mutations on networks that mimic biological populations. It is now well established that the structure of such networks can have dramatic effects on evolutionary dynamics. In particular, there are population structures that might amplify the fixation probabilities while simultaneously delaying the fixation events. However, the microscopic origins of such complex evolutionary dynamics remain not well understood. We present here a theoretical investigation of the microscopic mechanisms of mutation fixation processes on inhomogeneous networks. It views evolutionary dynamics as a set of stochastic transitions between discrete states specified by different numbers of mutated cells. By specifically considering star networks, we obtain a comprehensive description of evolutionary dynamics. Our approach allows us to employ physics-inspired free-energy landscape arguments to explain the observed trends in fixation times and fixation probabilities, providing a better microscopic understanding of evolutionary dynamics in complex systems.

Optimal pathways control fixation of multiple mutations during cancer initiation.

Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.

The role of spatial structures of tissues in cancer initiation dynamics.

It is widely believed that biological tissues evolved to lower the risks of cancer development. One of the specific ways to minimize the chances of tumor formation comes from proper spatial organization of tissues. However, the microscopic mechanisms of underlying processes remain not fully understood. We present a theoretical investigation on the role of spatial structures in cancer initiation dynamics. In our approach, the dynamics of single mutation fixations are analyzed using analytical calculations and computer simulations by mapping them to Moran processes on graphs with different connectivity that mimic various spatial structures. It is found that while the fixation probability is not affected by modifying the spatial structures of the tissues, the fixation times can change dramatically. The slowest dynamics is observed in 'quasi-one-dimensional' structures, while the fastest dynamics is observed in 'quasi-three-dimensional' structures. Theoretical calculations also suggest that there is a critical value of the degree of graph connectivity, which mimics the spatial dimension of the tissue structure, above which the spatial structure of the tissue has no effect on the mutation fixation dynamics. An effective discrete-state stochastic model of cancer initiation is utilized to explain our theoretical results and predictions. Our theoretical analysis clarifies some important aspects on the role of the tissue spatial structures in the cancer initiation processes.