Modeling Evolutionary Dynamics of Epigenetic Mutations in Hierarchically Organized Tumors

The cancer stem cell (CSC) concept is a highly debated topic in cancer research. While experimental evidence in favor of the cancer stem cell theory is apparently abundant, the results are often criticized as being difficult to interpret. An important reason for this is that most experimental data that support this model rely on transplantation studies. In this study we use a novel cellular Potts model to elucidate the dynamics of established malignancies that are driven by a small subset of CSCs. Our results demonstrate that epigenetic mutations that occur during mitosis display highly altered dynamics in CSC-driven malignancies compared to a classical, non-hierarchical model of growth. In particular, the heterogeneity observed in CSC-driven tumors is considerably higher. We speculate that this feature could be used in combination with epigenetic (methylation) sequencing studies of human malignancies to prove or refute the CSC hypothesis in established tumors without the need for transplantation. Moreover our tumor growth simulations indicate that CSC-driven tumors display evolutionary features that can be considered beneficial during tumor progression. Besides an increased heterogeneity they also exhibit properties that allow the escape of clones from local fitness peaks. This leads to more aggressive phenotypes in the long run and makes the neoplasm more adaptable to stringent selective forces such as cancer treatment. Indeed when therapy is applied the clone landscape of the regrown tumor is more aggressive with respect to the primary tumor, whereas the classical model demonstrated similar patterns before and after therapy. Understanding these often counter-intuitive fundamental properties of (non-)hierarchically organized malignancies is a crucial step in validating the CSC concept as well as providing insight into the therapeutical consequences of this model

Self-avoiding surfaces, topology, and lattice animals

With Monte Carlo simulation we study closed self-avoiding surfaces (SAS) of arbitrary genus on a cubic lattice. The gyration radius and entropic exponents are nu=0.506 +/- 0.005 and theta=1.50 +/- 0.06, respectively. Thus, SAS behave like lattice animals (LA) or branched polymers at criticality. This result, contradicting previous conjectures, is due to a mechanism of geometrical redundancy, which is tested by exact renormalization on a hierarchical vesicle model. By mapping SAS into restricted interacting site LA, we conjecture nu(THETA)=1/2 , phi(THETA)=1, and theta(THETA)=3/2 at the LA theta point

Bending-rigidity-driven transition and crumpling-point scaling of lattice vesicles

The crumpling transition of three-dimensional (3D) lattice vesicles subject to a bending fugacity rho = exp(- kappa/k(B)T) is investigated by Monte Carlo methods in a grand canonical framework. By also exploiting conjectures suggested by previous rigorous results, a critical regime with scaling behavior in the universality class of branched polymers is found to exist for rho > rho(c). For rho < rho(c) the vesicles undergo a first-order transition that has remarkable similarities to the line of droplet singularities of inflated 2D vesicles. At the crumpling point (rho = rho(c)), which has a tricritical character, the average radius and the canonical partition function of vesicles with n plaquettes scale as n(nu c) and n-(theta c), respectively, with nu(c) = 0.4825 +/- 0.0015 and theta(c) = 1.78 +/- 0.03. These exponents indicate a new class, distinct from that of branched polymers, for scaling at the crumpling point

Self-avoiding surfaces, topology, and lattice animals

With Monte Carlo simulation we study closed self-avoiding surfaces (SAS) of arbitrary genus on a cubic lattice.https://doi.org/10.1103/PhysRevLett.69.365

Bending-rigidity-driven transition and crumpling-point scaling of lattice vesicles

https://doi.org/10.1103/PhysRevE.53.580

Multisampling: A New Approach to Uniform Sampling and Approximate Counting

In this paper we present a new approach to uniform sampling and approximate counting. The presented method is called multisampling and is a generalization of the importance sampling technique. It has the same advantage as importance sampling, it is unbiased, but in contrary to it&apos;s prototype it is also an almost uniform sampler. The approach seams to be as universal as Markov Chain Monte Carlo approach, but simpler. Here we report very promising test results of using multisampling to the following problems: counting matchings in graphs, counting colorings of graphs, counting independent sets in graphs, counting solutions to knapsack problem, counting elements in graph matroids and computing the partition function of the Ising model