Evolutionary dynamics of adult stem cells: comparison of random and immortal-strand segregation mechanisms

Theoretical Models of Generalized Quasispecies

Theoretical modeling of quasispecies has progressed in several directions. In this chapter, we review the works of Emmanuel Tannenbaum, who, together with Eugene Shakhnovich at Harvard University and later with colleagues and students at Ben-Gurion University in Beersheva, implemented one of the more useful approaches, by progressively setting up various formulations for the quasispecies model and solving them analytically. Our review will focus on these papers that have explored new models, assumed the relevant mathematical approximations, and proceeded to analytically solve for the steady-state solutions and run stochastic simulations . When applicable, these models were related to real-life problems and situations, including changing environments, presence of chemical mutagens, evolution of cancer and tumor cells , mutations in Escherichia coli, stem cells , chromosomal instability (CIN), propagation of antibiotic drug resistance , dynamics of bacteria with plasmids , DNA proofreading mechanisms, and more.

Evolution and phenotypic selection of cancer stem cells

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change, and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cells(CSC), as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits, including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of non-stem cancer cells(CC) that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The sub-population of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.

We present an in silico computational model of tumor growth and evolution according to the cancer stem cell hypothesis. Inheritable traits of cells may be genetically or epigenetically altered, and traits that confer increased fitness to the cell will be selected for on the population level. Phenotypic evolution yields aggressive tumors with large heterogeneity, prompting the notion that the cancer stem cell population per se is highly heterogeneous. Within aggressive tumors cancer stem cells with low tumorigenic potential may be isolated. Simulations of our model suggest that the cells harvested in core needle biopsies represent less than 10% of the phenotypic heterogeneity of the total tumor population. Dependent on the cells captured in the sample, xenografted tumors may exhibit aggressive growth or long-term dormancy—dynamics that may suggest opposing treatment approaches for the same tumor when translated into clinical decision-making.

New cancer diagnostics and therapeutics from a ninth 'hallmark of cancer': symmetric self-renewal by mutated distributed stem cells

A total of eight cellular alterations associated with human carcinogenesis have been framed as the 'hallmarks of cancer'. This representation overlooks a ninth hallmark of cancer: the requirement for tumor-originating distributed stem cells to shift sufficiently from asymmetric to symmetric self-renewal kinetics for attainment of the high cell production rate necessary to form clinically significant tumors within a human lifespan. Overlooking this ninth hallmark costs opportunities for discovery of more selective molecular targets for development of improved cancer therapeutics and missing cancer stem cell biomarkers of greater specificity. Here, the biological basis for the ninth hallmark of cancer is considered toward highlighting its importance in human carcinogenesis and, as such, its potential for revealing unique molecules for targeting cancer diagnostics and therapeutics.

Stem cells propagate their DNA by random segregation in the flatworm Macrostomum lignano

Adult stem cells are proposed to have acquired special features to prevent an accumulation of DNA-replication errors. Two such mechanisms, frequently suggested to serve this goal are cellular quiescence, and non-random segregation of DNA strands during stem cell division, a theory designated as the immortal strand hypothesis. To date, it has been difficult to test the in vivo relevance of both mechanisms in stem cell systems. It has been shown that in the flatworm Macrostomum lignano pluripotent stem cells (neoblasts) are present in adult animals. We sought to address by which means M. lignano neoblasts protect themselves against the accumulation of genomic errors, by studying the exact mode of DNA-segregation during their division. In this study, we demonstrated four lines of in vivo evidence in favor of cellular quiescence. Firstly, performing BrdU pulse-chase experiments, we localized 'Label-Retaining Cells' (LRCs). Secondly, EDU pulse-chase combined with Vasa labeling demonstrated the presence of neoblasts among the LRCs, while the majority of LRCs were differentiated cells. We showed that stem cells lose their label at a slow rate, indicating cellular quiescence. Thirdly, CldU/IdU- double labeling studies confirmed that label-retaining stem cells showed low proliferative activity. Finally, the use of the actin inhibitor, cytochalasin D, unequivocally demonstrated random segregation of DNA-strands in LRCs. Altogether, our data unambiguously demonstrated that the majority of neoblasts in M. lignano distribute their DNA randomly during cell division, and that label-retention is a direct result of cellular quiescence, rather than a sign of co-segregation of labeled strands.

Semiconservative quasispecies equations for polysomic genomes: the general case

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analog of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for noncomplementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

Development of a two-dimensional agent-based model for chronic chagasic cardiomyopathy after stem cell transplantation

MOTIVATION

A significant issue in stem cell therapy is to understand the role of this type of cell in the tissue regeneration. To explain this mechanism, an experimental study has quantified that the bone marrow cell transplantation decreases the number of inflammatory cells and reduces the fibrosis area in chagasic mice. Using this experimental data, we have developed an agent-based computational model to investigate the regeneration of the chronic chagasic cardiomyopathy after bone marrow stem cell transplantation.

RESULTS

Our model includes six different types of agents: inflammatory cell, fibrosis area, cardiomyocyte, proinflammatory cytokine tumor necrosis factor-alpha, Trypanosoma cruzi parasite and bone marrow stem cell. This latter promotes apoptosis in inflammatory cells, reduction in the fibrosis area and can differentiate into cardiomyocyte. Proinflammatory cytokine tumor necrosis factor-alpha can increase the fibrosis area and T.cruzi can increase the number of inflammatory cells. Our results for both apoptosis of inflammatory cells and reduction in the fibrosis area were compared with experimental data. They suggest that the concentration pattern is the most important factor to characterize the kinetics of cardiac tissue regeneration after bone marrow stem cell transplantation.

AVAILABILITY

The source code of our software is available online at www.vivas.ufba.br/bone/bone.zip .br Supplementaty information: Supplementary data are available at Bioinformatics online.

Comparison of three replication strategies in complex multicellular organisms: asexual replication, sexual replication with identical gametes, and sexual replication with distinct sperm and egg gametes

This paper studies the mutation-selection balance in three simplified replication models. The first model considers a population of organisms replicating via the production of asexual spores. The second model considers a sexually replicating population that produces identical gametes. The third model considers a sexually replicating population that produces distinct sperm and egg gametes. All models assume diploid organisms whose genomes consist of two chromosomes, each of which is taken to be functional if equal to some master sequence, and defective otherwise. In the asexual population, the asexual diploid spores develop directly into adult organisms. In the sexual populations, the haploid gametes enter a haploid pool, where they may fuse with other haploids. The resulting immature diploid organisms then proceed to develop into mature organisms. Based on an analysis of all three models, we find that, as organism size increases, a sexually replicating population can only outcompete an asexually replicating population if the adult organisms produce distinct sperm and egg gametes. A sexual replication strategy that is based on the production of large numbers of sperm cells to fertilize a small number of eggs is found to be necessary in order to maintain a sufficiently low cost for sex for the strategy to be selected for over a purely asexual strategy. We discuss the usefulness of this model in understanding the evolution and maintenance of sexual replication as the preferred replication strategy in complex, multicellular organisms.

Asexual and sexual replication in sporulating organisms

Replication via sporulation is the replication strategy for all multicellular life, and may even be observed in unicellular life (such as with budding yeast). We consider diploid populations replicating via one of two possible sporulation mechanisms. (1) Asexual sporulation, whereby adult organisms produce single-celled diploid spores that grow into adults themselves. (2) Sexual sporulation, whereby adult organisms produce single-celled diploid spores that divide into haploid gametes. The haploid gametes enter a haploid "pool," where they may recombine with other haploids to form a diploid spore that then grows into an adult. We consider a haploid fusion rate given by second-order reaction kinetics. We work with a simplified model where the diploid genome consists of only two chromosomes, each of which may be rendered defective with a single point mutation of the wild-type. We find that the asexual strategy is favored when the rate of spore production is high compared to the characteristic growth rate from a spore to a reproducing adult. Conversely, the sexual strategy is favored when the rate of spore production is low compared to the characteristic growth rate from a spore to a reproducing adult. As the characteristic growth time increases, or as the population density increases, the critical ratio of spore production rate to organism growth rate at which the asexual strategy overtakes the sexual one is pushed to higher values. Therefore, the results of this model suggest that, for complex multicellular organisms, sexual replication is favored at high population densities and low growth and sporulation rates.

Dynamics, stability and inheritance of somatic DNA methylation imprints

Recent research highlights the role of CpG methylation in genomic imprinting, histone and chromatin modification, transcriptional regulation, and 'gene silencing' in cancer development. An unresolved issue, however, is the role of stable inheritance of factors that manage epigenetic imprints in renewing or expanding cell populations in soma. Here we propose a mathematical model of CpG methylation that is consistent with the cooperative roles of de novo and maintenance methylation. This model describes (1) the evolution of methylation imprints toward stable, yet noisy equilibria, (2) bifurcations in methylation levels, thus the dual stability of both hypo- and hypermethylated genomic regions, and (3) sporadic transitions from hypo- to hypermethylated equilibria as a result of methylation noise in a finite system of CpG sites. Our model not only affords an explanation of the persistent coexistence of these two equilibria, but also of sporadic changes of site-specific methylation levels that may alter preset epigenetic imprints in a renewing cell population.

Selective advantage for sexual reproduction

This paper develops a simplified model for sexual reproduction within the quasispecies formalism. The model assumes a diploid genome consisting of two chromosomes, where the fitness is determined by the number of chromosomes that are identical to a given master sequence. We also assume that there is a cost to sexual reproduction, given by a characteristic time tau(seek) during which haploid cells seek out a mate with which to recombine. If the mating strategy is such that only viable haploids can mate, then when tau(seek) = 0, it is possible to show that sexual reproduction will always out compete asexual reproduction. However, as tau(seek) increases, sexual reproduction only becomes advantageous at progressively higher mutation rates. Once the time cost for sex reaches a critical threshold, the selective advantage for sexual reproduction disappears entirely. The results of this paper suggest that sexual reproduction is not advantageous in small populations per se, but rather in populations with low replication rates. In this regime, the cost for sex is sufficiently low that the selective advantage obtained through recombination leads to the dominance of the strategy. In fact, at a given replication rate and for a fixed environment volume, sexual reproduction is selected for in high populations because of the reduced time spent finding a reproductive partner.

Simulation of proliferation of neural stem cells on a surface with emphasis on spatial constraints on cell division

We present Monte Carlo lattice simulations of proliferation of cells on a surface in the situation when the cell-cell adhesion is relatively strong and the cells may form islands and/or flattened hemispheres. The model parameters were chosen to mimic proliferation of adult rat neural stem cells (or, more specifically, adult hippocampal progenitor cells) deposited on polyornithine and laminin coated polystyrene. The results obtained show that the spatial constraints on cell division may result in slowdown of the exponential growth. Depending on the rules used for cell division, this effect may be either nearly negligible or appreciable. In the latter case, the scale of the deviations from the exponential growth is comparable with that observed in our experiments. In the simulations, the slowdown of the growth starts however somewhat earlier and occurs in a less abrupt manner. This seems to indicate that the spatial constraints on division of cells are not the main factor behind the experimentally observed termination of the growth.