Selection in spatial stochastic models of cancer: Migration as a key modulator of fitness

Thalhauser, Craig J.; Lowengrub, John; Stupack, Dwayne G.; Komarova, Natalia L.

doi:10.1186/1745-6150-5-21

Cited by 40 publications

(53 citation statements)

References 45 publications

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“…This very simple and relatively abstract system is an important case study because it allows a rigorous mathematical description of the ways of evolution in the simple case. It turns out that the results allow understanding of several more complex and more biologically relevant scenarios, including the mutation dynamics in spatial and hierarchically organized cell populations (12)(13)(14)(15).…”

Section: Resultsmentioning

confidence: 99%

“…Most tissue in the human body exhibits strong spatial structure; interestingly, our theory suggests that this can decrease the time until a certain number of mutations have accumulated in a cell, and this could reduce the time to cancer. At the same time, however, extensive cell migration occurs in many tissues, and migration has been shown to lead to similar properties as mass action (14). Also, it has recently been shown that a hierarchical organization of cell lineages can significantly reduce the rate of double-hit mutant generation (15).…”

Section: Resultsmentioning

confidence: 99%

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Spatial interactions and cooperation can change the speed of evolution of complex phenotypes

Komarova

2014

Proc. Natl. Acad. Sci. U.S.A.

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Complex traits arise from the interactions among multiple gene products. In the case where the complex phenotype is separated from the wild type by a fitness valley or a fitness plateau, the generation of a complex phenotype may take a very long evolutionary time. Interestingly, the rate of evolution depends in nontrivial ways on various properties of the underlying stochastic process, such as the spatial organization of the population and social interactions among cells. Here we review some of our recent work that investigates these phenomena in asexual populations. The role of spatial constraints is quite complex: there are realistic cases where spatial constrains can accelerate or delay evolution, or even influence it in a nonmonotonic fashion, where evolution works fastest for intermediate-range constraints. Social interactions among cells can be studied in the context of the division-of-labor games. Under a range of circumstances, cooperation among cells can lead to a relatively fast creation of a complex phenotype as an emerging (distributed) property. If we further assume the presence of cheaters, we observe the emergence of a fully mutated population of cells possessing the complex phenotype. Applications of these ideas to cancer initiation and biofilm formation in bacteria are discussed.mutations | stochastic modeling C omplex traits depend on several genes and their environments, and arise from the interactions among multiple gene products. Much research has been devoted to inheritance patterns of complex traits (1) and to identifying their genetic makeup (2). Here we will concentrate on the evolutionary process of the emergence of complex traits in asexual populations, and review some of our recent results in this context.In some cases, the evolution of complex traits involves the accumulation of several beneficial mutations. In other cases, however, their evolution requires the accumulation of multiple mutations, each of which is individually neutral or deleterious. A fitness advantage is only attained when all mutations have been acquired (sign epistasis). In such cases, evolution involves the crossing of a fitness valley or fitness plateau (3-5). We can talk about a "fitness foothill" when intermediate mutations are very slightly advantageous compared with the wild type, but not nearly as advantageous as the complex trait (Fig. 1). We will denote by m the number of mutations that need to be accumulated to reach the advantageous complex phenotype. Though recombination can bring together all m mutations within an organism, evolution in asexual populations depends on the sequential accumulation of these mutations within a lineage. The process of sequential accumulation (especially if it involves intermediate deleterious types, such as in the case of fitness valleys) can take a very long evolutionary time. In this paper we discuss how this process and its timing depend on the underlying evolutionary dynamics. In particular, we review recent results on the role of the spatial restrictions inherent in th...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Spatial interactions and cooperation can change the speed of evolution of complex phenotypes

Komarova

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…Interestingly, our theory suggests that this can minimize the time until a certain number of mutations have accumulated in a cell, and this could reduce the time to cancer. At the same time, however, extensive cell migration occurs in many tissues, and migration has been shown to lead to similar properties as mass action [23]. In addition, it has recently been shown that a hierarchical organization of cell lineages can significantly reduce the rate of double-hit mutant generation [40].…”

Section: Somatic Evolution In Tissuementioning

confidence: 99%

Complex role of space in the crossing of fitness valleys by asexual populations

Komarova

Shahriyari

Wodarz

2014

J. R. Soc. Interface.

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The evolution of complex traits requires the accumulation of multiple mutations, which can be disadvantageous, neutral or advantageous relative to the wild-type. We study two spatial (two-dimensional) models of fitness valley crossing (the constant-population Moran process and the non-constantpopulation contact process), varying the number of loci involved and the degree of mixing. We find that spatial interactions accelerate the crossing of fitness valleys in the Moran process in the context of neutral and disadvantageous intermediate mutants because of the formation of mutant islands that increase the lifespan of mutant lineages. By contrast, in the contact process, spatial structure can accelerate or delay the emergence of the complex trait, and there can even be an optimal degree of mixing that maximizes the rate of evolution. For advantageous intermediate mutants, spatial interactions always delay the evolution of complex traits, in both the Moran and contact processes. The role of the mutant islands here is the opposite: instead of protecting, they constrict the growth of mutants. We conclude that the laws of population growth can be crucial for the effect of spatial interactions on the rate of evolution, and we relate the two processes explored here to different biological situations.

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“…In addition, from microscopic dynamics utilizing the excluded volume approach, non-linear diffusion equations with diffusion coefficients depending on cellular volume fraction to prevent the collapse of cellular density were obtained [20]. These versatile models have been applied for interpreting different aspects of cell physiology [20][21][22][23][24][25][26][27][28]. Thus, an extended CPM version provided a strong correlation of cell migration directionality with topological surrounding extracellular matrix (ECM) distribution and a biphasic dependence of migration on the matrix structure and stiffness, cell density, and adhesion [27].…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media

et al. 2016

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To deal with complex systems, microscopic and global approaches become of particular interest. Our previous results from the dynamics of large cell colonies indicated that their 2D front roughness dynamics is compatible with the standard Kardar-Parisi-Zhang (KPZ) or the quenched KPZ equations either in plain or methylcellulose (MC)-containing gel culture media, respectively. In both cases, the influence of a non-uniform distribution of the colony constituents was significant. These results encouraged us to investigate the overall dynamics of those systems considering the morphology and size, the duplication rate, and the motility of single cells. For this purpose, colonies with different cell populations (N) exhibiting quasi-circular and quasi-linear growth fronts in plain and MC-containing culture media are investigated. For small N, the average radial front velocity and its change with time depend on MC concentration. MC in the medium interferes with cell mitosis, contributes to the local enlargement of cells, and increases the distribution of spatio-temporal cell density heterogeneities. Colony spreading in MC-containing media proceeds under two main quenching effects, I and II; the former mainly depending on the culture medium composition and structure and the latter caused by the distribution of enlarged local cell domains. For large N, colony spreading occurs at constant velocity. The characteristics of cell motility, assessed by measuring their trajectories and the corresponding velocity field, reflect the effect of enlarged, slowmoving cells and the structure of the medium. Local average cell size distribution and individual cell motility data from plain and MC-containing media are qualitatively consistent with the predictions of both the extended cellular Potts models and the observed transition of the front roughness dynamics from a standard KPZ to a quenched KPZ. In this case, quenching J Biol Phys (2016) 42:477-502 DOI 10.1007

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Selection in spatial stochastic models of cancer: Migration as a key modulator of fitness

Cited by 40 publications

References 45 publications

Spatial interactions and cooperation can change the speed of evolution of complex phenotypes

Spatial interactions and cooperation can change the speed of evolution of complex phenotypes

Complex role of space in the crossing of fitness valleys by asexual populations

Spatio-temporal morphology changes in and quenching effects on the 2D spreading dynamics of cell colonies in both plain and methylcellulose-containing culture media

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