The role of cell location and spatial gradients in the evolutionary dynamics of colon and intestinal crypts

BACKGROUND: Colon and intestinal crypts serve as an important model system for adult stem cell proliferation and differentiation. We develop a spatial stochastic model to study the rate of somatic evolution in a normal crypt, focusing on the production of two-hit mutants that inactivate a tumor suppressor gene. We investigate the effect of cell division pattern along the crypt on mutant production, assuming that the division rate of each cell depends on its location. RESULTS: We find that higher probability of division at the bottom of the crypt, where the stem cells are located, leads to a higher rate of double-hit mutant production. The optimal case for delaying mutations occurs when most of the cell divisions happen at the top of the crypt. We further consider an optimization problem where the “evolutionary” penalty for double-hit mutant generation is complemented with a “functional” penalty that assures that fully differentiated cells at the top of the crypt cannot divide. CONCLUSION: The trade-off between the two types of objectives leads to the selection of an intermediate division pattern, where the cells in the middle of the crypt divide with the highest rate. This matches the pattern of cell divisions obtained experimentally in murine crypts. REVIEWERS: This article was reviewed by David Axelrod (nominated by an Editorial Board member, Marek Kimmel), Yang Kuang and Anna Marciniak-Czochra. For the full reviews, please go to the Reviewers’ comments section. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13062-016-0141-6) contains supplementary material, which is available to authorized users

The Advancement of Biomaterials in Regulating Stem Cell Fate.

Stem cells are well-known to have prominent roles in tissue engineering applications. Embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs) can differentiate into every cell type in the body while adult stem cells such as mesenchymal stem cells (MSCs) can be isolated from various sources. Nevertheless, an utmost limitation in harnessing stem cells for tissue engineering is the supply of cells. The advances in biomaterial technology allows the establishment of ex vivo expansion systems to overcome this bottleneck. The progress of various scaffold fabrication could direct stem cell fate decisions including cell proliferation and differentiation into specific lineages in vitro. Stem cell biology and biomaterial technology promote synergistic effect on stem cell-based regenerative therapies. Therefore, understanding the interaction of stem cell and biomaterials would allow the designation of new biomaterials for future clinical therapeutic applications for tissue regeneration. This review focuses mainly on the advances of natural and synthetic biomaterials in regulating stem cell fate decisions. We have also briefly discussed how biological and biophysical properties of biomaterials including wettability, chemical functionality, biodegradability and stiffness play their roles

Symmetric vs. asymmetric stem cell divisions: an adaptation against cancer?

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a consequence of two "hits", and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more specialized cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common

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

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-constant-population 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

The probability of double-hit mutant generation as a function of , the probability of symmetric stem cell divisions.

<p>The results of numerical simulations are presented as points connected with dotted lines (standard deviations are included). Analytical results are given by solid lines (formula (11). The horizontal line represents the calculations for the homogeneous model. We ran batches of runs. The parameters are , , , .</p

The six different approximation regimes (Table 2) for solutions of system (2–3).

<p>Plotted is the quantity (a) and (b) as a function of the frequency of symmetric divisions, , for three different values of (solid lines), together with the approximations given by the formulas in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0076195#pone-0076195-t002" target="_blank">Table 2</a>. Approximations , , and are best demonstrated in panel (a), where the quantity is plotted. Approximations , , and are best demonstrated in panel (b), where the quantity is plotted. The other parameters are , .</p

Symmetric and asymmetric stem cell divisions.

<p>In the asymmetric division model, a stem cell produces one differentiated cell and one stem cell. In the symmetric division model, a stem cell produces two differentiated cells or two stem cells.</p

The probability of double-hit mutant generation in the symmetric division model.

<p>The case of symmetrically dividing stem cells, same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0076195#pone-0076195-g005" target="_blank">Figure 5</a>.</p

Model parameters.

<p>Notations used in the text and their brief description.</p