Determining the control networks regulating stem cell lineages in colonic crypts
Introduction
The stem cell lineage is a basic unit of hierarchical tissues and as such it has attracted the attention of both experimental biologists, and mathematical/computational modelers. The question of stem cell control is at the center of our understanding of tissue (mal-) functioning. Every day, cells in hierarchical tissues perform their specific functions and die to be replaced by new cell divisions. This process is stochastic in nature (see e.g. Arai, 2016, Wagers, Christensen, Weissman, 2002), and involves very large numbers of cellular events. The cells involved in the functioning and renewal of an organ differ from each other by their division and apoptosis capabilities, as well as the types of signals they send and the kinds of cell fate decisions they make.
In Komarova (2013) we developed a framework of reasoning about stem cell signaling networks. Let us suppose that there are three compartments in a set cell lineage: stem cells (SCs), transit amplifying cells (TACs) and differentiated cells (DCs). In the colon and intestinal crypts, as well as other structures, these are linearly ordered with SC at the bottom, DC cells at the top, and TAC in between. In order to maintain the number of each cell type, the rate of removal of the DCs from the top is balanced by division and differentiation of the SCs and TACs below.
Each cellular compartment may receive signals from other compartments (as well as from its own cells), which influence the rate of differentiation and proliferation. For example, having too few DCs may call for the need of faster differentiation of TACs into DCs. This faster differentiation of TACs may be achieved by relieving the negative control on the probability of TACs to differentiate exerted by DCs. Many molecules produced by these cells have been detected (Gregorieff, Pinto, Begthel, Destrée, Kielman, Clevers, 2005, Hsieh, 2012, Kosinski, Li, Chan, Zhang, Ho, Tsui, Chan, Mifflin, Powell, Yuen, et al., 2007), but their role in each step of the regulatory network is yet to be completely determined (Crosnier, Stamataki, Lewis, 2006, Medema, Vermeulen, 2011).
Theoretically, each cell population may influence (in a negative or positive way) each of the processes that happen in the system, which gives rise to a very large number of networks of cellular control. In Komarova (2013) we examined such controls from the (linear) stability point of view. We called the stable networks with the smallest possible number of loops the “minimal networks”. In a three-compartment system, assume that the following five processes can be controlled: divisions of SCs and TACs, differentiations of SCs and TACs, and death of DCs. It turns out that in this case, the smallest number of control loops is three, and there are exactly 32 different three-loop control networks that are stable. These 32 stable networks have different topologies and different signs of control loops (positive or negative).
In the present paper we are interested in determining the most likely control network(s) that govern the regulation of human colon crypt stem cell lineages. While the analysis of Komarova (2013) restricts the total number of possibilities to 20 (plus additional 12 networks with non constant DC death terms), the analysis did not indicate which of the 32 were most likely to describe the regulation in a real biological system.
We have now determined the most likely regulatory network(s), among the 32 three-compartment stable networks, by using actual measurements of the number of SCs, TACs, and DCs in biopsies of human colon crypts, and additional mathematical methodology. Bravo and Axelrod (2013) performed detailed measurements of the number of each of the three cell types (SCs, TACs, DCs) in 49 colon crypts in human biopsy specimens. In this paper we will examine each of the 32 possible networks (including the 20 networks explicitly presented in Komarova (2013) plus 12 additional ones) to determine whether it can produce the correct measured means and variances of cell population numbers. In addition to this static information we have also used data on the dynamics of injury recovery, as well as experimentally obtained intracrypt correlations. Using these criteria, a selection algorithm was devised that identified three of the 32 possible control networks as most likely the ones corresponding to the regulation of homeostasis of human colon crypts.
This paper contributes to the growing literature on the theory of stem cells, which ranges from ODE modeling (Nakata, Getto, Marciniak-Czochra, Alarcón, 2012, Stiehl, Marciniak-Czochra, 2011) to stochastic modeling (Dingli, Traulsen, Pacheco, 2007, Enderling, Anderson, Chaplain, Beheshti, Hlatky, Hahnfeldt, 2009, Enderling, Chaplain, Anderson, Vaidya, 2007, Enderling, Hlatky, Hahnfeldt, 2009, Enderling, Park, Hlatky, Hahnfeldt, 2009), and includes research of stem cells in the context of feedback mechanisms (Konstorum, Hillen, Lowengrub, 2016, Kunche, Yan, Calof, Lowengrub, Lander, 2016, Lander, Gokoffski, Wan, Nie, Calof, 2009, Youssefpour, Li, Lander, Lowengrub, 2012), carcinogenesis (Ashkenazi, Gentry, Jackson, 2008, Ashkenazi, Jackson, Dontu, Wicha, 2007, Boman, Fields, Cavanaugh, Guetter, Runquist, 2008, Enderling, Hahnfeldt, 2011, Ganguly, Puri, 2006, Ganguly, Puri, 2007, Hardy, Stark, 2002, Johnston, Edwards, Bodmer, Maini, Chapman, 2007, Yatabe, Tavare, Shibata, 2001), modeling hematopoietic SC dynamics (Foo, Drummond, Clarkson, Holyoake, Michor, 2009, Glauche, Cross, Loeffler, Roeder, 2007, Marciniak-Czochra, Stiehl, Ho, Jäger, Wagner, 2009, Stiehl, Marciniak-Czochra, 2012), and cancer stem cells (Dingli, Michor, 2006, Enderling, 2015, Enderling, Hahnfeldt, 2011, Hillen, Enderling, Hahnfeldt, 2013, Johnston, Maini, Chapman, Edwards, Bodmer, 2010, Scott, Hjelmeland, Chinnaiyan, Anderson, Basanta, 2014).
Section snippets
Data Description
We have measured the number and location of dividing cells (Ki-67 positively stained cells) and non-dividing cells (Ki-67 non-stained cells) in 49 colon crypts in human biopsy specimens. The non-dividing cells at the bottom of the crypt are considered quiescent stem cells, the non-dividing cells in the top two-thirds of the crypt are considered differentiated cells. The dividing cells near the bottom third of the crypt are considered to consist of transient amplifying cells and active stem
Selection Algorithm
In Komarova (2013), we have identified 20 different 3-compartment minimal control networks that are compatible with stable homeostatic control, see Fig. 2. These networks are characterized by constant death terms. In addition, there are 12 minimal control networks with non-constant death terms, see Fig. 3. Regulated death terms occur in different contexts and have been modelled in the past (Fuertinger, Kappel, Thijssen, Levin, Kotanko, 2012, Mahaffy, Bélair, Mackey, 1998, Stiehl, Baran, Ho,
Results and discussion
Investigating possible regulation of stem cell dynamics in colon and intestinal crypts has been a popular subject for computational and mathematical modeling (Carulli, Samuelson, Schnell, 2014, De Matteis, Graudenzi, Antoniotti, 2013, Kershaw, Byrne, Gavaghan, Osborne, 2013, Van Leeuwen, Byrne, Jensen, King, 2006). This is because crypts have a few distinguishable cell types organized in a hierarchy of fewer than 2500 cells that maintain homeostasis, and can recover after perturbation. It is
Acknowledgments
D.E.A. was supported by the Human Genetics Institute of New Jersey, the New Jersey Breast Cancer Research Fund, and the Rutgers Cancer Institute of New Jersey (PA30CA072720). He thanks Dr. Steven Schiff of the R-CINJ for provided biopsy specimens, and Dr. Michael de Frietas for informative discussions about modeling crypt cell dynamics. N.L.K gratefully acknowledges the support of NIH grant 1 U01 CA187956-01. We thank an anonymous reviewer for suggesting that we analyze networks with
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