Robustness of differentiation cascades with symmetric stem cell division

Abstract

Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.

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

“…In previous, non-spatial models, it was shown that symmetric stem cell divisions help delay the production of double-hit mutant compared to asymmetric stem cell divisions [ 19 , 20 , 22 ]. In the present model, the same trend is observed (see e.g.…”

“…Furthermore, for intestinal crypts there are reports that an age-dependent transition occurs from mainly asymmetric divisions to largely symmetric divisions [ 15 ], and opposing reports that a transition occurs from symmetric to asymmetric divisions [ 16 ]. The potential tradeoffs between symmetric and asymmetric stem cell divisions in tissues have previously been considered by many modelers using ODE models [ 17 ], stochastic space-free models [ 18 – 22 ], and in a spatial setting [ 23 ]. Several of these models consider the time to appearance of k consecutive mutations in a population of cells, and ask how mutation accumulation can be minimized.…”

“…Shahriyari and Komarova [ 20 ] found that symmetrically dividing cells may delay double hit mutations compared to an equivalent system with asymmetric mutations. The rationale is that symmetric division producing two progenitors flushes out mutations in the stem cell lineage, if progenitor turnover is fast [ 19 , 20 , 22 , 24 ].…”

Wnt Signaling: Role in Regulation of Haematopoiesis

“…In an asymmetric division, stem cells divide to generate one daughter cell with self renewal capacity and other which differentiates. In a symmetric division, there are two types-proliferation division, in which stem cell divide to generate two stem cells and differentiation division where parent cell gives rise to two differentiated cells [33][34][35]. Molecular mechanisms which underlie the regulation of self-renewal are yet ripe for research.…”

Andronov-Hopf’s Bifurcation in a Dynamic Model of Cell Population

“…Dynamic model of cell population can be represented by the following system of ordinary differential equations [2]:…”