Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect

Konstorum, Anna; Hillen, Thomas; Lowengrub, John

doi:10.1007/s11538-016-0161-5

Cited by 41 publications

(37 citation statements)

References 53 publications

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“…No studies have been conducted that systematically characterize the negative feedback loops still present in specific cancers, although it has been suggested that negative feedback has to be invoked to explain certain experimentally observed tumor growth patterns (18). The results reported here further emphasize the need to investigate which aspects of healthy tissue cell hierarchies remain active in tumors (23), and how this relates to treatment outcome. Not all feedback mechanisms, however, enable permanent shifts in tumor stem cell fractions after therapy, and further mathematical work should take a more comprehensive approach (34) to define possible feedback patterns that can and cannot induce this effect.…”

Section: Discussionmentioning

confidence: 54%

“…More precisely,

r_{1} = \frac{r_{1}^{false(0 false)}}{1 + h D^{k}}, r_{2} = \frac{r_{2}^{false(0 false)}}{1 + h D^{k}}

, where r 1 (0) and r 2 (0) are the division rates without negative feedback and the parameters k and h control the strength of the inhibitory signals (for a schematic representation see Figure 2A). The modeling of the division rates using Hill equations builds on previous work on feedback regulation by others and us (1–3,19–23). …”

Section: Resultsmentioning

confidence: 99%

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Cellular Hierarchy as a Determinant of Tumor Sensitivity to Chemotherapy

et al. 2017

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Chemotherapy has been shown to enrich cancer stem cells in tumors. Recently, we demonstrated that administration of chemotherapy to human bladder cancer xenografts could trigger a wound-healing response that mobilizes quiescent tumor stem cells into active proliferation. This phenomenon leads to a loss of sensitivity to chemotherapy partly due to an increase in the number of tumor stem cells, which typically respond to chemotherapy-induced cell death less than more differentiated cells. Different bladder cancer xenografts, however, demonstrate differential sensitivities to chemotherapy, the basis of which is not understood. Using mathematical models, we show that characteristics of the tumor cell hierarchy can be crucial for determining the sensitivity of tumors to drug therapy, under the assumption that stem cell enrichment is the primary basis for drug resistance. Intriguingly, our model predicts a weaker response to therapy if there is negative feedback from differentiated tumor cells that inhibits the rate of tumor stem cell division. If this negative feedback is less pronounced, the treatment response is predicted to be enhanced. The reason is that negative feedback on the rate of tumor cell division promotes a permanent rise of the tumor stem cell population over time both in the absence of treatment, and even more so during drug therapy. Model application to data from chemotherapy-treated patient-derived xenografts indicates support for model predictions. These findings call for further research into feedback mechanisms that might remain active in cancers, and potentially highlight the presence of feedback as an indication to combine chemotherapy with approaches that limit the process of tumor stem cell enrichment.

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Section: Discussionmentioning

confidence: 54%

“…More precisely,

r_{1} = \frac{r_{1}^{false(0 false)}}{1 + h D^{k}}, r_{2} = \frac{r_{2}^{false(0 false)}}{1 + h D^{k}}

Section: Resultsmentioning

confidence: 99%

Cellular Hierarchy as a Determinant of Tumor Sensitivity to Chemotherapy

et al. 2017

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“…7C, solid line). However, if the treatment stops at T=200 when the GSCs have been decreased to a sufficiently low level so as to induce an Allee effect (37), the tumor does not regrow. Therefore, the results suggest that a combination of anti-angiogenic, anti-mitotic, differentiation and anti-GEC therapy greatly reduces tumor growth and invasion, and could eradicate the tumor without recurrence when the treatment is stopped – achieving long-lasting remission.…”

Section: Resultsmentioning

confidence: 99%

3D Mathematical Modeling of Glioblastoma Suggests That Transdifferentiated Vascular Endothelial Cells Mediate Resistance to Current Standard-of-Care Therapy

et al. 2017

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Glioblastoma (GBM), the most aggressive brain tumor in human patients, is decidedly heterogeneous and highly vascularized. Glioma stem/initiating cells (GSC) are found to play a crucial role by increasing cancer aggressiveness and promoting resistance to therapy. Recently, crosstalk between GSC and vascular endothelial cells has been shown to significantly promote GSC self-renewal and tumor progression. Further, GSC also transdifferentiate into bona-fide vascular endothelial cells (GEC), which inherit mutations present in GSC and are resistant to traditional anti-angiogenic therapies. Here we use 3D mathematical modeling to investigate GBM progression and response to therapy. The model predicted that GSC drive invasive fingering and that GEC spontaneously form a network within the hypoxic core, consistent with published experimental findings. Standard-of-care treatments using DNA-targeted therapy (radiation/chemo) together with anti-angiogenic therapies, reduced GBM tumor size but increased invasiveness. Anti-GEC treatments blocked the GEC support of GSC and reduced tumor size but led to increased invasiveness. Anti-GSC therapies that promote differentiation or disturb the stem cell niche effectively reduced tumor invasiveness and size, but were ultimately limited in reducing tumor size because GEC maintain GSC. Our study suggests that a combinatorial regimen targeting the vasculature, GSC, and GEC, using drugs already approved by the FDA, can reduce both tumor size and invasiveness and could lead to tumor eradication.

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“…This paper contributes to the growing literature on the theory of stem cells, which ranges from ODE modeling (Stiehl and Marciniak-Czochra, 2011; Nakata et al, 2012) to stochastic modeling (Enderling et al, 2007, 2009a,b,c; Dingli et al, 2007), and includes research of stem cells in the context of feedback mechanisms (Lander et al, 2009; Youssefpour et al, 2012; Konstorum et al, 2016; Kunche et al, 2016), carcinogenesis (Yatabe et al, 2001; Hardy and Stark, 2002; Ganguly and Puri, 2006; Johnston et al, 2007; Ganguly and Puri, 2007; Boman et al, 2008; Ashkenazi et al, 2007, 2008; Enderling and Hahnfeldt, 2011), modeling hematopoietic SC dynamics (Glauche et al, 2007; Marciniak-Czochra et al, 2009; Foo et al, 2009; Stiehl and Marciniak-Czochra, 2012), and cancer stem cells (Dingli and Michor, 2006; Johnston et al, 2010; Enderling and Hahnfeldt, 2011; Hillen et al, 2013; Scott et al, 2014; Enderling, 2015). …”

Section: Introductionmentioning

confidence: 99%

Determining the control networks regulating stem cell lineages in colonic crypts

Yang

Axelrod

Komarova

2017

Journal of Theoretical Biology

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The question of stem cell control is at the center of our understanding of tissue functioning, both in healthy and cancerous conditions. It is well accepted that cellular fate decisions (such as divisions, differentiation, apoptosis) are orchestrated by a network of regulatory signals emitted by different cell populations in the lineage and the surrounding tissue. The exact regulatory network that governs stem cell lineages in a given tissue is usually unknown. Here we propose an algorithm to identify a set of candidate control networks that are compatible with (a) measured means and variances of cell populations in different compartments, (b) qualitative information on cell population dynamics, such as the existence of local controls and oscillatory reaction of the system to population size perturbations, and (c) statistics of correlations between cell numbers in different compartments. Using the example of human colon crypts, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells, we start with a theoretically known set of 32 smallest control networks compatible with tissue stability. Utilizing near-equilibrium stochastic calculus of stem cells developed earlier, we apply a series of tests, where we compare the networks’ expected behavior with the observations. This allows us to exclude most of the networks, until only three, very similar, candidate networks remain, which are most compatible with the measurements. This work demonstrates how theoretical analysis of control networks combined with only static biological data can shed light onto the inner workings of stem cell lineages, in the absence of direct experimental assessment of regulatory signaling mechanisms. The resulting candidate networks are dominated by negative control loops and possess the following properties: (1) stem cell division decisions are negatively controlled by the stem cell population, (2) stem cell differentiation decisions are negatively controlled by the transit amplifying cell population.

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Feedback Regulation in a Cancer Stem Cell Model can Cause an Allee Effect

Cited by 41 publications

References 53 publications

Cellular Hierarchy as a Determinant of Tumor Sensitivity to Chemotherapy

Cellular Hierarchy as a Determinant of Tumor Sensitivity to Chemotherapy

3D Mathematical Modeling of Glioblastoma Suggests That Transdifferentiated Vascular Endothelial Cells Mediate Resistance to Current Standard-of-Care Therapy

Determining the control networks regulating stem cell lineages in colonic crypts

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